From ac0c737c98f37665afab5d02d25b7258602c47ec Mon Sep 17 00:00:00 2001 From: ShadowMitia Date: Wed, 23 Aug 2023 13:19:41 +0000 Subject: [PATCH] =?UTF-8?q?Deploying=20to=20gh-pages=20from=20@=20algorith?= =?UTF-8?q?m-archivists/algorithm-archive@59c0b9d6b054488b134ea3159d192c84?= =?UTF-8?q?2c185328=20=F0=9F=9A=80?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Dockerfile | 1 - SConstruct | 3 + builders/mcs.py | 37 +++++ contents/IFS/IFS.html | 2 +- .../affine_transformations.html | 2 +- .../approximate_counting.html | 2 +- contents/barnsley/barnsley.html | 2 +- contents/bitlogic/bitlogic.html | 2 +- contents/box_muller/box_muller.html | 2 +- contents/box_muller/box_muller_rejection.html | 2 +- contents/code_reviews/code_reviewers.html | 2 +- .../computational_geometry.html | 2 +- .../computer_graphics/computer_graphics.html | 2 +- contents/computus/computus.html | 2 +- contents/convolutions/1d/1d.html | 2 +- contents/convolutions/2d/2d.html | 2 +- .../convolutional_theorem.html | 2 +- contents/convolutions/convolutions.html | 2 +- .../multiplication/multiplication.html | 2 +- contents/cooley_tukey/cooley_tukey.html | 2 +- contents/cryptography/cryptography.html | 2 +- .../data_compression/data_compression.html | 2 +- contents/data_structures/data_structures.html | 2 +- .../decision_problems/decision_problems.html | 2 +- contents/domain_coloring/domain_coloring.html | 2 +- .../euclidean_algorithm.html | 2 +- contents/flood_fill/flood_fill.html | 2 +- .../gaussian_elimination.html | 2 +- contents/gift_wrapping/gift_wrapping.html | 2 +- contents/graham_scan/graham_scan.html | 2 +- .../how_to_contribute/how_to_contribute.html | 2 +- .../code/csharp/HuffmanCoding.cs | 29 ++-- .../huffman_encoding/huffman_encoding.html | 29 ++-- contents/introduction/introduction.html | 2 +- contents/jarvis_march/jarvis_march.html | 2 +- .../mathematical_background.html | 2 +- contents/matrix_methods/matrix_methods.html | 2 +- contents/metropolis/metropolis.html | 2 +- .../monte_carlo_integration.html | 2 +- contents/notation/notation.html | 2 +- contents/physics_solvers/physics_solvers.html | 2 +- contents/plotting/plotting.html | 2 +- .../distributions.html | 2 +- .../quantum_information.html | 2 +- contents/quantum_systems/quantum_systems.html | 2 +- .../split-operator_method.html | 2 +- .../stable_marriage_problem.html | 2 +- .../stacks_and_queues/stacks_and_queues.html | 2 +- .../taylor_series_expansion.html | 2 +- .../thomas_algorithm/thomas_algorithm.html | 2 +- contents/tree_traversal/code/csharp/Tree.cs | 64 ++++---- contents/tree_traversal/tree_traversal.html | 153 +++++++++--------- .../verlet_integration.html | 2 +- index.html | 2 +- sconscripts/csharp_SConscript | 15 ++ search_index.json | 2 +- 56 files changed, 243 insertions(+), 184 deletions(-) create mode 100644 builders/mcs.py create mode 100644 sconscripts/csharp_SConscript diff --git a/Dockerfile b/Dockerfile index 714139a32..b648ea7d8 100644 --- a/Dockerfile +++ b/Dockerfile @@ -109,4 +109,3 @@ RUN apt-get update && export DEBIAN_FRONTEND=noninteractive \ RUN pip install wheel matplotlib numpy coconut scons RUN sudo sh -c 'npm install -g typescript' - diff --git a/SConstruct b/SConstruct index e5ecf82d9..74e05ea85 100644 --- a/SConstruct +++ b/SConstruct @@ -28,6 +28,7 @@ available_languages = { 'bash', 'c', 'cpp', + 'csharp', 'fortran', 'java', 'julia', @@ -43,6 +44,7 @@ available_languages = { languages_to_import = { 'coconut': ['coconut'], + 'csharp': ['mcs'], 'go': ['go'], 'rust': ['rustc', 'cargo'], 'kotlin': ['kotlin'], @@ -77,6 +79,7 @@ languages = { 'c': 'c', 'coconut': 'coco', 'cpp': 'cpp', + 'csharp': 'cs', 'fortran': 'f90', 'go': 'go', 'java': 'java', diff --git a/builders/mcs.py b/builders/mcs.py new file mode 100644 index 000000000..07f1bd76c --- /dev/null +++ b/builders/mcs.py @@ -0,0 +1,37 @@ +from SCons.Builder import Builder +import SCons.Util + +class ToolMCSWarning(SCons.Warnings.SConsWarning): + pass + +class MCSNotFound(ToolMCSWarning): + pass + +SCons.Warnings.enableWarningClass(ToolMCSWarning) + +def _detect(env): + try: + return env['mcs'] + except KeyError: + pass + + mcs = env.WhereIs('mcs') + if mcs: + return mcs + + SCons.Warnings.warn(MCSNotFound, 'Could not find mcs executable') + +def exists(env): + env.Detect('mcs') + +def generate(env): + env['MCS'] = _detect(env) + env['MCSFLAGS'] = [] + + mcs_builder = Builder( + action='"$MCS" -out:$TARGET $MCSFLAGS $SOURCES', + src_suffix='.cs', + suffix='$PROGSUFFIX', + ) + + env.Append(BUILDERS={'MCS': mcs_builder}) diff --git a/contents/IFS/IFS.html b/contents/IFS/IFS.html index 7ea606f22..908557728 100644 --- a/contents/IFS/IFS.html +++ b/contents/IFS/IFS.html @@ -1646,7 +1646,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Iterated Function Systems","level":"1.4.2","depth":2,"next":{"title":"The Barnsley Fern","level":"1.4.2.1","depth":3,"path":"contents/barnsley/barnsley.md","ref":"contents/barnsley/barnsley.md","articles":[]},"previous":{"title":"Domain Coloring","level":"1.4.1","depth":2,"path":"contents/domain_coloring/domain_coloring.md","ref":"contents/domain_coloring/domain_coloring.md","articles":[]},"articles":[{"title":"The Barnsley Fern","level":"1.4.2.1","depth":3,"path":"contents/barnsley/barnsley.md","ref":"contents/barnsley/barnsley.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/IFS/IFS.md","mtime":"2023-08-22T20:57:11.690Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Iterated Function Systems","level":"1.4.2","depth":2,"next":{"title":"The Barnsley Fern","level":"1.4.2.1","depth":3,"path":"contents/barnsley/barnsley.md","ref":"contents/barnsley/barnsley.md","articles":[]},"previous":{"title":"Domain Coloring","level":"1.4.1","depth":2,"path":"contents/domain_coloring/domain_coloring.md","ref":"contents/domain_coloring/domain_coloring.md","articles":[]},"articles":[{"title":"The Barnsley Fern","level":"1.4.2.1","depth":3,"path":"contents/barnsley/barnsley.md","ref":"contents/barnsley/barnsley.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/IFS/IFS.md","mtime":"2023-08-23T13:18:40.814Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/affine_transformations/affine_transformations.html b/contents/affine_transformations/affine_transformations.html index da57c818f..87c853acd 100644 --- a/contents/affine_transformations/affine_transformations.html +++ b/contents/affine_transformations/affine_transformations.html @@ -1286,7 +1286,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Affine Transformations","level":"1.6.2","depth":2,"next":{"title":"Bit Logic","level":"1.6.3","depth":2,"path":"contents/bitlogic/bitlogic.md","ref":"contents/bitlogic/bitlogic.md","articles":[]},"previous":{"title":"Complexity Notation","level":"1.6.1","depth":2,"path":"contents/notation/notation.md","ref":"contents/notation/notation.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/affine_transformations/affine_transformations.md","mtime":"2023-08-22T20:57:11.730Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Affine Transformations","level":"1.6.2","depth":2,"next":{"title":"Bit Logic","level":"1.6.3","depth":2,"path":"contents/bitlogic/bitlogic.md","ref":"contents/bitlogic/bitlogic.md","articles":[]},"previous":{"title":"Complexity Notation","level":"1.6.1","depth":2,"path":"contents/notation/notation.md","ref":"contents/notation/notation.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/affine_transformations/affine_transformations.md","mtime":"2023-08-23T13:18:40.850Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/approximate_counting/approximate_counting.html b/contents/approximate_counting/approximate_counting.html index a8bb86a47..7ef479a72 100644 --- a/contents/approximate_counting/approximate_counting.html +++ b/contents/approximate_counting/approximate_counting.html @@ -1752,7 +1752,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Approximate Counting Algorithm","level":"1.20","depth":1,"previous":{"title":"Computus","level":"1.19","depth":1,"path":"contents/computus/computus.md","ref":"contents/computus/computus.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/approximate_counting/approximate_counting.md","mtime":"2023-08-22T20:57:11.854Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Approximate Counting Algorithm","level":"1.20","depth":1,"previous":{"title":"Computus","level":"1.19","depth":1,"path":"contents/computus/computus.md","ref":"contents/computus/computus.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/approximate_counting/approximate_counting.md","mtime":"2023-08-23T13:18:40.950Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/barnsley/barnsley.html b/contents/barnsley/barnsley.html index eacd51678..403ba5ffd 100644 --- a/contents/barnsley/barnsley.html +++ b/contents/barnsley/barnsley.html @@ -1747,7 +1747,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"The Barnsley Fern","level":"1.4.2.1","depth":3,"next":{"title":"Data Structures","level":"1.5","depth":1,"path":"contents/data_structures/data_structures.md","ref":"contents/data_structures/data_structures.md","articles":[{"title":"Stacks and Queues","level":"1.5.1","depth":2,"path":"contents/stacks_and_queues/stacks_and_queues.md","ref":"contents/stacks_and_queues/stacks_and_queues.md","articles":[]}]},"previous":{"title":"Iterated Function Systems","level":"1.4.2","depth":2,"path":"contents/IFS/IFS.md","ref":"contents/IFS/IFS.md","articles":[{"title":"The Barnsley Fern","level":"1.4.2.1","depth":3,"path":"contents/barnsley/barnsley.md","ref":"contents/barnsley/barnsley.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/barnsley/barnsley.md","mtime":"2023-08-22T20:57:11.862Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"The Barnsley Fern","level":"1.4.2.1","depth":3,"next":{"title":"Data Structures","level":"1.5","depth":1,"path":"contents/data_structures/data_structures.md","ref":"contents/data_structures/data_structures.md","articles":[{"title":"Stacks and Queues","level":"1.5.1","depth":2,"path":"contents/stacks_and_queues/stacks_and_queues.md","ref":"contents/stacks_and_queues/stacks_and_queues.md","articles":[]}]},"previous":{"title":"Iterated Function Systems","level":"1.4.2","depth":2,"path":"contents/IFS/IFS.md","ref":"contents/IFS/IFS.md","articles":[{"title":"The Barnsley Fern","level":"1.4.2.1","depth":3,"path":"contents/barnsley/barnsley.md","ref":"contents/barnsley/barnsley.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/barnsley/barnsley.md","mtime":"2023-08-23T13:18:40.958Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/bitlogic/bitlogic.html b/contents/bitlogic/bitlogic.html index 1e0731149..bbf7897c2 100644 --- a/contents/bitlogic/bitlogic.html +++ b/contents/bitlogic/bitlogic.html @@ -1198,7 +1198,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Bit Logic","level":"1.6.3","depth":2,"next":{"title":"Taylor Series","level":"1.6.4","depth":2,"path":"contents/taylor_series_expansion/taylor_series_expansion.md","ref":"contents/taylor_series_expansion/taylor_series_expansion.md","articles":[]},"previous":{"title":"Affine Transformations","level":"1.6.2","depth":2,"path":"contents/affine_transformations/affine_transformations.md","ref":"contents/affine_transformations/affine_transformations.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/bitlogic/bitlogic.md","mtime":"2023-08-22T20:57:12.010Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Bit Logic","level":"1.6.3","depth":2,"next":{"title":"Taylor Series","level":"1.6.4","depth":2,"path":"contents/taylor_series_expansion/taylor_series_expansion.md","ref":"contents/taylor_series_expansion/taylor_series_expansion.md","articles":[]},"previous":{"title":"Affine Transformations","level":"1.6.2","depth":2,"path":"contents/affine_transformations/affine_transformations.md","ref":"contents/affine_transformations/affine_transformations.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/bitlogic/bitlogic.md","mtime":"2023-08-23T13:18:41.082Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/box_muller/box_muller.html b/contents/box_muller/box_muller.html index ffb8025b4..ba266a764 100644 --- a/contents/box_muller/box_muller.html +++ b/contents/box_muller/box_muller.html @@ -1321,7 +1321,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Box Muller Transform","level":"1.6.6","depth":2,"next":{"title":"How costly is rejection sampling?","level":"1.6.6.1","depth":3,"path":"contents/box_muller/box_muller_rejection.md","ref":"contents/box_muller/box_muller_rejection.md","articles":[]},"previous":{"title":"Convolutional Theorem","level":"1.6.5.4","depth":3,"path":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","articles":[]},"articles":[{"title":"How costly is rejection sampling?","level":"1.6.6.1","depth":3,"path":"contents/box_muller/box_muller_rejection.md","ref":"contents/box_muller/box_muller_rejection.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/box_muller/box_muller.md","mtime":"2023-08-22T20:57:12.014Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Box Muller Transform","level":"1.6.6","depth":2,"next":{"title":"How costly is rejection sampling?","level":"1.6.6.1","depth":3,"path":"contents/box_muller/box_muller_rejection.md","ref":"contents/box_muller/box_muller_rejection.md","articles":[]},"previous":{"title":"Convolutional Theorem","level":"1.6.5.4","depth":3,"path":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","articles":[]},"articles":[{"title":"How costly is rejection sampling?","level":"1.6.6.1","depth":3,"path":"contents/box_muller/box_muller_rejection.md","ref":"contents/box_muller/box_muller_rejection.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/box_muller/box_muller.md","mtime":"2023-08-23T13:18:41.082Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/box_muller/box_muller_rejection.html b/contents/box_muller/box_muller_rejection.html index 29e662d99..de8ff53b2 100644 --- a/contents/box_muller/box_muller_rejection.html +++ b/contents/box_muller/box_muller_rejection.html @@ -1212,7 +1212,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"How costly is rejection sampling?","level":"1.6.6.1","depth":3,"next":{"title":"Probability Distributions","level":"1.6.7","depth":2,"path":"contents/probability_distributions/distributions.md","ref":"contents/probability_distributions/distributions.md","articles":[]},"previous":{"title":"Box Muller Transform","level":"1.6.6","depth":2,"path":"contents/box_muller/box_muller.md","ref":"contents/box_muller/box_muller.md","articles":[{"title":"How costly is rejection sampling?","level":"1.6.6.1","depth":3,"path":"contents/box_muller/box_muller_rejection.md","ref":"contents/box_muller/box_muller_rejection.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/box_muller/box_muller_rejection.md","mtime":"2023-08-22T20:57:12.014Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"How costly is rejection sampling?","level":"1.6.6.1","depth":3,"next":{"title":"Probability Distributions","level":"1.6.7","depth":2,"path":"contents/probability_distributions/distributions.md","ref":"contents/probability_distributions/distributions.md","articles":[]},"previous":{"title":"Box Muller Transform","level":"1.6.6","depth":2,"path":"contents/box_muller/box_muller.md","ref":"contents/box_muller/box_muller.md","articles":[{"title":"How costly is rejection sampling?","level":"1.6.6.1","depth":3,"path":"contents/box_muller/box_muller_rejection.md","ref":"contents/box_muller/box_muller_rejection.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/box_muller/box_muller_rejection.md","mtime":"2023-08-23T13:18:41.082Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/code_reviews/code_reviewers.html b/contents/code_reviews/code_reviewers.html index 2c9b26ca6..c5c61a417 100644 --- a/contents/code_reviews/code_reviewers.html +++ b/contents/code_reviews/code_reviewers.html @@ -1146,7 +1146,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Code Reviewers","level":"1.3.1","depth":2,"next":{"title":"Plotting","level":"1.4","depth":1,"path":"contents/plotting/plotting.md","ref":"contents/plotting/plotting.md","articles":[{"title":"Domain Coloring","level":"1.4.1","depth":2,"path":"contents/domain_coloring/domain_coloring.md","ref":"contents/domain_coloring/domain_coloring.md","articles":[]},{"title":"Iterated Function Systems","level":"1.4.2","depth":2,"path":"contents/IFS/IFS.md","ref":"contents/IFS/IFS.md","articles":[{"title":"The Barnsley Fern","level":"1.4.2.1","depth":3,"path":"contents/barnsley/barnsley.md","ref":"contents/barnsley/barnsley.md","articles":[]}]}]},"previous":{"title":"How To Contribute","level":"1.3","depth":1,"path":"contents/how_to_contribute/how_to_contribute.md","ref":"contents/how_to_contribute/how_to_contribute.md","articles":[{"title":"Code Reviewers","level":"1.3.1","depth":2,"path":"contents/code_reviews/code_reviewers.md","ref":"contents/code_reviews/code_reviewers.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/code_reviews/code_reviewers.md","mtime":"2023-08-22T20:57:12.026Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Code Reviewers","level":"1.3.1","depth":2,"next":{"title":"Plotting","level":"1.4","depth":1,"path":"contents/plotting/plotting.md","ref":"contents/plotting/plotting.md","articles":[{"title":"Domain Coloring","level":"1.4.1","depth":2,"path":"contents/domain_coloring/domain_coloring.md","ref":"contents/domain_coloring/domain_coloring.md","articles":[]},{"title":"Iterated Function Systems","level":"1.4.2","depth":2,"path":"contents/IFS/IFS.md","ref":"contents/IFS/IFS.md","articles":[{"title":"The Barnsley Fern","level":"1.4.2.1","depth":3,"path":"contents/barnsley/barnsley.md","ref":"contents/barnsley/barnsley.md","articles":[]}]}]},"previous":{"title":"How To Contribute","level":"1.3","depth":1,"path":"contents/how_to_contribute/how_to_contribute.md","ref":"contents/how_to_contribute/how_to_contribute.md","articles":[{"title":"Code Reviewers","level":"1.3.1","depth":2,"path":"contents/code_reviews/code_reviewers.md","ref":"contents/code_reviews/code_reviewers.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/code_reviews/code_reviewers.md","mtime":"2023-08-23T13:18:41.094Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/computational_geometry/computational_geometry.html b/contents/computational_geometry/computational_geometry.html index 46fffed72..133ee7554 100644 --- a/contents/computational_geometry/computational_geometry.html +++ b/contents/computational_geometry/computational_geometry.html @@ -939,7 +939,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Computational Geometry","level":"1.11","depth":1,"next":{"title":"Gift Wrapping","level":"1.11.1","depth":2,"path":"contents/gift_wrapping/gift_wrapping.md","ref":"contents/gift_wrapping/gift_wrapping.md","articles":[{"title":"Jarvis March","level":"1.11.1.1","depth":3,"path":"contents/jarvis_march/jarvis_march.md","ref":"contents/jarvis_march/jarvis_march.md","articles":[]},{"title":"Graham Scan","level":"1.11.1.2","depth":3,"path":"contents/graham_scan/graham_scan.md","ref":"contents/graham_scan/graham_scan.md","articles":[]}]},"previous":{"title":"Thomas Algorithm","level":"1.10.2","depth":2,"path":"contents/thomas_algorithm/thomas_algorithm.md","ref":"contents/thomas_algorithm/thomas_algorithm.md","articles":[]},"articles":[{"title":"Gift Wrapping","level":"1.11.1","depth":2,"path":"contents/gift_wrapping/gift_wrapping.md","ref":"contents/gift_wrapping/gift_wrapping.md","articles":[{"title":"Jarvis March","level":"1.11.1.1","depth":3,"path":"contents/jarvis_march/jarvis_march.md","ref":"contents/jarvis_march/jarvis_march.md","articles":[]},{"title":"Graham Scan","level":"1.11.1.2","depth":3,"path":"contents/graham_scan/graham_scan.md","ref":"contents/graham_scan/graham_scan.md","articles":[]}]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/computational_geometry/computational_geometry.md","mtime":"2023-08-22T20:57:12.026Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Computational Geometry","level":"1.11","depth":1,"next":{"title":"Gift Wrapping","level":"1.11.1","depth":2,"path":"contents/gift_wrapping/gift_wrapping.md","ref":"contents/gift_wrapping/gift_wrapping.md","articles":[{"title":"Jarvis March","level":"1.11.1.1","depth":3,"path":"contents/jarvis_march/jarvis_march.md","ref":"contents/jarvis_march/jarvis_march.md","articles":[]},{"title":"Graham Scan","level":"1.11.1.2","depth":3,"path":"contents/graham_scan/graham_scan.md","ref":"contents/graham_scan/graham_scan.md","articles":[]}]},"previous":{"title":"Thomas Algorithm","level":"1.10.2","depth":2,"path":"contents/thomas_algorithm/thomas_algorithm.md","ref":"contents/thomas_algorithm/thomas_algorithm.md","articles":[]},"articles":[{"title":"Gift Wrapping","level":"1.11.1","depth":2,"path":"contents/gift_wrapping/gift_wrapping.md","ref":"contents/gift_wrapping/gift_wrapping.md","articles":[{"title":"Jarvis March","level":"1.11.1.1","depth":3,"path":"contents/jarvis_march/jarvis_march.md","ref":"contents/jarvis_march/jarvis_march.md","articles":[]},{"title":"Graham Scan","level":"1.11.1.2","depth":3,"path":"contents/graham_scan/graham_scan.md","ref":"contents/graham_scan/graham_scan.md","articles":[]}]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/computational_geometry/computational_geometry.md","mtime":"2023-08-23T13:18:41.094Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/computer_graphics/computer_graphics.html b/contents/computer_graphics/computer_graphics.html index c22e5f51e..a789f0a64 100644 --- a/contents/computer_graphics/computer_graphics.html +++ b/contents/computer_graphics/computer_graphics.html @@ -932,7 +932,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Computer Graphics","level":"1.16","depth":1,"next":{"title":"Flood Fill","level":"1.16.1","depth":2,"path":"contents/flood_fill/flood_fill.md","ref":"contents/flood_fill/flood_fill.md","articles":[]},"previous":{"title":"Huffman Encoding","level":"1.15.1","depth":2,"path":"contents/huffman_encoding/huffman_encoding.md","ref":"contents/huffman_encoding/huffman_encoding.md","articles":[]},"articles":[{"title":"Flood Fill","level":"1.16.1","depth":2,"path":"contents/flood_fill/flood_fill.md","ref":"contents/flood_fill/flood_fill.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/computer_graphics/computer_graphics.md","mtime":"2023-08-22T20:57:12.026Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Computer Graphics","level":"1.16","depth":1,"next":{"title":"Flood Fill","level":"1.16.1","depth":2,"path":"contents/flood_fill/flood_fill.md","ref":"contents/flood_fill/flood_fill.md","articles":[]},"previous":{"title":"Huffman Encoding","level":"1.15.1","depth":2,"path":"contents/huffman_encoding/huffman_encoding.md","ref":"contents/huffman_encoding/huffman_encoding.md","articles":[]},"articles":[{"title":"Flood Fill","level":"1.16.1","depth":2,"path":"contents/flood_fill/flood_fill.md","ref":"contents/flood_fill/flood_fill.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/computer_graphics/computer_graphics.md","mtime":"2023-08-23T13:18:41.094Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/computus/computus.html b/contents/computus/computus.html index 9f1626fd2..b0c6d1a25 100644 --- a/contents/computus/computus.html +++ b/contents/computus/computus.html @@ -2094,7 +2094,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Computus","level":"1.19","depth":1,"next":{"title":"Approximate Counting Algorithm","level":"1.20","depth":1,"path":"contents/approximate_counting/approximate_counting.md","ref":"contents/approximate_counting/approximate_counting.md","articles":[]},"previous":{"title":"Cryptography","level":"1.18","depth":1,"path":"contents/cryptography/cryptography.md","ref":"contents/cryptography/cryptography.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/computus/computus.md","mtime":"2023-08-22T20:57:12.026Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Computus","level":"1.19","depth":1,"next":{"title":"Approximate Counting Algorithm","level":"1.20","depth":1,"path":"contents/approximate_counting/approximate_counting.md","ref":"contents/approximate_counting/approximate_counting.md","articles":[]},"previous":{"title":"Cryptography","level":"1.18","depth":1,"path":"contents/cryptography/cryptography.md","ref":"contents/cryptography/cryptography.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/computus/computus.md","mtime":"2023-08-23T13:18:41.094Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/convolutions/1d/1d.html b/contents/convolutions/1d/1d.html index c54833d4b..3d88cf627 100644 --- a/contents/convolutions/1d/1d.html +++ b/contents/convolutions/1d/1d.html @@ -1603,7 +1603,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Convolutions in 1D","level":"1.6.5.1","depth":3,"next":{"title":"Multiplication as a Convolution","level":"1.6.5.2","depth":3,"path":"contents/convolutions/multiplication/multiplication.md","ref":"contents/convolutions/multiplication/multiplication.md","articles":[]},"previous":{"title":"Convolutions","level":"1.6.5","depth":2,"path":"contents/convolutions/convolutions.md","ref":"contents/convolutions/convolutions.md","articles":[{"title":"Convolutions in 1D","level":"1.6.5.1","depth":3,"path":"contents/convolutions/1d/1d.md","ref":"contents/convolutions/1d/1d.md","articles":[]},{"title":"Multiplication as a Convolution","level":"1.6.5.2","depth":3,"path":"contents/convolutions/multiplication/multiplication.md","ref":"contents/convolutions/multiplication/multiplication.md","articles":[]},{"title":"Convolutions of Images (2D)","level":"1.6.5.3","depth":3,"path":"contents/convolutions/2d/2d.md","ref":"contents/convolutions/2d/2d.md","articles":[]},{"title":"Convolutional Theorem","level":"1.6.5.4","depth":3,"path":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/convolutions/1d/1d.md","mtime":"2023-08-22T20:57:12.030Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Convolutions in 1D","level":"1.6.5.1","depth":3,"next":{"title":"Multiplication as a Convolution","level":"1.6.5.2","depth":3,"path":"contents/convolutions/multiplication/multiplication.md","ref":"contents/convolutions/multiplication/multiplication.md","articles":[]},"previous":{"title":"Convolutions","level":"1.6.5","depth":2,"path":"contents/convolutions/convolutions.md","ref":"contents/convolutions/convolutions.md","articles":[{"title":"Convolutions in 1D","level":"1.6.5.1","depth":3,"path":"contents/convolutions/1d/1d.md","ref":"contents/convolutions/1d/1d.md","articles":[]},{"title":"Multiplication as a Convolution","level":"1.6.5.2","depth":3,"path":"contents/convolutions/multiplication/multiplication.md","ref":"contents/convolutions/multiplication/multiplication.md","articles":[]},{"title":"Convolutions of Images (2D)","level":"1.6.5.3","depth":3,"path":"contents/convolutions/2d/2d.md","ref":"contents/convolutions/2d/2d.md","articles":[]},{"title":"Convolutional Theorem","level":"1.6.5.4","depth":3,"path":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/convolutions/1d/1d.md","mtime":"2023-08-23T13:18:41.098Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../../..","book":{"language":""}}); }); diff --git a/contents/convolutions/2d/2d.html b/contents/convolutions/2d/2d.html index 213212f61..f0cf2c9a1 100644 --- a/contents/convolutions/2d/2d.html +++ b/contents/convolutions/2d/2d.html @@ -1411,7 +1411,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Convolutions of Images (2D)","level":"1.6.5.3","depth":3,"next":{"title":"Convolutional Theorem","level":"1.6.5.4","depth":3,"path":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","articles":[]},"previous":{"title":"Multiplication as a Convolution","level":"1.6.5.2","depth":3,"path":"contents/convolutions/multiplication/multiplication.md","ref":"contents/convolutions/multiplication/multiplication.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/convolutions/2d/2d.md","mtime":"2023-08-22T20:57:12.034Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Convolutions of Images (2D)","level":"1.6.5.3","depth":3,"next":{"title":"Convolutional Theorem","level":"1.6.5.4","depth":3,"path":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","articles":[]},"previous":{"title":"Multiplication as a Convolution","level":"1.6.5.2","depth":3,"path":"contents/convolutions/multiplication/multiplication.md","ref":"contents/convolutions/multiplication/multiplication.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/convolutions/2d/2d.md","mtime":"2023-08-23T13:18:41.098Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../../..","book":{"language":""}}); }); diff --git a/contents/convolutions/convolutional_theorem/convolutional_theorem.html b/contents/convolutions/convolutional_theorem/convolutional_theorem.html index 56a207844..ee6ed9508 100644 --- a/contents/convolutions/convolutional_theorem/convolutional_theorem.html +++ b/contents/convolutions/convolutional_theorem/convolutional_theorem.html @@ -1027,7 +1027,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Convolutional Theorem","level":"1.6.5.4","depth":3,"next":{"title":"Box Muller Transform","level":"1.6.6","depth":2,"path":"contents/box_muller/box_muller.md","ref":"contents/box_muller/box_muller.md","articles":[{"title":"How costly is rejection sampling?","level":"1.6.6.1","depth":3,"path":"contents/box_muller/box_muller_rejection.md","ref":"contents/box_muller/box_muller_rejection.md","articles":[]}]},"previous":{"title":"Convolutions of Images (2D)","level":"1.6.5.3","depth":3,"path":"contents/convolutions/2d/2d.md","ref":"contents/convolutions/2d/2d.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","mtime":"2023-08-22T20:57:12.034Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Convolutional Theorem","level":"1.6.5.4","depth":3,"next":{"title":"Box Muller Transform","level":"1.6.6","depth":2,"path":"contents/box_muller/box_muller.md","ref":"contents/box_muller/box_muller.md","articles":[{"title":"How costly is rejection sampling?","level":"1.6.6.1","depth":3,"path":"contents/box_muller/box_muller_rejection.md","ref":"contents/box_muller/box_muller_rejection.md","articles":[]}]},"previous":{"title":"Convolutions of Images (2D)","level":"1.6.5.3","depth":3,"path":"contents/convolutions/2d/2d.md","ref":"contents/convolutions/2d/2d.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","mtime":"2023-08-23T13:18:41.098Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../../..","book":{"language":""}}); }); diff --git a/contents/convolutions/convolutions.html b/contents/convolutions/convolutions.html index a6673fc9f..1022a393e 100644 --- a/contents/convolutions/convolutions.html +++ b/contents/convolutions/convolutions.html @@ -955,7 +955,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Convolutions","level":"1.6.5","depth":2,"next":{"title":"Convolutions in 1D","level":"1.6.5.1","depth":3,"path":"contents/convolutions/1d/1d.md","ref":"contents/convolutions/1d/1d.md","articles":[]},"previous":{"title":"Taylor Series","level":"1.6.4","depth":2,"path":"contents/taylor_series_expansion/taylor_series_expansion.md","ref":"contents/taylor_series_expansion/taylor_series_expansion.md","articles":[]},"articles":[{"title":"Convolutions in 1D","level":"1.6.5.1","depth":3,"path":"contents/convolutions/1d/1d.md","ref":"contents/convolutions/1d/1d.md","articles":[]},{"title":"Multiplication as a Convolution","level":"1.6.5.2","depth":3,"path":"contents/convolutions/multiplication/multiplication.md","ref":"contents/convolutions/multiplication/multiplication.md","articles":[]},{"title":"Convolutions of Images (2D)","level":"1.6.5.3","depth":3,"path":"contents/convolutions/2d/2d.md","ref":"contents/convolutions/2d/2d.md","articles":[]},{"title":"Convolutional Theorem","level":"1.6.5.4","depth":3,"path":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/convolutions/convolutions.md","mtime":"2023-08-22T20:57:12.034Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Convolutions","level":"1.6.5","depth":2,"next":{"title":"Convolutions in 1D","level":"1.6.5.1","depth":3,"path":"contents/convolutions/1d/1d.md","ref":"contents/convolutions/1d/1d.md","articles":[]},"previous":{"title":"Taylor Series","level":"1.6.4","depth":2,"path":"contents/taylor_series_expansion/taylor_series_expansion.md","ref":"contents/taylor_series_expansion/taylor_series_expansion.md","articles":[]},"articles":[{"title":"Convolutions in 1D","level":"1.6.5.1","depth":3,"path":"contents/convolutions/1d/1d.md","ref":"contents/convolutions/1d/1d.md","articles":[]},{"title":"Multiplication as a Convolution","level":"1.6.5.2","depth":3,"path":"contents/convolutions/multiplication/multiplication.md","ref":"contents/convolutions/multiplication/multiplication.md","articles":[]},{"title":"Convolutions of Images (2D)","level":"1.6.5.3","depth":3,"path":"contents/convolutions/2d/2d.md","ref":"contents/convolutions/2d/2d.md","articles":[]},{"title":"Convolutional Theorem","level":"1.6.5.4","depth":3,"path":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/convolutions/convolutions.md","mtime":"2023-08-23T13:18:41.098Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/convolutions/multiplication/multiplication.html b/contents/convolutions/multiplication/multiplication.html index 129af8bb5..94b0f1191 100644 --- a/contents/convolutions/multiplication/multiplication.html +++ b/contents/convolutions/multiplication/multiplication.html @@ -1011,7 +1011,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Multiplication as a Convolution","level":"1.6.5.2","depth":3,"next":{"title":"Convolutions of Images (2D)","level":"1.6.5.3","depth":3,"path":"contents/convolutions/2d/2d.md","ref":"contents/convolutions/2d/2d.md","articles":[]},"previous":{"title":"Convolutions in 1D","level":"1.6.5.1","depth":3,"path":"contents/convolutions/1d/1d.md","ref":"contents/convolutions/1d/1d.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/convolutions/multiplication/multiplication.md","mtime":"2023-08-22T20:57:12.034Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Multiplication as a Convolution","level":"1.6.5.2","depth":3,"next":{"title":"Convolutions of Images (2D)","level":"1.6.5.3","depth":3,"path":"contents/convolutions/2d/2d.md","ref":"contents/convolutions/2d/2d.md","articles":[]},"previous":{"title":"Convolutions in 1D","level":"1.6.5.1","depth":3,"path":"contents/convolutions/1d/1d.md","ref":"contents/convolutions/1d/1d.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/convolutions/multiplication/multiplication.md","mtime":"2023-08-23T13:18:41.098Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../../..","book":{"language":""}}); }); diff --git a/contents/cooley_tukey/cooley_tukey.html b/contents/cooley_tukey/cooley_tukey.html index 281f34385..9d6fa944e 100644 --- a/contents/cooley_tukey/cooley_tukey.html +++ b/contents/cooley_tukey/cooley_tukey.html @@ -2844,7 +2844,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"FFT","level":"1.12","depth":1,"next":{"title":"Decision Problems","level":"1.13","depth":1,"path":"contents/decision_problems/decision_problems.md","ref":"contents/decision_problems/decision_problems.md","articles":[{"title":"Stable Marriage Problem","level":"1.13.1","depth":2,"path":"contents/stable_marriage_problem/stable_marriage_problem.md","ref":"contents/stable_marriage_problem/stable_marriage_problem.md","articles":[]}]},"previous":{"title":"Graham Scan","level":"1.11.1.2","depth":3,"path":"contents/graham_scan/graham_scan.md","ref":"contents/graham_scan/graham_scan.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/cooley_tukey/cooley_tukey.md","mtime":"2023-08-22T20:57:12.122Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"FFT","level":"1.12","depth":1,"next":{"title":"Decision Problems","level":"1.13","depth":1,"path":"contents/decision_problems/decision_problems.md","ref":"contents/decision_problems/decision_problems.md","articles":[{"title":"Stable Marriage Problem","level":"1.13.1","depth":2,"path":"contents/stable_marriage_problem/stable_marriage_problem.md","ref":"contents/stable_marriage_problem/stable_marriage_problem.md","articles":[]}]},"previous":{"title":"Graham Scan","level":"1.11.1.2","depth":3,"path":"contents/graham_scan/graham_scan.md","ref":"contents/graham_scan/graham_scan.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/cooley_tukey/cooley_tukey.md","mtime":"2023-08-23T13:18:41.174Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/cryptography/cryptography.html b/contents/cryptography/cryptography.html index 97c079153..86358fbfe 100644 --- a/contents/cryptography/cryptography.html +++ b/contents/cryptography/cryptography.html @@ -1259,7 +1259,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Cryptography","level":"1.18","depth":1,"next":{"title":"Computus","level":"1.19","depth":1,"path":"contents/computus/computus.md","ref":"contents/computus/computus.md","articles":[]},"previous":{"title":"Quantum Information","level":"1.17","depth":1,"path":"contents/quantum_information/quantum_information.md","ref":"contents/quantum_information/quantum_information.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/cryptography/cryptography.md","mtime":"2023-08-22T20:57:12.126Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Cryptography","level":"1.18","depth":1,"next":{"title":"Computus","level":"1.19","depth":1,"path":"contents/computus/computus.md","ref":"contents/computus/computus.md","articles":[]},"previous":{"title":"Quantum Information","level":"1.17","depth":1,"path":"contents/quantum_information/quantum_information.md","ref":"contents/quantum_information/quantum_information.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/cryptography/cryptography.md","mtime":"2023-08-23T13:18:41.174Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/data_compression/data_compression.html b/contents/data_compression/data_compression.html index 9742d0e2f..9d897ca94 100644 --- a/contents/data_compression/data_compression.html +++ b/contents/data_compression/data_compression.html @@ -1115,7 +1115,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Data Compression","level":"1.15","depth":1,"next":{"title":"Huffman Encoding","level":"1.15.1","depth":2,"path":"contents/huffman_encoding/huffman_encoding.md","ref":"contents/huffman_encoding/huffman_encoding.md","articles":[]},"previous":{"title":"Split-Operator Method","level":"1.14.2.1","depth":3,"path":"contents/split-operator_method/split-operator_method.md","ref":"contents/split-operator_method/split-operator_method.md","articles":[]},"articles":[{"title":"Huffman Encoding","level":"1.15.1","depth":2,"path":"contents/huffman_encoding/huffman_encoding.md","ref":"contents/huffman_encoding/huffman_encoding.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/data_compression/data_compression.md","mtime":"2023-08-22T20:57:12.126Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Data Compression","level":"1.15","depth":1,"next":{"title":"Huffman Encoding","level":"1.15.1","depth":2,"path":"contents/huffman_encoding/huffman_encoding.md","ref":"contents/huffman_encoding/huffman_encoding.md","articles":[]},"previous":{"title":"Split-Operator Method","level":"1.14.2.1","depth":3,"path":"contents/split-operator_method/split-operator_method.md","ref":"contents/split-operator_method/split-operator_method.md","articles":[]},"articles":[{"title":"Huffman Encoding","level":"1.15.1","depth":2,"path":"contents/huffman_encoding/huffman_encoding.md","ref":"contents/huffman_encoding/huffman_encoding.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/data_compression/data_compression.md","mtime":"2023-08-23T13:18:41.174Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/data_structures/data_structures.html b/contents/data_structures/data_structures.html index 6c311f50d..a9784e108 100644 --- a/contents/data_structures/data_structures.html +++ b/contents/data_structures/data_structures.html @@ -933,7 +933,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Data Structures","level":"1.5","depth":1,"next":{"title":"Stacks and Queues","level":"1.5.1","depth":2,"path":"contents/stacks_and_queues/stacks_and_queues.md","ref":"contents/stacks_and_queues/stacks_and_queues.md","articles":[]},"previous":{"title":"The Barnsley Fern","level":"1.4.2.1","depth":3,"path":"contents/barnsley/barnsley.md","ref":"contents/barnsley/barnsley.md","articles":[]},"articles":[{"title":"Stacks and Queues","level":"1.5.1","depth":2,"path":"contents/stacks_and_queues/stacks_and_queues.md","ref":"contents/stacks_and_queues/stacks_and_queues.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/data_structures/data_structures.md","mtime":"2023-08-22T20:57:12.126Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Data Structures","level":"1.5","depth":1,"next":{"title":"Stacks and Queues","level":"1.5.1","depth":2,"path":"contents/stacks_and_queues/stacks_and_queues.md","ref":"contents/stacks_and_queues/stacks_and_queues.md","articles":[]},"previous":{"title":"The Barnsley Fern","level":"1.4.2.1","depth":3,"path":"contents/barnsley/barnsley.md","ref":"contents/barnsley/barnsley.md","articles":[]},"articles":[{"title":"Stacks and Queues","level":"1.5.1","depth":2,"path":"contents/stacks_and_queues/stacks_and_queues.md","ref":"contents/stacks_and_queues/stacks_and_queues.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/data_structures/data_structures.md","mtime":"2023-08-23T13:18:41.174Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/decision_problems/decision_problems.html b/contents/decision_problems/decision_problems.html index abc12079e..9a73a7a38 100644 --- a/contents/decision_problems/decision_problems.html +++ b/contents/decision_problems/decision_problems.html @@ -939,7 +939,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Decision Problems","level":"1.13","depth":1,"next":{"title":"Stable Marriage Problem","level":"1.13.1","depth":2,"path":"contents/stable_marriage_problem/stable_marriage_problem.md","ref":"contents/stable_marriage_problem/stable_marriage_problem.md","articles":[]},"previous":{"title":"FFT","level":"1.12","depth":1,"path":"contents/cooley_tukey/cooley_tukey.md","ref":"contents/cooley_tukey/cooley_tukey.md","articles":[]},"articles":[{"title":"Stable Marriage Problem","level":"1.13.1","depth":2,"path":"contents/stable_marriage_problem/stable_marriage_problem.md","ref":"contents/stable_marriage_problem/stable_marriage_problem.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/decision_problems/decision_problems.md","mtime":"2023-08-22T20:57:12.126Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Decision Problems","level":"1.13","depth":1,"next":{"title":"Stable Marriage Problem","level":"1.13.1","depth":2,"path":"contents/stable_marriage_problem/stable_marriage_problem.md","ref":"contents/stable_marriage_problem/stable_marriage_problem.md","articles":[]},"previous":{"title":"FFT","level":"1.12","depth":1,"path":"contents/cooley_tukey/cooley_tukey.md","ref":"contents/cooley_tukey/cooley_tukey.md","articles":[]},"articles":[{"title":"Stable Marriage Problem","level":"1.13.1","depth":2,"path":"contents/stable_marriage_problem/stable_marriage_problem.md","ref":"contents/stable_marriage_problem/stable_marriage_problem.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/decision_problems/decision_problems.md","mtime":"2023-08-23T13:18:41.174Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/domain_coloring/domain_coloring.html b/contents/domain_coloring/domain_coloring.html index cd551c54e..bd68ab05e 100644 --- a/contents/domain_coloring/domain_coloring.html +++ b/contents/domain_coloring/domain_coloring.html @@ -1253,7 +1253,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Domain Coloring","level":"1.4.1","depth":2,"next":{"title":"Iterated Function Systems","level":"1.4.2","depth":2,"path":"contents/IFS/IFS.md","ref":"contents/IFS/IFS.md","articles":[{"title":"The Barnsley Fern","level":"1.4.2.1","depth":3,"path":"contents/barnsley/barnsley.md","ref":"contents/barnsley/barnsley.md","articles":[]}]},"previous":{"title":"Plotting","level":"1.4","depth":1,"path":"contents/plotting/plotting.md","ref":"contents/plotting/plotting.md","articles":[{"title":"Domain Coloring","level":"1.4.1","depth":2,"path":"contents/domain_coloring/domain_coloring.md","ref":"contents/domain_coloring/domain_coloring.md","articles":[]},{"title":"Iterated Function Systems","level":"1.4.2","depth":2,"path":"contents/IFS/IFS.md","ref":"contents/IFS/IFS.md","articles":[{"title":"The Barnsley Fern","level":"1.4.2.1","depth":3,"path":"contents/barnsley/barnsley.md","ref":"contents/barnsley/barnsley.md","articles":[]}]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/domain_coloring/domain_coloring.md","mtime":"2023-08-22T20:57:12.126Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Domain Coloring","level":"1.4.1","depth":2,"next":{"title":"Iterated Function Systems","level":"1.4.2","depth":2,"path":"contents/IFS/IFS.md","ref":"contents/IFS/IFS.md","articles":[{"title":"The Barnsley Fern","level":"1.4.2.1","depth":3,"path":"contents/barnsley/barnsley.md","ref":"contents/barnsley/barnsley.md","articles":[]}]},"previous":{"title":"Plotting","level":"1.4","depth":1,"path":"contents/plotting/plotting.md","ref":"contents/plotting/plotting.md","articles":[{"title":"Domain Coloring","level":"1.4.1","depth":2,"path":"contents/domain_coloring/domain_coloring.md","ref":"contents/domain_coloring/domain_coloring.md","articles":[]},{"title":"Iterated Function Systems","level":"1.4.2","depth":2,"path":"contents/IFS/IFS.md","ref":"contents/IFS/IFS.md","articles":[{"title":"The Barnsley Fern","level":"1.4.2.1","depth":3,"path":"contents/barnsley/barnsley.md","ref":"contents/barnsley/barnsley.md","articles":[]}]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/domain_coloring/domain_coloring.md","mtime":"2023-08-23T13:18:41.174Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/euclidean_algorithm/euclidean_algorithm.html b/contents/euclidean_algorithm/euclidean_algorithm.html index 6881950de..cd1230c61 100644 --- a/contents/euclidean_algorithm/euclidean_algorithm.html +++ b/contents/euclidean_algorithm/euclidean_algorithm.html @@ -3369,7 +3369,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Euclidean Algorithm","level":"1.8","depth":1,"next":{"title":"Monte Carlo","level":"1.9","depth":1,"path":"contents/monte_carlo_integration/monte_carlo_integration.md","ref":"contents/monte_carlo_integration/monte_carlo_integration.md","articles":[{"title":"Metropolis","level":"1.9.1","depth":2,"path":"contents/metropolis/metropolis.md","ref":"contents/metropolis/metropolis.md","articles":[]}]},"previous":{"title":"Tree Traversal","level":"1.7","depth":1,"path":"contents/tree_traversal/tree_traversal.md","ref":"contents/tree_traversal/tree_traversal.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/euclidean_algorithm/euclidean_algorithm.md","mtime":"2023-08-22T20:57:12.138Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Euclidean Algorithm","level":"1.8","depth":1,"next":{"title":"Monte Carlo","level":"1.9","depth":1,"path":"contents/monte_carlo_integration/monte_carlo_integration.md","ref":"contents/monte_carlo_integration/monte_carlo_integration.md","articles":[{"title":"Metropolis","level":"1.9.1","depth":2,"path":"contents/metropolis/metropolis.md","ref":"contents/metropolis/metropolis.md","articles":[]}]},"previous":{"title":"Tree Traversal","level":"1.7","depth":1,"path":"contents/tree_traversal/tree_traversal.md","ref":"contents/tree_traversal/tree_traversal.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/euclidean_algorithm/euclidean_algorithm.md","mtime":"2023-08-23T13:18:41.186Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/flood_fill/flood_fill.html b/contents/flood_fill/flood_fill.html index 6a45bc93f..1c6b6e18a 100644 --- a/contents/flood_fill/flood_fill.html +++ b/contents/flood_fill/flood_fill.html @@ -2249,7 +2249,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Flood Fill","level":"1.16.1","depth":2,"next":{"title":"Quantum Information","level":"1.17","depth":1,"path":"contents/quantum_information/quantum_information.md","ref":"contents/quantum_information/quantum_information.md","articles":[]},"previous":{"title":"Computer Graphics","level":"1.16","depth":1,"path":"contents/computer_graphics/computer_graphics.md","ref":"contents/computer_graphics/computer_graphics.md","articles":[{"title":"Flood Fill","level":"1.16.1","depth":2,"path":"contents/flood_fill/flood_fill.md","ref":"contents/flood_fill/flood_fill.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/flood_fill/flood_fill.md","mtime":"2023-08-22T20:57:12.142Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Flood Fill","level":"1.16.1","depth":2,"next":{"title":"Quantum Information","level":"1.17","depth":1,"path":"contents/quantum_information/quantum_information.md","ref":"contents/quantum_information/quantum_information.md","articles":[]},"previous":{"title":"Computer Graphics","level":"1.16","depth":1,"path":"contents/computer_graphics/computer_graphics.md","ref":"contents/computer_graphics/computer_graphics.md","articles":[{"title":"Flood Fill","level":"1.16.1","depth":2,"path":"contents/flood_fill/flood_fill.md","ref":"contents/flood_fill/flood_fill.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/flood_fill/flood_fill.md","mtime":"2023-08-23T13:18:41.190Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/gaussian_elimination/gaussian_elimination.html b/contents/gaussian_elimination/gaussian_elimination.html index 92deb322a..64da8277f 100644 --- a/contents/gaussian_elimination/gaussian_elimination.html +++ b/contents/gaussian_elimination/gaussian_elimination.html @@ -3269,7 +3269,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Gaussian Elimination","level":"1.10.1","depth":2,"next":{"title":"Thomas Algorithm","level":"1.10.2","depth":2,"path":"contents/thomas_algorithm/thomas_algorithm.md","ref":"contents/thomas_algorithm/thomas_algorithm.md","articles":[]},"previous":{"title":"Matrix Methods","level":"1.10","depth":1,"path":"contents/matrix_methods/matrix_methods.md","ref":"contents/matrix_methods/matrix_methods.md","articles":[{"title":"Gaussian Elimination","level":"1.10.1","depth":2,"path":"contents/gaussian_elimination/gaussian_elimination.md","ref":"contents/gaussian_elimination/gaussian_elimination.md","articles":[]},{"title":"Thomas Algorithm","level":"1.10.2","depth":2,"path":"contents/thomas_algorithm/thomas_algorithm.md","ref":"contents/thomas_algorithm/thomas_algorithm.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/gaussian_elimination/gaussian_elimination.md","mtime":"2023-08-22T20:57:12.146Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Gaussian Elimination","level":"1.10.1","depth":2,"next":{"title":"Thomas Algorithm","level":"1.10.2","depth":2,"path":"contents/thomas_algorithm/thomas_algorithm.md","ref":"contents/thomas_algorithm/thomas_algorithm.md","articles":[]},"previous":{"title":"Matrix Methods","level":"1.10","depth":1,"path":"contents/matrix_methods/matrix_methods.md","ref":"contents/matrix_methods/matrix_methods.md","articles":[{"title":"Gaussian Elimination","level":"1.10.1","depth":2,"path":"contents/gaussian_elimination/gaussian_elimination.md","ref":"contents/gaussian_elimination/gaussian_elimination.md","articles":[]},{"title":"Thomas Algorithm","level":"1.10.2","depth":2,"path":"contents/thomas_algorithm/thomas_algorithm.md","ref":"contents/thomas_algorithm/thomas_algorithm.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/gaussian_elimination/gaussian_elimination.md","mtime":"2023-08-23T13:18:41.194Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/gift_wrapping/gift_wrapping.html b/contents/gift_wrapping/gift_wrapping.html index ebb00dd75..a4691ca11 100644 --- a/contents/gift_wrapping/gift_wrapping.html +++ b/contents/gift_wrapping/gift_wrapping.html @@ -940,7 +940,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Gift Wrapping","level":"1.11.1","depth":2,"next":{"title":"Jarvis March","level":"1.11.1.1","depth":3,"path":"contents/jarvis_march/jarvis_march.md","ref":"contents/jarvis_march/jarvis_march.md","articles":[]},"previous":{"title":"Computational Geometry","level":"1.11","depth":1,"path":"contents/computational_geometry/computational_geometry.md","ref":"contents/computational_geometry/computational_geometry.md","articles":[{"title":"Gift Wrapping","level":"1.11.1","depth":2,"path":"contents/gift_wrapping/gift_wrapping.md","ref":"contents/gift_wrapping/gift_wrapping.md","articles":[{"title":"Jarvis March","level":"1.11.1.1","depth":3,"path":"contents/jarvis_march/jarvis_march.md","ref":"contents/jarvis_march/jarvis_march.md","articles":[]},{"title":"Graham Scan","level":"1.11.1.2","depth":3,"path":"contents/graham_scan/graham_scan.md","ref":"contents/graham_scan/graham_scan.md","articles":[]}]}]},"articles":[{"title":"Jarvis March","level":"1.11.1.1","depth":3,"path":"contents/jarvis_march/jarvis_march.md","ref":"contents/jarvis_march/jarvis_march.md","articles":[]},{"title":"Graham Scan","level":"1.11.1.2","depth":3,"path":"contents/graham_scan/graham_scan.md","ref":"contents/graham_scan/graham_scan.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/gift_wrapping/gift_wrapping.md","mtime":"2023-08-22T20:57:12.186Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Gift Wrapping","level":"1.11.1","depth":2,"next":{"title":"Jarvis March","level":"1.11.1.1","depth":3,"path":"contents/jarvis_march/jarvis_march.md","ref":"contents/jarvis_march/jarvis_march.md","articles":[]},"previous":{"title":"Computational Geometry","level":"1.11","depth":1,"path":"contents/computational_geometry/computational_geometry.md","ref":"contents/computational_geometry/computational_geometry.md","articles":[{"title":"Gift Wrapping","level":"1.11.1","depth":2,"path":"contents/gift_wrapping/gift_wrapping.md","ref":"contents/gift_wrapping/gift_wrapping.md","articles":[{"title":"Jarvis March","level":"1.11.1.1","depth":3,"path":"contents/jarvis_march/jarvis_march.md","ref":"contents/jarvis_march/jarvis_march.md","articles":[]},{"title":"Graham Scan","level":"1.11.1.2","depth":3,"path":"contents/graham_scan/graham_scan.md","ref":"contents/graham_scan/graham_scan.md","articles":[]}]}]},"articles":[{"title":"Jarvis March","level":"1.11.1.1","depth":3,"path":"contents/jarvis_march/jarvis_march.md","ref":"contents/jarvis_march/jarvis_march.md","articles":[]},{"title":"Graham Scan","level":"1.11.1.2","depth":3,"path":"contents/graham_scan/graham_scan.md","ref":"contents/graham_scan/graham_scan.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/gift_wrapping/gift_wrapping.md","mtime":"2023-08-23T13:18:41.226Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/graham_scan/graham_scan.html b/contents/graham_scan/graham_scan.html index 8fce9cdbe..d6f016c25 100644 --- a/contents/graham_scan/graham_scan.html +++ b/contents/graham_scan/graham_scan.html @@ -2084,7 +2084,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Graham Scan","level":"1.11.1.2","depth":3,"next":{"title":"FFT","level":"1.12","depth":1,"path":"contents/cooley_tukey/cooley_tukey.md","ref":"contents/cooley_tukey/cooley_tukey.md","articles":[]},"previous":{"title":"Jarvis March","level":"1.11.1.1","depth":3,"path":"contents/jarvis_march/jarvis_march.md","ref":"contents/jarvis_march/jarvis_march.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/graham_scan/graham_scan.md","mtime":"2023-08-22T20:57:12.186Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Graham Scan","level":"1.11.1.2","depth":3,"next":{"title":"FFT","level":"1.12","depth":1,"path":"contents/cooley_tukey/cooley_tukey.md","ref":"contents/cooley_tukey/cooley_tukey.md","articles":[]},"previous":{"title":"Jarvis March","level":"1.11.1.1","depth":3,"path":"contents/jarvis_march/jarvis_march.md","ref":"contents/jarvis_march/jarvis_march.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/graham_scan/graham_scan.md","mtime":"2023-08-23T13:18:41.226Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/how_to_contribute/how_to_contribute.html b/contents/how_to_contribute/how_to_contribute.html index cdfd79e3c..1f5a90d75 100644 --- a/contents/how_to_contribute/how_to_contribute.html +++ b/contents/how_to_contribute/how_to_contribute.html @@ -961,7 +961,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"How To Contribute","level":"1.3","depth":1,"next":{"title":"Code Reviewers","level":"1.3.1","depth":2,"path":"contents/code_reviews/code_reviewers.md","ref":"contents/code_reviews/code_reviewers.md","articles":[]},"previous":{"title":"Introduction","level":"1.2","depth":1,"path":"contents/introduction/introduction.md","ref":"contents/introduction/introduction.md","articles":[]},"articles":[{"title":"Code Reviewers","level":"1.3.1","depth":2,"path":"contents/code_reviews/code_reviewers.md","ref":"contents/code_reviews/code_reviewers.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/how_to_contribute/how_to_contribute.md","mtime":"2023-08-22T20:57:12.190Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"How To Contribute","level":"1.3","depth":1,"next":{"title":"Code Reviewers","level":"1.3.1","depth":2,"path":"contents/code_reviews/code_reviewers.md","ref":"contents/code_reviews/code_reviewers.md","articles":[]},"previous":{"title":"Introduction","level":"1.2","depth":1,"path":"contents/introduction/introduction.md","ref":"contents/introduction/introduction.md","articles":[]},"articles":[{"title":"Code Reviewers","level":"1.3.1","depth":2,"path":"contents/code_reviews/code_reviewers.md","ref":"contents/code_reviews/code_reviewers.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/how_to_contribute/how_to_contribute.md","mtime":"2023-08-23T13:18:41.226Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/huffman_encoding/code/csharp/HuffmanCoding.cs b/contents/huffman_encoding/code/csharp/HuffmanCoding.cs index ef711af26..cc8a711cd 100644 --- a/contents/huffman_encoding/code/csharp/HuffmanCoding.cs +++ b/contents/huffman_encoding/code/csharp/HuffmanCoding.cs @@ -133,25 +133,26 @@ private Node CreateTree(string input) return nodePriorityList.Pop(); } + + private void CreateDictionary(Node node, string bitString, Dictionary localDictionary) + { + if (node.IsLeaf) + localDictionary.Add(node.Key[0], bitString); + else + { + if (node.LeftChild != null) + CreateDictionary(node.LeftChild, bitString + '0', localDictionary); + if (node.RightChild != null) + CreateDictionary(node.RightChild, bitString + '1', localDictionary); + } + } + private Dictionary CreateDictionary(Node root) { // We're using a string instead of a actual bits here, since it makes the code somewhat more readable and this is an educational example. var dictionary = new Dictionary(); CreateDictionary(root, "", dictionary); return dictionary; - - void CreateDictionary(Node node, string bitString, Dictionary localDictionary) - { - if (node.IsLeaf) - localDictionary.Add(node.Key[0], bitString); - else - { - if (node.LeftChild != null) - CreateDictionary(node.LeftChild, bitString + '0', localDictionary); - if (node.RightChild != null) - CreateDictionary(node.RightChild, bitString + '1', localDictionary); - } - } } @@ -165,4 +166,4 @@ private string CreateBitString(string input, Dictionary dictionary return bitString; } } -} \ No newline at end of file +} diff --git a/contents/huffman_encoding/huffman_encoding.html b/contents/huffman_encoding/huffman_encoding.html index d270fa949..494a79f31 100644 --- a/contents/huffman_encoding/huffman_encoding.html +++ b/contents/huffman_encoding/huffman_encoding.html @@ -1697,25 +1697,26 @@

Example Code

return nodePriorityList.Pop(); } + + private void CreateDictionary(Node node, string bitString, Dictionary<char, string> localDictionary) + { + if (node.IsLeaf) + localDictionary.Add(node.Key[0], bitString); + else + { + if (node.LeftChild != null) + CreateDictionary(node.LeftChild, bitString + '0', localDictionary); + if (node.RightChild != null) + CreateDictionary(node.RightChild, bitString + '1', localDictionary); + } + } + private Dictionary<char, string> CreateDictionary(Node root) { // We're using a string instead of a actual bits here, since it makes the code somewhat more readable and this is an educational example. var dictionary = new Dictionary<char, string>(); CreateDictionary(root, "", dictionary); return dictionary; - - void CreateDictionary(Node node, string bitString, Dictionary<char, string> localDictionary) - { - if (node.IsLeaf) - localDictionary.Add(node.Key[0], bitString); - else - { - if (node.LeftChild != null) - CreateDictionary(node.LeftChild, bitString + '0', localDictionary); - if (node.RightChild != null) - CreateDictionary(node.RightChild, bitString + '1', localDictionary); - } - } } @@ -3525,7 +3526,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Huffman Encoding","level":"1.15.1","depth":2,"next":{"title":"Computer Graphics","level":"1.16","depth":1,"path":"contents/computer_graphics/computer_graphics.md","ref":"contents/computer_graphics/computer_graphics.md","articles":[{"title":"Flood Fill","level":"1.16.1","depth":2,"path":"contents/flood_fill/flood_fill.md","ref":"contents/flood_fill/flood_fill.md","articles":[]}]},"previous":{"title":"Data Compression","level":"1.15","depth":1,"path":"contents/data_compression/data_compression.md","ref":"contents/data_compression/data_compression.md","articles":[{"title":"Huffman Encoding","level":"1.15.1","depth":2,"path":"contents/huffman_encoding/huffman_encoding.md","ref":"contents/huffman_encoding/huffman_encoding.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/huffman_encoding/huffman_encoding.md","mtime":"2023-08-22T20:57:12.190Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Huffman Encoding","level":"1.15.1","depth":2,"next":{"title":"Computer Graphics","level":"1.16","depth":1,"path":"contents/computer_graphics/computer_graphics.md","ref":"contents/computer_graphics/computer_graphics.md","articles":[{"title":"Flood Fill","level":"1.16.1","depth":2,"path":"contents/flood_fill/flood_fill.md","ref":"contents/flood_fill/flood_fill.md","articles":[]}]},"previous":{"title":"Data Compression","level":"1.15","depth":1,"path":"contents/data_compression/data_compression.md","ref":"contents/data_compression/data_compression.md","articles":[{"title":"Huffman Encoding","level":"1.15.1","depth":2,"path":"contents/huffman_encoding/huffman_encoding.md","ref":"contents/huffman_encoding/huffman_encoding.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/huffman_encoding/huffman_encoding.md","mtime":"2023-08-23T13:18:41.230Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/introduction/introduction.html b/contents/introduction/introduction.html index f1449eeec..bbde9d79b 100644 --- a/contents/introduction/introduction.html +++ b/contents/introduction/introduction.html @@ -940,7 +940,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Introduction","level":"1.2","depth":1,"next":{"title":"How To Contribute","level":"1.3","depth":1,"path":"contents/how_to_contribute/how_to_contribute.md","ref":"contents/how_to_contribute/how_to_contribute.md","articles":[{"title":"Code Reviewers","level":"1.3.1","depth":2,"path":"contents/code_reviews/code_reviewers.md","ref":"contents/code_reviews/code_reviewers.md","articles":[]}]},"previous":{"title":"Algorithm Archive","level":"1.1","depth":1,"path":"README.md","ref":"README.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/introduction/introduction.md","mtime":"2023-08-22T20:57:12.194Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Introduction","level":"1.2","depth":1,"next":{"title":"How To Contribute","level":"1.3","depth":1,"path":"contents/how_to_contribute/how_to_contribute.md","ref":"contents/how_to_contribute/how_to_contribute.md","articles":[{"title":"Code Reviewers","level":"1.3.1","depth":2,"path":"contents/code_reviews/code_reviewers.md","ref":"contents/code_reviews/code_reviewers.md","articles":[]}]},"previous":{"title":"Algorithm Archive","level":"1.1","depth":1,"path":"README.md","ref":"README.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/introduction/introduction.md","mtime":"2023-08-23T13:18:41.230Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/jarvis_march/jarvis_march.html b/contents/jarvis_march/jarvis_march.html index 6ae0ccfed..e839d852d 100644 --- a/contents/jarvis_march/jarvis_march.html +++ b/contents/jarvis_march/jarvis_march.html @@ -1801,7 +1801,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Jarvis March","level":"1.11.1.1","depth":3,"next":{"title":"Graham Scan","level":"1.11.1.2","depth":3,"path":"contents/graham_scan/graham_scan.md","ref":"contents/graham_scan/graham_scan.md","articles":[]},"previous":{"title":"Gift Wrapping","level":"1.11.1","depth":2,"path":"contents/gift_wrapping/gift_wrapping.md","ref":"contents/gift_wrapping/gift_wrapping.md","articles":[{"title":"Jarvis March","level":"1.11.1.1","depth":3,"path":"contents/jarvis_march/jarvis_march.md","ref":"contents/jarvis_march/jarvis_march.md","articles":[]},{"title":"Graham Scan","level":"1.11.1.2","depth":3,"path":"contents/graham_scan/graham_scan.md","ref":"contents/graham_scan/graham_scan.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/jarvis_march/jarvis_march.md","mtime":"2023-08-22T20:57:12.194Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Jarvis March","level":"1.11.1.1","depth":3,"next":{"title":"Graham Scan","level":"1.11.1.2","depth":3,"path":"contents/graham_scan/graham_scan.md","ref":"contents/graham_scan/graham_scan.md","articles":[]},"previous":{"title":"Gift Wrapping","level":"1.11.1","depth":2,"path":"contents/gift_wrapping/gift_wrapping.md","ref":"contents/gift_wrapping/gift_wrapping.md","articles":[{"title":"Jarvis March","level":"1.11.1.1","depth":3,"path":"contents/jarvis_march/jarvis_march.md","ref":"contents/jarvis_march/jarvis_march.md","articles":[]},{"title":"Graham Scan","level":"1.11.1.2","depth":3,"path":"contents/graham_scan/graham_scan.md","ref":"contents/graham_scan/graham_scan.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/jarvis_march/jarvis_march.md","mtime":"2023-08-23T13:18:41.230Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/mathematical_background/mathematical_background.html b/contents/mathematical_background/mathematical_background.html index e3f9f612a..3961d6f04 100644 --- a/contents/mathematical_background/mathematical_background.html +++ b/contents/mathematical_background/mathematical_background.html @@ -940,7 +940,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Mathematical Background","level":"1.6","depth":1,"next":{"title":"Complexity Notation","level":"1.6.1","depth":2,"path":"contents/notation/notation.md","ref":"contents/notation/notation.md","articles":[]},"previous":{"title":"Stacks and Queues","level":"1.5.1","depth":2,"path":"contents/stacks_and_queues/stacks_and_queues.md","ref":"contents/stacks_and_queues/stacks_and_queues.md","articles":[]},"articles":[{"title":"Complexity Notation","level":"1.6.1","depth":2,"path":"contents/notation/notation.md","ref":"contents/notation/notation.md","articles":[]},{"title":"Affine Transformations","level":"1.6.2","depth":2,"path":"contents/affine_transformations/affine_transformations.md","ref":"contents/affine_transformations/affine_transformations.md","articles":[]},{"title":"Bit Logic","level":"1.6.3","depth":2,"path":"contents/bitlogic/bitlogic.md","ref":"contents/bitlogic/bitlogic.md","articles":[]},{"title":"Taylor Series","level":"1.6.4","depth":2,"path":"contents/taylor_series_expansion/taylor_series_expansion.md","ref":"contents/taylor_series_expansion/taylor_series_expansion.md","articles":[]},{"title":"Convolutions","level":"1.6.5","depth":2,"path":"contents/convolutions/convolutions.md","ref":"contents/convolutions/convolutions.md","articles":[{"title":"Convolutions in 1D","level":"1.6.5.1","depth":3,"path":"contents/convolutions/1d/1d.md","ref":"contents/convolutions/1d/1d.md","articles":[]},{"title":"Multiplication as a Convolution","level":"1.6.5.2","depth":3,"path":"contents/convolutions/multiplication/multiplication.md","ref":"contents/convolutions/multiplication/multiplication.md","articles":[]},{"title":"Convolutions of Images (2D)","level":"1.6.5.3","depth":3,"path":"contents/convolutions/2d/2d.md","ref":"contents/convolutions/2d/2d.md","articles":[]},{"title":"Convolutional Theorem","level":"1.6.5.4","depth":3,"path":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","articles":[]}]},{"title":"Box Muller Transform","level":"1.6.6","depth":2,"path":"contents/box_muller/box_muller.md","ref":"contents/box_muller/box_muller.md","articles":[{"title":"How costly is rejection sampling?","level":"1.6.6.1","depth":3,"path":"contents/box_muller/box_muller_rejection.md","ref":"contents/box_muller/box_muller_rejection.md","articles":[]}]},{"title":"Probability Distributions","level":"1.6.7","depth":2,"path":"contents/probability_distributions/distributions.md","ref":"contents/probability_distributions/distributions.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/mathematical_background/mathematical_background.md","mtime":"2023-08-22T20:57:12.194Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Mathematical Background","level":"1.6","depth":1,"next":{"title":"Complexity Notation","level":"1.6.1","depth":2,"path":"contents/notation/notation.md","ref":"contents/notation/notation.md","articles":[]},"previous":{"title":"Stacks and Queues","level":"1.5.1","depth":2,"path":"contents/stacks_and_queues/stacks_and_queues.md","ref":"contents/stacks_and_queues/stacks_and_queues.md","articles":[]},"articles":[{"title":"Complexity Notation","level":"1.6.1","depth":2,"path":"contents/notation/notation.md","ref":"contents/notation/notation.md","articles":[]},{"title":"Affine Transformations","level":"1.6.2","depth":2,"path":"contents/affine_transformations/affine_transformations.md","ref":"contents/affine_transformations/affine_transformations.md","articles":[]},{"title":"Bit Logic","level":"1.6.3","depth":2,"path":"contents/bitlogic/bitlogic.md","ref":"contents/bitlogic/bitlogic.md","articles":[]},{"title":"Taylor Series","level":"1.6.4","depth":2,"path":"contents/taylor_series_expansion/taylor_series_expansion.md","ref":"contents/taylor_series_expansion/taylor_series_expansion.md","articles":[]},{"title":"Convolutions","level":"1.6.5","depth":2,"path":"contents/convolutions/convolutions.md","ref":"contents/convolutions/convolutions.md","articles":[{"title":"Convolutions in 1D","level":"1.6.5.1","depth":3,"path":"contents/convolutions/1d/1d.md","ref":"contents/convolutions/1d/1d.md","articles":[]},{"title":"Multiplication as a Convolution","level":"1.6.5.2","depth":3,"path":"contents/convolutions/multiplication/multiplication.md","ref":"contents/convolutions/multiplication/multiplication.md","articles":[]},{"title":"Convolutions of Images (2D)","level":"1.6.5.3","depth":3,"path":"contents/convolutions/2d/2d.md","ref":"contents/convolutions/2d/2d.md","articles":[]},{"title":"Convolutional Theorem","level":"1.6.5.4","depth":3,"path":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","articles":[]}]},{"title":"Box Muller Transform","level":"1.6.6","depth":2,"path":"contents/box_muller/box_muller.md","ref":"contents/box_muller/box_muller.md","articles":[{"title":"How costly is rejection sampling?","level":"1.6.6.1","depth":3,"path":"contents/box_muller/box_muller_rejection.md","ref":"contents/box_muller/box_muller_rejection.md","articles":[]}]},{"title":"Probability Distributions","level":"1.6.7","depth":2,"path":"contents/probability_distributions/distributions.md","ref":"contents/probability_distributions/distributions.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/mathematical_background/mathematical_background.md","mtime":"2023-08-23T13:18:41.230Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/matrix_methods/matrix_methods.html b/contents/matrix_methods/matrix_methods.html index fd683bcf2..ccb40b8c4 100644 --- a/contents/matrix_methods/matrix_methods.html +++ b/contents/matrix_methods/matrix_methods.html @@ -942,7 +942,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Matrix Methods","level":"1.10","depth":1,"next":{"title":"Gaussian Elimination","level":"1.10.1","depth":2,"path":"contents/gaussian_elimination/gaussian_elimination.md","ref":"contents/gaussian_elimination/gaussian_elimination.md","articles":[]},"previous":{"title":"Metropolis","level":"1.9.1","depth":2,"path":"contents/metropolis/metropolis.md","ref":"contents/metropolis/metropolis.md","articles":[]},"articles":[{"title":"Gaussian Elimination","level":"1.10.1","depth":2,"path":"contents/gaussian_elimination/gaussian_elimination.md","ref":"contents/gaussian_elimination/gaussian_elimination.md","articles":[]},{"title":"Thomas Algorithm","level":"1.10.2","depth":2,"path":"contents/thomas_algorithm/thomas_algorithm.md","ref":"contents/thomas_algorithm/thomas_algorithm.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/matrix_methods/matrix_methods.md","mtime":"2023-08-22T20:57:12.194Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Matrix Methods","level":"1.10","depth":1,"next":{"title":"Gaussian Elimination","level":"1.10.1","depth":2,"path":"contents/gaussian_elimination/gaussian_elimination.md","ref":"contents/gaussian_elimination/gaussian_elimination.md","articles":[]},"previous":{"title":"Metropolis","level":"1.9.1","depth":2,"path":"contents/metropolis/metropolis.md","ref":"contents/metropolis/metropolis.md","articles":[]},"articles":[{"title":"Gaussian Elimination","level":"1.10.1","depth":2,"path":"contents/gaussian_elimination/gaussian_elimination.md","ref":"contents/gaussian_elimination/gaussian_elimination.md","articles":[]},{"title":"Thomas Algorithm","level":"1.10.2","depth":2,"path":"contents/thomas_algorithm/thomas_algorithm.md","ref":"contents/thomas_algorithm/thomas_algorithm.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/matrix_methods/matrix_methods.md","mtime":"2023-08-23T13:18:41.230Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/metropolis/metropolis.html b/contents/metropolis/metropolis.html index d0070e3ac..8ab0148b6 100644 --- a/contents/metropolis/metropolis.html +++ b/contents/metropolis/metropolis.html @@ -1263,7 +1263,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Metropolis","level":"1.9.1","depth":2,"next":{"title":"Matrix Methods","level":"1.10","depth":1,"path":"contents/matrix_methods/matrix_methods.md","ref":"contents/matrix_methods/matrix_methods.md","articles":[{"title":"Gaussian Elimination","level":"1.10.1","depth":2,"path":"contents/gaussian_elimination/gaussian_elimination.md","ref":"contents/gaussian_elimination/gaussian_elimination.md","articles":[]},{"title":"Thomas Algorithm","level":"1.10.2","depth":2,"path":"contents/thomas_algorithm/thomas_algorithm.md","ref":"contents/thomas_algorithm/thomas_algorithm.md","articles":[]}]},"previous":{"title":"Monte Carlo","level":"1.9","depth":1,"path":"contents/monte_carlo_integration/monte_carlo_integration.md","ref":"contents/monte_carlo_integration/monte_carlo_integration.md","articles":[{"title":"Metropolis","level":"1.9.1","depth":2,"path":"contents/metropolis/metropolis.md","ref":"contents/metropolis/metropolis.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/metropolis/metropolis.md","mtime":"2023-08-22T20:57:12.194Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Metropolis","level":"1.9.1","depth":2,"next":{"title":"Matrix Methods","level":"1.10","depth":1,"path":"contents/matrix_methods/matrix_methods.md","ref":"contents/matrix_methods/matrix_methods.md","articles":[{"title":"Gaussian Elimination","level":"1.10.1","depth":2,"path":"contents/gaussian_elimination/gaussian_elimination.md","ref":"contents/gaussian_elimination/gaussian_elimination.md","articles":[]},{"title":"Thomas Algorithm","level":"1.10.2","depth":2,"path":"contents/thomas_algorithm/thomas_algorithm.md","ref":"contents/thomas_algorithm/thomas_algorithm.md","articles":[]}]},"previous":{"title":"Monte Carlo","level":"1.9","depth":1,"path":"contents/monte_carlo_integration/monte_carlo_integration.md","ref":"contents/monte_carlo_integration/monte_carlo_integration.md","articles":[{"title":"Metropolis","level":"1.9.1","depth":2,"path":"contents/metropolis/metropolis.md","ref":"contents/metropolis/metropolis.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/metropolis/metropolis.md","mtime":"2023-08-23T13:18:41.230Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/monte_carlo_integration/monte_carlo_integration.html b/contents/monte_carlo_integration/monte_carlo_integration.html index cb88bf0d7..0795a2fa9 100644 --- a/contents/monte_carlo_integration/monte_carlo_integration.html +++ b/contents/monte_carlo_integration/monte_carlo_integration.html @@ -2188,7 +2188,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Monte Carlo","level":"1.9","depth":1,"next":{"title":"Metropolis","level":"1.9.1","depth":2,"path":"contents/metropolis/metropolis.md","ref":"contents/metropolis/metropolis.md","articles":[]},"previous":{"title":"Euclidean Algorithm","level":"1.8","depth":1,"path":"contents/euclidean_algorithm/euclidean_algorithm.md","ref":"contents/euclidean_algorithm/euclidean_algorithm.md","articles":[]},"articles":[{"title":"Metropolis","level":"1.9.1","depth":2,"path":"contents/metropolis/metropolis.md","ref":"contents/metropolis/metropolis.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/monte_carlo_integration/monte_carlo_integration.md","mtime":"2023-08-22T20:57:12.214Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Monte Carlo","level":"1.9","depth":1,"next":{"title":"Metropolis","level":"1.9.1","depth":2,"path":"contents/metropolis/metropolis.md","ref":"contents/metropolis/metropolis.md","articles":[]},"previous":{"title":"Euclidean Algorithm","level":"1.8","depth":1,"path":"contents/euclidean_algorithm/euclidean_algorithm.md","ref":"contents/euclidean_algorithm/euclidean_algorithm.md","articles":[]},"articles":[{"title":"Metropolis","level":"1.9.1","depth":2,"path":"contents/metropolis/metropolis.md","ref":"contents/metropolis/metropolis.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/monte_carlo_integration/monte_carlo_integration.md","mtime":"2023-08-23T13:18:41.250Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/notation/notation.html b/contents/notation/notation.html index 3fa9a38ca..667d7d204 100644 --- a/contents/notation/notation.html +++ b/contents/notation/notation.html @@ -1114,7 +1114,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Complexity Notation","level":"1.6.1","depth":2,"next":{"title":"Affine Transformations","level":"1.6.2","depth":2,"path":"contents/affine_transformations/affine_transformations.md","ref":"contents/affine_transformations/affine_transformations.md","articles":[]},"previous":{"title":"Mathematical Background","level":"1.6","depth":1,"path":"contents/mathematical_background/mathematical_background.md","ref":"contents/mathematical_background/mathematical_background.md","articles":[{"title":"Complexity Notation","level":"1.6.1","depth":2,"path":"contents/notation/notation.md","ref":"contents/notation/notation.md","articles":[]},{"title":"Affine Transformations","level":"1.6.2","depth":2,"path":"contents/affine_transformations/affine_transformations.md","ref":"contents/affine_transformations/affine_transformations.md","articles":[]},{"title":"Bit Logic","level":"1.6.3","depth":2,"path":"contents/bitlogic/bitlogic.md","ref":"contents/bitlogic/bitlogic.md","articles":[]},{"title":"Taylor Series","level":"1.6.4","depth":2,"path":"contents/taylor_series_expansion/taylor_series_expansion.md","ref":"contents/taylor_series_expansion/taylor_series_expansion.md","articles":[]},{"title":"Convolutions","level":"1.6.5","depth":2,"path":"contents/convolutions/convolutions.md","ref":"contents/convolutions/convolutions.md","articles":[{"title":"Convolutions in 1D","level":"1.6.5.1","depth":3,"path":"contents/convolutions/1d/1d.md","ref":"contents/convolutions/1d/1d.md","articles":[]},{"title":"Multiplication as a Convolution","level":"1.6.5.2","depth":3,"path":"contents/convolutions/multiplication/multiplication.md","ref":"contents/convolutions/multiplication/multiplication.md","articles":[]},{"title":"Convolutions of Images (2D)","level":"1.6.5.3","depth":3,"path":"contents/convolutions/2d/2d.md","ref":"contents/convolutions/2d/2d.md","articles":[]},{"title":"Convolutional Theorem","level":"1.6.5.4","depth":3,"path":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","articles":[]}]},{"title":"Box Muller Transform","level":"1.6.6","depth":2,"path":"contents/box_muller/box_muller.md","ref":"contents/box_muller/box_muller.md","articles":[{"title":"How costly is rejection sampling?","level":"1.6.6.1","depth":3,"path":"contents/box_muller/box_muller_rejection.md","ref":"contents/box_muller/box_muller_rejection.md","articles":[]}]},{"title":"Probability Distributions","level":"1.6.7","depth":2,"path":"contents/probability_distributions/distributions.md","ref":"contents/probability_distributions/distributions.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/notation/notation.md","mtime":"2023-08-22T20:57:12.226Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Complexity Notation","level":"1.6.1","depth":2,"next":{"title":"Affine Transformations","level":"1.6.2","depth":2,"path":"contents/affine_transformations/affine_transformations.md","ref":"contents/affine_transformations/affine_transformations.md","articles":[]},"previous":{"title":"Mathematical Background","level":"1.6","depth":1,"path":"contents/mathematical_background/mathematical_background.md","ref":"contents/mathematical_background/mathematical_background.md","articles":[{"title":"Complexity Notation","level":"1.6.1","depth":2,"path":"contents/notation/notation.md","ref":"contents/notation/notation.md","articles":[]},{"title":"Affine Transformations","level":"1.6.2","depth":2,"path":"contents/affine_transformations/affine_transformations.md","ref":"contents/affine_transformations/affine_transformations.md","articles":[]},{"title":"Bit Logic","level":"1.6.3","depth":2,"path":"contents/bitlogic/bitlogic.md","ref":"contents/bitlogic/bitlogic.md","articles":[]},{"title":"Taylor Series","level":"1.6.4","depth":2,"path":"contents/taylor_series_expansion/taylor_series_expansion.md","ref":"contents/taylor_series_expansion/taylor_series_expansion.md","articles":[]},{"title":"Convolutions","level":"1.6.5","depth":2,"path":"contents/convolutions/convolutions.md","ref":"contents/convolutions/convolutions.md","articles":[{"title":"Convolutions in 1D","level":"1.6.5.1","depth":3,"path":"contents/convolutions/1d/1d.md","ref":"contents/convolutions/1d/1d.md","articles":[]},{"title":"Multiplication as a Convolution","level":"1.6.5.2","depth":3,"path":"contents/convolutions/multiplication/multiplication.md","ref":"contents/convolutions/multiplication/multiplication.md","articles":[]},{"title":"Convolutions of Images (2D)","level":"1.6.5.3","depth":3,"path":"contents/convolutions/2d/2d.md","ref":"contents/convolutions/2d/2d.md","articles":[]},{"title":"Convolutional Theorem","level":"1.6.5.4","depth":3,"path":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","articles":[]}]},{"title":"Box Muller Transform","level":"1.6.6","depth":2,"path":"contents/box_muller/box_muller.md","ref":"contents/box_muller/box_muller.md","articles":[{"title":"How costly is rejection sampling?","level":"1.6.6.1","depth":3,"path":"contents/box_muller/box_muller_rejection.md","ref":"contents/box_muller/box_muller_rejection.md","articles":[]}]},{"title":"Probability Distributions","level":"1.6.7","depth":2,"path":"contents/probability_distributions/distributions.md","ref":"contents/probability_distributions/distributions.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/notation/notation.md","mtime":"2023-08-23T13:18:41.258Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/physics_solvers/physics_solvers.html b/contents/physics_solvers/physics_solvers.html index f74686e69..4d93f41f0 100644 --- a/contents/physics_solvers/physics_solvers.html +++ b/contents/physics_solvers/physics_solvers.html @@ -937,7 +937,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Physics Solvers","level":"1.14","depth":1,"next":{"title":"Verlet Integration","level":"1.14.1","depth":2,"path":"contents/verlet_integration/verlet_integration.md","ref":"contents/verlet_integration/verlet_integration.md","articles":[]},"previous":{"title":"Stable Marriage Problem","level":"1.13.1","depth":2,"path":"contents/stable_marriage_problem/stable_marriage_problem.md","ref":"contents/stable_marriage_problem/stable_marriage_problem.md","articles":[]},"articles":[{"title":"Verlet Integration","level":"1.14.1","depth":2,"path":"contents/verlet_integration/verlet_integration.md","ref":"contents/verlet_integration/verlet_integration.md","articles":[]},{"title":"Quantum Systems","level":"1.14.2","depth":2,"path":"contents/quantum_systems/quantum_systems.md","ref":"contents/quantum_systems/quantum_systems.md","articles":[{"title":"Split-Operator Method","level":"1.14.2.1","depth":3,"path":"contents/split-operator_method/split-operator_method.md","ref":"contents/split-operator_method/split-operator_method.md","articles":[]}]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/physics_solvers/physics_solvers.md","mtime":"2023-08-22T20:57:12.226Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Physics Solvers","level":"1.14","depth":1,"next":{"title":"Verlet Integration","level":"1.14.1","depth":2,"path":"contents/verlet_integration/verlet_integration.md","ref":"contents/verlet_integration/verlet_integration.md","articles":[]},"previous":{"title":"Stable Marriage Problem","level":"1.13.1","depth":2,"path":"contents/stable_marriage_problem/stable_marriage_problem.md","ref":"contents/stable_marriage_problem/stable_marriage_problem.md","articles":[]},"articles":[{"title":"Verlet Integration","level":"1.14.1","depth":2,"path":"contents/verlet_integration/verlet_integration.md","ref":"contents/verlet_integration/verlet_integration.md","articles":[]},{"title":"Quantum Systems","level":"1.14.2","depth":2,"path":"contents/quantum_systems/quantum_systems.md","ref":"contents/quantum_systems/quantum_systems.md","articles":[{"title":"Split-Operator Method","level":"1.14.2.1","depth":3,"path":"contents/split-operator_method/split-operator_method.md","ref":"contents/split-operator_method/split-operator_method.md","articles":[]}]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/physics_solvers/physics_solvers.md","mtime":"2023-08-23T13:18:41.258Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/plotting/plotting.html b/contents/plotting/plotting.html index d0022b319..fdaaaf378 100644 --- a/contents/plotting/plotting.html +++ b/contents/plotting/plotting.html @@ -1407,7 +1407,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Plotting","level":"1.4","depth":1,"next":{"title":"Domain Coloring","level":"1.4.1","depth":2,"path":"contents/domain_coloring/domain_coloring.md","ref":"contents/domain_coloring/domain_coloring.md","articles":[]},"previous":{"title":"Code Reviewers","level":"1.3.1","depth":2,"path":"contents/code_reviews/code_reviewers.md","ref":"contents/code_reviews/code_reviewers.md","articles":[]},"articles":[{"title":"Domain Coloring","level":"1.4.1","depth":2,"path":"contents/domain_coloring/domain_coloring.md","ref":"contents/domain_coloring/domain_coloring.md","articles":[]},{"title":"Iterated Function Systems","level":"1.4.2","depth":2,"path":"contents/IFS/IFS.md","ref":"contents/IFS/IFS.md","articles":[{"title":"The Barnsley Fern","level":"1.4.2.1","depth":3,"path":"contents/barnsley/barnsley.md","ref":"contents/barnsley/barnsley.md","articles":[]}]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/plotting/plotting.md","mtime":"2023-08-22T20:57:12.226Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Plotting","level":"1.4","depth":1,"next":{"title":"Domain Coloring","level":"1.4.1","depth":2,"path":"contents/domain_coloring/domain_coloring.md","ref":"contents/domain_coloring/domain_coloring.md","articles":[]},"previous":{"title":"Code Reviewers","level":"1.3.1","depth":2,"path":"contents/code_reviews/code_reviewers.md","ref":"contents/code_reviews/code_reviewers.md","articles":[]},"articles":[{"title":"Domain Coloring","level":"1.4.1","depth":2,"path":"contents/domain_coloring/domain_coloring.md","ref":"contents/domain_coloring/domain_coloring.md","articles":[]},{"title":"Iterated Function Systems","level":"1.4.2","depth":2,"path":"contents/IFS/IFS.md","ref":"contents/IFS/IFS.md","articles":[{"title":"The Barnsley Fern","level":"1.4.2.1","depth":3,"path":"contents/barnsley/barnsley.md","ref":"contents/barnsley/barnsley.md","articles":[]}]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/plotting/plotting.md","mtime":"2023-08-23T13:18:41.262Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/probability_distributions/distributions.html b/contents/probability_distributions/distributions.html index 139c4742a..5aad38e93 100644 --- a/contents/probability_distributions/distributions.html +++ b/contents/probability_distributions/distributions.html @@ -1082,7 +1082,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Probability Distributions","level":"1.6.7","depth":2,"next":{"title":"Tree Traversal","level":"1.7","depth":1,"path":"contents/tree_traversal/tree_traversal.md","ref":"contents/tree_traversal/tree_traversal.md","articles":[]},"previous":{"title":"How costly is rejection sampling?","level":"1.6.6.1","depth":3,"path":"contents/box_muller/box_muller_rejection.md","ref":"contents/box_muller/box_muller_rejection.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/probability_distributions/distributions.md","mtime":"2023-08-22T20:57:12.230Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Probability Distributions","level":"1.6.7","depth":2,"next":{"title":"Tree Traversal","level":"1.7","depth":1,"path":"contents/tree_traversal/tree_traversal.md","ref":"contents/tree_traversal/tree_traversal.md","articles":[]},"previous":{"title":"How costly is rejection sampling?","level":"1.6.6.1","depth":3,"path":"contents/box_muller/box_muller_rejection.md","ref":"contents/box_muller/box_muller_rejection.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/probability_distributions/distributions.md","mtime":"2023-08-23T13:18:41.266Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/quantum_information/quantum_information.html b/contents/quantum_information/quantum_information.html index 22a66cddb..5d9761257 100644 --- a/contents/quantum_information/quantum_information.html +++ b/contents/quantum_information/quantum_information.html @@ -954,7 +954,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Quantum Information","level":"1.17","depth":1,"next":{"title":"Cryptography","level":"1.18","depth":1,"path":"contents/cryptography/cryptography.md","ref":"contents/cryptography/cryptography.md","articles":[]},"previous":{"title":"Flood Fill","level":"1.16.1","depth":2,"path":"contents/flood_fill/flood_fill.md","ref":"contents/flood_fill/flood_fill.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/quantum_information/quantum_information.md","mtime":"2023-08-22T20:57:12.234Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Quantum Information","level":"1.17","depth":1,"next":{"title":"Cryptography","level":"1.18","depth":1,"path":"contents/cryptography/cryptography.md","ref":"contents/cryptography/cryptography.md","articles":[]},"previous":{"title":"Flood Fill","level":"1.16.1","depth":2,"path":"contents/flood_fill/flood_fill.md","ref":"contents/flood_fill/flood_fill.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/quantum_information/quantum_information.md","mtime":"2023-08-23T13:18:41.266Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/quantum_systems/quantum_systems.html b/contents/quantum_systems/quantum_systems.html index abfa2cfd5..57fcce43f 100644 --- a/contents/quantum_systems/quantum_systems.html +++ b/contents/quantum_systems/quantum_systems.html @@ -1231,7 +1231,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Quantum Systems","level":"1.14.2","depth":2,"next":{"title":"Split-Operator Method","level":"1.14.2.1","depth":3,"path":"contents/split-operator_method/split-operator_method.md","ref":"contents/split-operator_method/split-operator_method.md","articles":[]},"previous":{"title":"Verlet Integration","level":"1.14.1","depth":2,"path":"contents/verlet_integration/verlet_integration.md","ref":"contents/verlet_integration/verlet_integration.md","articles":[]},"articles":[{"title":"Split-Operator Method","level":"1.14.2.1","depth":3,"path":"contents/split-operator_method/split-operator_method.md","ref":"contents/split-operator_method/split-operator_method.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/quantum_systems/quantum_systems.md","mtime":"2023-08-22T20:57:12.234Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Quantum Systems","level":"1.14.2","depth":2,"next":{"title":"Split-Operator Method","level":"1.14.2.1","depth":3,"path":"contents/split-operator_method/split-operator_method.md","ref":"contents/split-operator_method/split-operator_method.md","articles":[]},"previous":{"title":"Verlet Integration","level":"1.14.1","depth":2,"path":"contents/verlet_integration/verlet_integration.md","ref":"contents/verlet_integration/verlet_integration.md","articles":[]},"articles":[{"title":"Split-Operator Method","level":"1.14.2.1","depth":3,"path":"contents/split-operator_method/split-operator_method.md","ref":"contents/split-operator_method/split-operator_method.md","articles":[]}],"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/quantum_systems/quantum_systems.md","mtime":"2023-08-23T13:18:41.266Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/split-operator_method/split-operator_method.html b/contents/split-operator_method/split-operator_method.html index 92d622dba..9fa9e3a6d 100644 --- a/contents/split-operator_method/split-operator_method.html +++ b/contents/split-operator_method/split-operator_method.html @@ -2661,7 +2661,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Split-Operator Method","level":"1.14.2.1","depth":3,"next":{"title":"Data Compression","level":"1.15","depth":1,"path":"contents/data_compression/data_compression.md","ref":"contents/data_compression/data_compression.md","articles":[{"title":"Huffman Encoding","level":"1.15.1","depth":2,"path":"contents/huffman_encoding/huffman_encoding.md","ref":"contents/huffman_encoding/huffman_encoding.md","articles":[]}]},"previous":{"title":"Quantum Systems","level":"1.14.2","depth":2,"path":"contents/quantum_systems/quantum_systems.md","ref":"contents/quantum_systems/quantum_systems.md","articles":[{"title":"Split-Operator Method","level":"1.14.2.1","depth":3,"path":"contents/split-operator_method/split-operator_method.md","ref":"contents/split-operator_method/split-operator_method.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/split-operator_method/split-operator_method.md","mtime":"2023-08-22T20:57:12.246Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Split-Operator Method","level":"1.14.2.1","depth":3,"next":{"title":"Data Compression","level":"1.15","depth":1,"path":"contents/data_compression/data_compression.md","ref":"contents/data_compression/data_compression.md","articles":[{"title":"Huffman Encoding","level":"1.15.1","depth":2,"path":"contents/huffman_encoding/huffman_encoding.md","ref":"contents/huffman_encoding/huffman_encoding.md","articles":[]}]},"previous":{"title":"Quantum Systems","level":"1.14.2","depth":2,"path":"contents/quantum_systems/quantum_systems.md","ref":"contents/quantum_systems/quantum_systems.md","articles":[{"title":"Split-Operator Method","level":"1.14.2.1","depth":3,"path":"contents/split-operator_method/split-operator_method.md","ref":"contents/split-operator_method/split-operator_method.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/split-operator_method/split-operator_method.md","mtime":"2023-08-23T13:18:41.278Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/stable_marriage_problem/stable_marriage_problem.html b/contents/stable_marriage_problem/stable_marriage_problem.html index d128cdedf..5e16a5b92 100644 --- a/contents/stable_marriage_problem/stable_marriage_problem.html +++ b/contents/stable_marriage_problem/stable_marriage_problem.html @@ -2119,7 +2119,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Stable Marriage Problem","level":"1.13.1","depth":2,"next":{"title":"Physics Solvers","level":"1.14","depth":1,"path":"contents/physics_solvers/physics_solvers.md","ref":"contents/physics_solvers/physics_solvers.md","articles":[{"title":"Verlet Integration","level":"1.14.1","depth":2,"path":"contents/verlet_integration/verlet_integration.md","ref":"contents/verlet_integration/verlet_integration.md","articles":[]},{"title":"Quantum Systems","level":"1.14.2","depth":2,"path":"contents/quantum_systems/quantum_systems.md","ref":"contents/quantum_systems/quantum_systems.md","articles":[{"title":"Split-Operator Method","level":"1.14.2.1","depth":3,"path":"contents/split-operator_method/split-operator_method.md","ref":"contents/split-operator_method/split-operator_method.md","articles":[]}]}]},"previous":{"title":"Decision Problems","level":"1.13","depth":1,"path":"contents/decision_problems/decision_problems.md","ref":"contents/decision_problems/decision_problems.md","articles":[{"title":"Stable Marriage Problem","level":"1.13.1","depth":2,"path":"contents/stable_marriage_problem/stable_marriage_problem.md","ref":"contents/stable_marriage_problem/stable_marriage_problem.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/stable_marriage_problem/stable_marriage_problem.md","mtime":"2023-08-22T20:57:12.246Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Stable Marriage Problem","level":"1.13.1","depth":2,"next":{"title":"Physics Solvers","level":"1.14","depth":1,"path":"contents/physics_solvers/physics_solvers.md","ref":"contents/physics_solvers/physics_solvers.md","articles":[{"title":"Verlet Integration","level":"1.14.1","depth":2,"path":"contents/verlet_integration/verlet_integration.md","ref":"contents/verlet_integration/verlet_integration.md","articles":[]},{"title":"Quantum Systems","level":"1.14.2","depth":2,"path":"contents/quantum_systems/quantum_systems.md","ref":"contents/quantum_systems/quantum_systems.md","articles":[{"title":"Split-Operator Method","level":"1.14.2.1","depth":3,"path":"contents/split-operator_method/split-operator_method.md","ref":"contents/split-operator_method/split-operator_method.md","articles":[]}]}]},"previous":{"title":"Decision Problems","level":"1.13","depth":1,"path":"contents/decision_problems/decision_problems.md","ref":"contents/decision_problems/decision_problems.md","articles":[{"title":"Stable Marriage Problem","level":"1.13.1","depth":2,"path":"contents/stable_marriage_problem/stable_marriage_problem.md","ref":"contents/stable_marriage_problem/stable_marriage_problem.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/stable_marriage_problem/stable_marriage_problem.md","mtime":"2023-08-23T13:18:41.278Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/stacks_and_queues/stacks_and_queues.html b/contents/stacks_and_queues/stacks_and_queues.html index 5944b06e3..22de83897 100644 --- a/contents/stacks_and_queues/stacks_and_queues.html +++ b/contents/stacks_and_queues/stacks_and_queues.html @@ -1552,7 +1552,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Stacks and Queues","level":"1.5.1","depth":2,"next":{"title":"Mathematical Background","level":"1.6","depth":1,"path":"contents/mathematical_background/mathematical_background.md","ref":"contents/mathematical_background/mathematical_background.md","articles":[{"title":"Complexity Notation","level":"1.6.1","depth":2,"path":"contents/notation/notation.md","ref":"contents/notation/notation.md","articles":[]},{"title":"Affine Transformations","level":"1.6.2","depth":2,"path":"contents/affine_transformations/affine_transformations.md","ref":"contents/affine_transformations/affine_transformations.md","articles":[]},{"title":"Bit Logic","level":"1.6.3","depth":2,"path":"contents/bitlogic/bitlogic.md","ref":"contents/bitlogic/bitlogic.md","articles":[]},{"title":"Taylor Series","level":"1.6.4","depth":2,"path":"contents/taylor_series_expansion/taylor_series_expansion.md","ref":"contents/taylor_series_expansion/taylor_series_expansion.md","articles":[]},{"title":"Convolutions","level":"1.6.5","depth":2,"path":"contents/convolutions/convolutions.md","ref":"contents/convolutions/convolutions.md","articles":[{"title":"Convolutions in 1D","level":"1.6.5.1","depth":3,"path":"contents/convolutions/1d/1d.md","ref":"contents/convolutions/1d/1d.md","articles":[]},{"title":"Multiplication as a Convolution","level":"1.6.5.2","depth":3,"path":"contents/convolutions/multiplication/multiplication.md","ref":"contents/convolutions/multiplication/multiplication.md","articles":[]},{"title":"Convolutions of Images (2D)","level":"1.6.5.3","depth":3,"path":"contents/convolutions/2d/2d.md","ref":"contents/convolutions/2d/2d.md","articles":[]},{"title":"Convolutional Theorem","level":"1.6.5.4","depth":3,"path":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","articles":[]}]},{"title":"Box Muller Transform","level":"1.6.6","depth":2,"path":"contents/box_muller/box_muller.md","ref":"contents/box_muller/box_muller.md","articles":[{"title":"How costly is rejection sampling?","level":"1.6.6.1","depth":3,"path":"contents/box_muller/box_muller_rejection.md","ref":"contents/box_muller/box_muller_rejection.md","articles":[]}]},{"title":"Probability Distributions","level":"1.6.7","depth":2,"path":"contents/probability_distributions/distributions.md","ref":"contents/probability_distributions/distributions.md","articles":[]}]},"previous":{"title":"Data Structures","level":"1.5","depth":1,"path":"contents/data_structures/data_structures.md","ref":"contents/data_structures/data_structures.md","articles":[{"title":"Stacks and Queues","level":"1.5.1","depth":2,"path":"contents/stacks_and_queues/stacks_and_queues.md","ref":"contents/stacks_and_queues/stacks_and_queues.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/stacks_and_queues/stacks_and_queues.md","mtime":"2023-08-22T20:57:12.246Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Stacks and Queues","level":"1.5.1","depth":2,"next":{"title":"Mathematical Background","level":"1.6","depth":1,"path":"contents/mathematical_background/mathematical_background.md","ref":"contents/mathematical_background/mathematical_background.md","articles":[{"title":"Complexity Notation","level":"1.6.1","depth":2,"path":"contents/notation/notation.md","ref":"contents/notation/notation.md","articles":[]},{"title":"Affine Transformations","level":"1.6.2","depth":2,"path":"contents/affine_transformations/affine_transformations.md","ref":"contents/affine_transformations/affine_transformations.md","articles":[]},{"title":"Bit Logic","level":"1.6.3","depth":2,"path":"contents/bitlogic/bitlogic.md","ref":"contents/bitlogic/bitlogic.md","articles":[]},{"title":"Taylor Series","level":"1.6.4","depth":2,"path":"contents/taylor_series_expansion/taylor_series_expansion.md","ref":"contents/taylor_series_expansion/taylor_series_expansion.md","articles":[]},{"title":"Convolutions","level":"1.6.5","depth":2,"path":"contents/convolutions/convolutions.md","ref":"contents/convolutions/convolutions.md","articles":[{"title":"Convolutions in 1D","level":"1.6.5.1","depth":3,"path":"contents/convolutions/1d/1d.md","ref":"contents/convolutions/1d/1d.md","articles":[]},{"title":"Multiplication as a Convolution","level":"1.6.5.2","depth":3,"path":"contents/convolutions/multiplication/multiplication.md","ref":"contents/convolutions/multiplication/multiplication.md","articles":[]},{"title":"Convolutions of Images (2D)","level":"1.6.5.3","depth":3,"path":"contents/convolutions/2d/2d.md","ref":"contents/convolutions/2d/2d.md","articles":[]},{"title":"Convolutional Theorem","level":"1.6.5.4","depth":3,"path":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","articles":[]}]},{"title":"Box Muller Transform","level":"1.6.6","depth":2,"path":"contents/box_muller/box_muller.md","ref":"contents/box_muller/box_muller.md","articles":[{"title":"How costly is rejection sampling?","level":"1.6.6.1","depth":3,"path":"contents/box_muller/box_muller_rejection.md","ref":"contents/box_muller/box_muller_rejection.md","articles":[]}]},{"title":"Probability Distributions","level":"1.6.7","depth":2,"path":"contents/probability_distributions/distributions.md","ref":"contents/probability_distributions/distributions.md","articles":[]}]},"previous":{"title":"Data Structures","level":"1.5","depth":1,"path":"contents/data_structures/data_structures.md","ref":"contents/data_structures/data_structures.md","articles":[{"title":"Stacks and Queues","level":"1.5.1","depth":2,"path":"contents/stacks_and_queues/stacks_and_queues.md","ref":"contents/stacks_and_queues/stacks_and_queues.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/stacks_and_queues/stacks_and_queues.md","mtime":"2023-08-23T13:18:41.278Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/taylor_series_expansion/taylor_series_expansion.html b/contents/taylor_series_expansion/taylor_series_expansion.html index f87e816f9..29c3f493e 100644 --- a/contents/taylor_series_expansion/taylor_series_expansion.html +++ b/contents/taylor_series_expansion/taylor_series_expansion.html @@ -970,7 +970,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Taylor Series","level":"1.6.4","depth":2,"next":{"title":"Convolutions","level":"1.6.5","depth":2,"path":"contents/convolutions/convolutions.md","ref":"contents/convolutions/convolutions.md","articles":[{"title":"Convolutions in 1D","level":"1.6.5.1","depth":3,"path":"contents/convolutions/1d/1d.md","ref":"contents/convolutions/1d/1d.md","articles":[]},{"title":"Multiplication as a Convolution","level":"1.6.5.2","depth":3,"path":"contents/convolutions/multiplication/multiplication.md","ref":"contents/convolutions/multiplication/multiplication.md","articles":[]},{"title":"Convolutions of Images (2D)","level":"1.6.5.3","depth":3,"path":"contents/convolutions/2d/2d.md","ref":"contents/convolutions/2d/2d.md","articles":[]},{"title":"Convolutional Theorem","level":"1.6.5.4","depth":3,"path":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","articles":[]}]},"previous":{"title":"Bit Logic","level":"1.6.3","depth":2,"path":"contents/bitlogic/bitlogic.md","ref":"contents/bitlogic/bitlogic.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/taylor_series_expansion/taylor_series_expansion.md","mtime":"2023-08-22T20:57:12.250Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Taylor Series","level":"1.6.4","depth":2,"next":{"title":"Convolutions","level":"1.6.5","depth":2,"path":"contents/convolutions/convolutions.md","ref":"contents/convolutions/convolutions.md","articles":[{"title":"Convolutions in 1D","level":"1.6.5.1","depth":3,"path":"contents/convolutions/1d/1d.md","ref":"contents/convolutions/1d/1d.md","articles":[]},{"title":"Multiplication as a Convolution","level":"1.6.5.2","depth":3,"path":"contents/convolutions/multiplication/multiplication.md","ref":"contents/convolutions/multiplication/multiplication.md","articles":[]},{"title":"Convolutions of Images (2D)","level":"1.6.5.3","depth":3,"path":"contents/convolutions/2d/2d.md","ref":"contents/convolutions/2d/2d.md","articles":[]},{"title":"Convolutional Theorem","level":"1.6.5.4","depth":3,"path":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.md","articles":[]}]},"previous":{"title":"Bit Logic","level":"1.6.3","depth":2,"path":"contents/bitlogic/bitlogic.md","ref":"contents/bitlogic/bitlogic.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/taylor_series_expansion/taylor_series_expansion.md","mtime":"2023-08-23T13:18:41.278Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/thomas_algorithm/thomas_algorithm.html b/contents/thomas_algorithm/thomas_algorithm.html index 6568b7912..1c3855e3c 100644 --- a/contents/thomas_algorithm/thomas_algorithm.html +++ b/contents/thomas_algorithm/thomas_algorithm.html @@ -1705,7 +1705,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Thomas Algorithm","level":"1.10.2","depth":2,"next":{"title":"Computational Geometry","level":"1.11","depth":1,"path":"contents/computational_geometry/computational_geometry.md","ref":"contents/computational_geometry/computational_geometry.md","articles":[{"title":"Gift Wrapping","level":"1.11.1","depth":2,"path":"contents/gift_wrapping/gift_wrapping.md","ref":"contents/gift_wrapping/gift_wrapping.md","articles":[{"title":"Jarvis March","level":"1.11.1.1","depth":3,"path":"contents/jarvis_march/jarvis_march.md","ref":"contents/jarvis_march/jarvis_march.md","articles":[]},{"title":"Graham Scan","level":"1.11.1.2","depth":3,"path":"contents/graham_scan/graham_scan.md","ref":"contents/graham_scan/graham_scan.md","articles":[]}]}]},"previous":{"title":"Gaussian Elimination","level":"1.10.1","depth":2,"path":"contents/gaussian_elimination/gaussian_elimination.md","ref":"contents/gaussian_elimination/gaussian_elimination.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/thomas_algorithm/thomas_algorithm.md","mtime":"2023-08-22T20:57:12.250Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Thomas Algorithm","level":"1.10.2","depth":2,"next":{"title":"Computational Geometry","level":"1.11","depth":1,"path":"contents/computational_geometry/computational_geometry.md","ref":"contents/computational_geometry/computational_geometry.md","articles":[{"title":"Gift Wrapping","level":"1.11.1","depth":2,"path":"contents/gift_wrapping/gift_wrapping.md","ref":"contents/gift_wrapping/gift_wrapping.md","articles":[{"title":"Jarvis March","level":"1.11.1.1","depth":3,"path":"contents/jarvis_march/jarvis_march.md","ref":"contents/jarvis_march/jarvis_march.md","articles":[]},{"title":"Graham Scan","level":"1.11.1.2","depth":3,"path":"contents/graham_scan/graham_scan.md","ref":"contents/graham_scan/graham_scan.md","articles":[]}]}]},"previous":{"title":"Gaussian Elimination","level":"1.10.1","depth":2,"path":"contents/gaussian_elimination/gaussian_elimination.md","ref":"contents/gaussian_elimination/gaussian_elimination.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/thomas_algorithm/thomas_algorithm.md","mtime":"2023-08-23T13:18:41.278Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/contents/tree_traversal/code/csharp/Tree.cs b/contents/tree_traversal/code/csharp/Tree.cs index 28df47c91..5e8bc263c 100644 --- a/contents/tree_traversal/code/csharp/Tree.cs +++ b/contents/tree_traversal/code/csharp/Tree.cs @@ -30,29 +30,51 @@ private Tree(int id, int depthCount, int childrenCount) } } + private void DFSRecursive(Tree tree) { + Console.Write(tree.Id + " "); + + foreach (var c in tree._children) + DFSRecursive(c); + } + public void DFSRecursive() { DFSRecursive(this); - void DFSRecursive(Tree tree) - { - Console.Write(tree.Id + " "); + } - foreach (var c in tree._children) - DFSRecursive(c); - } + private void DFSRecursivePostorder(Tree tree) + { + foreach (var c in tree._children) + DFSRecursivePostorder(c); + + Console.Write(tree.Id + " "); } public void DFSRecursivePostorder() { DFSRecursivePostorder(this); - void DFSRecursivePostorder(Tree tree) - { - foreach (var c in tree._children) - DFSRecursivePostorder(c); + } - Console.Write(tree.Id + " "); + private void DFSRecursiveInorderBinary(Tree tree) + { + switch (tree._children.Count) + { + case 2: + DFSRecursiveInorderBinary(tree._children[0]); + Console.Write(tree.Id + " "); + DFSRecursiveInorderBinary(tree._children[1]); + break; + case 1: + DFSRecursiveInorderBinary(tree._children[0]); + Console.Write(tree.Id + " "); + break; + case 0: + Console.Write(tree.Id + " "); + break; + default: + throw new Exception("Not binary tree!"); } } @@ -60,26 +82,6 @@ public void DFSRecursiveInorderBinary() { DFSRecursiveInorderBinary(this); - void DFSRecursiveInorderBinary(Tree tree) - { - switch (tree._children.Count) - { - case 2: - DFSRecursiveInorderBinary(tree._children[0]); - Console.Write(tree.Id + " "); - DFSRecursiveInorderBinary(tree._children[1]); - break; - case 1: - DFSRecursiveInorderBinary(tree._children[0]); - Console.Write(tree.Id + " "); - break; - case 0: - Console.Write(tree.Id + " "); - break; - default: - throw new Exception("Not binary tree!"); - } - } } public void DFSStack() diff --git a/contents/tree_traversal/tree_traversal.html b/contents/tree_traversal/tree_traversal.html index a072d17cb..93a3ecc7e 100644 --- a/contents/tree_traversal/tree_traversal.html +++ b/contents/tree_traversal/tree_traversal.html @@ -1059,17 +1059,17 @@

Tree Traversal

} } -
public void DFSRecursive()
+
private void DFSRecursive(Tree tree) {
+    Console.Write(tree.Id + " ");
+
+    foreach (var c in tree._children)
+        DFSRecursive(c);
+}
+
+public void DFSRecursive()
 {
     DFSRecursive(this);
 
-    void DFSRecursive(Tree tree)
-    {
-        Console.Write(tree.Id + " ");
-
-        foreach (var c in tree._children)
-            DFSRecursive(c);
-    }
 }
 
void dfs_recursive(struct node n) {
@@ -1244,18 +1244,17 @@ 
Tree Traversal

   std::cout << n.value << ' ';
 }
-
public void DFSRecursivePostorder()
+
private void DFSRecursivePostorder(Tree tree)
 {
-    DFSRecursivePostorder(this);
+    foreach (var c in tree._children)
+        DFSRecursivePostorder(c);
 
-    void DFSRecursivePostorder(Tree tree)
-    {
-        foreach (var c in tree._children)
-            DFSRecursivePostorder(c);
-
-        Console.Write(tree.Id + " ");
-    }
+    Console.Write(tree.Id + " ");
 }
+
+public void DFSRecursivePostorder()
+{
+    DFSRecursivePostorder(this);
 
void dfs_recursive_postorder(struct node n) {
     for (size_t i = 0; i < n.children_size; ++i) {
@@ -1450,31 +1449,31 @@ 
Tree Traversal

   }
 }
-
public void DFSRecursiveInorderBinary()
+

+private void DFSRecursiveInorderBinary(Tree tree)
 {
-    DFSRecursiveInorderBinary(this);
-
-    void DFSRecursiveInorderBinary(Tree tree)
+    switch (tree._children.Count)
     {
-        switch (tree._children.Count)
-        {
-            case 2:
-                DFSRecursiveInorderBinary(tree._children[0]);
-                Console.Write(tree.Id + " ");
-                DFSRecursiveInorderBinary(tree._children[1]);
-                break;
-            case 1:
-                DFSRecursiveInorderBinary(tree._children[0]);
-                Console.Write(tree.Id + " ");
-                break;
-            case 0:
-                Console.Write(tree.Id + " ");
-                break;
-            default:
-                throw new Exception("Not binary tree!");
-        }
+        case 2:
+            DFSRecursiveInorderBinary(tree._children[0]);
+            Console.Write(tree.Id + " ");
+            DFSRecursiveInorderBinary(tree._children[1]);
+            break;
+        case 1:
+            DFSRecursiveInorderBinary(tree._children[0]);
+            Console.Write(tree.Id + " ");
+            break;
+        case 0:
+            Console.Write(tree.Id + " ");
+            break;
+        default:
+            throw new Exception("Not binary tree!");
     }
 }
+
+public void DFSRecursiveInorderBinary()
+{
+    DFSRecursiveInorderBinary(this);
 
void dfs_recursive_inorder_btree(struct node n) {
     switch (n.children_size) {
@@ -1824,7 +1823,9 @@ 
Tree Traversal

   }
 }
-
public void DFSStack()
+
}
+
+public void DFSStack()
 {
     var stack = new Stack<Tree>();
     stack.Push(this);
@@ -1836,8 +1837,6 @@ 
Tree Traversal

 
         foreach (var c in temp._children)
             stack.Push(c);
-    }
-}
 
void dfs_stack(struct node n) {
     struct stack stk = get_stack(sizeof(struct node*));
@@ -2114,7 +2113,9 @@ 
Tree Traversal

   }
 }
-
public void BFSQueue()
+
}
+
+public void BFSQueue()
 {
     var queue = new Queue<Tree>();
     queue.Enqueue(this);
@@ -2126,8 +2127,6 @@ 
Tree Traversal

 
         foreach (var c in temp._children)
             queue.Enqueue(c);
-    }
-}
 
void bfs_queue(struct node n) {
     struct queue q = get_queue(sizeof(struct node*));
@@ -2651,29 +2650,51 @@ 
Example Code

             }
         }
 
+        private void DFSRecursive(Tree tree) {
+            Console.Write(tree.Id + " ");
+
+            foreach (var c in tree._children)
+                DFSRecursive(c);
+        }
+
         public void DFSRecursive()
         {
             DFSRecursive(this);
 
-            void DFSRecursive(Tree tree)
-            {
-                Console.Write(tree.Id + " ");
+        }
 
-                foreach (var c in tree._children)
-                    DFSRecursive(c);
-            }
+        private void DFSRecursivePostorder(Tree tree)
+        {
+            foreach (var c in tree._children)
+                DFSRecursivePostorder(c);
+
+            Console.Write(tree.Id + " ");
         }
 
         public void DFSRecursivePostorder()
         {
             DFSRecursivePostorder(this);
 
-            void DFSRecursivePostorder(Tree tree)
-            {
-                foreach (var c in tree._children)
-                    DFSRecursivePostorder(c);
+        }
 
-                Console.Write(tree.Id + " ");
+        private void DFSRecursiveInorderBinary(Tree tree)
+        {
+            switch (tree._children.Count)
+            {
+                case 2:
+                    DFSRecursiveInorderBinary(tree._children[0]);
+                    Console.Write(tree.Id + " ");
+                    DFSRecursiveInorderBinary(tree._children[1]);
+                    break;
+                case 1:
+                    DFSRecursiveInorderBinary(tree._children[0]);
+                    Console.Write(tree.Id + " ");
+                    break;
+                case 0:
+                    Console.Write(tree.Id + " ");
+                    break;
+                default:
+                    throw new Exception("Not binary tree!");
             }
         }
 
@@ -2681,26 +2702,6 @@ 
Example Code

         {
             DFSRecursiveInorderBinary(this);
 
-            void DFSRecursiveInorderBinary(Tree tree)
-            {
-                switch (tree._children.Count)
-                {
-                    case 2:
-                        DFSRecursiveInorderBinary(tree._children[0]);
-                        Console.Write(tree.Id + " ");
-                        DFSRecursiveInorderBinary(tree._children[1]);
-                        break;
-                    case 1:
-                        DFSRecursiveInorderBinary(tree._children[0]);
-                        Console.Write(tree.Id + " ");
-                        break;
-                    case 0:
-                        Console.Write(tree.Id + " ");
-                        break;
-                    default:
-                        throw new Exception("Not binary tree!");
-                }
-            }
         }
 
         public void DFSStack()
@@ -5112,7 +5113,7 @@ 
No results matching "
         var gitbook = gitbook || [];
         gitbook.push(function() {
-            gitbook.page.hasChanged({"page":{"title":"Tree Traversal","level":"1.7","depth":1,"next":{"title":"Euclidean Algorithm","level":"1.8","depth":1,"path":"contents/euclidean_algorithm/euclidean_algorithm.md","ref":"contents/euclidean_algorithm/euclidean_algorithm.md","articles":[]},"previous":{"title":"Probability Distributions","level":"1.6.7","depth":2,"path":"contents/probability_distributions/distributions.md","ref":"contents/probability_distributions/distributions.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n    \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas  and Rosenbluth,Arianna W.  and Rosenbluth,Marshall N.  and Teller,Augusta H.  and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n    \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/tree_traversal/tree_traversal.md","mtime":"2023-08-22T20:57:12.258Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}});
+            gitbook.page.hasChanged({"page":{"title":"Tree Traversal","level":"1.7","depth":1,"next":{"title":"Euclidean Algorithm","level":"1.8","depth":1,"path":"contents/euclidean_algorithm/euclidean_algorithm.md","ref":"contents/euclidean_algorithm/euclidean_algorithm.md","articles":[]},"previous":{"title":"Probability Distributions","level":"1.6.7","depth":2,"path":"contents/probability_distributions/distributions.md","ref":"contents/probability_distributions/distributions.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n    \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas  and Rosenbluth,Arianna W.  and Rosenbluth,Marshall N.  and Teller,Augusta H.  and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n    \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/tree_traversal/tree_traversal.md","mtime":"2023-08-23T13:18:41.286Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}});
         });
diff --git a/contents/verlet_integration/verlet_integration.html b/contents/verlet_integration/verlet_integration.html index 1e0008f1e..48b6a9970 100644 --- a/contents/verlet_integration/verlet_integration.html +++ b/contents/verlet_integration/verlet_integration.html @@ -2921,7 +2921,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Verlet Integration","level":"1.14.1","depth":2,"next":{"title":"Quantum Systems","level":"1.14.2","depth":2,"path":"contents/quantum_systems/quantum_systems.md","ref":"contents/quantum_systems/quantum_systems.md","articles":[{"title":"Split-Operator Method","level":"1.14.2.1","depth":3,"path":"contents/split-operator_method/split-operator_method.md","ref":"contents/split-operator_method/split-operator_method.md","articles":[]}]},"previous":{"title":"Physics Solvers","level":"1.14","depth":1,"path":"contents/physics_solvers/physics_solvers.md","ref":"contents/physics_solvers/physics_solvers.md","articles":[{"title":"Verlet Integration","level":"1.14.1","depth":2,"path":"contents/verlet_integration/verlet_integration.md","ref":"contents/verlet_integration/verlet_integration.md","articles":[]},{"title":"Quantum Systems","level":"1.14.2","depth":2,"path":"contents/quantum_systems/quantum_systems.md","ref":"contents/quantum_systems/quantum_systems.md","articles":[{"title":"Split-Operator Method","level":"1.14.2.1","depth":3,"path":"contents/split-operator_method/split-operator_method.md","ref":"contents/split-operator_method/split-operator_method.md","articles":[]}]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/verlet_integration/verlet_integration.md","mtime":"2023-08-22T20:57:12.266Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":"../..","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Verlet Integration","level":"1.14.1","depth":2,"next":{"title":"Quantum Systems","level":"1.14.2","depth":2,"path":"contents/quantum_systems/quantum_systems.md","ref":"contents/quantum_systems/quantum_systems.md","articles":[{"title":"Split-Operator Method","level":"1.14.2.1","depth":3,"path":"contents/split-operator_method/split-operator_method.md","ref":"contents/split-operator_method/split-operator_method.md","articles":[]}]},"previous":{"title":"Physics Solvers","level":"1.14","depth":1,"path":"contents/physics_solvers/physics_solvers.md","ref":"contents/physics_solvers/physics_solvers.md","articles":[{"title":"Verlet Integration","level":"1.14.1","depth":2,"path":"contents/verlet_integration/verlet_integration.md","ref":"contents/verlet_integration/verlet_integration.md","articles":[]},{"title":"Quantum Systems","level":"1.14.2","depth":2,"path":"contents/quantum_systems/quantum_systems.md","ref":"contents/quantum_systems/quantum_systems.md","articles":[{"title":"Split-Operator Method","level":"1.14.2.1","depth":3,"path":"contents/split-operator_method/split-operator_method.md","ref":"contents/split-operator_method/split-operator_method.md","articles":[]}]}]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"contents/verlet_integration/verlet_integration.md","mtime":"2023-08-23T13:18:41.290Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":"../..","book":{"language":""}}); }); diff --git a/index.html b/index.html index 5d7ddf974..97b3db0ed 100644 --- a/index.html +++ b/index.html @@ -945,7 +945,7 @@

No results matching " var gitbook = gitbook || []; gitbook.push(function() { - gitbook.page.hasChanged({"page":{"title":"Algorithm Archive","level":"1.1","depth":1,"next":{"title":"Introduction","level":"1.2","depth":1,"path":"contents/introduction/introduction.md","ref":"contents/introduction/introduction.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"README.md","mtime":"2023-08-22T20:57:11.690Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-22T20:57:39.049Z"},"basePath":".","book":{"language":""}}); + gitbook.page.hasChanged({"page":{"title":"Algorithm Archive","level":"1.1","depth":1,"next":{"title":"Introduction","level":"1.2","depth":1,"path":"contents/introduction/introduction.md","ref":"contents/introduction/introduction.md","articles":[]},"dir":"ltr"},"config":{"plugins":["mathjax@https://github.com/algorithm-archivists/plugin-mathjax","bibtex-cite","wordcount","api-language-selector@https://github.com/algorithm-archivists/gitbook-plugin-api-language-selector.git","include-codeblock","bulk-redirect","prism","-highlight"],"root":"./","styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"api-language-selector":{"languages":[{"lang":"jl","name":"Julia","default":true},{"lang":"bash","name":"Bash"},{"lang":"cs","name":"C#"},{"lang":"cpp","name":"C++"},{"lang":"c","name":"C"},{"lang":"c8","name":"chip-8"},{"lang":"py","name":"Python"},{"lang":"js","name":"JavaScript"},{"lang":"scratch","name":"Scratch"},{"lang":"hs","name":"Haskell"},{"lang":"rs","name":"Rust"},{"lang":"ml","name":"OCaml"},{"lang":"java","name":"Java"},{"lang":"clj","name":"Clojure"},{"lang":"elm","name":"Elm"},{"lang":"LabVIEW","name":"LabVIEW"},{"lang":"d","name":"D"},{"lang":"go","name":"Go"},{"lang":"swift","name":"Swift"},{"lang":"racket","name":"Racket"},{"lang":"m","name":"Matlab"},{"lang":"r","name":"R"},{"lang":"ti83b","name":"TI-83 Basic"},{"lang":"lua","name":"Lua"},{"lang":"crystal","name":"Crystal"},{"lang":"php","name":"PHP"},{"lang":"lisp","name":"Common Lisp"},{"lang":"nim","name":"Nim"},{"lang":"asm-x64","name":"X86-64 Assembly"},{"lang":"f90","name":"Fortran90"},{"lang":"factor","name":"Factor"},{"lang":"ws","name":"Whitespace"},{"lang":"scala","name":"Scala"},{"lang":"emojic","name":"Emojicode"},{"lang":"lolcode","name":"LOLCODE"},{"lang":"piet","name":"Piet"},{"lang":"ss","name":"Scheme"},{"lang":"ps1","name":"PowerShell"},{"lang":"v","name":"Vlang"},{"lang":"coffee","name":"CoffeeScript"},{"lang":"kotlin","name":"Kotlin"},{"lang":"ts","name":"TypeScript"},{"lang":"vim","name":"VimL"},{"lang":"coco","name":"Coconut"},{"lang":"dart","name":"Dart"}]},"prism":{"lang":{"asm-x64":"nasm"},"ignore":["emojicode","text"],"css":["prismjs/themes/prism-tomorrow.css"]},"wordcount":{},"search":{},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"fontsettings":{"theme":"white","family":"sans","size":2},"bulk-redirect":{"basepath":"/","redirectsFile":"redirects.json"},"bibtex-cite":{},"mathjax":{"forceSVG":false,"version":"2.6.1"},"include-codeblock":{"check":false,"edit":false,"lang":"","fixlang":true,"template":"default","theme":"chrome","unindent":true},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"showLevel":false}},"theme":"default","lunr":{"maxIndexSize":1000000000},"honkit":">= 3.0.0","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56},"embedFonts":false},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"bibCount":0,"variables":{},"title":"Arcane Algorithm Archive","bib":[{"citationKey":"CT1965","entryType":"ARTICLE","entryTags":{"TITLE":"An algorithm for the machine calculation of complex Fourier series","AUTHOR":"Cooley, James W and Tukey, John W","JOURNAL":"Mathematics of computation","VOLUME":"19","NUMBER":"90","PAGES":"297--301","YEAR":"1965","PUBLISHER":"JSTOR"}},{"citationKey":"JM1973","entryType":"ARTICLE","entryTags":{"TITLE":"On the identification of the convex hull of a finite set of points in the plane","AUTHOR":"Jarvis, Ray A","JOURNAL":"Information processing letters","VOLUME":"2","NUMBER":"1","PAGES":"18--21","YEAR":"1973","PUBLISHER":"Elsevier"}},{"citationKey":"GS1972","entryType":"ARTICLE","entryTags":{"TITLE":"An efficient algorithm for determining the convex hull of a finite planar set","AUTHOR":"Graham, Ronald L","JOURNAL":"Information processing letters","VOLUME":"1","NUMBER":"4","PAGES":"132--133","YEAR":"1972","PUBLISHER":"Elsevier"}},{"citationKey":"GNUPLOT","entryType":"MISC","entryTags":{"TITLE":"Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation","AUTHOR":"Williams, T and Kelley, C","YEAR":"2015"}},{"citationKey":"BEDE725","entryType":"BOOK","entryTags":{"TITLE":"Bede, the Reckoning of Time","AUTHOR":"Venerabilis, Beda and others","VOLUME":"29","YEAR":"1999","PUBLISHER":"Liverpool University Press"}},{"citationKey":"DICTCOMPUTUS","entryType":"MISC","entryTags":{"TITLE":"Dictionary.com definition of computus","URL":"https://www.merriam-webster.com/dictionary/computus","YEAR":"2020"}},{"citationKey":"COMPUTUS1876","entryType":"ARTICLE","entryTags":{"TITLE":"To find Easter: a new York correspondent sends us the following","AUTHOR":"unknown","JOURNAL":"Nature","YEAR":"1876"}},{"citationKey":"BIEN2004","entryType":"ARTICLE","entryTags":{"TITLE":"Gauss and beyond: The making of Easter algorithms","AUTHOR":"Bien, Reinhold","JOURNAL":"Archive for history of exact sciences","VOLUME":"58","NUMBER":"5","PAGES":"439--452","YEAR":"2004","PUBLISHER":"Springer"}},{"citationKey":"SERVOIS","entryType":"INPROCEEDINGS","entryTags":{"TITLE":"84 Calendrier","AUTHOR":"Servois, M","BOOKTITLE":"Annales de Mathématiques pures et appliquées","VOLUME":"4","NUMBER":"1813-1814","PAGES":"84--90"}},{"citationKey":"STANDISH2004","entryType":"ARTICLE","entryTags":{"TITLE":"The astronomical unit now","AUTHOR":"Standish, EM","JOURNAL":"Proceedings of the International Astronomical Union","VOLUME":"2004","NUMBER":"IAUC196","PAGES":"163--179","YEAR":"2004","PUBLISHER":"Cambridge University Press"}},{"citationKey":"LUNAR_MONTH_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Lunar Month","URL":"https://en.wikipedia.org/wiki/Lunar_month","YEAR":"2020"}},{"citationKey":"SELF-SIMILAR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Self-similarity","URL":"https://en.wikipedia.org/wiki/Self-similarity","YEAR":"2019"}},{"citationKey":"HAUSDORFF","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hausdorff dimension","URL":"https://en.wikipedia.org/wiki/Hausdorff_dimension","YEAR":"2019"}},{"citationKey":"3B1BFRACTAL","entryType":"MISC","entryTags":{"AUTHOR":"Sanderson, G","TITLE":"3blue1brown: Fractals are typically not self-similar","URL":"https://www.youtube.com/watch?v=gB9n2gHsHN4","YEAR":"2017"}},{"citationKey":"MANDELBROT1983FRACTAL","entryType":"BOOK","entryTags":{"TITLE":"The fractal geometry of nature","AUTHOR":"Mandelbrot, Benoit B","VOLUME":"173","YEAR":"1983","PUBLISHER":"WH freeman New York"}},{"citationKey":"MANDELBROT1967LONG","entryType":"ARTICLE","entryTags":{"TITLE":"How long is the coast of Britain? Statistical self-similarity and fractional dimension","AUTHOR":"Mandelbrot, Benoit","JOURNAL":"science","VOLUME":"156","NUMBER":"3775","PAGES":"636--638","YEAR":"1967","PUBLISHER":"American Association for the Advancement of Science"}},{"citationKey":"JAMPOUR2010NEW","entryType":"ARTICLE","entryTags":{"TITLE":"A new fast technique for fingerprint identification with fractal and chaos game theory","AUTHOR":"Jampour, Mahdi and Yaghoobi, Mahdi and Ashourzadeh, Maryam and Soleimani, Adel","JOURNAL":"Fractals","VOLUME":"18","NUMBER":"03","PAGES":"293--300","YEAR":"2010","PUBLISHER":"World Scientific"}},{"citationKey":"FRACTAL-COMPRESSION","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Fractal Compression","URL":"https://en.wikipedia.org/wiki/Fractal_compression","YEAR":"2019"}},{"citationKey":"SAUPE1994REVIEW","entryType":"ARTICLE","entryTags":{"TITLE":"A review of the fractal image compression literature","AUTHOR":"Saupe, Dietmar and Hamzaoui, Raouf","JOURNAL":"ACM SIGGRAPH Computer Graphics","VOLUME":"28","NUMBER":"4","PAGES":"268--276","YEAR":"1994","PUBLISHER":"ACM"}},{"citationKey":"GNEITING2012ESTIMATORS","entryType":"ARTICLE","entryTags":{"TITLE":"Estimators of fractal dimension: Assessing the roughness of time series and spatial data","AUTHOR":"Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B","JOURNAL":"Statistical Science","PAGES":"247--277","YEAR":"2012","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON1981FRACTALS","entryType":"ARTICLE","entryTags":{"TITLE":"Fractals and self similarity","AUTHOR":"Hutchinson, John E","JOURNAL":"Indiana University Mathematics Journal","VOLUME":"30","NUMBER":"5","PAGES":"713--747","YEAR":"1981","PUBLISHER":"JSTOR"}},{"citationKey":"HUTCHINSON-OPERATOR","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hutchinson Operator","URL":"https://en.wikipedia.org/wiki/Hutchinson_operator","YEAR":"2019"}},{"citationKey":"CHAOS-GAME","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Chaos Game","URL":"https://en.wikipedia.org/wiki/Chaos_game","YEAR":"2019"}},{"citationKey":"CHAOS-GAME-WOLF","entryType":"MISC","entryTags":{"TITLE":"Wolfram: Chaos Game","URL":"http://mathworld.wolfram.com/ChaosGame.html","YEAR":"2019"}},{"citationKey":"BARNSLEY2014FRACTALS","entryType":"BOOK","entryTags":{"TITLE":"Fractals everywhere","AUTHOR":"Barnsley, Michael F","YEAR":"2014","PUBLISHER":"Academic press"}},{"citationKey":"HSV","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: HSL and HSV","URL":"https://en.wikipedia.org/wiki/HSL_and_HSV","YEAR":"2020"}},{"citationKey":"SCHLOSS2019","entryType":"ARTICLE","entryTags":{"TITLE":"Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units","AUTHOR":"Schloss, James","YEAR":"2019"}},{"citationKey":"PETHICK2008","entryType":"BOOK","entryTags":{"TITLE":"Bose--Einstein condensation in dilute gases","AUTHOR":"Pethick, Christopher J and Smith, Henrik","YEAR":"2008","PUBLISHER":"Cambridge university press"}},{"citationKey":"WEGERT2012","entryType":"BOOK","entryTags":{"TITLE":"Visual complex functions: an introduction with phase portraits","AUTHOR":"Wegert, Elias","YEAR":"2012","PUBLISHER":"Springer Science \\& Business Media"}},{"citationKey":"POELKEDOMAIN","entryType":"ARTICLE","entryTags":{"TITLE":"Domain Coloring of Complex Functions","AUTHOR":"Poelke, Konstantin and Polthier, Konrad"}},{"citationKey":"LUNDMARK2004","entryType":"ARTICLE","entryTags":{"TITLE":"Visualizing complex analytic functions using domain coloring","AUTHOR":"Lundmark, Hans","JOURNAL":"Recuperado el","VOLUME":"24","YEAR":"2004"}},{"citationKey":"GIMP_BUCKET","entryType":"MISC","entryTags":{"TITLE":"Bucket Fill in Gimp","URL":"https://docs.gimp.org/2.10/en/gimp-tool-bucket-fill.html","YEAR":"2020"}},{"citationKey":"TORBERT2016","entryType":"BOOK","entryTags":{"TITLE":"Applied computer science","AUTHOR":"Torbert, Shane","YEAR":"2016","PAGES":"158","PUBLISHER":"Springer"}},{"citationKey":"CANNY1986COMPUTATIONAL","entryType":"ARTICLE","entryTags":{"TITLE":"A computational approach to edge detection","AUTHOR":"Canny, John","JOURNAL":"IEEE Transactions on pattern analysis and machine intelligence","NUMBER":"6","PAGES":"679--698","YEAR":"1986","PUBLISHER":"Ieee"}},{"citationKey":"MORRIS1978COUNTING","entryType":"ARTICLE","entryTags":{"TITLE":"Counting large numbers of events in small registers","AUTHOR":"Morris, R","JOURNAL":"Communications of the ACM","VOLUME":"21","NUMBER":"10","PAGES":"840--842","YEAR":"1978","PUBLISHER":"ACM New York, NY, USA"}},{"citationKey":"FLAJOLET1985APPROXIMATE","entryType":"ARTICLE","entryTags":{"TITLE":"Approximate counting: a detailed analysis","AUTHOR":"Flajolet, P","JOURNAL":"BIT Numerical Mathematics","VOLUME":"25","NUMBER":"1","PAGES":"113--134","YEAR":"1985","PUBLISHER":"Springer"}},{"citationKey":"ARPIT_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Morris's Algorithm for Approximate Counting","AUTHOR":"Bhayani, A","URL":"https://arpitbhayani.me/blogs/morris-counter","YEAR":"2020"}},{"citationKey":"GREGGUNDERSON_COUNTING","entryType":"MISC","entryTags":{"TITLE":"Approximate Counting with Morris's Algorithm","AUTHOR":"Gundersen, G","URL":"http://gregorygundersen.com/blog/2019/11/11/morris-algorithm/","YEAR":"2019"}},{"citationKey":"3B1B_FINGER_COUNT","entryType":"MISC","entryTags":{"TITLE":"How to count to 1000 on two hands","AUTHOR":"Sanderson, G","URL":"https://youtu.be/1SMmc9gQmHQ","YEAR":"2015"}},{"citationKey":"METROPOLIS1953EQUATION","entryType":"ARTICLE","entryTags":{"PAGES":"1087-1092","EPRINT":"https://doi.org/10.1063/1.1699114\n \n","NUMBER":"6","AUTHOR":"Metropolis,Nicholas and Rosenbluth,Arianna W. and Rosenbluth,Marshall N. and Teller,Augusta H. and Teller,Edward ","URL":"https://doi.org/10.1063/1.1699114\n \n","JOURNAL":"The Journal of Chemical Physics","TITLE":"Equation of State Calculations by Fast Computing Machines","VOLUME":"21","YEAR":"1953","DOI":"10.1063/1.1699114"}},{"citationKey":"ROSENTHAL2011OPTIMAL","entryType":"ARTICLE","entryTags":{"TITLE":"Optimal proposal distributions and adaptive MCMC","AUTHOR":"Rosenthal, Jeffrey S and others","JOURNAL":"Handbook of Markov Chain Monte Carlo","VOLUME":"4","NUMBER":"10.1201","YEAR":"2011","PUBLISHER":"Chapman & Hall/CRC Boca Raton, FL"}},{"citationKey":"GARETH2001OPTIMAL","entryType":"ARTICLE","entryTags":{"PAGES":"351 -- 367","NUMBER":"4","AUTHOR":"Gareth O. Roberts and Jeffrey S. Rosenthal","URL":"https://doi.org/10.1214/ss/1015346320","JOURNAL":"Statistical Science","TITLE":"Optimal scaling for various Metropolis-Hastings algorithms","VOLUME":"16","PUBLISHER":"Institute of Mathematical Statistics","YEAR":"2001","DOI":"10.1214/ss/1015346320"}},{"citationKey":"POTENTIAL_ENERGY_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Potential Energy","URL":"https://en.wikipedia.org/wiki/Potential_energy","YEAR":"2021"}},{"citationKey":"LUDWIG_BOLTZMANN_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ludwig Boltzmann","URL":"https://en.wikipedia.org/wiki/Ludwig_Boltzmann","YEAR":"2021"}},{"citationKey":"BOLTZMANN_DISTRIBUTION_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Boltzmann distribution","URL":"https://en.wikipedia.org/wiki/Boltzmann_distribution","YEAR":"2021"}},{"citationKey":"HASTINGS1970MONTE","entryType":"ARTICLE","entryTags":{"MONTH":"04","ABSTRACT":"{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}","PAGES":"97-109","ISSN":"0006-3444","EPRINT":"https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf","NUMBER":"1","AUTHOR":"Hastings, W. K.","URL":"https://doi.org/10.1093/biomet/57.1.97","JOURNAL":"Biometrika","TITLE":"Monte Carlo sampling methods using Markov chains and their applications","VOLUME":"57","YEAR":"1970","DOI":"10.1093/biomet/57.1.97"}},{"citationKey":"MALA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Metropolis-adjusted Langevin Algorithm","URL":"https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm","YEAR":"2021"}},{"citationKey":"HMC_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Hamiltonian Monte Carlo","URL":"https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo","YEAR":"2021"}},{"citationKey":"RMSD_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Root Mean Square Deviation","URL":"https://en.wikipedia.org/wiki/Root-mean-square_deviation","YEAR":"2021"}},{"citationKey":"CEASAR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Ceasar Cipher","URL":"https://en.wikipedia.org/wiki/Caesar_cipher","YEAR":"2022"}},{"citationKey":"POST-QUANTUM_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Post-quantum Cryptography","URL":"https://en.wikipedia.org/wiki/Post-quantum_cryptography","YEAR":"2022"}},{"citationKey":"KERCKHOFFS_PRINCIPLE_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Kerckhoffs's principle","URL":"https://en.wikipedia.org/wiki/Kerckhoffs%27s_principle","YEAR":"2022"}},{"citationKey":"ROT13_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: ROT13","URL":"https://en.wikipedia.org/wiki/ROT13","YEAR":"2022"}},{"citationKey":"CC_PERMUTATION","entryType":"MISC","entryTags":{"TITLE":"Crypto Corner: Permutation Cipher","URL":"https://crypto.interactive-maths.com/permutation-cipher.html","YEAR":"2022"}},{"citationKey":"XOR_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: XOR cipher","URL":"https://en.wikipedia.org/wiki/XOR_cipher","YEAR":"2022"}},{"citationKey":"DES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Data Encryption Standard","URL":"https://en.wikipedia.org/wiki/Data_Encryption_Standard","YEAR":"2022"}},{"citationKey":"AES_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Advanced Encryption Standard","URL":"https://en.wikipedia.org/wiki/Advanced_Encryption_Standard","YEAR":"2022"}},{"citationKey":"BLOWFISH_CIPHER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Blowfish (cipher)","URL":"https://en.wikipedia.org/wiki/Blowfish_(cipher)","YEAR":"2022"}},{"citationKey":"RSA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: RSA (cryptosystem)","URL":"https://en.wikipedia.org/wiki/RSA_(cryptosystem)","YEAR":"2022"}},{"citationKey":"ECC_CRYPTO_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Elliptic-curve cryptography","URL":"https://en.wikipedia.org/wiki/Elliptic-curve_cryptography","YEAR":"2022"}},{"citationKey":"BOX1958","entryType":"ARTICLE","entryTags":{"TITLE":"A note on the generation of random normal deviates","AUTHOR":"Box, George EP","JOURNAL":"Ann. Math. Statist.","VOLUME":"29","PAGES":"610--611","YEAR":"1958"}},{"citationKey":"MARSAGLIA_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Marsaglia Transform","URL":"https://en.wikipedia.org/wiki/Marsaglia_polar_method","YEAR":"2022"}},{"citationKey":"BOX_MULLER_WIKI","entryType":"MISC","entryTags":{"TITLE":"Wikipedia: Box-Muller Transform","URL":"https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform","YEAR":"2022"}}],"gitbook":"*"},"file":{"path":"README.md","mtime":"2023-08-23T13:18:40.814Z","type":"markdown"},"gitbook":{"version":"3.7.5","time":"2023-08-23T13:19:05.016Z"},"basePath":".","book":{"language":""}}); }); diff --git a/sconscripts/csharp_SConscript b/sconscripts/csharp_SConscript new file mode 100644 index 000000000..366471f19 --- /dev/null +++ b/sconscripts/csharp_SConscript @@ -0,0 +1,15 @@ +Import('files_to_compile env') + +language = files_to_compile[0].language +chapter = files_to_compile[0].chapter + +from collections import defaultdict +chapter_files = defaultdict(list) + +for file_info in files_to_compile: + chapter_files[file_info.chapter].append(file_info.path) + +for chapter, files in chapter_files.items(): + build_target = f'#/build/{language}/{chapter}/{chapter}' + build_result = env.MCS(build_target, [str(file) for file in files]) + env.Alias(str(chapter), build_result) diff --git a/search_index.json b/search_index.json index 9baa2055a..c1493caaa 100644 --- a/search_index.json +++ b/search_index.json @@ -1 +1 @@ -{"index":{"version":"0.5.12","fields":[{"name":"title","boost":10},{"name":"keywords","boost":15},{"name":"body","boost":1}],"ref":"url","documentStore":{"store":{"./":["(found","(leiosos):","(potentially)","/","4.0","adventur","algorithm","allow","ambiti","anyth","arcan","archiv","archive.org/","archivists/algorithm","associ","attribut","available.","becom","book","chang","channel","chapter","chapter.","code","collabor","common","commun","community.","content","contribut","contribute,","cover","creat","creativ","differ","discord","effort","else,","end","enjoy","entry.","essenti","exampl","favorit","feel","few","find","focu","fortunately,","free","fun","future!","future.","github","go","goal","graphic","great","grow","guid","hand","help","here","hopefulli","hopefully,","https://discord.gg/pr2e9s6","https://github.com/algorithm","https://www.algorithm","https://www.twitch.tv/leioslab","https://www.youtube.com/user/leioso","implement","import","incred","individu","instead","instruct","intern","jame","know","language,","languages.","learn","licens","license.md).","links:","little,","livestream:","lot","materi","mean","mit","necessary.","need","never","note","noth","obvious","onlin","out","pleas","practic","probabl","process","programm","project","projects.","pull","purpose.","read","regard","repository:","request.","resourc","said,","schloss.","see","server:","sharealik","site:","size,","someth","specifi","specified,","state","still","submit","text","thank","there'","there,","top","tri","twitch","ui","under","unfortunately,","us","veri","via","want","we'll","website:","wiki","work","written","wrong","youtub"],"contents/introduction/introduction.html":["\"languag","\"textbook\"","(#560),","(and","(found","(or","/","4.0","5","5:00am","abil","addition,","advanc","adventur","age,","agnostic.\"","ago,","ahem","algorithm","algorithm;","algorithms.","all,","along","anyon","appendix.","arcan","archiv","around","arxiv,","attribut","author","author.","avail","away","back","background","basic","be,","becom","befor","before.","begin","between","big)","bit","blissfulli","blog","book","book,","book.","both","brows","bulk","call","can.","case","challeng","chanc","chapter","chapter:","chip","choic","class.","classic","clear,","code","collect","combin","comment","common","commun","community,","complet","comprehens","comput","concerns,","conglomer","content","cool","counter","creat","creativ","day,","deeper","degre","delv","develop","differently,","discoveri","doubt","each","echo","effort","end","end,","enjoy","enjoy.","entir","era","everyone'","everything,","exampl","example,","example.","excit","express","extens","fact,","fantast","favorit","feel","few","fill","final","find","fingertips,","first","flexibl","focus","follow","forward.","found","free","freeli","fun","fun.","gener","genuin","github","graphic","great","greatest","guess","guid","hard","harsh","heavili","hero","hesit","high","hobbi","hobbies:","honest","hope","hour","however,","human","idea","ignor","implement","improv","inclined,","incred","initi","interest","intern","introduc","introduct","intuitive,","is)","it!","it'","jame","journey.","jr.","keep","know.","knowledg","lab","lack","languag","latest","learn","learning!","learning.","lecture.","lectures,","left?","licens","license.","license.md).","line","littl","live","livecod","look","lose","lot.","love","main","manag","mani","master","material;","mathematics.","matter","mayb","mean","meaning","mention","mentioned,","mind,","mine.","mit","modern","modifi","more","morsel","motiv","move","much","myself","natur","nearli","never","nice","none","note","notebook","noth","now","now,","now.","nowaday","offer","on","one,","online,","outsid","overwhelm","pages.","paper","part,","pass","past","peopl","perfectli","person","phd","physic","physics.","piec","place","pleas","please.","pleasur","point","poor","pore","possibl","post","posts,","power","prefer","problem","professor","program","programmers.","project","prospect!","provid","pseudocod","public.","pull","push","puzzl","quantum","question","quickly,","read","reader.","reality.","realli","really,","reason,","redefin","request","research","right","right.","rigor","schloss","school","scienc","science,","science.","scientist.","see","see,","seem","shame.","sharealik","show","signific","significantly,","slowli","small","solve;","someth","sometim","sorts.","sourc","spend","spent","stage","start","still","stori","storytel","straddl","stream","streaming.","studi","subject","submit","sum","suppos","sure,","systems;","tackl","teacher","tend","tests,","text","text,","text.","that'","that.","theme,","there'","there.","think","this,","those","though","through","throughout","throw","time","time.","train","twitch","two","type","unawar","under","understand","understood!","uniqu","up","us","version","villain","wait","want","way","ways,","well","well,","well.","what'","wish","without","work","work.","world","write","writing,","written","year","years,","you!","you,","younger,","youtube,"],"contents/how_to_contribute/how_to_contribute.html":["\"","%}","(#560),","(and","(found","(where","1","17","17,","4.0","80",">>","[import:1","abil","accept","add","addition,","algorithm","algorithm,","algorithms.","allow","anoth","anyon","api","api,","api.","archiv","archive!","archive.","archive:","around","ask","associ","attribut","basic","be","befor","between","book,","browser","build","c++,","capit","certain","chapter","chapter:","check","choice.","clean","cleanli","clutter,","code","code,","code/","codeblock","columns,","common","commun","community.","consid","consist","consult","contribut","contribute,","contributors.md","contributors.md.","contributors.md:","control,","cpp","creativ","current","currently,","depend","detail","details.","develop","differ","directori","directory.","discord","discussion,","display","each","echo","effort","end","endmethod","especi","etc.","exampl","example,","extens","faq","far.","feel","file","flip","follow","found","free","future.","git","gitbook","go","graphic","grows.","guid","guide,","guide.","guidelin","haskell,","have","help","here","however,","hs","https://discord.gg/pb976sy.","i'll","import","includ","initi","instal","intern","is).","jame","join","julia","keep","lang","lang:\"julia\"](code/julia/conv.jl)","lang=\"jl\"","languag","language'","language.","languages.","learn","level","licens","license.","license.md).","license.md;","licensing:","line","list","local","machine.","main","make","markdown","members.","method","mit","modifi","more","name","name\"","near","need","new","node","noncommerci","none","note","now,","npm","on","ongo","out","page","part","part,","pleas","plugin","project","provid","pull","readabl","readme.md","rememb","remov","request","requir","review","run","sampl","schemes,","schloss","seri","serv","server","server:","sharealik","snippet","so),","specif","standard","start","statement","style","style:","submission,","submissions;","submit","such,","support","sure","teach","text","thank","theme","this,","those","titl","together:","tri","troubl","trust","two","under","understand","understandable.","updat","updating!","url","us","user","variabl","version","video","view","visual","want","whatev","work","written","written.","yourself","{%"],"contents/code_reviews/code_reviewers.html":["@amara","@amaras,@peanutbutterwarrior","@leio","@ntindl","@ntindle,","@ntindle,@shadowmitia","@ntindle,@shadowmitia,@amaras,@peanutbutterwarrior","@shadowmitia","@shadowmitia,@peanutbutterwarrior","action","add","asm","bash","below:","c","c#","c++","change,","chapter","clojur","coconut","code","comfort","contain","crystal","d","dart","dev","docker","elm","emojicod","factor","featur","fortran","github","gnuplot","go","haskel","honkit","java","javascript","julia","kotlin","labview","languag","language,","lisp","list","lolcod","lua","matlab","nim","ocaml","php","piet","pleas","powershel","python","r","racket","review","rubi","rust","scala","scheme","scon","scratch","smalltask","swift","tabl","toolchain","typescript","v","viml","whitespac","x64","yourself"],"contents/data_structures/data_structures.html":["(#560),","(found","4.0","ad","algorithm","algorithms.","archive,","attribut","block","book","build","chapter","chapter:","code","common","creativ","data","exampl","follow","fundament","graphic","initi","intern","jame","licens","license.","license.md).","mit","modifi","more","none","pull","request","schloss","section.","sharealik","structur","structures,","text","thu","under","written"],"contents/stacks_and_queues/stacks_and_queues.html":["!=","\"__main__\":","\"call","\"michael","#!/usr/bin/env","#includ","&&","'dequeue'","'enqueue'","'front'","'pop'","'push'","'size'","'top'","(#560),","(count","(fifo),","(found","(front","(front_pointer.get()","(intermediat","(lifo),","(pop())","(push())","(rear","(top","(top())","(top_pointer.get()","*","*/","+","...","/*","/**","//","0","0)","0;","1)","1);","1;","1]","1];","2","4","4.0","5","6",":","=","==",">",">next",">next);",">next;",">value;","[]","[];","[value][next]","__author__","__init__(self)","__len__(self)","__name__","__str__(self)","`dequeue`","`enqueue`","`front`","`pop`","`push`","`size`","`top`","access","act","ad","add","address","algorithm","allow","args)","array","arraylist<>();","assert(count","attend","attent","attribut","auto","basic","between","biggest","book","book,","books,","bool","both","camp\"","chapter","chapter:","ciccotosto","class","code","coin","common","comput","console.log(numberqueue.dequeue());","console.log(numberqueue.front());","console.log(numberqueue.size());","console.log(numberstack.pop());","console.log(numberstack.size());","console.log(numberstack.top());","const","const&","contrast","count","count(0ull)","count:","count;","creativ","current","data","def","depend","dequeu","dequeue(&mut","dequeue()","dequeue():","dequeue();","dequeue(self)","detail","differ","element","element)","element);","element:","elements,","empti","empty()","end","enqueue(&mut","enqueue(const","enqueue(data:","enqueue(self,","enqueue(t","exactli","exampl","example,","examplequeue()","examplequeue();","examplestack()","examplestack();","final","first","fn","follow","front","front(&self)","front()","front():","front();","front(self)","front_point","front_pointer.reset();","front_pointer:","front_pointer;","frontel","function","gener","give","graphic","groceri","held","here","hold","i32queu","i32queue.dequeue().unwrap());","i32queue.enqueue(4);","i32queue.enqueue(5);","i32queue.enqueue(6);","i32queue.front().unwrap());","i32queue.size());","i32stack.pop().unwrap());","i32stack.push(4);","i32stack.push(5);","i32stack.push(6);","i32stack.size());","i32stack.top().unwrap());","i32stack:","imagin","impl","implement","import","in,","initi","instead","int","int:","int_queue.enqueue(4)","int_queue.enqueue(5)","int_queue.enqueue(9)","int_queue:","int_stack.push(4)","int_stack.push(5)","int_stack.push(9)","int_stack:","interfac","intern","intqueu","intqueue.dequeue();","intqueue.enqueue(4);","intqueue.enqueue(5);","intqueue.enqueue(9);","intqueue.front();","intqueue;","intstack","intstack.pop();","intstack.push(4);","intstack.push(5);","intstack.push(9);","intstack.top();","intstack;","iqueu","istack","it'","item:","jame","java.util.arraylist;","java.util.list;","keep","know","languag","last","left","len(self)","len(self.__list)","length","licens","license.","license.md).","life.","line","link","list","list()","list:","list;","list[t]","look","main()","main(string[]","mean","mit","modifi","multipl","mut","mutabl","my::queu","my::stack","namespac","new","new()","new_nod","new_node;","next:","next;","node","node(const","node)","nodes)","none","none:","notat","note","now","nullptr)","number","number;","numberqueu","numberqueue.enqueue(4);","numberqueue.enqueue(5);","numberqueue.enqueue(9);","numberstack","numberstack.push(4);","numberstack.push(5);","numberstack.push(9);","onc","onto","option","order","out","out.","ownership","part,","people.","person","point","pop","pop(&mut","pop()","pop():","pop();","pop(self)","present","print(int_queue.dequeue())","print(int_queue.front())","print(int_stack.pop())","print(int_stack.top())","print(len(int_queue))","print(len(int_stack))","println!(\"{:?}\",","privat","private:","public","public:","pull","push","push(&mut","push(const","push(data:","push(self,","push(t","put","python3","queue","queue\");","queue()","queue();","queue(generic[t]):","queue,","queue:","queue::new();","queue<>();","queue[int]","queues,","queuetest","queue{","readonli","real","rear_point","rear_pointer.reset();","rear_pointer:","rear_pointer;","receiv","recent","refer","remov","repres","request","return","right","same","schloss","science.","see","self","self)","self,","self.__list.append(element)","self.__list.pop()","self.__list.pop(0)","self.__list:","self.__list[","self.__list[0]","self.list.front()","self.list.last()","self.list.len()","self.list.pop()","self.list.pop_front()","self.list.push(item);","self.list.push_back(item);","sharealik","show","side","sift","simpl","simpli","singl","size","size(&self)","size()","size():","size();","size_t","someon","sourc","specif","stack","stack\");","stack()","stack();","stack(generic[t]):","stack.","stack:","stack::new();","stack<>();","stack[int]","stacks,","stacktest","static","std::collections::vecdeque;","std::cout","std::make_shared>(element);","std::make_unique>(element);","std::move(new_node);","std::move(top_point","std::move(top_pointer);","std::shared_ptr>","std::unique_ptr>","store","str(self.__list)","str:","struct","structur","structure.","system.out.println(intqueue.dequeue());","system.out.println(intqueue.front());","system.out.println(intqueue.size());","system.out.println(intstack.pop());","system.out.println(intstack.size());","system.out.println(intstack.top());","t","t&","t)","t):","t:","t;","take","templat","text","them.","this.list","this.list.add(element);","this.list.get(0);","this.list.get(this.size()","this.list.length;","this.list.pop();","this.list.push(data);","this.list.remove(0);","this.list.remove(this.size()","this.list.shift();","this.list.size();","this.list[0];","this.list[this.list.length","this.size();","though,","through","time.","to:","top","top(&self)","top()","top().","top():","top();","top(self)","top_point","top_pointer:","top_pointer;","topel","track","treat","two","type","typevar(\"t\")","typevar,","under","unfair","up.","us","useful","using.","usiz","v)","valu","value(v)","value;","vec","vec::new(),","vecdequ","vecdeque::new(),","veri","void","way","way.","whichev","within","without","written","{","}","};","~queue()","~stack()"],"contents/mathematical_background/mathematical_background.html":["(#560),","(found","4.0","add","algorithm","algorithms,","algorithms.","ask,","attempt","attribut","away","background","bioinformatics.","book","calculu","case","cases,","certain","chapter","chapter:","class","code","common","creativ","deeper","depend","differenti","doesn't","domain","equations.","exampl","except","follow","foundat","graphic","high","honestly,","however,","initi","intern","jame","knowledge,","learn","licens","license.","license.md).","littl","math.","mathemat","mathematics.","matter","method","mit","modifi","more","much","much.","need","new","none","notabl","part,","place","probabl","program","programmers,","provid","pull","quantum","relev","request","requir","rule","said,","schloss","school.","section","section.","sections.","see","sharealik","simul","sometim","specialty,","specif","text","those","tools,","under","understand","written"],"contents/tree_traversal/tree_traversal.html":["!=","!==","\"","\"\"\"a","\"\"\"creat","\"#{node.id}","\"#{temp.id}","\"%d","\")","\"),","\");","\",","\"[#]\\nqueue","\"[#]\\nrecurs","\"[#]\\nstack","\"[#]~%queue","\"[#]~%recurs","\"[#]~%stack","\"a","\"bfssimple\"","\"children","\"creat","\"data","\"depth","\"dfsinorder\"","\"dfspostorder\"","\"dfspreorder\"","\"fmt\"","\"invalid","\"levels\"","\"not","\"recurs","\"thi","\"tree\"","\"utility.h\"","\"~%\")","\"~a","#","#[derive(debug)]","#defin","#endif","#ifndef","#includ","#node","$","$child)","$child):","$child;","$children","$children;","$i","$id,","$id;","$node","$node;","$numofchildren):","$numofrows,","$stack","$stack[]","$temp","$thi","$tree","$tree):","%","%%","🆔","🆕","🆕🌲🆕","🆕🌲⭐️","🆕⏩⏩","🆕⏹⏫❗️","🌀","🌀tree❗️","🌌","🌌🐕","🌲","🍆","🍇","🍉","🍥","🍥tree❗️","🍨","🍨🍆","🍨🐚🌲🍆","🍬⏹","🍭","🍭🐽","🍭binary_tree❗️","🍭tree❗️","🏁","🏢","🏢tree❗️","🐇","🐔","🐕","🐨","🐻","🐽","💭","📗","🔁","🔂","🔐","🔘","🔡","🔡return❗❗️️","🔢","🔤🌀","🔤🍥","🔤🍭","🔤🏢","🔤🔤","🔤🥞","🔤the","🔤tree","🖍🆕","🖍children","🖍id","😀","🙅","🙌","🤜depth_count","🤜id","🤷‍♀️","🥞","🥞tree❗️","🦃","🧒","&n);","&n.children","&n.children[..]","&node)","&node{id:","&tmp","'","''","')","',","';","'[#]'","'__main__':","'children","'children'","'id'","'num","'num_child'","'num_rows'","'queue","'recurs","'stack","'thi","(!queue_empty(&q))","(!stack_empty(&stk))","(!tmp)","(!tree)","(#560),","($i","($numofrow","($temp","($tree","((node","())","(),","();","(0","(0..num_child)","(1","(2","(>","(auto","(bf","(bfs)","(case","(child","(children","(concatmap","(count($tre","(createtre","(current","(defstruct","(defun","(defvar","(depthcount","(df","(dfs)","(eql","(fail)\");","(first","(float)","(format","(found","(if","(int","(length","(length(n.children)","(list","(loop","(make","(n.children)","(n.children.size())","(n.children_size)","(nconc","(node","(node)","(node.children.size())","(null","(num","(num_row","(numrow","(output","(pop","(post","(print","(push","(q","(queue.count","(queue.length","(queue.size()","(queue_empty(q))","(row","(rowcount","(second","(setf","(show)","(size_t","(stack.count","(stack.length","(stack.size()","(stack_empty(stk))","(stk","(struct","(t","(temp","(top","(tree._children.count)","(tree.children.length)","(var","(when","*","**data;","**tmp","*=","*children;","*dequeue(struct","*element)","*node","*node)","*q)","*q,","*queue.front();","*ret","*stack.top();","*stack_pop(struct","*stk)","*stk,","*tmp;","+","++","++i)",".","...",".collect();",".equ",".extern",".global",".intel_syntax",".map(|_|",".rodata",".section",".string",".text","//","//system.out.println(\"us","//tree.dfsrecursiveinorderbinary();","//utility_h","0","0)","0,","0:","0;","0]","0}","0};","0❗️","0❗️❗️","1","1🤛","1)","1))","1);","1,","1...numchildren","10","10❗️❗️","12","128","12]","12]#","12],","15","16","16]","16]#","16],","1:","1:num_child","1;","1]","1❗️","1❗️❗️","2","2)","2))","2),","2);","2,","2.","20","24]","2:","2;","2❗️","3","3)","3))","3);","3,","32","36","3❗️","4","4.","4.0","4;","5.","64","7","8","8]","8],",":","::",":=",":child",":children",":data",";;",";;;;","=","==","=='__main__':","===","=>",">",">=",">back",">back;",">back]",">capac",">capacity)",">capacity;",">children",">children,",">children;",">children[]",">children[i]);",">data",">data);",">data,",">data[",">data[0]));",">data[0]);",">data[q",">data[stk",">front",">front)",">front,",">front];",">getchildren()",">getchildren()))",">getchildren()[0]);",">getchildren()[1]);",">getid()",">id",">id);",">id,",">id;",">top",">top++]",">top];","@(a,","@(k,v)","@children","@overrid","[","[$tree];","[&]","[...array(children).keys()].map(()","[]","[])","[]*node","[]*node{n}","[];","[a]","[l,","[l])","[left,","[left]","[node]","[node])","[node]?","[r12","[r12]","[r12],","[r13","[r13]","[r14","[r14]","[r14],","[rax","[rax]","[rax],","[rbx","[rbx],","[rdi","[rdi]","[stack","[t]","[tree","[tree];","[x]","\\n\"","]","].","];","^","^self.","_","_,","__construct(int","__init__(self):","__name__","_children","`children`","a,","a]","abov","above,","access","account","action","actual","add","addchild($child);","addchild(tre","addit","addition,","addlast:","address","alloc","allow","append(cur.children,","append(queue,","approach","args)","argu","around","array","array(node))","array.","array_pop($stack)))","array_shift($stack)))","arraylist","arraylist();","ask","assum","at:","attribut","auto","avoid","a{b};","b)","back","back,","balanc","base","befor","below.","bf","bfs(root);","bfs(tree)","bfs.","bfs:\"","bfs:\")","bfs:\");","bfs:'","bfs:\\n\");","bfs:~%\")","bfs_queue","bfs_queue(&root);","bfs_queue(n)","bfs_queue(n:","bfs_queue(n::node)","bfs_queue(nod","bfs_queue(node)","bfs_queue(node):","bfs_queue(root)","bfs_queue(root);","bfs_queue(struct","bfs_queue(tree)","bfs_queue:","bfs_queue_end_push","bfs_queue_end_push:","bfs_queue_loop","bfs_queue_loop:","bfs_queue_push_child","bfs_queue_push_child:","bfs_queue_return","bfs_queue_return:","bfsqueue()","bfsqueue(n","bfsqueue(node:","bigger","binari","binary!🔤","binary🔤❗️","binary_root","binary_tre","bit","bits),","bool","bottom","bottom.","bottom.\"","bottom.\"\"\"","branch","branch.","branches.","breadth","break;","btree","byte","c","calcul","call","calle","calloc((q","calloc(4,","can't","capac","capacity,","capacity;","capcaiti","care","case","case!","case,","cdq","cell_index","cell_index(keys(n),","cell_index(keys(parent),","cell_index(values(n),","cell_index(values(parent),","chapter","chapter:","cheatsheet","check","child","child'","child)","child))","child)))","child)))))","child.","children","children'","children)","children))","children)):","children,","children.","children:","children::vector{node}","children;","children_count","children_count❗️","children_count❗️❗️","children_s","children_size,","children_size;","childrencount)","childrencount);","children|value|children_s","children❗️","child};","child❗️","class","classvariablenames:","cleanup:","cmp","code","code,","collect","collect:","comment","common","compar","compareto(nod","compos","concatmap","console.log(\"[#]\\nqueu","console.log(\"[#]\\nrecurs","console.log(\"[#]\\nstack","console.log();","console.log(tree.id);","console.write(queue.peek().id","console.write(stack.peek().id","console.write(tree.id","console.writeline(\"[#]\\nqueu","console.writeline(\"[#]\\nrecurs","console.writeline(\"[#]\\nstack","console.writeline();","const","const&","constructed.","containers.map(k,v);","convent","copi","cr.","creat","create_btree()","create_btree();","create_tre","create_tree()","create_tree();","create_tree(2,","create_tree(3,","create_tree(3,2)","create_tree(int","create_tree(levels,","create_tree(node(),","create_tree(node,","create_tree(num_row","create_tree(num_row:","create_tree(num_row::int64,","create_tree(num_rows,","create_tree:","create_tree_children","create_tree_children:","create_tree_leaf","create_tree_leaf:","create_tree_return","create_tree_return:","createallchildren(nod","created.","createtre","createtree(2,","createtree(3,","createtree(numrow,","createtree(numrows:","createtree(row","createtree(rows,","creativ","crucial","cur","cur.children...)","cur.id","cur.id)","current","current.value);","current_nod","current_node.children:","data","data'","data);","data;","datastructures,","deep.\"","deep.\"\"\"","def","default:","depend","depth","depth_count","depthcount,","dequ","deque([node])","deque.new","dequeu","dequeue!(q)","dequeue:","dequeue_return","dequeue_return:","deriv","describ","destroy_tree(root);","destroy_tree(root_binary);","detail","df","dfs.","dfs:\"","dfs:\")","dfs:\");","dfs:'","dfs:\\n\");","dfs:~%\")","dfs_recurs","dfs_recursive(&root);","dfs_recursive(...)","dfs_recursive(child)","dfs_recursive(child);","dfs_recursive(n)","dfs_recursive(n:","dfs_recursive(n::node)","dfs_recursive(nod","dfs_recursive(node(value,","dfs_recursive(node)","dfs_recursive(node):","dfs_recursive(root)","dfs_recursive(root);","dfs_recursive(struct","dfs_recursive(tree)","dfs_recursive:","dfs_recursive_bt_return","dfs_recursive_bt_return:","dfs_recursive_bt_size0","dfs_recursive_bt_size0:","dfs_recursive_bt_size1","dfs_recursive_bt_size1:","dfs_recursive_bt_size2","dfs_recursive_bt_size2:","dfs_recursive_children","dfs_recursive_children:","dfs_recursive_inorder_btre","dfs_recursive_inorder_btree(&root_binary);","dfs_recursive_inorder_btree(binary_tree)","dfs_recursive_inorder_btree(children[0])","dfs_recursive_inorder_btree(children[1])","dfs_recursive_inorder_btree(children{1})","dfs_recursive_inorder_btree(children{2})","dfs_recursive_inorder_btree(left);","dfs_recursive_inorder_btree(n)","dfs_recursive_inorder_btree(n.children[0]);","dfs_recursive_inorder_btree(n.children[1])","dfs_recursive_inorder_btree(n.children[1]);","dfs_recursive_inorder_btree(n.children[2])","dfs_recursive_inorder_btree(n:","dfs_recursive_inorder_btree(n::node)","dfs_recursive_inorder_btree(nod","dfs_recursive_inorder_btree(node(value,","dfs_recursive_inorder_btree(node)","dfs_recursive_inorder_btree(node):","dfs_recursive_inorder_btree(node.children[0])","dfs_recursive_inorder_btree(node.children[1])","dfs_recursive_inorder_btree(right);","dfs_recursive_inorder_btree(root_binary)","dfs_recursive_inorder_btree(root_binary);","dfs_recursive_inorder_btree(rootb)","dfs_recursive_inorder_btree(struct","dfs_recursive_inorder_btree:","dfs_recursive_po_children","dfs_recursive_po_children:","dfs_recursive_po_return","dfs_recursive_po_return:","dfs_recursive_postord","dfs_recursive_postorder(&root);","dfs_recursive_postorder(child)","dfs_recursive_postorder(child);","dfs_recursive_postorder(n)","dfs_recursive_postorder(n:","dfs_recursive_postorder(n::node)","dfs_recursive_postorder(nod","dfs_recursive_postorder(node(value,","dfs_recursive_postorder(node)","dfs_recursive_postorder(node):","dfs_recursive_postorder(root)","dfs_recursive_postorder(root);","dfs_recursive_postorder(struct","dfs_recursive_postorder(tree)","dfs_recursive_postorder:","dfs_recursive_return","dfs_recursive_return:","dfs_stack","dfs_stack(&root);","dfs_stack(...)","dfs_stack(n)","dfs_stack(n:","dfs_stack(n::node)","dfs_stack(nod","dfs_stack(node)","dfs_stack(node):","dfs_stack(root)","dfs_stack(root);","dfs_stack(struct","dfs_stack(tree)","dfs_stack:","dfs_stack_end_push","dfs_stack_end_push:","dfs_stack_loop","dfs_stack_loop:","dfs_stack_push_child","dfs_stack_push_child:","dfs_stack_return","dfs_stack_return:","dfsinord","dfsinorder(root_binary);","dfsinorder(tree)","dfsinorder(tree.children[0]);","dfsinorder(tree.children[1]);","dfsinorderbinarytree.","dfsinorderbinarytree:","dfsiterative(root);","dfsiterative(tree)","dfspostord","dfspostorder(root);","dfspostorder(tree)","dfspreorder(root);","dfspreorder(tree)","dfsqueue(tre","dfsrecurs","dfsrecursive()","dfsrecursive(c);","dfsrecursive(child)","dfsrecursive(n","dfsrecursive(n);","dfsrecursive(nod","dfsrecursive(node:","dfsrecursive(this);","dfsrecursive(tre","dfsrecursive.","dfsrecursiveinorderbinari","dfsrecursiveinorderbinary()","dfsrecursiveinorderbinary()!\");","dfsrecursiveinorderbinary(nod","dfsrecursiveinorderbinary(node.children.get(0));","dfsrecursiveinorderbinary(node.children.get(1));","dfsrecursiveinorderbinary(node:","dfsrecursiveinorderbinary(this);","dfsrecursiveinorderbinary(this.root);","dfsrecursiveinorderbinary(tre","dfsrecursiveinorderbinary(tree._children[0]);","dfsrecursiveinorderbinary(tree._children[1]);","dfsrecursiveinorderbtree(n","dfsrecursiveinorderbtree(n.children[0])","dfsrecursiveinorderbtree(n.children[1])","dfsrecursivepostorder()","dfsrecursivepostorder(c);","dfsrecursivepostorder(child)","dfsrecursivepostorder(n","dfsrecursivepostorder(n);","dfsrecursivepostorder(nod","dfsrecursivepostorder(node:","dfsrecursivepostorder(this);","dfsrecursivepostorder(tre","dfsrecursivepostorder)].","dfsrecursivepostorder.","dfsstack","dfsstack()","dfsstack(n","dfsstack(node:","dfsstack(tre","dfsstack.","differ","discuss","do","does!","doesn't","down","dword","each","eax","eax,","echo","edi","edi,","edx","edx,","element","element.","element;","elements,","elif","else:","elseif","empti","empty,","end","end,","end='","enqueu","enqueue!(q,","enqueue(&q,","enqueue(struct","enqueue:","enqueue_append","enqueue_append:","equal","error","error🔤❗️","error(\"postord","error,","errors!","esi","esi,","exactli","exampl","example,","except","exception(\"not","exists!","explan","explicitli","few","fight","fill","first","first,","first.","flip(children)","fmt.printf(\"%d","fmt.println(\"thi","fmt_tree","fmt_tree:","fn","follow","foreach","forest","fprintf(\"not","fprintf('%u","fprintf('\\n')","fprintf('\\nbf","fprintf('\\ndf","free","free(q","free(q.data);","free(stk.data);","free,","free_queu","free_queue(q);","free_queue(struct","free_queue:","free_stack","free_stack(stk);","free_stack(struct","free_stack:","free_tre","free_tree:","free_tree_free_array","free_tree_free_array:","free_tree_free_kid","free_tree_free_kid:","free_tree_return","free_tree_return:","front","front,","func","function","function,","further","gener","generate_tree(2,","generate_tree(3,","generate_tree(int","get;","get_queu","get_queue(size_t","get_queue(sizeof(struct","get_queue:","get_stack","get_stack(size_t","get_stack(sizeof(struct","get_stack:","getchildren():","getid():","getter\"","getter.\"","given","given_id","go","goe","graphic","greatli","handl","here","hold","hous","however,","human","id","id)","id);","id,","id:","id::int64","id;","idea","ideal,","idiv","iftrue:","imag","images/graph","implement","implies:","import","in.","inbetween","incred","init","init(value:","initi","initialize(@id","initialized;","inord","instancevariablenames:","instead","instead,","int","int)","int,","int32,","integer.compare(this.id,","interact","interest","intern","invalidargumentexception('not","is.","i{1};","jame","java.util.arraylist;","java.util.linkedlist;","java.util.queue;","java.util.stack;","javascript,","je","jmp","jne","jsonserializ","jsonserialize():","jz","know","known","l","languag","last","last.","lea","lead","leaf","leav","left","len(children):","len(n.children)","len(node.children)","len(queue)","len(stack)","length(children)","level","levels:","licens","license.","license.md).","like:","line","linkedlist","linkedlist();","lisp","list","list();","long","look","loop","lot","made","main","main()","main():","main(string[]","main:","make","malloc","malloc(4","malloc,","mani","map","match","mathjax.hub.queue([\"typeset\",mathjax.hub]);","me,","memcpi","memcpy(tmp","memcpy(tmp,","memori","method","method:","miss","mit","mix","modifi","more","mov","move","multipl","mut","n","n'","n)","n.children","n.children)","n.children_s","n.id)","n.id);","n.value),","n.value);","name","namespac","natur","necessari","necessarili","need","new","new(node)","new(vector{node}(),","new.","new:","newchildren","newchildren.","newdata","newdata.","next_nod","next_nodes;","nil","nil)","node","node(0,","node(1,","node(10,","node(11,","node(12,","node(2,","node(3,","node(4,","node(5,","node(6,","node(7,","node(8,","node(9,","node(id::int64)","node(int","node(num_row)","node(num_rows,","node(rowcount);","node(value:","node)","node))","node)))","node))))","node));","node):","node*));","node*)dequeue(&q);","node*)malloc(num_children","node*)stack_pop(&stk);","node,","node.children!","node.children![0])","node.children![1])","node.children)","node.children.append(child)","node.children.each{","node.children.s","node.children:","node.children?.append(child)","node.children?.count","node.children[0]","node.children[1]","node.data","node.new(levels,","node1","node10","node11","node11,","node12","node12});","node2","node3","node3,","node3});","node4","node4});","node5","node5,","node6","node6});","node7","node7,","node8","node8});","node9","node9});","node:","node>>bf","node>>children","node>>children:","node>>data","node>>data:","node>>dfsinorderbinarytre","node>>dfsrecurs","node>>dfsrecursivepostord","node>>dfsstack","node[])","node_queu","node_stack","node_stack(end)","node_stack{end};","nodes,","nodes.","node{std::move(vec),","non","none","none:","noprefix","not_bt","not_bt:","note","note,","now,","null","null)","null;","num","num_child","num_child)","num_child))","num_child):","num_child);","num_child,","num_child:","num_child::int64)","num_children)","num_children;","num_childs)","num_childs.times{children.push","num_childs:","num_row","num_row,","num_row};","number","numchild","numchildren)","numchildren:","numrow","numrows,","object","offset","old","on","onc","order","order🔤❗️","order).\"","order.\"","other)","other,","other.id);","out","output","overrid","packag","package:","paramet","params:","parent","parent_cel","parent_cell{1};","perform","php_eol","php_eol;","place","point","point,","pointer","pop","pop!(s)","pop.","possibl","post","postord","postorder\\n')","pre","primarili","print","print!(\"thi","print!(\"{}","print(\"[#]\\nqueu","print(\"[#]\\nrecurs","print(\"[#]\\nstack","print(\"not","print('invalid","print()","print(current_node.value,","print(first(q).id,","print(n.id,","print(node.data)","print(node.data,","print(node.value,","print(temp.value,","print(top(s).id,","print(value,","print:","printf","printf(\"%d","printf(\"[#]\\nqueu","printf(\"[#]\\nrecurs","printf(\"[#]\\nstack","printf(\"\\n\");","printf(\"thi","printf,","println!(\"[#]\\nqueu","println!(\"[#]\\nrecurs","println!(\"[#]\\nstack","println!();","println(\"[#]\\nqueu","println(\"[#]\\nrecurs","println(\"[#]\\nstack","println(\"not","println()","privat","process.stdout.write(current.id","process.stdout.write(tree.id","program","program.c","project","properti","ptr","ptr[r12]","public","pull","push","push!(ret.children,","push!(s,","push:","put","putstrln","q","q)","q.back","q.capac","q.data","q.front","q;","queue","queue🔤❗️","queue();","queue)","queue))","queue)))","queue,","queue.add(c);","queue.add(this.root);","queue.append(child)","queue.count","queue.dequeue();","queue.empty?","queue.enqueue(c);","queue.enqueue(this);","queue.extend(¤t.children);","queue.extend(node.children)","queue.poll();","queue.pop();","queue.pop(0)","queue.pop_front()","queue.popleft()","queue.push","queue.push(&n);","queue.push(...current.children);","queue.push_back(n);","queue.remove(at:","queue.shift","queue.shift();","queue:","queue;","queue[0]","queue[1:]","queue\\n')","queue_array,","queue_back,","queue_cap,","queue_empty(struct","queue_front,","queue_res","queue_resize(q);","queue_resize(struct","queue_resize:","queue_size,","queues.\"","queue{node}()","queue❗️","qword","r","r10,","r11","r12","r12,","r12]","r12d","r12d,","r13","r13,","r13]","r13d","r13d,","r14","r14,","r14]","r14d","r14d,","r15","r15,","r15]","r15d,","r8,","r9,","r])","rang","range(num_child)))","range(num_child):","rax","rax,","rax:rdx","rax]","rbp,","rbx","rbx,","rcx,","rdi","rdi,","rdx","rdx,","reach","realloc","realloc(stk","recurs","recursion!","recursion,","recursive.","recursive\\n')","regist","relat","removefirst.","repeat","replic","request","resiz","rest","restrict","result","ret","ret;","return","return:","return;","reus","reversedo:","right.","right]","root","root)","root;","root_bin","root_binari","rootb","rootbinari","rootbinary)","row","rowcount","rowcount,","rows'","rows)","rows,","rows};","rsi","rsi,","rsi]","rsp","rsp,","run","s","said,","same","save","scheme","schloss","scratch","scratch:","search","search.","search.\"","see","seem","self.","self.children","self.data","self.valu","sense.","set;","setter\"","setter.\"","shape","sharealik","shift","shl","show","show:","shownod","shr","similar","simpl","simple,","simple:","simpli","singl","situation.","size","size)","size);","size;","size_t","sizeof(q","sizeof(stk","sizeof(struct","sizeof(tree)","snippet","so:","some(current)","someth","something...","spend","stack","stack🔤❗️","stack();","stack)","stack))","stack)))","stack))))","stack,","stack.\"","stack.\"\"\"","stack...)","stack.append(child)","stack.count","stack.empty?","stack.extend(¤t.children);","stack.extend(node.children)","stack.pop","stack.pop()","stack.pop();","stack.poplast()!","stack.push","stack.push(&n);","stack.push(...current.children);","stack.push(c);","stack.push(this);","stack.push(this.root);","stack:","stack;","stack[0]","stack[1:]","stack\\n')","stack_array,","stack_cap,","stack_empty(struct","stack_pop","stack_pop:","stack_pop_el","stack_pop_element:","stack_pop_return","stack_pop_return:","stack_push","stack_push(&stk,","stack_push(struct","stack_push:","stack_push_append","stack_push_append:","stack_size,","stack_top,","stack{node}()","stack❗️","start","static","static::dfsrecursive($child);","static::dfsrecursiveinorderbinary($tre","static::dfsrecursivepostorder($child);","std::collections::vecdeque;","std::cout","std::generate_n(std::back_inserter(vec),","std::queue","std::size_t;","std::stack","std::vector","step:","still","stk","stk)","stk.capac","stk.data","stk.top","stk;","store","straightforward","struct","structur","structure.","structures,","sub","subclass:","subtract","sure","surprisingly,","swap","switch","system","system.collections.generic;","system.err.println(\"not","system.out.print(node.id","system.out.print(queue.peek().id","system.out.print(stack.peek().id","system.out.println(\"[#]\\nqueu","system.out.println(\"[#]\\nrecurs","system.out.println(\"[#]\\nstack","system.out.println();","system;","t","take","taken","temp","temp)","temp))","temp)))))","temp._children)","temp.children","temp.children!","temp.children)","temp.children.each{","temp:","temp_children","temp❗️","terminator:\"","ternari","test","testtre","text","that,","therefor","this,","this.","this.children","this.createallchildren(this.root,","this.dfsrecursive(this.root);","this.dfsrecursivepostorder(this.root);","this.id","this.root","this:","thought","through","throw","thrown","time","tmp","tmp.children)","tmp;","top","top,","transcript","travers","traversal🔤️❗️","traversal,","traversal:","tree","tree!\"","tree!\")","tree!\");","tree!');","tree!';","tree\"","tree\")","tree'","tree')","tree($numofrows);","tree(2,","tree(3,","tree(int","tree)","tree,","tree.","tree.\"","tree.\"\"\"","tree.\"))))","tree.\\n\"","tree.\\n\");","tree._children)","tree.bfsqueue();","tree.c","tree.children.foreach(dfspostorder);","tree.children.foreach(dfspreorder);","tree.dfsrecursive();","tree.dfsrecursiveinorderbinary();","tree.dfsrecursivepostorder();","tree.dfsstack();","tree.java","tree:\"","tree:\")","tree:\");","tree:'","tree:\\n\");","tree:~%\")","tree\\n')","tree_children,","tree_num_children,","tree_siz","tree_size,","tree_traversal.c","tree_value,","trees\");","treetravers","treetraversal::dfsqueue($node);","treetraversal::dfsrecursive($node);","treetraversal::dfsrecursiveinorderbinary($node);","treetraversal::dfsrecursivepostorder($node);","treetraversal::dfsstack($node);","tri","ts","ts)","tuple(create_tree(num_row","twice,","two","type","types,","u64)","u64,","uncom","under","unless","until","unword","up","upper","us","used;","using,","utility.h","utility_h","v","valid","valu","value,","value.","value:","value;","value|children_s","var","vari","variabl","vec![],","vec![n];","vec,","vec;","vecdeque::new();","vector","vector,","vector.","veri","video","visit","void","want","warn","way","we'll","while(length(q)","while(length(s)","whiletrue:","with:","without","won't","work","work.","would'v","write","written","x","xmm0","xor","zero","{","{next_nodes{:},","{node1,","{node10,","{node2,","{node5,","{node6,","{node_stack{:}","{null,","{n};","{{}});","{};","|","|child|","}","});","}.","};","~isempty(child)","~isempty(children{1})","~isempty(node_queue)","~isempty(node_stack)","↩️","↪️","⏫","⏹","▶️","◀️🙌","✖️","❎","❗️","➕","➖","➡️","⭐️","️↪️"],"contents/euclidean_algorithm/euclidean_algorithm.html":["!","!=","!==","\"$1\")","\"$2\")","\"$a\"","\"%s\"","\"[#]\\nmodulu","\"[#]\\nsubtract","\"[#]`nmodulu","\"[#]`nsubtract","\"[#]~%modulu","\"[#]~%subtract","\"euclidean","\"euclidmod\"","\"euclidsub\"","\"find","\"fmt\"","\"~d~%\"","#","#!/usr/bin/env","#includ","#lang","$((128","$((64","$(128","$(64","$a","$a)","$a,","$a;","$b","$b)","$b):","$b,","$b;","$b];","$tmp","%","🍇","🍉","🏁","🏧","🏧a","🏧b","🐇","💭","🔡","🔢","🔼","🖍🆕var_a","🖍🆕var_b","🖍var_a","🖍var_b","😀","🙅","🙌","🚮","🤜128","🤜64","'(g0)')","',num2str(euclidmod(64","',num2str(euclidsub(128","'[#]'","'modulu","'subtract","(","(#560),","($a","($b","(%","(%)","((","((128","((64","((a","((b","((defin","((tmp","()","(*","(0,","(128","(64","(=","(>","(_,","(a","(a,","(ab","(ad)","(almost","(assert","(b","(chin123)","(cond","(defin","(defn","(defun","(display","(displayln","(dp","(end","(envis","(eql","(euclid","(euclid_mod","(euclid_mod*","(euclid_sub","(euclid_sub*","(format","(found","(gcd","(gcd)","(if","(inner","(jspp)","(like","(local","(loop","(math.abs(a),","(math/ab","(mod","(modulo","(negative?","(newline)","(on","(print","(recur","(return","(ubsan)","(x","(x,","(zero?","(zerop","(~",")","))","));","*","*)",".",".extern",".global",".intel_syntax",".rodata",".section",".string",".text","//","/=","0","0)","0,","0/1","0/1a","0:","0;","0aa","1","1.2","1/0","10","11aa","12","12🤛","12)","12))","12,","128","128*77)","12ab","12ba","13aab","13bba","13tba","14","1536","180","1800's.","1:","1aa","2","2ab","2ba","2dup","3","300","31","3aab","3bba","3tba","4.0","42","4288","48","5184","56","64","64*81)","67","67🤛","67)","67))","67,","71)","77","77🤛","77)","77))","77))\"","77)))","77)).","77));","77))]","77);","81","81🤛","81)","81))","81))\"","81)))","81))))","81)).","81));","81))]","81);","9856",":","::",":=",";",";;",";;;;","=","==","=>",">",">=","[","[$a","['[#]","[(>","[(eq?","[(or","[a","[els","[i","[lf][lf][lf]","[lf][lf][lf][lf]","[lf][space][lf][lf]","[lf][space][space][lf]","[lf][space][space][tab][lf]","[lf][space][space][tab][space][lf]","[lf][tab][space][tab][lf]","[lf][tab][tab][tab][space][lf]","[math]::abs($a)","[math]::abs($b)","[space][lf][space]","[space][lf][tab]","[space][space][space][lf]","[space][space][space][tab][lf]","[tab][lf][space][tab]","[tab][lf][tab][tab]","[tab][space][space][tab]","[tab][space][tab][tab]","[tab][tab][space]","[tab][tab][tab]","]","].","^a.","_","_)","_________________________________________________________________________","__name__==\"__main__\":","`b`","`mod`","a%b","a%b,b","a)","a)(ab","a)(negative?","a))","a)))))","a))]))","a,","a.","a.ab","a.abs();","a.absolutevalu","a:","a;","a=$(ab","a=abs(a);","a=b","a>b:","a]","aa","aab","ab","aba","abs($a);","abs($b);","abs()","abs(a","abs(a)","abs(a);","abs(a:a)","abs(a:b)","abs(b)","abs(b);","abs(in1)","abs(in2)","abs.","absolut","abz","addpattern","again","algorithm","algorithm,","algorithm.","algorithm:","amaz","ancient","appeal.","applic","args)","arguabl","array)","array[string]):","attribut","auto","b","b)","b)(euclid","b))","b))(euclid","b)))","b))))","b))]","b):","b);","b)]","b,","b,a","b.","b.ab","b.abs();","b.absolutevalu","b.zero?","b:","b::int64)","b;","b=$(ab","b=0","b=abs(b);","b]","ba","bab","back","base","bash","bat","bba","bc)","becom","befor","better","bi@","bigger","biggr","both","call","case","certain","chang","chapter","chapter:","check","check1","check1);","check2","check2);","check:","chinmaya","chk1","chk1);","chk2","chk2);","class","clockwise)","clockwise,","cmp","code","come","command","comments.","common","comput","conceptu","console.log('[#]\\nmodulu","console.log('[#]\\nsubtract","console.log(euclidmod(64","console.log(euclidsub(128","console.writeline(\"[#]\\nmodulu","console.writeline(\"[#]\\nsubtract","console.writeline(check);","console.writeline(check2);","contribut","cool.","cr.","creat","creativ","death","deeper","def","definit","definition)","describ","devic","diff","differ","difficult","diffrint","discuss","div","divid","divisor","divisor.","divsor","done","done.","down","dp","drop","dup","duplic","e","earthfail","echo","element","elif","else:","empty:","end","end.","endfunct","endif","endwhil","enter","equal","equal,","era","euclid","euclid%","euclid'","euclid($a,","euclid()","euclid)","euclid_mod","euclid_mod()","euclid_mod(0,","euclid_mod(128","euclid_mod(64","euclid_mod(a","euclid_mod(a,","euclid_mod(a:","euclid_mod(a::int64,","euclid_mod(b,","euclid_mod(in1,","euclid_mod(int","euclid_mod:","euclid_mod_fmt","euclid_mod_fmt:","euclid_rem(64","euclid_rem(mut","euclid_sub","euclid_sub()","euclid_sub(0,","euclid_sub(128","euclid_sub(64","euclid_sub(a","euclid_sub(a,","euclid_sub(a:","euclid_sub(a::int64,","euclid_sub(in1,","euclid_sub(int","euclid_sub(mut","euclid_sub(x","euclid_sub(x,","euclid_sub,","euclid_sub:","euclid_sub_fmt","euclid_sub_fmt:","euclidean","euclideanalgo","euclideanalgorithm","euclideanalgorithm();","euclideanalgorithm.c","euclideanalgorithm.euclidmod(64","euclideanalgorithm.euclidsub(128","euclidian","euclidmod","euclidmod(64*67,","euclidmod(a,","euclidmod(a,b)","euclidmod(a:","euclidmod(int","euclidmod:","euclidsub","euclidsub(128*12,","euclidsub(a,","euclidsub(a,b)","euclidsub(a:","euclidsub(int","euclidsub:","exampl","exist","exit","explan","fact","fals","few","fewer","fi","find","first","first,","fmt.println(\"[#]\\nmodulu","fmt.println(\"[#]\\nsubtract","fmt.println(check1)","fmt.println(check2)","fn","follow","found","fractions).","fun","func","function","fundament","gcd","gcd_minus(128","gcd_minus(a,","gcd_mod(64","gcd_mod(a,","go","goe","graph","graphic","greater","greatest","gt","hai","here","here'","here,","higher","histori","host","i))))))","i64","i64)","i64,","if_tru","if_true:","iffalse:","iftrue:","im","imag","images/graph","implement","implementation,","implementations,","implicit","import","in(number)","in2:","incredibly,","inform","initi","inner","input","input:","int","int)","int):","int,","integ","integer,","integer>>euclidmod:","integer>>euclidsub:","integers\"","integers.","intent(inout)","intern","io","is.","ismainmodule:","it'","itz","iz","j","j)","j)))))","jame","jle","jmp","jne","julian","known","kotlin.math.absolutevalu","kthxbye","l:a","l:b","l:c","label_0","label_0:","label_1","label_1:","label_2","label_2:","last","later.","leav","licens","license.","license.md).","line","lisp","list($b,","live","local","lolatomroflsinnlos,","look","loop","loop)","loop:","lower","mahesh","main","main()","main(args:","main(string[]","main:","make","mani","match","math.ab","math.abs(a)","math.abs(a);","math.abs(b)","math.abs(b))","math.abs(b);","mathemat","mathjax.hub.queue([\"typeset\",mathjax.hub]);","max","mazzuca","me,","method","method.","method:","millennia","millennia.","mit","mkay","mod","mod(a,b);","mod_check","mod_check:","mod_loop","mod_loop:","modern","modifi","modulo","modulo(a,b)","modulu","modulus.\"","mov","much","mut","namespac","ne","neg","new","nicol","non","none","noprefix","now,","num","num1","num2","num2,","number","numbers,","numbers.","o","object","offset","oic","oldb","oldb.","older","on","onc","oper","origin","otherwise,","out","out(number)","output","outta","over","p","packag","php_eol;","pointer","pop","posit","pretti","print","print(\"[#]\\nmodulu","print(\"[#]\\nsubtract","print('[#]\\nmodulu","print('[#]\\nsubtract","print(euclid_mod(64","print(euclid_sub(128","print(euclidmod(a:","print(euclidsub(a:","print_int","print_newlin","print_newline;","printf","printf(\"[#]\\nmodulu","printf(\"[#]\\nsubtract","printf('[#]'.php_eol.'modulu","printf('[#]'.php_eol.'subtract","printf.printf","printi","println!(\"[#]\\nmodulu","println!(\"[#]\\nsubtract","println(\"[#]\\nmodulu","println(\"[#]\\nsubtract","println(euclid_mod(64","println(euclid_sub(128","println(euclidmod(64","println(euclidsub(128","produkt","program","program.c","project","provid","public","pull","push","putstrln","quick","r","racket","rax","rax,","rdi","rdi,","rdx","rdx,","read","readabl","readi","rec","recurs","reduc","remaind","request","result","result:","result:\"","result:\")","result:\");","result:'","result:')","result:'),","result:'.php_eol.'%s',","result:\\n\"","result:\\n\",","result:\\n\";","result:\\n$(check1)\")","result:\\n$(check2)\")","result:\\n$result\"","result:\\n%d\\n\"","result:\\n%d\\n\",","result:\\n{}\",","result:`n$(mod","result:`n$(sub","result:~%\")","result=$(euclid_mod","result=$(euclid_sub","ret","ret=$1","retriev","return","revolutionary,","rid","right","rly,","rly?","roll","rot","rsi","rsi,","s:check_1","s:check_2","s:euclid_mod(64","s:euclid_mod(a,","s:euclid_sub(128","s:euclid_sub(a,","saem","said,","same","same)","same.","sar","schacher","schloss","scienc","scratch","secondnumb","see","self","set","sharealik","show","show:","simpl","simpli","smallr","snippet","someth","stack","start","state","static","stay","std.math;","std.stdio;","std::abs(a);","std::abs(b);","std::cout","std::exchange(b,","step","steps:","still","store","sub","sub(","sub*","submit","subtract","subtraction\"","subtraction:","such","support","sure","swap","system.out.println(\"[#]\\nmodulu","system.out.println(\"[#]\\nsubtract","system.out.println(euclidmod(64","system.out.println(euclidsub(128","system;","t","take","taken","tba","temp","temp:","temp;","test","text","that'","them.","think","this:","though,","throughout","time,","timeless","timestep.","tmp","tmp))","tmp;","today","today.","top)","top,","transcript","true;","truli","twice","two","u","uklidmod","uklidsup","under","unit","univers","until","up","us","val","valu","value)","var","var_a","var_b","version","versions.","video","visibl","void","wai,","way","weinstein","whatev","while(b","whilefalse:","without","works,","world","write","write(*,","write(*,'(a)')","writeln(\"[#]\\nmodulu","writeln(\"[#]\\nsubtract","written","x","x)","x))","xam4lor","xor","y","y)","y,","ya","yr","zero","zero?","{","|","|>","}","~=","↩️","↪️","≠","⏫","▶️","✖️","❎","❗️","❗️❗️","➖","➡️","⬅️","⬆️","️🔁","️🔼🐇⬆️","️⏫🐇⬆️"],"contents/matrix_methods/matrix_methods.html":["(#560),","(found","/","4.0","algorithms.","along!","applic","area","attribut","categories:","certainli","chapter","chapter:","code","common","creat","creativ","diagon","divid","don't","eigenvalu","engineering,","equat","everyth","exampl","fail","favorit","feel","fill","find","follow","form.","foundat","go","graphic","initi","intern","jame","larg","licens","license.","license.md).","list","lower","mani","manipul","mathemat","mathematical.","mathematics,","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matric","matrices.","matrix","method","mit","modifi","more","none","offend","on","out","part,","pull","reason,","request","requir","schloss","scienc","sharealik","solv","system","text","there,","though","tour","type","uncommon","under","upper","us","usabl","we'll","written"],"contents/computational_geometry/computational_geometry.html":["(#560),","(found","4.0","add","algorithm","archiv","area","arxiv.org","attribut","automat","bring","chapter","chapter:","code","come","common","comput","cover","creativ","definit","differ","dimension","evolves,","exampl","follow","foundat","future!","gener","geometri","geometry.","go","graphic","graphics.","initi","interest","intern","jame","joy","know","licens","license.","license.md).","mathematics,","mathjax.hub.queue([\"typeset\",mathjax.hub]);","mit","modifi","more","none","pore","pull","recommend","request","research,","schloss","section","sector","sense,","sharealik","spend","text","three","through","time","two","under","written"],"contents/gift_wrapping/gift_wrapping.html":["\"gift\",","(#560),","(found","4.0","accur","algorithm","algorithm;","allow","attribut","case","chapter","chapter:","classifi","code","code.","common","complic","convex","creativ","defin","dimens","dimensions,","distribut","entir","exampl","fair,","find","follow","gift","give","given","graphic","here","histori","hold","however,","hull","incred","initi","interior","intern","it'","jame","jarvi","lead","leap","licens","license.","license.md).","mani","march","mathjax.hub.queue([\"typeset\",mathjax.hub]);","methods.","mit","modifi","more","name","neat","none","on","point","points.","problem.","programm","pull","random","request","rich","said,","schloss","shape","sharealik","smallest","solv","speaking,","strictli","term","text","though,","three","two","under","wrap","written"],"contents/decision_problems/decision_problems.html":["(#560),","(candid","(found","4.0","algorithm","all;","appropri","assign","associ","attribut","bunch","certain","certainli","chang","chapter","chapter:","classifi","code","come","common","comput","cost","creativ","decis","design","each","everyth","exampl","example,","follow","future.","graphic","here:","honest","however,","hungarian","i'll","i'm","in,","inform","initi","input","intern","jame","job","licens","license.","license.md).","make","mathematics,","mathjax.hub.queue([\"typeset\",mathjax.hub]);","minim","mit","modifi","near","none","now,","output","outputs.","over","overall,","perform","place","positions)","problem","pull","put","read","relat","request","right!","schloss","section","sharealik","studi","sure","task","task.","text","under","up","whether","worth","written"],"contents/physics_solvers/physics_solvers.html":["(#560),","(found","4.0","algorithm","along","archiv","area","area.","attribut","benefit","biologi","certain","chapter","chapter:","chemistry.","code","common","comput","creat","creativ","differ","differenti","drawback","equat","equation,","exampl","example,","follow","future,","gener","graphic","heat","initi","integr","intern","it'","itself","jame","kinemat","lend","licens","license.","license.md).","mani","method","mit","modifi","more","none","note","particular","physic","place","pull","readili","request","research,","schloss","schrödinger","scientif","section,","sever","sharealik","solv","solver","solvers.","specif","such","system","systems.","text","throughout","under","uniqu","us","verlet","way","ways.","worth","written"],"contents/huffman_encoding/huffman_encoding.html":["!=","!input[start..].is_empty()","!node.right)","!t","\"","\"\"","\"\")","\"\"))","\"\",","\"\",:code","\"\";","\"\"}","\"(bibbiti","\"0\"","\"0\")","\"0\"),","\"0\",","\"0\":","\"1\"","\"1\")","\"1\")))))","\"1\"),","\"1\",","\"1\":","\"?\"))","\"\\\":","\"\\ndecoding...\")","\"\\t\"","\"b","\"b\"","\"bbbbbbbb\"","\"bibbiti","\"bibbity_bobbity\"","\"coding...\")","\"container/heap\"","\"decod","\"decoding:","\"encod","\"endod","\"fmt\"","\"huffman_tree\"","\"length:","\"make","\"origin","\"remov","\"take","\"test\"","\"the","#","#(+","#(appli","#(str","#[derive(debug)]","#freq","#includ","#messag","$","%","%1","%1))","%1)))]","%2)","%2))","%s\\n\"","%t\\n\",","&&","&builder,","&cb,","&codebook);","&count)|","&encoder](char","&heap","&mut","&result);","&self)","&self.codebook[&c]).join(\"\")","&str)","&str,","&tree,","'","''","''.join(decoded_message)","''.join(messag","'':","'(((node1","'0'","'0')","'0'),","'0',","'0';","'1')","'1',","'1';","'100'),","'1000'),","'1001'),","'101'),","'110'),","'1100'),","'1101'),","'111')]","'\\0';","'__main__':","'a')","'a',","'bibbity_bobbity'","'i']]]","'o'],","'y'],","(","(!heap","(!isa(current,","(!node.left","(!tree)","(#560),","('_',","('i',","('o',","('t',","('y',","(*cb)[node.char]","(*dst)[len","(*dst)[len]","(*input","(*input);","(*it)","(+)","(5","(;","(;;)","(a,","(appli","(assoc","(auto","(bit","(char)i;","(char,","(char?","(clojure.pprint/pprint","(clojure.set/map","(coder","(complement","(concat","(cond","(const","(counts[char]","(decod","(def","(default","(defn","(drop","(eq","(first","(float)","(fn","(found","(freq","(freq.empty())","(func","(get","(hash","(haskey(weights,","(heap","(heap.length","(i","(i,","(if","(inc","(index","(index)","(insert,","(int","(integer?","(interleav","(is_leaf(tree))","(it","(it',","(jspp),","(just","(key","(last","(leaf","(leav","(left","(length","(let","(list","(loop","(m","(map","(map.entri","(map[c]","(mayb","(merg","(n","(node","(node.isleaf)","(node.left","(node.left)","(node.leftchild","(node.right","(node.right)","(node.rightchild","(node2","(nodeprioritylist.count","(one:","(ord","(partial","(println","(priorityqueue.data.length","(priorityqueue.size()","(ptr)","(recur","(reduc","(remov","(repeat","(ret.size()","(right","(second","(set","(show","(show,","(size_t","(sometim","(sort","(split","(str","(string,","(t,","(t1:t2:ts)","(t2,","(tabl","(take","(target","(thi","(tree","(tree,","(tree.siz","(uncurri","(updat","(val","(var","(vec","(we","(zero:","({",")","*","*/","*=","*codebook","*codebook,","*dst","*huffman_tre","*input));","*input;","*lh","*lhs;","*map.entry(c).or_insert(0)","*n","*node","*node)","*node,","*nodeheap)","*rh","*rhs;","*self","*str","+","++","++=","++input)","++it)","++str)","+=",".","..","...this.data.slice(target)];",".code",".collect::>();",".equ",".extern",".flatmap(bit",".global",".groupby(identity)",".intel_syntax",".iter()",".map(|(&value,",".mapvalues(_.length)",".map{",".next_index",".rodata",".section",".select(n",".str",".string",".text",".tolist();","/","/*","//","0","0)","0))","0))))","0),","0,","01000010010111011110111000100101110.","01110011110110011010110000111101100","01110011111010110000100100111110101","0;","0x1","1","1)","1)),","1),","1);","1,","100","101","1024","1040","110","1110","1111","12","128","15","16","16]","16],","1:","1;","1]","1],","2","2)),","2),","2);","2.7+","20","24","255","256","2;","3","3))))","301","32","32]","32],","4","4*r12]","4*r8]","4*rax]","4*rdi]","4.0","40","4096","512","5128","6","6),","63","64","64,","7","7]","8","8*r13],","8*rax]","8*rcx]","8*rcx],","8*rdx]","8]",":","::",":=",":code",":code)",":els",":messag",":message))",";",";;",";add",";extract",";of",";remov",";to","=","==","===","=>",">",">\",",">>",">capac",">codes)",">codes[(unsign",">codes[0]);",">count",">count)",">count;",">data",">data);",">data,",">data[",">data[0],",">data[0];",">data[heap",">data[index]);",">data[index],",">data[left]",">data[parent_index]",">data[parent_index],",">data[right]",">data[target]);",">decoder.get();",">encoder;",">frequenc",">frequency),",">frequency;",">key);",">key,",">left",">left);",">left,",">length",">length)",">length++]",">length]);",">lhs.get(),",">lhs.get();",">next_index",">next_index++]",">next_index]",">rhs.get(),",">rhs.get();",">right",">right);",">right,",">right;",">second;",">str);",">str[builder",">value);",">value]","?","@test","@testset","[&freq](char","[&ret,","['b',","['t',","[('b',","[(a,","[(char,","[(int,","[(t1,","[...bitstring])","[...iterable].sort((a,","[...str].map(c","[...str];","[...this.data.slice(0,","[0]","[64","[[['_',","[[noreturn]]","[]","[](auto","[])","[]*node","[];","[]rune)","[a]","[bit","[bit]","[bit])","[c](auto","[charact","[code","[codebook]","[ecx","[it',","[it,","[left","[letter","[m","[middl","[new","[new_freq](auto","[r10","[r10]","[r10],","[r11","[r12","[r12]","[r13","[r14","[r14]","[r14],","[r8","[r8]","[r9","[r9]","[r9],","[rax","[rax],","[rcx","[rcx]","[rdi","[rdx","[rdx]","[rdx],","[rsi","[rsp","[rsp],","[s","[st]","[t]","[top](it","[tree","[tree]","[tree_left,","\\\"\"","_","_)","_,","_.weight))","__name__","__repr__","__str__","__str__(self):","_}","a)","a),","a)]","a,","a.weight","a[2]","accept","accord","achiev","actual","ad","add","add(nod","addition,","addpattern","address","advanc","again","al","al,","algorithm","align","alloc","allow","alphabet,","alreadi","alway","amount","anoth","anything.","anyway","appar","appear","append","append(*n,","append(code,","append(code[:len(code)","appli","appropriate.","args)","argument","arithmet","arr","arr[#arr","array","array[string]):","assign","at.","attribut","auto","auto&","b","b)","b.weight),","b[2]","back","backward","backwards,","base","becom","befor","begin","begin(freq),","between","bibbity_bobb","bibbity_bobbity:","bigger","biggest","binari","bisect","bisect(tre","bit","bitmask","bits),","bits,","bits.","bits.push_back(b);","bits;","bitstr","bitstr_len,","bitstr_len]","bitstr_siz","bitstr_size,","bitstring)","bitstring);","bitstring,","bitstring.","bitstring::string)","bitstring;","bitstring_build","bitstring_builder*","block","bobbity\"","bobbity\")","bobbity\");","bobbity\",","bobbity\";","bobbity)\")","bobbity)\";","book\");","bool","both","bottom","box,","box::new(left),","box::new(right),","branch","branch(left,","branch(left:","branch(node1,","branch(node_ptr","branch)","branch))","branch);","branch.","branch.freq","branch.left","branch.right","branch:","branch}","break;","build","build_codebook(empty(),","build_codebook(leaf(char,","build_codebook(left,","build_codebook(node(left,","build_codebook(right,","build_codebook(tree)","build_huffman_tree(message)","build_huffman_tree(message):","builder","builder,","buildtre","buildtree(messag","buildtree(message)","byte","c","c)","c);","c;","c]","calcul","call","calle","calloc","calloc(0,","calloc(1,","calloc,","capacity;","case","cases,","cases.","cb","cb,","cb[char]","cf","chang","chapter","chapter:","char","char)","char)*str]","char)c];","char)tre","char*","char**","char,","charact","character.","charcount","chars.reduce((counts,","cheatsheet","check","child","child,","children","choosetreebranch(bit)","choosetreebranch(bit:","chunk","cl","class","claud","cleanup:","clear","clobber","cmovnz","cmp","cmp(&self,","code","code)","code)))))","code);","code)]","code+'0')","code+'1')","code,","code.append(0));","code.append(1));","code.deletecharat(code.length()","code.tostring());","code:","code::string,","code='')","code]","codearr","codearr)","codebook","codebook'","codebook(it","codebook)","codebook);","codebook*","codebook,","codebook.","codebook.decode(&encoded);","codebook.encode(input);","codebook.entryset())","codebook.getorelse(c,","codebook.insert(value,","codebook.put(node.letter,","codebook.put(symbol,","codebook/tre","codebook:","codebook::codebook(it","codebook::decode(it","codebook::encode(it","codebook::node::~node()","codebook;","codebook[0][0]","codebook[c]).join(\"\"),","codebook[i]","codebook[n.key]=\"0\"","codebook])","codebook_free(struct","codebook_ptr","codebook_recurse!(branch.left,","codebook_recurse!(branch.right,","codebook_recurse!(branch::branch,","codebook_recurse!(leaf::leaf,","codebook_recurse!(n,","codebook_recurse(const","codebook_recurse(tre","codebook_recurse(tree,","codebook_s","codebook_size,","codebook_size]","codebookrecurse(c,","codebookrecurse(left,","codebookrecurse(nod","codebookrecurse(node.left,","codebookrecurse(node.right,","codebookrecurse(node:","codebookrecurse(right,","codebookrecurse(root,","codebookreverse()","coder","coder))","coder]","codes(begin(s),","codes(codes),","codes,","codes.decode(begin(string),","codes;","codes[256];","codes[i]);","codeword","codeword.","collect","combin","common","compar","compareto(nod","complet","complete.","compress","compression.","comput","concat","concat(&result,","concat(char**","concat_char(char**","concat_char(result,","concaten","concatmap","conceptu","consist","console.log(decoded);","console.log(encoded.string);","const","const&","const*","const;","construct","contain","contains?","continu","convent","convert","copi","correct","count","count(&self)","count)","count,","count:","count;","counter","counter(message)","counter,","counter.","counts,","counts;","counts[(unsign","counts[256]","counts[char]","counts[i];","counts_size,","counts_size]","counts_size],","cours","crate","creat","create_codebook(huffman_tree)","create_codebook(n::node)","create_tree(phrase)","create_tree(phrase::string)","createbitstring(str","createbranch","createbranch(nod","createcodebook(mayberoot:","createcodebook(tree)","createcodebook(tree);","createdictionary(nod","createdictionary(node.leftchild,","createdictionary(node.rightchild,","createdictionary(root,","createleaf(char","createtree()","createtree(originaltext)","createtree(phrase:","createtree(str)","createtree(str);","creativ","cur","cur.char","cur.left","cur.right","current","current.left","current.right","current_nod","currentnod","c|","data","data.","data.list","data.map","data:","data;","data[index]","data[target]","datastructur","data{std::move(decoder),","david","dead","dec","decod","decode(&self,","decode(bitstring,","decode(const","decode(enc,","decode(encoded,","decode(encoded.string,","decode(encoded:","decode(huffman_tree,","decode(huffman_tree::node,","decode(it","decode(messag","decode:","decode_dfs(&self,","decode_don","decode_done:","decode_loop","decode_loop:","decode_loop_char","decode_loop_char:","decode_loop_char_branch","decode_loop_char_branch:","decode_recurse(const","decode_recurse(input","decode_recurse(input,","decode_singl","decode_single(it,","decoded()","decoded)","decoded);","decoded:","decoded_messag","decoded_message)","decoded_message.append(inverse_dict[key])","decoded_message:","decoder)","decoder))","decoder;","decoder]","decreas","decrement","def","depend","depth","dequ","dequeue!(nodes)","dequeue!(weights)[1]","dequeue()","deriv","descend","describ","destroy","devis","dfs(&self,","dict","dict((v,","dict([(v,","dict(codebook)","dict)","dict);","dict::dict{char,string})","dict;","dict[leaf.key]","dict[node.key]","dictionari","dictionary();","dictionary)","dictionary);","dictionary,","dictionary.","dictionary;","dictionary[character];","dict{char,string}()","difficult","dil","dil,","display","distinctli","divid","do","doesn't","don't","done","dst","dst,","dst;","dst_len","dump","duplicate(build","duplicate(const","duplicate(get_code(codebook,","dword","dynamic_cast(cur))","dynamic_cast(current_node))","e.g","each","earthfail","easier","easiest","ecx","ecx,","edit","educ","edx","edx,","element","elif","empti","empty()","enc)","enc,","encod","encode(\"bibb","encode(\"bibbity_bobbity\")","encode(&self,","encode()","encode(codebook,","encode(codebook::dict{char,","encode(const","encode(it","encode(messag","encode(originaltext,","encode(phrase:","encode(str)","encode:","encode_calculate_length","encode_calculate_length:","encode_calculate_new_bit_offset","encode_calculate_new_bit_offset:","encode_don","encode_done:","encode_messag","encode_message:","encode_message_bit","encode_message_bits:","encode_message_bits_qword","encode_message_bits_qword:","encode_message_bits_try_overflow","encode_message_bits_try_overflow:","encoded)","encoded);","encoded.tree);","encoded:","encoded_messag","encoded_message)","encoded_message):","encoded_message:","encoded_str","encoded_string(codebook","encoded_string(std::str","encoder;","encoder_rec(&decoder,","encoder_rec(b","encoder_t","encoder_t&","encoder_t();","encoding.","encoding:","encodingresult","encodingresult(str","end","end(code),","end(encoder))","end(encoder),","end(freq))","end(freq),","end(ret),","end(s)))","end(s)),","end(string));","end)","enough","enqueue!(nodes,","enqueue(value)","ensur","entri","enum","enumerate(encoded_message):","enumerate(trees)","eq","eq(&self,","eq)","equal","esi","esi,","exampl","example.","exist","exit","experiments.core)","explan","explanation.","explicit","extend","extern","extra","extraordinari","f'leaf({self.char},","f'node({str(self.left)},","f1)","f1+f2)","f2))","fact","fact,","fano","fano,","field","fields:","final","final_bitstr","final_str","find","first","first,","first;","firsti","fit","flatmap","flip","fmt.printf(\"i","fmt.println(\"\\nencoded:\",","fmt.println(\"codebook:\")","fmt.println(\"decoded:\",","fmt.println(string(r),","fn","follow","following:","foreach","forward_dict","forward_dict[char]","found,","free","free(heap","free(tree);","free_tre","freq","freq,","freq.emplace_back(1,","freqmap","freqmap[char]","freqmap[char].freq++","freqmap[char];","frequenc","frequencies,","frequencies.most_common()","frequency)","frequency,","frequency.","frequency;","frequency]","frequency_array(message)","frequency_array(str)","frequencymap","frequencymap.entryset())","frequent","from(input:","func","function","function(a,","function,","gathro","gener","generate_codebook","generate_codebook(*huffman_tree);","generate_codebook(const","generate_codebook:","generate_codebook_branch","generate_codebook_branch:","generate_codebook_recurs","generate_codebook_recurse:","generate_codebook_recurse_don","generate_codebook_recurse_done:","generate_tre","generate_tree(const","generate_tree(input);","generate_tree:","generate_tree_branch","generate_tree_branches:","generate_tree_count_char","generate_tree_count_chars:","generate_tree_don","generate_tree_done:","generate_tree_leav","generate_tree_leaves:","generate_tree_leaves_count","generate_tree_leaves_counters:","generate_tree_leaves_setup","generate_tree_leaves_setup:","generate_tree_one_leaf","generate_tree_one_leaf:","generate_tree_ret","generate_tree_ret:","generatecodebook(root","generatecodebook(root)","generation:","get;","get_code(codebook,","get_code(const","getfrequ","giallouraki","given","givennodes)","givennodes.tolist();","go","gotten","graphic","great","group","guarante","guston","gustorn","h","h.len()","h.pop().(*node)","h.pop().(*node),","handl","happen","hash","hashmap","hashmap)","hashmap,","hashmap::new();","hashmap<>(),","hashmap<>();","hashmap};","heap","heap'","heap)","heap*","heap,","heap.init(h)","heap.pop(h).(*node)","heap.push(h,","heap_data,","heap_data]","heap_free(&heap);","heap_free(struct","heap_len,","heap_len]","heap_len],","heap_pop","heap_pop(&heap);","heap_pop(struct","heap_push","heap_push(&heap,","heap_push(struct","heap_push:","heap_push_don","heap_push_sift_up:","heap_size,","heart","heart.","help","helper","helper::make_decoder(first,","helper::make_encoder(*decoder);","here","here'","here,","here.","himself!","hoist","hold","horribl","huffman","huffman.","huffman::encoded_string(to_be_encoded);","huffman_decode(codebook,","huffman_encode(codebook,","huffman_tre","huffman_tree,","huffman_tree:","huffmancod","huffmancoding();","huffmancoding.c","huffmancoding.decode(result);","huffmancoding.encode(\"bibb","huffmancoding.nod","huffmanencod","huffmantre","huffmantree(\"bibbity_bobbity\");","huffmantree(str","huffmantree,","huffmantree.createtree();","huffmantree.decode(encoded));","huffmantree.encode();","huffmantree::branch","huffmantree::from(input);","huffmantree::leaf","i)","i,","i.e.,","i32","i32,","icompar","idea","ignor","imag","images/graph","immedi","impl","implement","implement,","implemented.","import","inc","included\"","increas","increment","index","index)","index).","index,","index.","index:","index;","indic","indici","ineffici","inefficient,","inform","information.","initi","inlin","input","input\"),","input)","input,","input.chars().fold(hashmap::new(),","input.chars().map(|c|","input.chars().next();","input:","input;","insert","instanc","instead","instruct","int","int)","int64}()","interest","interface{}","interface{})","interleav","intern","introduc","inverse_dict","inverse_dict:","inverse_dict['']","inverse_dict[key]","invert","is:","is_leaf(const","isa(huffman_tree,","isa(n,","isleaf","it'","it,","it.","iter","itertools::itertools;","itertools;","ith","itself","j","jame","java.util.*;","jge","jl","jle","jmp","jne","jnz","julian","jz","k)","k,","keep","key","key(key)","key)","key,","key::char","key;","keyword","kid","knew","l","l)","languag","language,","last","last)","last);","last,","last;","last;)","lasty))))))","lasty]","later","lea","leader","leaf","leaf(*t))","leaf(_,","leaf(c,","leaf(char,","leaf(char:","leaf(i,","leaf(int","leaf(symbol,","leaf(t,","leaf(weight,","leaf)","leaf.","leaf;","left","left,","left.count()","left.decode_dfs(&input[1..],","left.dfs(code.clone()","left.freq","left.weight","left:","left::union{leaf,","left;","leftchild","leftchild,","leftchild.weight","leftchild;","len","len()","len(codebook)","len(encoded_message)","len(message)","len(n)","len(old)","len(trees)","length","length,","length;","length]","less","less(i,","letter","letter))","letter,","letter;","lh","lhs(std::move(lhs)),","lhs,","lhs.frequenc","lhs;","licens","license.","license.md).","like.","line","list","list();","list,","list.","littl","load","local","localdictionary)","localdictionary);","localdictionary.add(node.key[0],","longer","look","loop","lose","lossless","m","m)","m.!)","m.empti","m.fromlist","m.fromlistwith","m.getkey());","m.getvalue()));","m.getvalue());","m.tolist","made","main","main()","main():","main(args:","main(string[]","main:","make","make([]rune,","make(codebook)","make(map[rune]*node)","make_codebook(self)","make_decoder(it","make_encoder(nod","makequeue(iterable)","makequeue(nodes);","malloc","malloc(length","malloc,","manag","manipul","map","map$(forward_dict[]))","map$(t","map$(weight)","map,","map[c]","map[char,","map[rune]str","mask","mask:","match","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matthew","mayb","maybegetacharact","mayberoot.foreach(c","mayberoot.getorelse(leaf('?',","mayberoot:","member","memcpy(dst,","memori","memory,","memset","memset,","mention","messag","message)","message):","message,:cod","message:","message:',","method","method.","mid","mid)","mid))","middl","middle)))","minimum","mit","mix:","mktabl","modifi","moment,","more","mov","movap","move","movup","msg","msg)","msg_data,","msg_data]","msg_len,","mut","n","n)","n))","n),","n.count()))","n[i]","n[i],","n[i].freq","n[j]","n[j],","n[j].freq","namespac","necessari","need","needed?","never","new","new(node)","new(nodeheap)","new_freq","new_nod","new_tre","new_tree)","new_weight","newnod","newnode)","newnode.char","newnode.freq","next","next((i","next_index;","nil","node","node'","node(freq),","node(key.tostring(),","node(leaf(b,","node(left","node(leftchild.key","node(lh","node(node(leaf(o,","node(node(leaf(y,","node(str","node(tree_left,","node)","node,","node.","node.createbranch(leftchild,","node.createleaf(n.key,","node.left","node.right","node.right;","node1","node1,","node1.weight","node1[2]","node2","node2,","node2.weight)","node2[1]","node2[2]","node3","node_ptr","nodeheap","nodeheap)","nodeprioritylist","nodeprioritylist()","nodeprioritylist(list","nodeprioritylist(nodes);","nodeprioritylist.","nodeprioritylist.add(parentnode);","nodeprioritylist.pop();","nodes)","nodes.count;","non","none","noprefix","not,","note:","noth","now","now)","null","null)","null);","null,","null;","number","o","o.frequency));","object","object.entries(charcounts).map(([key,","occur","offset","offset]","ok","old","old[0","old[l","on","on.","one:p)]","onto","option","option[node]","option[node]):","ord","order","ordering,","origin","original:","originalstr","originaltext","originaltext)","other)","other.count()","other.count().cmp(&self.count())","other.count().partial_cmp(&self.count())","other.weight;","other:","otherwis","out","out)","out);","out.push_back(std::make_pair(l","output","outright","over","overflow","p","p)","p)]","p.first","p.first;","p.key","packag","pad","pair","pair:","pairs(map)","panic!(\"unexpect","paramet","params:","parent","parent_index","parent_index;","parentnod","part","partial_cmp(&self,","partialeq","partialord","partialord};","path","patholog","peek(weights)[2]","phrase","phrase)","phrase.flatmap(c","phrase::string)","place","pointer","pop","pop()","posit","possibl","practice.","principle,","print","print('codebook:","print('codebook:',","print('decod","print('encod","print('huffman","print('message:","print('message:',","print_codebook","print_messag","printcodebook()","printf","printf(\"codebook:\\n\");","printf,","println!(\"{:#?}\",","println!(\"{}\",","println(\"codebook","println(\"decod","println(\"encod","println(\"origin","prioriti","priorityqueu","priorityqueue()","priorityqueue.add(new","priorityqueue.dequeue();","priorityqueue.enqueue({","priorityqueue.remove();","priorityqueue<>(comparator.comparingint(o","priorityqueue[node]()(ordering.by(","priorityqueue{node,","priorityqueue}","privat","problem","process","professor","program","program.c","project","project!","proper,","provabl","provid","ptr","ptr,","pub","public","public:","pull","push","push(x","push/pop","put","putstrln","python","qualifi","question","queue","queue,","queue.len()","queue.pop().expect(\"th","queue.pop().unwrap();","queue.push(huffmantree::branch","quick","qword","qword]","r\"(bibbiti","r,","r10,","r10b,","r11","r11,","r11]","r12","r12,","r12:","r12d","r13","r13,","r13:","r13d","r13d,","r14","r14,","r8","r8,","r8d,","r9","r9,","r9b","r9d,","rang","range\");","rax","rax,","rax:","rax:rdx","rbp","rbp,","rbx","rbx,","rcx","rcx,","rdi","rdi,","rdx","rdx,","reach","read","readabl","readi","realli","realloc(*dst,","realloc(heap","recurs","recurse(node,","recurse(node.left,","recurse(node.right,","recurse(tree,","reduc","ref","regist","registers:","remain","rememb","remov","repeat","replac","repres","represent","request","requir","resourc","respect","restor","result","result)","result);","result.dictionary)","result.join(\"\");","result.push(node.key);","result.push(value);","result:","result;","results,","ret","ret);","ret,","ret.pop_back();","ret.push_back(p.second);","ret;","return","return:","return;","revers","reversecodebook","reversecodebook.put(m.getvalue(),","revert","rh","rhs(std::move(rhs))","rhs)","rhs.frequency;","rhs;","right","right)","right))","right));","right),","right,","right.count(),","right.decode_dfs(&input[1..],","right.dfs(code.clone()","right.freq","right.frequency,","right.weight,","right:","right::union{leaf,","right;","rightchild","rightchild)","rightchild);","rightchild.key,","rightchild.weight,","rightchild;","rip","robert","robust","root","root\")","root)","root))","root,","root.left","root.right","root;","round","rsi","rsi,","rsp","rsp,","rune","s","s\"","s)","s)))","save","scala.collection.mutable.{map,","schacher","schloss","school","scratch","scratch:","search","second","section.","see","self","self,","self.count()","self.decode_dfs(&input[start..],","self.dfs(string::from(\"\"),","self.tree.decode(input)","seq","set","set\");","set;","shannon","share","sharealik","shl","shouldn't","show","shr","simpl","simpli","singl","sit","size","size_t","sizeof(codebook","sizeof(struct","skip","small","smaller","smallest","snippet","so:","some('0')","some('1')","some(c)","somewhat","sort","sort)","space","special","specif","src)","src);","src,","src_len","st","st)))","stack","start","static","std::back_inserter(ret));","std::back_inserter(ret),","std::begin;","std::cerr","std::cmp::{ord,","std::collections::{binaryheap,","std::copy(begin(code),","std::cout","std::end;","std::find_if(","std::find_if(begin(encoder),","std::find_if(begin(ret),","std::for_each(first,","std::invalid_argument(","std::invalid_argument(\"attempt","std::make_pair(it,","std::make_pair(last,","std::make_shared(","std::make_unique(l);","std::make_unique(std::move(lhs),","std::move(bits)));","std::move(encoder)});","std::move(ret.back());","std::move(rhs));","std::pair","std::shared_ptr","std::sort(begin(freq),","std::string","std::transform(","std::vector","std::vector(),","std::vector();","std::vector;","std::vector>();","std::vector>;","step","still","store","storm,","str","str(codebook))","str(tree))","str)","str:gmatch(\".\")","str[257];","straight","straightforward","strcat(*dst,","string","string\"","string(char)","string(code)","string(code,","string(codes.encode(begin(s),","string(cur.char)","string(current.key)","string(huffman_tree.key)","string(i)","string)","string):","string,","string:","string::from(\"\");","string;","string]","string]()","string]):","stringbuild","stringbuilder());","stringbuilder();","stringtoencode)","stringtoencode;","string},","strlen(*dst);","strlen(src);","struct","sub","submit","subtract","success","such","suddenli","sum","sure","swap","swap(&heap","swap(i,","swap(struct","switch","system","system.","system.collections.generic;","system.collections;","system.console.writeline($\"{entry.key}","system.console.writeline($\"{result.bitstring}","system.console.writeline(originalstring);","system.linq;","system.out.println(\"cod","system.out.println(\"decod","system.out.println(\"encod","system.out.println();","system.out.println(m.getkey()","system;","t","t)","t1","t1)","t2","t2)","t2,","tabl","table.remove(freq)","table.remove(freq),","table.sort(arr,","take","taken","talk","target","target),","target;","temp_nod","temp_node,","temp_node.weight)","temp_str","temp_string))","templat","temporarili","termin","test","tests\"","text","text.","text:","thank","that'","theorist","thing","this.bitstr","this.data","this.data.findindex(x","this.data.push(value);","this.data.shift();","this.dictionari","this.frequ","this.key","this.left","this.leftchild","this.lett","this.nod","this.nodes.binarysearch(newnode);","this.nodes.sort();","this.right","this.rightchild","this.stringtoencod","this.tre","this.weight","this:","through","throw","time","time.","tmp","tmp;","to_be_encod","togeth","together.","together.)","too!","top","top.","top;","tosortedlist","total","touch","track","trait","traverse(node.left,","traverse(node.right,","traverse(root,","traverse(treenod","treat","tree","tree\"","tree'","tree)","tree))","tree)))))","tree));","tree))]","tree);","tree*","tree*));","tree**","tree,","tree.","tree.dequeue()","tree.headopt","tree.make_codebook();","tree:","tree:',","tree;","tree?","tree[1]","tree_count,","tree_count]","tree_count],","tree_free(struct","tree_free(tre","tree_left","tree_left,","tree_left,weight_left","tree_left]","tree_left],","tree_right","tree_right)","tree_right,","tree_right,weight_right","tree_right]","tree_right],","tree_siz","tree_size,","tree_value,","tree_value]","tree_value],","treenod","treenode(int","treenode(left.frequ","treenode(m.getkey(),","treenode(str","trees.insert(index,","trees.pop()","trees.popleft()","trees:","trees[0]","tree}","tricky.","ts","two","two_pass_huffman(\"b\")","two_pass_huffman(\"bbbbbbbb\")","two_pass_huffman(\"bibb","two_pass_huffman(phrase::string)","type","uncom","under","underlying_","underlying_;","understand","union{leaf,","uniqu","unit","unititialized,","unreachable()","unreachable();","until","up","us","use:","usiz","usual","v","val","valu","value\"","value)","value,","value.weight);","value:","value;","values.","var","vec","vec)]","vector","video","void","v}","want","way","we'll","we'r","we'v","weight","weight(leaf(char,","weight(left)","weight(new_tree))","weight(node(left,","weight(right)","weight(tree())","weight)","weight,","weight:","weight::int64","weight;","weight])","weight_left","weight_right","weights[temp_string]","weird","well,","whether","while(length(nodes)","while(length(weights)","whole","with.","with_new_bit(bits,","with_new_bit(std::move(bits),","with_new_bit(std::vector","without","word","work","world","write","written","x","x)","x.(*node);","x.weight","xmm0","xmm0,","xmm1","xmm1,","xmmword","xor","xorp","y","zero","zero:p),","zip","{","{\"\"","{:messag","{entry.value}\");","{k,","{node1[1],","{result.bitstring.length}\");","{self.n})'","{str(self.right)})'","{}","{});","|","|>","|mut","||","}","})","}));","});","},","};"],"contents/computer_graphics/computer_graphics.html":["activ","algorithm","anyth","appear","appli","applic","approxim","archive,","area","argu","around","art","art.","be.","beautifulli","between","bit","boundari","broadli","canni","change,","classifi","climate,","closest","complet","comput","consid","convolutions,","cover","creat","current","desktop","detail","details,","detect","differ","direct","distinctli","edg","effort","end,","enough","example,","eye.","fastest","feel","field","find","fluid","focus","free","further","game","good","graphic","graphics.","hand","hardwar","high","hire","however,","imag","images.","immedi","impact","instead","instead,","interest","know","known","learn","look","machin","man","mani","media,","more","movi","multimedia","none","paint","part","pixar","plot","possibl","precisely.","progress","provid","publish","purpos","rang","realist","released.","render","repres","research","research,","research;","resolut","rigor","run","scienc","scientist","section","simpli","simul","simulation.","softwar","spend","stori","studio","sub","subject","support.","tell","think!","those","though","truth!","untrain","us","vague,","via","video","visual","wavey,","wide","without","work","world.","write","year"],"contents/quantum_information/quantum_information.html":["(#560),","(found","128","3","4.0","add","adequ","advantag","ago,","agree;","algorithm","algorithm?","algorithms,","algorithms:","already.","always,","amount","ask","attempt","attribut","basically,","be","being,","bit?","bitlogic:","boast","book","build","c.","chang","chapter","chapter:","circuit","circuits:","classic","closest","code","code.","common","commun","compil","compiler,","comput","computers.","creat","creativ","current","d","deserv","differ","discuss","distil","done","exampl","exist.","expect","experiment","fact,","fantast","far","field","final","first","follow","fundament","further","futur","gate","go","graphic","hard","head","help","home.","hope","however,","ill","imagin","implement","import","imposs","impress","industri","inform","information.","initi","instead,","intense.","interfac","intern","introduct","intuit","is...","isn't","it'","item","jame","knowledg","knowledge.","languag","language.","licens","license.","license.md).","list.","look","machine,","make","mani","market","mechanics.","mit","model","modifi","more","none","note,","now,","number","numer","obviou","on","out","outdo","own.","peopl","perform","phenomen","place","point","potenti","promis","pull","purpos","purpose.","pursu","quantum","qubit","qubits!","qubits,","readi","real","realiz","realized.","realli","relat","request","requir","research","schloss","section","seem","shake","sharealik","shor'","short,","simul","simulator,","spice","start","step","strong","subject","suit","summary,","survey","system","techniqu","tell","tend","text","textbook","theori","theory,","think","through","time","time,","time:","topic","tri","true","truli","under","understand","univers","up","updat","wave,","way","we'll","wild:","work","writing,","written"],"contents/stable_marriage_problem/stable_marriage_problem.html":["!!this.fiance;","!=","!==","!haskey(pairs,","\"","\"\"\"determin","\"\"\"find","\"\"\"pick","\"\"\"propos","\"\"\"return","\"\"\"set","\"#{@name.rjust(20)}:","\"#{prefix}","\"(\"","\")\";","\".join(p.nam","\":\");","\"b\",","\"c\",","\"d\"]","\"f\",","\"g\",","\"h\"]","\"lonely\"","\"man\",","\"round","\"stable\"","\"unstable\")","\"woman\",","#","#includ","#{i}\",","#{round}\"","#{self.lonely?","$","$fianc","$groupsiz","$i","$man","$man)","$man):","$man;","$match","$match)","$match):","$match;","$men","$men,","$men;","$name;","$prefer","$preference)","$preferences):","$preferences;","$thi","$unmarri","$woman","$woman)","$woman,","$women","$women):","$women);","${girl.preferences.map(p","${guy.fiance.name}`);","${guy.preferences.map(p","%","%s',","&&","&women[man","'","'%","'__main__':","'a';","(!))","(!empty($thi","(!girl.hasfiance)","(!preferredmates.isempty())","(!prefers_partner(woman","(!woman","(#560),","($i","($man","($men","($prefer","($thi","($unmarried);","($woman","($women","((man,","(0","(20","(\\(w,","(a,","(bachelors.nonempty)","(boyfriend,","(char","(const","(elemindex)","(follow.partn","(found","(girl.prefers(guy))","(husband,","(i","(interest.partn","(jspp)","(let","(lonelyfollows.count","(m,","(m,_))","(m.fromlist","(man,","(map","(map,","(mate","(mostdesir","(ord","(person","(propos","(size_t","(size_t)rand()","(tail","(this.mat","(var","(w,","(which","(woman)","(woman.prefers(this))","(women!theone)",")","*","*/","*array,","*group,","*man","*partner;","*prefers;","*sooner*","*woman","+","++=","+=",".","...","/*","//","//alway","0","0)","0,","0;","1","1));","1);","1.step","10;","1;","1]","1];","2","2)","20","26","4.0","5","5);","5;",":","::",":id,",":name",":partner","=","==","===","=>",">",">>=",">choosematch();",">getmatch());",">getname(),",">getpreferences()));",">id,",">index++;",">index]];",">issingle())",">match",">match;",">name;",">partner",">partner)",">partner;",">prefer",">preferences))",">preferences);",">preferences;",">prefers,",">prefers[man",">propose();",">receiveproposal($this);",">setmatch($preference);",">setmatch($this);",">setpreferences($preferences);",">suitor",">suitors))",">suitors[]",">unmatch();","?","?person","@choic","@id","@name","@partner","@partner.name}\"","@partner.nil?","@partner.partn","@partner.sett","@pref","@prefs.index(partner.id)","@prefs.siz","@prefs[@choices]","@properti","[\"a\",","[\"e\",","[&]","[(a,","[(b,","[...\"abcde\"].map(nam","[...\"fghij\"].map(nam","[...iterable];","[0,","[]","[];","[a]","[a])]","[array[i],","[array[j],","[b]))","[b])]","[m","[person(name)","\\mathcal{o}(n^2)","_","__init__(self,","__name__","__str__(self):","__tostring():","`and`","`first`","`not`","`number_of_partners`.","`person`","`preference_list`","`second`","a,","a.prefer","act","again","aim","algorithm","algorithm,","algorithm.","all((man.has_partn","allow","alreadi","alway","amara","anymore.","appear","args)","around","array","array.length","array.new(size){|i|","array;","array[i]","array[i];","array[i]];","array[j]","array[j];","array[j]]","array[string]):","array_shift($thi","arraylist<>();","arraylist<>(mates);","ascii_lowercas","ascii_lowercase[:num_pairs]]","ascii_uppercase,","ascii_uppercase[:num_pairs]]","associ","assum","attempt","attr_read","attr_writ","attribut","auto","b","b)","b)]","b,","b.prefer","bachelor","bachelor,","bachelors.dequeue.propose()","bachelors.enqueue(this)","bachelors.push(girl.fiance);","bachelors.shift();","bachelors[","bachelors[bachelors_s","bachelors_size]","back","back,","base(name)","becker","becom","belt.","bool","boolean","both","boyfriend","break","break;","c","c)","c++14,","c,","c.prefer","call","candid","candidate,","carri","case","case,","chanc","chang","change.","chapter","chapter:","charact","choic","choice,","choice.","choices,","choices:","choices[currenttopchoiceindex++];","choosematch():","choosemate()","claim","class","clear,","code","collections.shuffle(preferredmates);","column","come","common","compil","conceptu","consid","console.log(\"\\ngirls\");","console.log(\"\\npairings\");","console.log(\"guys\");","console.log(`${girl.name}:","console.log(`${guy.name}:","console.println(","console.write(choice.name);","console.writeline(\"galeshapleyalgorithm\");","console.writeline();","console.writeline(man.nam","console.writeline(woman.nam","const","constructor(name)","continu","control.monad.st","copi","copy(men)","copy(women)","correctly.","counted.","coupl","creat","create_group(struct","creativ","current","currenttopchoic","currenttopchoiceindex","data.list","data.map","decreas","def","definit","delete!(mentowomen,","describ","determin","determinist","dict(map(m","dict(map(w","dictionary,","dict{string,string}","dict{string,string}()","dict{string,vector{string}}","doesn't","don't","don't.","duplicates.","each","echo","effici","elegantli","elemindex","elif","elseif","end","end(ret),","engag","equal","evalst","even","everybodi","everyon","everyone'","exampl","example.","except","explan","extend","f'{self.name}:","fals","false;","favorit","feel","female,","fianc","fiance.recieveproposal(this);","fiance:","final","find","findfirst(m","findstablemarriages(list","findstablemarriages(women,","findstablematches(men:","finished;","first","first,","follow","followit","follows)","follows,","follows:","foreach","free","free_group(men,","free_group(struct","free_group(women,","function","futur","gale","galeshapley(men,","galeshapley(men::preferences,","galeshapleyalgorithm","galeshapleyalgorithm.c","galeshapleyalgorithm.rungaleshapleyalgorithm(women,","gave","gender","gener","generators.","genpreferences(mannames::vector{string},","genpreferences(mnames,","get","get;","getclass().getname()","getmatch():","getmate()","getname():","getnexttopchoice();","getpreferences():","getpreferredmates()","girl","girl.prefer","girls)","girls);","give","given","global_random_device;","global_rng(global_random_device());","global_rng);","go","graphic","great","group","group.","groups,","guarante","gustorn","guy","guy.engageto(girl);","guy.prefer","guy.preferences)","guys)","has_partner(self):","hasfiance()","have","head","header","help","henc","here","however,","husband,","i)","i,","id","id);","id;","ilist","imagin","implement","implode(',',","import","in_array($preference,","incred","index","index;","indexerror:","individu","initi","initialize(id,","instead","int","interest","interest'","interest.choices.indexof(thi","intern","isfree(candidate,","isfree(m,","isfree(person,","islonely()","issingle():","isstable(men::preferences,","it.","iter","j","jame","java.util.arraylist;","java.util.collections;","java.util.list;","julian","keys(men)","lead,","leadit","leads'","leads)","leads,","leads;","leads_end","leads_end,","leastcommongend","left","length(bachelors)","less","licens","license.","license.md).","list","list\"\"\"","list()","list())","list(),","list();","list(a,","list(b,","list(c,","list(follows);","list(men).shuffle(random);","list(women).shuffle(random);","list(x,","list(y,","list,","list[man]","list[woman]","listextens","listextensions.c","lone","lonely!'","lonely.","lonely?","lonelyfollow","lonelyfollow.proposetonext();","lonelyfollows)","longer","look","m","m.assoc","m.empti","m.getpreferredmates());","m.insert","m.propose(women)","m.receiveoptions(women);","main()","main():","main(args:","main(string[]","make","make_person_list(size_t","male,","man","man(\"a\"),","man(\"b\"),","man(\"c\"),","man(\"d\"),","man(\"e\")","man(name:","man(str","man):","man*):","man.choic","man.choices)","man.has_partner:","man.prefer","man.propose_to_next()","man;","mani","mannames))","map","mariu","marri","marriag","marriages\"\"\"","married,","match","mate","mate)","mate,","mate.","mate.m","mate;","mates)","math.floor(math.random()","mathjax.hub.queue([\"typeset\",mathjax.hub]);","mean","member","men","men)","men)):","men);","men,","men.foreach(m","men.select(&:lonely?)","men.to[queue]","men/women","men:","men:')","men[bachelor]","men[husband]","mentowomen","mentowomen)]","mentowomen,","mentowomen::pairs,","mentowomen[bachelor]","mit","mname","modifi","more","mostdesir","msvc","much","n.","name","name)","name):","name,","name;","namespac","need","new","newlonelyfollow","newlonelyfollows.add(follow);","newlonelyfollows;","next","next_choice(self):","nil","nobodi","none","none)","none:","not.\"\"\"","noth","now","now,","npair","null","null)","null;","num_pair","number","number_of_partn","number_of_partners)","number_of_partners),","number_of_partners,","numer","object","offer","old","on","one.","onpropose(partner)","oppos","option[man]","ord","order","output","output,","over","p","p.name).join()}`)","pair","paired,","pairs)","pairs.","partner","partner(self):","partner(self,","partner.nil?","partner.partn","partners.","partners[choice].onpropose(self)","pass","peopl","person","person'","person(name));","person(str","person)","person):","person,","person.","person._partner)","person.c","person.candidates.append(self)","person.generate(4,","person.new(","person:","person{false,","php_eol;","pick","pick_preferred(self):","planb)","poor","possibl","possible.","pref","pref))","pref):bachelors)","prefer","prefer,","preference;","preference_list;","preferences.indexof(man)","preferences:","preferred\"\"\"","preferredm","preferredmates)","preferredmates.remove(0);","preferredmates;","prefers(man:","prefers(men,","prefers(other)","prefers(prefs,","prefers(women,","prefix,","prefs)","prefs[person])","print","print('\\n')","print('prefer","print('th","print()","print(f'{man.name}","print(man)","print(woman)","printf('%","printf('%s\\'","println(isstable(men,","println(mentowomen)","privat","problem","problem.","problem:","process","program","program.","program.c","propos","proposal_index","proposals(number_of_partners);","propose()","propose():","propose(partners)","propose_to_next(self):","proposetonext()","protect","provid","public","pull","put","qualifi","queue[man]()","r","r)","rais","random","random();","random.new(42)","random_pref_list","random_pref_list()};","randomli","rang","rank","receiveoptions(list","receiveproposal(person","recieveproposal(man","reject","remainingprefer","remov","request","result","ret(number_of_partners);","ret;","return","rng)","run","rungaleshapleyalgorithm(list","runtime.","scala.collection.mutable._","schacher","schloss","score(@partner)","score(partner)","second","second)","second,","see","seed","seem","select","self","self._partn","self._partner._partn","self._partner:","self.candid","self.candidates.clear()","self.candidates:","self.generate(size,","self.has_partn","self.has_partner()","self.lonely?","self.nam","self.next_choic","self.partn","self.partner:","self.pref_index","self.prefer","self.preference)}'","self.preference:","self.preference[self.pref_index]","set","set;","setmatch(person","setmate(mostdesired);","setmate(person","setpreferences($preferences);","setpreferences(array","shapley","sharealik","shuffl","shuffle($preferences);","shuffle(girls);","shuffle(guys);","shuffle(iterable)","shuffle(man.preference)","shuffle(mannames)),","shuffle(size_t","shuffle(thi","shuffle(woman.preference)","shuffle(womannames)),","simple,","simpler,","simpli","singl","singles.each","singles.empty?","size","size)","size))","size).to_a.shuffle(random:","size_t","size_t(0));","solution:')","solv","some(otherman)","some(this)","someon","someone,","sort","spacer","stabl","stable.","stable_marriage($men,","stable_marriage(array","stable_marriage(men,","stable_match(leadit","stablemarriag","stablemarriage(guys,","stablemarriage.findstablematches(a,","stablemarriage.man(\"adam\")","stablemarriage.man(\"bart\")","stablemarriage.man(\"colm\")","stablemarriage.woman(\"xena\")","stablemarriage.woman(\"yeva\")","stablemarriage.woman(\"zara\")","stablemarriageexampl","stablemarriageproblem","stablematch","state","static","stay","std::generate_n(std::back_inserter(ret),","std::iota(begin(ret),","std::mt19937","std::optional,","std::random_devic","std::shuffle(begin(ret),","std::size_t;","std::vector","still","story.","string","string,","struct","subjective.","submit","suitor","suitor)","suitors.add(suitor);","suitors.contains(mostdesired))","super(name);","symmetrical,","system.collections.generic;","system.out.println(m","system.out.println(w","system;","templat","tent","text","tfollow","that'","them.","theon","this.mat","this.mate.m","this.nam","this.preferences.indexof(other)","this;","though","thread_loc","through","tlead","tmp","tmp;","to.","to_","told","tool","top","topchoice,","tostring()","tpref","translat","tri","tricki","true","true:","true;","try:","tself","tself)","two","under","unit","unless","unmatch():","until","up","updat","upon","us","val","var","video","void","w","w))","w.fiance.getorelse(stablemarriage.man(\"nobody\")).name))","w.getmate()));","w.getpreferredmates());","w.name","w.receiveoptions(men);","want,","we'll","we'r","well\"\"\"","whether","whichev","wife","wife)","within","without","wname","wnames)","woman","woman(\"f\"),","woman(\"g\"),","woman(\"h\"),","woman(\"i\"),","woman(\"j\"),","woman(name:","woman(str","woman.choic","woman.choices)","woman.fi","woman.pick_preferred()","woman.prefer","woman;","woman?.partner.name);","womannames))","womannames::vector{string})","women","women)","women):","women,","women.","women.size()","women/men.","women:","women:')","women::preferences)","women::preferences,","womentoman::pairs)","womentoman[candidate])","womentomen","womentomen)","womentomen[candidate]","womentomen[candidate])","won't","worri","written","x","x)","x,","x.prefer","y","y)","y,","y.prefer","z","z)","z).foreach(","z,","z.prefer","{","{\",","{man.partner.name}')","|m|","|round|","||","}","});","};"],"contents/flood_fill/flood_fill.html":["\"bucket","\"circl","\"exampl","\"fill","\"grid","\"queue","\"stack","\"x","#","#includ","%","&&","'__main__':","'pass","(!queue_empty(q))","(!stack_empty(stk))","((point(0,","(auto","(c.data[cur_loc.x","(canva","(found","(grid[x][y]","(inbounds(canvas.shape,","(inbounds(size,","(int","(loc[0]","(old_val","(old_valu","(p.x","(q","(q.size()","(s.size()",")","*","*));","*/)","*=","*data;","*neighbors)","*q)","*stk)","*tmp","+","+=",".=","/*","0","0)","0))","0),","0)]","0,","0.","0.0,","0.75.","0;","0},","0}};","1","1\"","1)","1),","1,","1,1","1.0","1.0)","1.0);","1.0.","1.bucket","1;","1},","1};","2","2\"","2),","2016.","2020.2.torbert,","2;","3","3\"","4","4\"","4.0","5\"","5))","5x5","6\"","8",":",":]","=","==",">",">=",">back",">back]",">capac",">capacity)",">capacity;",">data",">data);",">data,",">data[",">data[0]));",">data[0]);",">data[q",">data[stk",">front",">front)",">front,",">front];",">top++]",">top];","?","?,","@test","@testset","[","[1].","[2].","[]","[loc","[location]","[p]","]","__add__(self,","__name__","abil","about.","abov","above.","actual","ad","add","additionally,","adequ","after,","again","again.","algorithm","alreadi","alway","anim","anoth","answer","answer_grid","answer_grid[1:3,","appli","applic","appropriately.","archiv","archive.","are:","area,","around","array","art","ask","aspect","assert(test_grid","attribut","auto","avail","back,","base","basics:","be","becom","befor","before,","before.","before;","begin","below:","beneath","best","better","between","beyond","bibliographi","bit","border","both!","bound","boundari","breadth","browser","bucket","c)","c,","c.data[cur_loc.x","c.data[p.x","c.max_i","c.max_x","c.max_x)","call","calloc((q","canva","canvas[cur_loc]","canvas[current_loc]","canvas[current_location]","canvas[loc]","canvas[location]","canvas[neighbor]","canvas[neighbour]","canvas[p]","canvas[possible_neighbor]","canvas[x]","canvas_size[1]","canvas_size[2]","capacity;","cartesianindex","cartesianindex(","cartesianindex(0,","cartesianindex(1,","cartesianindex(1,1)","cartesianindex{","case","case,","cases.","caveats.","center","center,","certain","chang","chapter","chapter,","chapter:","chapters,","chapters.","check","choos","chunks.","circl","circle,","close","cnt","coconut.","code","code,","collect","color","colored.","come","common","common,","commonli","complet","complic","compos","comput","conclus","connect","consid","consist","const","const&","constraint","consum","consume(","content","continu","correct","cover","creat","creation","creativ","cur_loc","cur_loc,","cur_loc.y]","current","current_loc","current_loc,","current_location,","data","datastructur","decid","def","defin","depth","dequ","deque()","dequeue!(q)","dequeue(&q);","dequeue(struct","describ","determin","diagon","differ","differences:","difficult","dimension","direct","directions,","dirti","discuss","disguise.","dissimilar","distinct","do","do,","do?","domain","domain,","domains\"","domains:","doubli","down,","duplic","each","easi","easier","easiest","east","east,","effici","efficient.","element","element.","element;","elements,","else:","elseif","embed","enclos","end","end='')","enough","enqueu","enqueue!(q,","enqueue!(q,neighbor)","enqueue(&q,","enqueued,","enqueued:","ensur","essenti","evenli","everyone.","exampl","example,","exclud","exclus","exist","exist,","exit_success;","explain.","explan","extent","failure_count","failure_count))","failures')","fals","false;","fashion.","featur","feel","few","fewer","fill","fill\"","fill,","fill.","fill?","filter$(x","final","final_canvas).all()","final_canvas,","find","find_neighbors(","find_neighbors(c,","find_neighbors(canvas,","find_neighbors(grid,","find_neighbors(struct","find_neighbours(canvas,","first","first.","fix","flavor.","float","floats,","flood","focu","follow","food","four","free(q","free(q.data);","free(stk.data);","free_queue(struct","free_stack(struct","front","front,","function","function(canvas)","function):","further","game,","gener","get_queue(sizeof(struct","get_stack();","gimp,","girlfriend,","glance,","go","go.","graph","grid","grid,","grid;","grid[1:2,:]","grid[2,:]","grid[3,:]","grid[neighbor_x][neighbor_y]","grid[x][y]","grid{","hand","hardwar","help","here","here,","hop","however,","iceberg","icon","idea","imag","image,","images/graph","imagin","immedi","implement","import","inbounds(canvas.shape,","inbounds(canvas_shape,","inbounds(canvas_size,","inbounds(cartesianindex","inbounds(size(canvas),","inbounds(struct","includ","increases,","incred","indic","individu","initi","initial_canva","initial_canvas.copy()","insid","instead","int","intens","intern","intuit","issue,","it!","it'","itself,","jame","journey","keep","kinda","known","languag","larg","leav","left","left,","length(q)","length(s)","less","lest","let","let'","licens","license.","license.md).","line","list","loc","loc)","loc,","loc::cartesianindex,","loc[1]","loc[1]},","loc[1]}};","locat","location!","location):","location,","location.x","long","look","lot","main()","make","manag","mani","manual","map$(location.__add__))","map$(recursive_fill$(canvas,","mask","mathjax.hub.queue([\"typeset\",mathjax.hub]);","max_x,","max_y;","maximum","me,","mean","memcpy(tmp","memcpy(tmp,","memori","method","method,","method.","methods\"","methods,","methods.","min(location)","min(p)","minesweep","minimum(tuple(loc))","mit","months,","more","n","namedtupl","namedtuple(\"point\",","namedtuple('testresults',","namely,","necessary,","need","neg","neighbor","neighbor,","neighbor_i","neighbor_x","neighbors);","neighbors,","neighbors.","neighbors.append(possible_neighbor)","neighbors.push_back(possible_neighbor);","neighbors:","neighbors;","neighbors[4];","neighbour","new_val","new_val)","new_val):","new_val:","new_val;","new_valu","new_value)","new_value))","new_value):","new_value);","new_value;","next","next.","node","node!.","node,","node.","nodes.","nodes:","north","north,","northeast,","northwest","now","now,","np","np.zeros((5,","number","numpi","obviou","old","old_val","old_val)","old_val,","old_val:","old_valu","old_value)","old_value))","old_value):","old_value,","old_value:","on","oper","optim","optimally.","other.x,","other.y)","others.","otherwise,","out","outsid","own,","p):","p);","p,","p.i","p.x","p.y),","p.y+1),","p.y]","p.y}","p.y},","parts:","pass_count","pattern","pattern.","phd,","pixel","pixel.","play","point","point(","point(0,","point(1,","point(p.x","point(p.x+1,","point(p.x,","point(self.x","point(x,","point)","point,","points[4]","pop!(s)","possibl","possible_neighbor","possible_neighbor)","possible_neighbor):","possible_neighbor,","possible_neighbors)","possible_neighbors:","possible_neighbors{","possible_neighbour","potenti","predefin","prevalent.","previou","print('.',","print('f',","print()","print(testresults(pass_count,","probabl","problem","proce","process","program","progress","properti","property.","purpos","purposes.","push","push!(neighbors,","push!(s,","push!(s,neighbor)","put:","q","q)","q.empty():","q.front();","q.get()","q.pop();","q.push(loc);","q.push(neighbor);","q.put(neighbor)","q.put(p)","queri","queue","queue()","queue.","queue.append(location)","queue.append(neighbour)","queue.popleft()","queue:","queue_fill!(canvas,","queue_fill!(grid,","queue_fill$(?,","queue_fill(","queue_fill(canvas,","queue_fill(struct","queue_fill(test_grid,","queue_test_func","queue_test_func):","queue{cartesianindex}()","quick","rang","reach","readi","realloc(stk","reasons:","recurs","recursion.","recursive_fill!(canvas,","recursive_fill!(grid,","recursive_fill$(?,","recursive_fill(","recursive_fill(canvas,","recursive_fill(grid,","recursive_fill(struct","recursive_fill(test_grid,","recursive_test_func","recursive_test_func):","red.","regularli","reiniti","remaind","replac","restrict","ret","ret;","return","return;","review","rgb.","right","row","run","s","s.pop();","s.push(loc);","s.push(neighbor);","s.top();","same","savor","scale","scanlin","scheme","schloss","science,","sections.","see","seem","select","self.i","sens","separ","set","setup","sever","shane,","share","sharealik","show","shown","side","similarli","simpl","simpler","simplest","simpli","simulation.","singl","sit","situat","six","size","size);","size,","size[0]","size[1])","size_t","sizeof(q","sizeof(stk","slightli","slower","small","so,","so:","solut","solution_grid","solution_grid);","solution_grid,","solution_grid[:3,]","solution_grid{","someon","someth","somewhat","sort","south,","southeast,","southwest,","space","space,","split","spread","springer,","stack","stack,","stack.extend(find_neighbours(canvas,","stack.pop()","stack:","stack_fill!(canvas,","stack_fill!(grid,","stack_fill$(?,","stack_fill(","stack_fill(canvas,","stack_fill(struct","stack_fill(test_grid,","stack_pop(&stk);","stack_pop(struct","stack_push(&stk,","stack_test_func","stack_test_func):","stack{cartesianindex}()","stage,","start","start_loc","start_loc,","start_loc{1,","starting_loc","starting_location,","state","static_cast(current_loc[0]);","static_cast(current_loc[1]);","static_cast(grid.size())};","static_cast(grid[0].size()),","static_cast(loc[0]);","static_cast(loc[1]);","static_cast(neighbor[0]);","static_cast(neighbor[1]);","static_cast(possible_neighbor[0]);","static_cast(possible_neighbor[1]);","std::array;","std::queue{};","std::stack{};","std::vector","std::vector>","std::vector>&","step","still","stk","stk)","stop","straightforward","straightforward.","strategi","strategy,","strategy?","struct","structure,","sub","submit","subsect","subsequ","such,","superfluid","superimpos","support","sure","surprisingli","suspect","switch","tag.","take","termin","test","test()","test():","test_grid","test_grid(grid,","test_grid(initial_canvas,","testresult","text","them.","there.","this,","this:","those","though","thought","thought:","three","threshold.","through","throughout","time","time.","tip","tmp;","top","top,","track","travel","travers","traversal,","traversal:","tree","tri","trick","true","true;","two","type","ultim","unchang","under","understand","uniqu","unit","unless","unnecessari","up","up,","us","user","usual","valu","vari","variat","vector","version","vertic","vicinity,","video","visit","void","vortic","walk","want","wasn't","way","way,","way.","way:","west","west,","west.","wherev","whose","within","without","work","worri","worth","wrap","write","write,","written","x","x)","x,","y","y\")","y):","y;","yield","zeros(5,5)","{","{0,","{1,","{loc[0]","{loc[0],","{p.x","{p.x,","|>","||","}","};"],"contents/jarvis_march/jarvis_march.html":["!(*thi","!(a","!=","!counterclockwise(p,","\"","\",","\"]\");","\"__main__\":","\"angle\"","\"check","\"find","\"fmt\"","\"return","#","#includ","${p.y})`));","&&","&[point])","'__main__':","(","(!equal(end_point,","(#560),","((ab.getx()","(*","(0,","(15,","(17","(2,","(5,","(6,","(7,","(9,","(:constructor","(>","(\\(x,y)","(ab.gety()","(ab.magnitude()","(b.i","(b.x","(compar","(curr_point","(defstruct","(defun","(double,","(endpoint","(first","(found","(gift)","(hull[i]","(i","(i64,","(if","(jspp)","(lambda","(next","(null","(on)","(p.getx()","(p.i","(p.x","(p1","(p2.0","(p2.1","(p2.i","(p2.x","(p2[0]","(p2[1]","(p3.0","(p3.1","(p3.i","(p3.x","(p3[0]","(p3[1]","(point","(pointonhul","(pointonhull.equals(hull.get(0)))","(potentialnextpointonhul","(product","(reduc","(rest","(size_t","(sort,","(var","(x","(x,",")",");","*","*first_point_it);","*points,","+","+=","/","//","//add","//find","//found","//print","//test","0","0)","0);","0,","0.0","0.0)","0.0,","0;","1","1)","1));","1),","1)]","1,","1.0","1.0,","1.jarvis,","10,","10.0,","11","11));","11),","11.0","11},","12","12));","12),","12.0","12},","14","14));","14),","14,","14.0","14.0,","14},","15","15));","15),","15);","15,","15.0","15.0,","15},","1973","1973.","1;","1]","1],","1},","2","2)","2));","2),","2,","2.0","2.0,","23","2},","4),","4.0","5","5));","5),","5,","5.0","5.0,","5},","6,","6.0,","7","7));","7),","7,","7.0","7.0,","7},","8","8)","8));","8),","8.0","8},","9","9));","9),","9,","9.0","9.0,","9},",":","::",":=",";;;;","=","==","=>",">",">=","[","[1].","[]","[](const","[];","[]point","[]point)","[]point{{","[hull_point]","[point]","[point_on_hull]","[pos(2,1.5),","\\","\\mathcal{o}(nh),","]","];","_,","__name__","__str__(self):","`on`","a,","a.","a.equals(b);","a.getx(),","a.gety());","a.x","a.x)","a.y)","a.y);","a;","a==b","a@(xa,","ab","advanc","again","algorithm","algorithm,","algorithm.","angl","angle(endpoint,","angle(point","append(hullpoints,","approxim","are:\")","are:\\n\");","args)","arr)","array","arraylist","arraylist();","attribut","auto","b)","b);","b){","b,","b.","b.getx(),","b.gety()","b.gety());","b.x","b.y;","b;","b@(xb,","base","bc","bc.getx())","bc.gety()))","bc.magnitude()));","behind","between","bibliographi","bool","boolean","break","break;","c)","c.gety()","c==b","c@(xc,","calcul","call","candid","ccw(gift[j],","ccw(p1,","chan'","chapter","chapter:","check","choos","chosen","class","clockwise?","code","common","complet","completed.","console.log(`(${p.x},","const","convex","convexhul","convexhull.foreach(p","convexhull;","convexhull[0]);","counter","counter_clockwise(p,","counter_clockwise(p1","covered.","creat","creativ","cross","curr_point","curr_point)","curr_product","curr_product)","current","current)","current))","current;","data","data.funct","data.list","def","defin","develop","dimension","dimensions.","discuss","distribut","doesn't","dot","doubl","double)","draw","due","effici","else:","elsevier,","end","end_point","end_point;","endpoint","endpoint)","endpoint)):","endpoint):","endpoint.equal(hullpoint)","endpoint.equal(hullpoints[0])","endpoint:","endpoint;","equal","equals(object","equals(point","exampl","exist,","expect,","f'({self.x},","false;","field","filter","find","finit","first","first_point_it","float64","fmt.printf(\"x=%f","fmt.println(\"th","fn","follow","foreach","forward,","forward.","func","function","gener","gethashcode()","getx()","gety()","gift","gift\"","gift)","gift))","gift)))))","gift.add(new","gift.len()","gift:","gift[0]","gift[j]","giftwrap","giftwrap)","graham","graphic","great","greater","guarante","gustorn","h","help","here,","here.","higher","hull","hull)","hull.","hull.add(pointonhull);","hull.append(point_on_hull)","hull:","hull;","hull[","hull[0]","hull[1])","hull[1],","hull[i","hull[i],","hull_point","hull_points,","hull_points;","hull_points[0]));","hull_points[15];","hullpoint","hullpoint)","hullpoints[len(hullpoints)","i++;","i64);","i;","idea","identif","if(points.empty())","implement","import","includ","incred","initi","int","interior","intern","intial","isleftof(pointonhull,","isleftof(vector","item","item.x)","j","jame","jarvi","jarvis_cross(hull[i","jarvis_cross(point1::pos,","jarvis_cross(pos(0,0),","jarvis_march(const","jarvis_march(gift):","jarvis_march(gift:","jarvis_march(point","jarvis_march(points)","jarvis_march(points);","jarvis_march(points,","jarvis_march(points::vector{pos})","jarvis_march(test_gift)","jarvismarch","jarvismarch();","jarvismarch(arraylist","jarvismarch(gift);","jarvismarch(point","jarvismarch(points)","jarvismarch(points);","jarvismarch.c","jarvismarch.run(points);","java.util.*;","julian","keep","known","largest","lefmost","left","left_most_point(point","left_most_point(points)","left_most_point(struct","leftmost","leftmost.x","leftmostpoint(point","leftmostpoint(points)","len(gift)","licens","license.","license.md).","line","list","list()","list();","list,","lowest.","magnitude()","main","main()","main():","main(string[]","make","make([]point,","mani","map$(t","march","math.acos(","math.pow(y,","math.sqrt(math.pow(x,","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matter.","maximumbi","maximumby)","min(gift)","minimum","mit","modifi","more","move","mut","n","n):","namespac","new","next","none","note,","num_hull_point","num_points)","number","obj","obj)","operator!=(const","operator!=(vector","operator==(const","operator==(vector","option>","origin","otherwis","overrid","p","p)","p.getx()","p.gety()","p.x,","p.y)","p0","p0@(x,","p1","p1))","p1)))","p1)))))","p1.0)","p1.1)","p1.x)","p1.y)","p1.y)*(p3.x","p1.y);","p1[0])","p1[1])","p2","p2\"","p2)","p2,","p2:","p3","p3)","p3):","p3:","p:","p;","packag","plane,","pm","po","point","point&","point(","point(*t))","point(0,","point(15,","point(2,","point(5,","point(6,","point(7,","point(9,","point(b.getx()","point(c.getx()","point(doubl","point(double.max_value,","point(x=0,","point)","point,","point.","point1.x,","point1.y)","point2.i","point2.x,","point2.y)","point2::pos,","point3.i","point3::pos)","point[])","point[]:","point_on_hul","pointonhul","pointonhull,","points)","points,","points.","points.aggregate((leftmost,","points.end(),","points.reduce((leftmost,","points[0]","points[0];","points[1:]","points[1])","points[2]","points[]","points[j];","pos(1,","pos(2,","pos(3,","pos(point2.x","pos(point3.x","posit","potentialnextpointonhul","potentialnextpointonhull,","potentialnextpointonhull.","potentialnextpointonhull;","print","print(\"[#]","print(\"th","print(point)","printf(\"th","println(hull)","privat","process","product","product,","program","program.c","properti","pt","public","pull","push!(hull,","r.","random","rang","range(1,","ray","readonli","realli","ref))","repeat","repres","request","ret","ret_cross","ret_cross*ret_cross","return","roughli","run(list","runtim","scan","schacher","schloss","set","setup","sharealik","simple.","simul","simulation.","size","size_t","sort","sort!(points,","start","static","std::cout","std::min_element(points.begin(),","std::vector","std::vector&","struct","submit","system.collections.generic;","system.console.writeline(\"jarvismarch\");","system.console.writeline($\"{point.x},","system.linq;","system.out.println(\"[\"","system.out.println(\"gift:\");","system.out.println(\"wrapping:\");","system;","test_gift","text","there,","theta","this.i","this.x","this.x)","this.y;","though","time.","true,","true:","true;","turn","turn_counter_clockwise(p1:","two","type","under","until","us","v","v.x","v.y;","var","vec1","vec1.x*vec2.i","vec1.y*vec2.x","vec2","vector","vector(","vector(0,","vector(15,","vector(2,","vector(5,","vector(6,","vector(7,","vector(9,","vector(int","vector{pos}()","void","whichev","while(*next_point_it","wrap","wrap.","written","x","x,","x,y;","x:","x::float64","x;","x^2+y^2","xvalue,","xvalue;","y","y)","y)))","y)=","y:","y::float64","y;","y=%f\\n\",","y=0):","ya)","yb)","yc)","yvalue)","yvalue;","{","{0,","{15,","{2,","{5,","{6,","{7,","{9,","{point.y}\");","{self.y})'","|","|>","||","}","});","},","};"],"contents/graham_scan/graham_scan.html":["!=","\"\"\"comput","\"\"\"find","\"\"\"i","\"\\n\".join(map(str,","\"calcul","\"determin","\"fmt\"","\"left\"","\"math\"","\"right\"","\"sort\"","\"the","#","#[derive(debug,","#includ","$","${p.y})`));","%","&&","&hull[hull.len()","&point)","&point,","&self)","&start);","'__main__':","(","(!(o","(#560),","((>","((and","((b.x","((wrap","(*","(+","(/","(/=p0)","(0,","(15,","(2,","(5,","(6,","(7,","(9,","(:constructor","(=","(\\(px,","(a.i","(atan","(auto","(b.i","(b.x","(c.i","(c.x","(ccw(points[m","(compar","(cond","(defstruct","(defun","(double,","(eql","(found","(i","(if","(int","(label","(length","(let","(m","(o","(on)","(p.x,","(p1","(p1:p2:ps)","(p2.i","(p2.x","(p2:ps)","(p2[0]","(p2[1]","(p3.i","(p3.x","(p3[0]","(p3[1]","(p[1],","(pa","(pi","(point","(point)o;","(point.i","(px","(rest","(s:p1:p2:ps)","(s:ss)","(size","(size_t","(sort","(sorton,","(struct","(the","(x","(xa,","(xb","(xb,","(xc","(xc,","(y","(yb","(yc",")","*","*a,","*b)","*points,","*points.iter().min().unwrap();","+","+=",".collect(collectors.tolist());",".distinct()",".sorted(comparator.comparingdouble(point","//","0","0)","0)'.","0))","0,","0;","1","1)","1));","1),","1);","1,","1.0f,","1.0f\\n\",","1.graham,","10,","10,11),","11","11));","11),","11},","12","12));","12),","12},","14","14));","14),","14,","14},","15","15));","15),","15,","15;","15},","1972.","1:length(other_points)","1:n","1;","1]","1],","1];","1},","2","2)","2))","2));","2),","2,","2;","2],","2},","4.0","5","5));","5),","5,","5,2),","5},","6,","6,15),","7","7));","7),","7,","7},","8","8));","8),","8},","8}};","9","9));","9),","9,","9},",":","::",";",";;",";;;;","=","==","===","=>",">",">=",">y",">y)","@overrid","[","[(x,y)","[...points].sort((a,","[1].","[]","[]point","[]point)","[hull[i],","[hull[m],","[p0]","[p]","[point]","[s,","[start,","\\mathcal{o}(n\\log(n)),","\\mathcal{o}(nh)","]","];","__name__","__str__(self):","`on`","a).partial_cmp(&polar_angle(&start,","a,","a.x","a.x)","a.x))","a.x)*(c.i","a.x);","a.y)","a.y)*(c.x","a.y);","a;","abc","accord","algorithm","alway","angl","angle(self,","angle.","any.","append()","are:\"","are:\")","are:\");","aren't","args)","around","array","array.","arraylist","arraylist<>();","atan(item.i","atan2","atan2(p.i","atan2(point[1]","atan2(y1","attribut","b","b)","b)).unwrap());","b,","b.x);","b.y));","b.y,","b:","b::point,","b;","back","base","basic","be","between","bibliographi","bool","boolean","bottom","bottom.","break","break;","build","b|","c)","c:","c::point)","calcul","case","ccw","ccw(a,","ccw(a::point,","ccw(const","ccw(point","ccw(struct","chapter","chapter:","circl","class","clockwis","clockwise,","clockwise?","clockwise?\"\"\"","clone)]","cmp(&self,","cmp_points(const","cmp_points);","code","colinear","collinear","collinear.","come","common","complex","concav","concern","console.log(\"th","console.log(`(${p.x},","const","continue;","convex","convex,","convexhul","convexhull.foreach(p","coordin","copy,","counter","counter_clockwise(&hull[hull.len()","counter_clockwise(a:","counter_clockwise(hull[","counter_clockwise(p1,","counterclockwise\"","counterclockwise(p1,","cover","creativ","cross","data","data.funct","data.list","def","defin","del","depend","determin","develop","distribut","doubl","double)","duplic","each","effici","element","element.","elseif","elsevier,","empti","empty,","end","end,","eq","equals(object","euclidean","exampl","expens","f'({self.x},","f64","f64,","false;","field","filter","find","finit","first","first,","float64","float64(point.x","fn","follow","form","found,","func","func(a,","function","gift","gift)","gift.","gift.get(0);","gift.remove(start)","gift.size());","gift.stream()","gift.sublist(1,","given","go","graham","graham_scan!(points)","graham_scan!(points::vector{point})","graham_scan(gift):","graham_scan(mut","graham_scan(points);","graham_scan(std::vector&","graham_scan(struct","graham_scan(test_gift)","grahamscan","grahamscan(list","grahamscan(point","grahamscan(points)","grahamscan(points);","graphic","h","hull","hull)","hull))","hull,","hull.","hull.add(0,","hull.append(point)","hull.append(pt)","hull.get(i);","hull.get(m));","hull.length;","hull.set(i,","hull.set(m,","hull.size();","hull.slice(0,","hull.sort(comparator.comparingdouble(point","hull.sublist(0,","hull.unshift(pivot);","hull:","hull[","hull[i]];","hull[m]]","i)","i);","i++;","i,","impl","implement","import","initi","instanceof","int","int)","integ","interior","intern","inward,","item","item.x","item.y)","itself","j","j)","jame","jarvi","java.util.arraylist;","java.util.comparator;","java.util.list;","java.util.stream.collectors;","key=(p","key=(point","key=lambda","know","l,","l.","leftmost","length","length(points)","licens","license.","license.md).","lisp","list","list(set(gift))","look","low_index","lowest","m","m++;","m;","main","main()","main():","main(string[]","make","map$(p","march","march,","match","math","math.atan2(a.i","math.atan2(float64(point.i","math.atan2(p.i","mathjax.hub.queue([\"typeset\",mathjax.hub]);","mean","memcpy(points,","memcpy(tmp_point","memori","min(gift,","minimumbi","minimumby)","mit","modifi","more","moreover,","mut","n","n)","nan,","negative,","never","new","none","null)","num_initial_point","number","o)","obvious","on","operation,","operations,","operator&","optimal,","option","ord","order","origin,","origin.x);","origin.y,","os","other):","other.i","other:","other_point","other_points[i]","otherwis","out","out.","output","p","p)","p.i","p.x","p.x,","p.y)))","p.y));","p0@(x,","p1","p1))","p1)))","p1)))))","p1.x)","p1.y)","p1.y)*(p2.x","p1.y)*(p3.x","p1[0])","p1[1])","p2","p2)","p2,","p3","p3)","p3):","p:","p[0]))","p]","pa","packag","partial_cmp(&self,","partialeq,","partialord","pb","pi","pi))","pivot","pivot)","pivot)));","pivot));","pivot);","pivot_angle)","place","planar","plane","point","point\"\"\"","point&","point(","point(*p))","point(0,","point(0,14),","point(15,","point(2,","point(2,8)","point(5,","point(5,7),","point(6,","point(7,","point(9,","point(9,9),","point(doubl","point(x1,","point(x=0,","point)","point))","point));","point),","point):","point*","point*)","point,","point.","point.y))","point:","point[0]","points\"\"\"","points)","points,","points.","points.add(new","points.begin()","points.is_empty()","points.retain(|a|","points.size())","points.slice(1).sort((a,","points.sort_unstable_by(|a,","points:","points[0],","points[0];","points[1:m]","points[1].x))","points[1].y,","points[1]];","points[2..points.len()].iter()","points[]","points[a].i","points[i+1]","points[i]","points[i])","points[i],","points[i];","points[j]","points[j];","points[m]","points[m]);","points[m],","polar","polar_angle(&start,","polar_angle(ref,","polar_angle(reference:","polar_angle(start,","polar_angle(struct","polar_angles_sort(point","polar_angles_sort(points,","polar_angles_sort(struct","polarangle(a,","polarangle(b,","polarangle(point","polarangle(point,","polarangle(ref,","positive,","print","print(\"th","print(point)","printf(\"points:\\n\");","println(hull)","product,","ps","pt","pt)","pt):","public","pull","py)","qsort(points,","r.","radians\"","radiu","random","ref.x))","ref.y),","ref[0])","ref[1],","refer","reference.x)","reference.y).atan2(point.x","rel","remain","remov","request","result","return","ronald","rotat","rotations,","rotations.","s","s[0],","s[1]]","s[2:]:","safe","same","save","scan","schloss","search","select","self.i","self.partial_cmp(other).unwrap()","self.x)","self.x.partial_cmp(&other.x)","self.y,","self.y.partial_cmp(&other.y)","sensitive;","set","set,","shape","sharealik","simpl","size","size)","size);","size,","size_t","sizeof(struct","snd)","so:","someth","sort","sort!(points,","sort(points[2:end],","sort.slice(points,","sorted(gift,","sortedpt","sorting,","sorton","ss","start","start.angle(point)))","static","std::cmp::ordering;","std::cout","std::ostream&","std::swap(points[i],","std::vector","std::vector(points.begin(),","struct","swap","system.out.printf(\"%","temp","temp);","test","test_gift","text","this)","this.i","this.x","this.y;","this:","three","through","throw","time","tmp","tmp;","tmp_point","tmp_points[0]","tmp_points[i]","tmp_points[i];","tmp_points[m]","tmp_points[m];","tmp_points[siz","tmp_points[size];","trigonometr","true;","turn","turn.","two","type","ultim","under","unlik","unwrap","updat","us","vec","vec![start,","vec)","vec::new();","vector","void","want","whether","within","wrap","wrap.","written","x","x)","x))","x,","x1","x:","x::float64","x;","xa)","y","y)","y)))","y)=","y1)","y:","y::float64","y;","y=0):","ya)","yb)","yc)","{","{0,","{15,","{2,","{5,","{6,","{7,","{9,","{self.y})'","{{","{}","|","|>","}","},","};"],"contents/data_compression/data_compression.html":["\"fact.\"","\"it'","\"what'","&=","(#560),","(a,","(assum","(found","(it","+",",",".1",".2",".3",".4","0","0.","0.1\\time","0.2","0.3","0.4","00","000","001","01","0100101010110100","0111101,","1","1,","1.9","10","11","2","3","4","4.0","=","\\\\","\\begin{align}","\\end{align}","\\sum_{i=0}^{n}w_i\\tim","\\text{length}(c_i)","\\time","a,","a.","abbbbab","abbbbab.","abbcccdddd","abbcccdddd.","above,","absolutes.","acknowledg","actual","add","algorithm","all.","alphabet","alphabets:","altogether,","alway","ambigu","anoth","answer","appear","ask","ask,","assum","assumpt","attribut","b","b!","b,","b.","bacccdba.","back","bag","basement","basic","basically,","be","befor","before.","better","between","binari","bit","bit,","bitlogic,","bits,","bitstr","bitstring,","bitstring?","bright","bright,","c","c,","c?","c_i","case,","case.","case:","cases,","categori","cbbbc!","certain","certainti","certainty.","chapter","chapter:","charact","character,","characters,","characters:","child","clear","clearli","code","codeword","codewords.","coding.","colloqui","combin","common","complet","compress","compression!","compression.","comput","conclud","conclusion,","consid","construct","contact.","contain","context","correspond","course,","cover","creat","creativ","d","d),","data","data;","day","day,","debat","decod","decode,","decoding.","deepli","defin","definit","definition,","degre","depth","describ","determin","development.","devic","differ","direct","discuss","distinct","distinguish","don't","door","easili","either.","encod","even","exampl","example,","exist","face","fact,","fall","fano,","far","field","field,","final","find","first","first,","first.","follow","food","free","free.","furious","further","future.","genet","get","given","go","gone","good,","graphic","great,","hand","happens).","hardwar","haven't","hear","heart","here,","honest,","hot","however,","huffman","huffman,","human","i'll","imagin","import","incred","individu","inform","information,","information.","information:","initi","intens","interact","intern","interpret","is.","it'","it,","itself","jame","kid","l","l(c(w))","l_1","l_2","learn","learning,","leav","length","less","let'","letter","letters:","level","licens","license.","license.md).","limit","logic","long","look","lossless","lot","machin","market","match","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matter","mean","measur","memori","mention","method","minim","mit","mix,","modifi","month","month,","more","mother","mother'","move","much","naiv","need","need.","new","none","notabl","now","now,","number","obviou","odd","on","on.","out","out.","outsid","overal","overcompl","overjoy","perfect","perfectli","piec","piece.","place","plenti","point,","possibl","power","prefix","pretend","probabl","programm","prospect","provid","pull","purposes,","put","quantiti","quantity:","question","question.","question:","random,","ratios.","reach","read","realiz","reason","reasons,","relat","relax!\"","repres","represent","request","requir","requires.","restrict","revolutionari","room,","said,","say,","schloss","search","second","see,","seem","set","set.","shannon,","sharealik","shorter","show","silly,","simpl","singl","slip","something,","soon!","specif","start","statements:","storage.","stori","string","summer","summer,","summer.","sunni","systems.","take","talk","techniques,","test","text","theori","thing","things,","think","third","this,","this:","those","through","thu","today","today?\"","topic,","tri","true","two","ultimately,","unawar","uncertain","under","undoubtedli","unfortunately,","uniqu","unit","unitless","until","us","usual","vague,","valid","value),","w","w_i","want","warm","warm.","wavey","way","way,","we'll","we'v","well,","without","word","word.","work","works,","written","year!"],"contents/cryptography/cryptography.html":["\"caesar","\"public","\"rijndael\"","\"rot13\"","(cipher),","(cryptosystem),","(depend","(found","(hopefully)","(i.e.","(in","(or","(probabl","(receiver).","(sender)","0","1.wikipedia:","128/192","13,","14","18","1977","2","2022.","2022.10.wikipedia:","2022.11.wikipedia:","2022.2.wikipedia:","2022.3.wikipedia:","2022.4.wikipedia:","2022.5.crypto","2022.6.wikipedia:","2022.7.wikipedia:","2022.8.wikipedia:","2022.9.wikipedia:","21","24","256","4.0","[10].","[11].","[1].","[2].","[3].","[4]","[5].","[6].","[7].","[8].","[9].","\\pi","\\pi=(3,1,2,4))","accept","accord","achiev","actual","addresses.","advanc","ae","aes.","again","again.","algorithm","algorithms,","alic","alice'","alice,","alphabet","alreadi","alter","alway","amount","analyz","ancient","anoth","another.","anymore.","anyon","anyway.","applications,","are:","art","ask","assum","asymmetr","asymmetric.","attack","attribut","b","back","banking.","base","becom","befor","behind","better.","between","beyond","bibliographi","big","bit","blowfish","blowfish:","bob","bob'","both","break","bunch","c","caesar","caeser","calcul","call","case","case,","caus","ceasar","certainli","chapter","charact","charli","chart","choos","chosen","cipher","cipher\"","cipher,","cipher:","close","code","combin","come","common","communicating.","communication,","complic","comprehension,","comput","computing.","consist","contend","context.","corner:","cornerston","correspond","couldn't","crack","creat","creativ","cryptograph","cryptographi","cryptography\"","cryptography,","cryptography.","cryptography:","current","curv","cypher.","d","damage.","data","de","dead","decod","decrypt","decrypt,","decrypting.","deem","defin","describ","determin","develop","developed.","differ","different?","digit","discuss","distance.","doesn't","doors,","e","earli","easiest","eavesdropp","eavesdropper.","ecc","effect","elabor","elementari","ellipt","encod","encrypt","encryption:","enough","entir","equal","especi","ev","even","everyth","evil","evil.","exampl","example,","extens","f","face","fact,","factor","faster","feasibl","few","field","figur","find","fine","first","follow","forg","formerli","forth","friend","future.","g","gener","general,","given","gobbledygook","good","gotten","greec","grown","h","hand.","happen","hash","have.","heart","henc","here","here,","hit","honestly,","however,","human","idea","impact","import","imposs","includ","inform","insecur","instead","instead,","interest","intern","it'","it.","j","juliu","k","keep","kept","kerckhoffs'","key","key,","key.","keys.","kid","kill","know","l","larg","layer","length","let'","letter","level","librari","licens","license.","license.md).","lie","liikt","limits.","literature,","long)","lost","m","mailman","make","manag","mani","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matter","mean","meanwhile,","messag","message,","message.","messeng","messenger'","messenger).","messenger;","method","mind:","mit","modern","n","name","near","necessari","need","negoti","never","newer","night","non","now","number","o","obsolet","obvious:","obviously,","on","onlin","oper","out","p","parti","parties.","path","peopl","permut","pk","point","posit","possible,","post","pre","prime","principl","principle,","privat","private,","problem","procedur","product","profession","progress,","progress.","properli","provid","public","purpos","q","quantum","question","r","read","reason","reason,","receiv","receiver,","receiver.","reli","remain","rememb","reorder","replac","replaced,","rijndael","robust","robust.","rome.","rot13,","rot13:","rotat","rsa","rsa:","ruse),","s","same","scheme","scheme,","school","school,","scrambl","secret","secret.","secretli","section","sections.","security.","see","seem","send","sender","sender,","sent","separ","seriou","set","share","sharealik","short)","side","signific","signing,","simple:","simpli","simplicity,","slip","smaller","sometim","spaces,","special","spy?","standard","standard,","standard:","state","stay.","stolen?","string","such","summar","supersed","supposedli","sure","symmetr","system","t","tabl","tactic","talk","technolog","technology,","tent","test","text","themselv","themselves.","there,","thing","third","time.","train","tri","trust","two","type","u","under","undergo","understand.","unscrambl","unsurprisingly,","up","us","usual","utter","v","veri","versa.","vetting.","vice","w","war","way","way,","whenev","whole","wide","wifi","won't","work","write","written","x","xor","y","z"],"contents/taylor_series_expansion/taylor_series_expansion.html":["\"taylor","&=","(#560),","(found","+","0,","1.","4.0","=","\\\\","\\begin{align}","\\end{align}","\\frac{1}{2}\\frac{d^2f(a)}{dx^2}(x","\\frac{1}{2}at^2","\\frac{d^2x(t)}{dt^2}","\\frac{df(a)}{dx}(x","\\frac{dx(t)}{dt}","\\frac{f^{(n)}(a)}{n!}(x","\\rightarrow","\\simeq","\\sum_{n=0}^{\\infty}","\\text{acceleration}","\\text{velocity}","a)","a)^2","a)^n","acceler","actual","algorithm","allow","along","approxim","approximation\"","assum","attribut","becomes!","better","between","blur","book.","boundari","bunch","chapter","chapter:","classic","close","code","common","complex","complic","consid","constant,","creat","creativ","definition:","denot","deriv","derivatives:","differ","easili","equation!","evalu","exampl","example,","expand","expans","expansion,","expansion.","f(a)","f(x)","f(x).","f^{(n)}(x)","few","figur","first","first,","follow","formal","formula","found","foundat","from,","function","function.","graphic","hand,","here","here,","higher","imag","images/graph","imagine!","include,","incomplete!","initi","intern","jame","kinemat","let'","licens","license.","license.md).","look","mani","mathemat","mathematical.","mathjax.hub.queue([\"typeset\",mathjax.hub]);","mean,","mind,","mit","modifi","more","n^{\\text{th}}","none","note","note:","obviou","on","order","perspective,","physic","physicist.","physics,","physics.","physics?","place","point","point,","power","pull","pure","quantiti","real","request","schloss","see","seem","seri","set","sever","sharealik","show","smooth","space,","strung","substitut","sum","tackl","take","taylor","technic","term","terms.","text","those","throughout","together!","told,","topic","topics.","train","true","truth","turn","under","unusu","us","v(t)","v_0t","well,","where'","why,","written","x(t)","x(t),","x_0"],"contents/convolutions/convolutions.html":["(#560),","(*)","(addition,","(get","1d","4.0","\\circ","addit","addition,","after,","algorithm.","always,","anim","anoth","answer","anyth","applic","attribut","back","basic","beyond","blend","bluntly,","brief","c,","call","chapter","chapter:","clarification.)","clear","combin","come","common","composit","comput","confusing.","convolut","convoluted!","convolutions.","convolutions?","correl","cover","creativ","definit","describ","describe,","detail","difficult","dimens","dimension","dimensions,","discuss","division),","even","example,","extend","f","f*g=c","f.","few","filters:","follow","fourier","function","function,","functions,","functions?","future.","g","g(x)","g,","g.","gaussian","go","good","graphic","great","hard","here","however,","imag","import","incred","initi","integ","interest","intern","intuit","it?","jame","joke","kernel","know","known","left","licens","license.","man","mathemat","mathjax.hub.queue([\"typeset\",mathjax.hub]);","modifi","move","multipl","multiplication,","n","near","need","needed,","needed.","none","notat","note:","now","number","numbers.","on","onc","oper","operation,","operator,","operator.","plug","possibl","power","practice,","provid","pull","put","question,","question:","reader","relat","request","schloss","section","section,","section.","see","sharealik","show","side","similar","simpl","sobel","special","standard","star","start","start.","stereotyp","subtraction,","take","talk","text","them.","theorem","third","three","told","topic","touch","transforms.","two","unclear,","under","understand","unless","up.","us","vagu","variabl","version","way","way;","wise","work","written"],"contents/convolutions/1d/1d.html":["\"applic","\"blend\"","\"blurred.\"","\"cyclic\"","\"doubl","\"full","\"gaussian","\"period","\"ramp","\"sawtooth","\"shift","\"simpl","\"squar","\"triangl","#","%","(#560),","((x","([0.5,","(a","(f*g)(x)","(f*g)[n]","(filter[i","(found","(length(filter)/2)","(sum)","(var","+","//","0","0.","0.0;","0.5]),","0;","0s","1","1)","1):","1);","1,","1.","100%","1d","1})","1},","1}}{2}","3","4.0","=","=>","\\frac{a_{n","\\frac{a_{n+1}}{2},","\\infty}^{\\infty}f(\\xi)g(x","\\infty}^{\\infty}f(x","\\infty}^{\\infty}f[m]g[n","\\infty}^{\\infty}f[n","\\int_{","\\sum_{m","\\xi","\\xi)d\\xi","\\xi)g(\\xi)d\\xi","a_{n}","abov","acceler","accelerating,","act","action","actual","ad","addition,","again","algorithm","all!","allow","along","alreadi","alway","amount","anim","animation,","animation.","animation:","animations,","animations.","anoth","appear","appli","applic","area","around","array","array,","arrays.","associ","assum","attent","attribut","base","be.","befor","before,","before.","before:","behavior","below:","best","better","between","beyond","bit","black","blend","blue","blur","blurrier","both","bound","boundari","boundaries.","boundaries:","boundary.","bring","browser","busi","c","c,","c_n","calcul","call","care","case","case,","case.","caveat","center","center,","center.","certain","certainly,","chang","chapter","chapter,","chapter.","chapter:","check,","chosen","clarity:","class","clearli","close","code","code,","common","compar","complic","comput","concept","condit","condition\"","conditions,","conditions.","constantli","continu","continuing:","contrast","convolut","convolution!","convolution\"","convolution,","convolution.","convolution1d","convolutions,","convolv","convolve_cyclic(signal,","convolve_cyclic(signal::array{t,","convolve_linear(signal,","convolve_linear(signal::array{t,","convolve_linear(x,","convolvecyclic(double[]","convolvelinear(double[]","convolvelinear(x,","copi","correct,","correlation,","count","course,","creat","createsawtooth(int","creativ","cyclic","dash","data","deal","debat","def","definit","delimitedfil","depend","descript","detail","determin","differ","dimension","directions.","directli","disappears.","discret","discuss","distinct","distinct.","distribut","domain","domain,","domain.","domain;","don't","done","double[]","double[length];","double[outputsize];","down\"","down.\"","dramat","each","easiest","edg","edge.","effect.","element","elements,","end","ensur","entir","entireti","equat","essenti","everyth","exactli","exampl","example,","example.","except","exist","expect","expect,","extend","f[n]","fact,","few","file","filter","filter)","filter,","filter,\"","filter.","filter.length);","filter:","filter::array{t,","filter?","filter_array):","filter_array,","filters,","filters.","final","finally,","first","first.","follow","form","form.","found","frequent","full","full,","full_linear_output","fulllinearoutput","function","function,","functions,","functions;","further","g[n]","gaussian","gaussian,","gaussian?","gener","general,","given","go","goe","good","graphic","greater","green","half","hand,","happen","happen!","here","here,","here.","here:","hit","honestly,","hotli","however,","i+(length(filter)/2)","i.","idea","ident","if(mod1(i","ignor","imag","image),","image,","image.","images,","images/graph","images:","images?","implement.","import","infin","initi","inner,","input","insid","instead,","instead.","int","integr","interact","interest","intern","interpret","introduc","introductori","is,","iter","itself","j","j,","j]).","jame","kernel","known","larg","larger","later","learn","leav","left","len(filter_array))","len(filter_array)),","len(x)","len(x))","len(y)","length","length(filter)","length(filter)):i","length(x)","length(x))","length(y)","length)","length,","length.","let'","licens","license.","license.md).","like:","line","line:","linear\"","linearalgebra","linger","littl","locat","location.","longer","longer.","look","loop","loop.","lot","m","m?","m]","m]g[m]","main","make","mani","math.max(0,","math.max(signal.length,","mathemat","mathematician","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matter","max(1,","max(len(signal),","mean","mention","method","middl","mind,","missed.","mit","mod(int","mod1(x,","modifi","modulu","more","move","much","multipl","multipli","multiply,","n","n,","namespac","necessarili","need","need.","neg","neighbor","neighbors,","neighbors.","new","next","nois","non","none","notat","note","note,","notic","now","np","np.zeros(output_size)","number","numpi","on","one.","opaque,","oper","operation,","operation.","operations,","opposit","origin","other,","otherwis","otherwise,","out","output","output.","output_s","output_size)","output_size):","outputs","outputsize)","outsid","over,","overlap","part","particular","particularli","past","pay","perform","period","periodic,","phase","physic","pick","place","play","point","point.","portion","posit","possibl","practic","practice,","precis","predefin","present","previou","processing),","produc","programmer,","properli","public","pull","purple,","put","questions:","random","range(max(0,","range(output_size):","read","realli","reappear","reason","reason,","red","rel","relat","rememb","request","requir","research","return","revers","right","rigorous,","s","said,","same","saniti","sawtooth","schloss","scope.","screen,","sea","second","section","section,","section.","see","seem","seemingli","seen","select","sens","sense,","separ","set","sharealik","sharp","shift","show","shown","side.","signal","signal,","signal,\"","signal.","signal?","signals,","signals.","similar","similarly,","simpl","simple_linear_output","simplelinearoutput","simplest","simpli","simul","size","slope","small","smaller","smallest","smooth","snippet,","so:","someth","somewhat","somewher","sort.","space,","spatial","specifi","squar","square,","square.","stage,","start","starts.","static","step","step,","step.","still","still,","stop","straightforward","strip","stronger","subset","subtract","such","sum","sum.","summat","support","sure","symmetr","system.io;","system;","tag.","take","talk","test","text","textbook.","that,","theorem,","therefore,","thing","think","this,","this:","those","though","through","time,","time.","together,","together:","topic","transcrib","treat","triangl","triangular,","tricki","trivial","trope","true;","two","type","typic","unbound","under","unrel","up","up\"","up,\"","us","us,","used,","user","value,","value.","var","veri","version","vertic","via","video","visual","visualization,","want","wants,","wave","wave\"","wave;","way","way,","weight","well,","whenev","white","white,","wider","wider.","wild","wise","within","without","work","worry!","worthwhil","wrap","write","written","x","x,","x.length","x.length);","y","y)","y):","y,","y.length","y;","you,","zero","{","{t"],"contents/convolutions/multiplication/multiplication.html":["&","&&&\\color{blue}6&5&4","&&&\\color{green}6&\\color{blue}5&4","&&&\\color{red}1&2&3","&&&\\color{red}1&\\color{green}2&3","&&&\\color{red}1&\\color{green}2&\\color{blue}3","&&&\\color{red}6&\\color{green}5&\\color{blue}4","&&1&2&3","&&1&\\color{green}2&\\color{blue}3&","&&6&\\color{red}5&\\color{green}4&","&1&2&\\color{blue}3&&","&4","&4&5&6","&6&5&\\color{red}4&&","&\\time","(#560),","0","0.","1","10","10,","100,","10s,","123","123,","123\\times456=56088,","13","18","18\\\\","18]=[4+1,","1s.","2","27","28","3","3+2","4","4.0","456","5","5+1","56088.","58.","6","7+1","8","8+2","8\\\\","8]=[5,8]","=","=&4+1","=&5","[4,","\\\\","\\begin{matrix}","\\color{blue}3\\times\\color{blue}6=18","\\color{green}2\\times\\color{green}6+\\color{blue}3\\times\\color{blue}5=27","\\color{red}1\\times\\color{red}5+\\color{green}2\\times\\color{green}4=13","\\color{red}1\\times\\color{red}6+\\color{green}2\\times\\color{green}5+\\color{blue}3\\times\\color{blue}4=28","\\color{red}{1}\\times\\color{red}{4}","\\end{matrix}","\\end{matrix}\\\\","\\hline","\\time","algorithm,","anoth","answer","aside,","attribut","between","blank","bound","brief","carri","case,","chapter","chapter:","column","common","consid","convolut","convolution,","convolution.","convolutions,","correct","creativ","detail","digit","discuss","each","element","elementari","end,","example,","fact","feel","follow","further","give","graphic","here,","incred","initi","integ","integers.","interest","intern","jame","know:","larg","learn","left","licens","license.","line","mathjax.hub.queue([\"typeset\",mathjax.hub]);","modifi","move","multipl","multiplication.","multiplication:","neighbor.","new","none","notat","now","number","numbers,","numbers:","oper","operations,","peopl","perform","power","pull","relat","repres","request","revers","right,","schloss","schonhag","school","second","set","sharealik","side","similar","so:","space","step:","strassen","student","such","suggest","talk","teach","text","topic:","touch","under","up","us","wise","written"],"contents/convolutions/convolutional_theorem/convolutional_theorem.html":["\"cyclic\"","\"wrap","#","(#560),","(fft)","(found","/","/=","10","10.","4.0","=","[float(i)/200","\\cdot","\\hat","\\mathcal{f}","\\mathcal{f}(f)","\\mathcal{f}(f*g)","\\mathcal{f}(g)","\\mathcal{o}(n\\log(n)).","\\mathcal{o}(n^2)","ad","add","advantag","allow","alway","anoth","around\"","array","attribut","back","base","best.","bit","blend","boundari","case","certain","chapter","chapter:","code","code,","common","complex","compos","comput","concept","condit","convolut","convolution,","convolution.","convolutions:","convolv","convolve_fft(signal1,","convolve_fft(signal1::array{t},","convolve_fft(x,","crazy,","creat","creativ","cyclic","def","delimitedfil","denot","describ","descript","differ","dimension","domain,","e^{2\\pi","each","edg","element'","equal","essenti","exampl","expand","explain,","explanation,","exponential.","exponentials,","exponentials.","extend","f(\\xi)","f(x)","fast","fft,","fft_output","fftw","first,","follow","fourier","frequenc","frequency.","function","functions.","fundament","g(\\xi),","g(x)","graphic","hard","here'","however,","idea:","ifft","ifft(np.multiply(fft(signal1),fft(signal2)))","imag","images/graph","import","incred","initi","input","inputs.","instead","intern","interpret","intuitive,","jame","k","known","lack","larg","length","licens","license.","license.md).","linearalgebra","look","magic:","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matter","mean","mention","method","method,","mit","modifi","more","move","multipl","multipli","n","n,","need","none","note","note:","now,","np","np.linalg.norm(x)","np.linalg.norm(y)","np.real(fft_output))","np.savetxt(\"fft.dat\",","numpi","n}","obviously,","on","operation,","output","output:","overal","pad","parameter","particular","particularli","peak","perform","period","process,","produc","programm","promis","pull","range(1,101)]","real","relat","rememb","request","return","revis","revised.","sawtooth","schloss","scipy.fft","section","sections!","see","seem","seen","send","seri","set","sharealik","show","side,","signal","signal.","signal2):","signal2::array{t})","signal;","singl","size","size,","smaller","someth","space","space,","space.","specifi","standard","still","take","tell","term,","text","theorem","third","this:","those","time","together.","transform","transform,","transform.","transforms!","transforms,","two","under","upon","us","valu","wave","wave.","way,","written","x","y","y)","zeros.","{t"],"contents/plotting/plotting.html":["\"2d_sample_low_res.dat\"","\"beautiful.\"","\"black\"","\"bottom\"","\"check.png\"","\"check.png\".","\"check.tex\"","\"cos(x)\"","\"exp_fn\"","\"exp_fn_log\"","\"fillsteps\"","\"gnuplot","\"gnuplot_1d_sample\"","\"gnuplot_2d_sample\"","\"gnuplot_2d_sample_colorbar\"","\"gnuplot_exp_tex\"","\"gnuplot_histogram\"","\"gnuplot_scatterplot\"","\"gnuplot_sine_cosine_customtics\"","\"gnuplot_sine_cosine_label\"","\"gnuplot_sine_cosine_linetype\"","\"gnuplot_sine_cosine_log\"","\"gnuplot_sine_cosine_movekey\"","\"gnuplot_sine_cosine_movekey2\"","\"gnuplot_sine_cosine_nokey\"","\"gnuplot_sine_cosine_notics\"","\"gnuplot_sine_cosine_square\"","\"gnuplot_sine_cosine_title\"","\"gnuplot_sine_cosine_wave\"","\"gnuplot_sine_cosine_wave_range\"","\"gnuplot_sine_wave\"","\"gnuplot_test\"","\"how","\"out.tex\"","\"purple\"","\"sample_data.dat\"","\"scatterplot_data.dat\"","\"sin(x)\"","\"sin(x)\",","\"sine","\"sine_cosine_plot.png\"","\"top\"","#","$1","'#0000ff',","'#00ff00')","'#00ff00',","'../../data/rand.dat'","'data'","'red',","(","(\"bottom\"","('#ff0000',","(0","(1","(1,0.5),","(bin($1)):(1)","(blue,","(found","(let'","(littl","(or","(read,","(to","(which",")","*","*.aux,","*.ep","+",",",".",".csv",".dat",".png",".tex",".tsv","0","0,","0.13307711243511333","0.18541942067815853","0.23648916187439406","0.23842162678327328","0.27999628668153087","0.30699091691896263","0.3548405553754319","0.35589625594005647","0.361307926046027","0.3692102429804389","0.40610861857701597","0.5","0.587785252292473","0.5877852522924731","0.5877852522924732","0.5877852522924734","0.6075688534409027","0.6338943724188091","0.6351126027850458","0.7605752608745506","0.7796784902862803","0.789554555806735","0.7972009737623846","0.8661873069668018","0.8686860241215444","0.9510565162951535","0.9510565162951536","1","1)","1,","1,0.5","1.0","1.00","1.2246467991473532e","1.williams,","10","10.","100","10cm","10cm,","12cm,","16","16:9)","17","1;","1s","2","2.0","2.4492935982947064e","2015.","2s","3","3.0","3s","4.0","480","4s,","5","5,","5.0","5.0:","6","6.0","622:","640,","6:9","7","7,","7.0","8.0","8cm","9.0","9:","=","[0:10]","[0:1]","[0:]","[1]","[n:m],","\\","\\begin{document}","\\documentclass[11pt]{article}","\\end{document}","\\input{out}","\\time","\\usepackage{gnuplottex}","abbrevi","abov","above,","above.","above:","academ","accord","actual","ad","add","addit","addition,","admittedly,","again","agnostic,","aim","algorithm","alia","alias","aliases,","allow","along","alreadi","anoth","anyon","anyth","appropri","archiv","archive,","archive.","area","argument","array","articles,","as:","ascii","ask,","aspect","associ","assum","attribut","audienc","auxiliari","avail","available.","aw","ax","axes.","axi","axis,","axis.","axis:","back","background","bar","bar.","basic","beauti","beautiful,","becom","befor","before,","begin,","behavior","beholder,","better","between","bibliographi","bin","bin(x)","bin_id(x)","bin_width","black","border","bottom,","box","bunch","c,","c.","c/c++,","cairo","call","capabl","case","case,","case:","categorized.","center","center,","certain","certainli","chang","chapter","chapter,","chapter.","chapter:","character.","check.tex","choic","choice,","choice.","choos","chore.","chosen","cleaner,","clear","clear.","clear:","clearli","cm,","code","color","colored,","column","come","command","command,","command.","command:","commands:","common","commonli","compar","comparison","complex","complic","complicated.","comput","conclus","condon","cool","coordin","copyright.","correct","correspond","cos(x)","cosin","cosine,","cover","creat","create.","creativ","cross","crosses.","current","custom","dash","dashtyp","data","data,","data.","data;","datasets.","decid","default","defin","depend","detail","determin","differ","dimens","dimension","dimension.","dimensional;","directli","discuss","do","document","document,","documentation,","documents,","don't","done","draw","each","easi","easier","easiest","easili","either:","else).","end","end,","enough","enter","entir","entri","epslatex","epslatex.","essenti","etc).","etc.),","etc.).","evaluate,","even","everyth","exact","exampl","example,","example:","exist","exist,","exp(x)","expect","expect:","explain","explan","explicitly:","extens","extern","ey","facet","fairli","fall","far","favor","featur","feel","few","file","file),","file,","file.gp","file_0000.dat,","file_0001.dat,","file_0002.dat,","files,","files;","fill","fillstep","finally,","find","first","first,","firstly,","fit","fledgl","fli","float","floor(x/bin_width)","focu","follow","following:","format","format,","fortran,","found","fractal","frequenc","frequency,","from,","from.","function","function.","futur","gener","gnuplot","gnuplot,","graphic","green,","guid","hand.","have","held","help","here","here,","here.","here:","highlight","histep","histogram","however,","html","id","ignor","imag","image,","image.","images/graph","implement","implementations.","import","inches,","includ","individu","inform","initi","input","instead","instead,","instead.","integ","intend","intens","interact","interest","intern","interpret","introduc","it!","it'","it:","iter","itself,","itself.","jame","java,","journal","julia,","keep","kelley,","key","keyword","keywords,","know","known","l","l,","label","label,","labels,","labels.","languag","languages,","larg","later.","latex","latex.","lc","learn","left","left,","legend","legend,","legend.","let'","librari","licens","license.","license.md).","like,","limit","line","line,","linecolor","littl","locat","log","logscal","look","loop","lot","m","mainli","make","mani","manually.","map","math","matlab,","matrix","matter","mean.","meant","measur","mention","method","methods.","mismatch","misrepresent","miss","missed,","mit","mode","modif","modifi","more","move","much","multipl","n","name","near","necessari","necessarili","necessary.","need","neg","new","newlin","newline,","nokey","notat","notation,","notches)","note","note,","note:","notifi","now","now,","number","number.","numbers,","numbers.","numbers?\"","object","obviously,","offici","on","on.","one...","onlin","open","option","option,","organ","otherwise,","out","out.pdf.","out.tex","output","output,","output.","output:","over","p","p,","pad","page,","pairs,","palett","paper","part,","particular","patterns,","pdf","pdflatex","peopl","perform","phrase","pixel","place","pleas","plenti","plot","plot,","plot.","plot:","plot;","plots,","plots.","plotted,","plotter","plotting,","plotting.","png","pngcairo","point","point,","pointtyp","posit","possibl","possible.","power","pr","predefin","prefer","prevent","print,","probabl","process","process,","produc","program,","project","provid","pt","pull","purpl","purpos","purpose.","purposes;","put","put,","python,","quickli","randomli","rang","rare","ratio","read","reader","reader'","real","reason,","recogn","red,","rel","relev","remov","rep","repl","replot","repositori","repres","represents,","request","requir","required.","research","resolut","rgb","rgb.","right","right,","round","rounded.","row","rows,","run","said,","same","scale","scale.","scales,","scatter","schemes.","schloss","science.","scientif","scope","screen;","script","script,","script.gp","script.gp)","script:","scripts,","section","section,","section.","see","seen","select","sens","sense,","separ","sequenti","seri","set","sever","sharealik","shell)","short","show","showcas","shown","similar,","similarly,","simpl","simplest","simpli","sin(x)","sine","singl","site.","size","skill","slowli","small","small,","smooth","so:","solid","someon","someth","sometim","space","space.","sparingly.","specif","specifi","specifiers,","splot","spot,","spruce","squar","standalon","start","state","stay","storag","store","straight","straightforward","string","strive","studi","stuff,","stun","style","such","such,","such.","sure","systems.","t","tab","tabl","take","takes.","task","tasks:","tastes.","techniqu","term","termin","terminal,","test","test\"","tex","tex,","text","text,","text.","that:","theme","themes,","thing","third,","this,","this:","though","three","through","tic","tics,","time","time,","times,","titl","title,","title.","titles,","told","tool","top","top,","tri","trouble.","turn","two","type","types.","typesetting,","u","under","understand","unit","unless","unnecessary.","unrel","unset","up","up.","updat","us","user","using,","usual","valu","value,","values,","vari","variou","vector","veri","view","visual","w","want","want.","wave","wave\",","way","way.","ways.","we'll","well","well.","whatev","whenev","widescreen","width","wish","without","word","work","work:","worse,","worth","write","written","x","x/ytic","xrang","xtic","y","yourself","yrang","ytic","z","zero","zoom"],"contents/monte_carlo_integration/monte_carlo_integration.html":["!","\"","\"\"\"return","\",","\",error:","\",our","\"check","\"error:\"","\"estim","\"fmt\"","\"how","\"math\"","\"math/rand\"","\"mont","\"percent","\"percentag","\"return","\"simplemontecarlo\"","\"squarecircle\"","\"take","\"the","\"time\"","\"world'","\"y\")(uniform01,","#","#!/usr/bin/env","#(*","#(rand","#includ","#lang","$","$(100","$2","$i","$i++)","$n","$n;","$percenterror\")","$picount","$picount++","$piestim","$piestimate\"","$piestimate\")","$positionx,","$positiony,","$radiu","$radius=1)","$x","$y","$y)","$y,","%","%))","%0.2f\\n\"","%f%%\\n\",","%f\\n\",","%lf\\n\"","🆕","🆕🌕🆕","🆕🎰🆕","🆕⏩⏩","🆕☝️🆕","🌕","🍇","🍉","🍪🔤th","🍼","🏁","🏃‍♀️","🏃‍♀️🐇🤡","🏧","🐇","👌","💯","💯samples❗️","📥","📪","📫","🔂","🔡","🔢","🔤","🔤%🔤🍪❗️","🔤run","🖍🆕","🖍radiu","😀","🤜pi_estim","🤜point_x","🤜radiu","🤡","🥧🕊💯","'__main__':","(","(#560),","($i","(($1","((ret","(*","(*'","(/","(0,","(0,0)","(100.0","(4","(>","([math]::pi))","([math]::pi))\"","([math]::pow($x,","(a","(ab","(chin123)","(dec","(defin","(defn","(defun","(displayln","(doubl","(float):","(found","(i","(if","(in","(inc","(int","(let","(like","(loop","(map","(math/ab","(mont","(n","(number","(optional)","(pi_estim","(pos_x","(println","(r,r)","(rand","(randomr","(real","(recur","(reduc","(repeatedli","(requir","(self.x,","(shown","(string","(unsign","(x","(x*x","(x*x)","(x,","(x,y)","(x:y:rest)","(y*y)","(zero?",")",");","*","**","*/","+","+))","+=",".",".count!(a",".doubl",".extern",".global",".intel_syntax",".long",".rodata",".section",".string",".take(n)",".text","/","/**","//","///return","0","0))","0..","0...n","0..n","0.0","0;","0]","1","1)","1):","1);","1.0","1.0)","10,000,000","100","100))))","100*abs(math.pi","100.0","10000000","10000000❗️","100_000","100}%\");","10❗","10❗🍪❗️","1105199103","1;","2","2)","2))","2147483647","3.141592653589793","3.14159265358979323846264338;","3jane","4","4.","4.0","4290772992","4294967295","4r^2",":","::",";",";;",";;;;","=","==","=>",">",">float",">singl",">string","?","@param","@return","[","[]","[constant","[float])","[i","[math]::abs($piestim","[math]::pow($radius,","[math]::pow($y,","[n","[pv","[r]","\\frac{\\text{area}_{\\text{circle}}}{\\text{area}_{\\text{square}}}","\\frac{\\text{count","\\pi,","\\text{area}_{\\text{circle}}","\\text{area}_{\\text{circle}}.","\\text{area}_{\\text{circle}}=\\pi","\\text{area}_{\\text{square}}","\\text{area}_{\\text{square}}=4r^2.","\\text{area}_{\\text{square}}\\times\\text{ratio}","\\text{length}","\\text{length}^2.","\\text{ratio}","\\text{ratio}?\"","\\text{width}","\\text{width}.","\\tfrac{length}{2}","\\time","]","^","^^","_","__abs__(self)","__name__","a.y));","ab","above;","abs(p","abs(p)","abs(pi_estim","abs,","ad","addsd","again","all,","anim","append","approx","approxim","approximation,","arbitrari","area","args)","array","array,","attribut","auto","bash","basic","becom","before,","below)!","below),","better","bi@","bit","bool","boolean","bunch","calcul","call","carlo","carlo\"","carlo([int]$n)","carlo.core)","case),","catch","center","chapter","chapter:","check","chinmaya","circl","circle\"","circle(1.0);","circle(doubl","circle,","circle.","circle.c","circle:","circle?","circle}}{\\text{tot","class","code","come","comisd","common","comput","constant","constexpr","coord","coordin","count","count)","count))))))","count❗️","crate","crazi","creat","creativ","crop","data","def","describ","determin","differ","dist(0,","distanc","doesn't","doubl","double)","double,","double.random(in:","drop","dup","each","easili","element","emb","embed","end","end,","engineering.","entir","equation.","error","error)))","error:","error_fmt:","estaim","estim","estimate)))","estimate))))","estimate_fmt:","exampl","exclusive\"","explan","extern","f64","f64)","f64,","fabs_const:","fact","fals","famou","feel","filter","filter$(in_circle$(?,","find","first","first.","float","float):","float64)","flonum","fn","follow","formula","four:","fprintf(\"perc","fprintf(\"th","free","fun","func","function","future!","g","get;","give","given","given_radiu","given_radius❗️","going.","graphic","guarante","here","here,","host","however,","hundred:","i)","idea","imag","images/graph","imagin","implicit","import","in_circl","in_circle()","in_circle(doubl","in_circle(float","in_circle(p","in_circle(pos_x,","in_circle(x,","in_circle(x:","in_circle(x_pos::float64,","in_circle:","incircl","incircle($x,","incircle()","incircle(a.x,","incircle(doubl","incircle(r","incircle(x,","incircle(x:","incircle(xpos,","incircle_array","inclus","increas","incred","initi","inlin","insid","instead","int","integr","integration!","integration:","intent(in)","intern","is,","is:","isinme(point","it!","it'","it,","jame","java.util.random","java.util.random;","jess","know","learn","len)","let'","licens","license.","license.md).","line","liter","local","logic","long","lower","lt","machin","mag","magic.","mahesh","main","main()","main(string[]","makepair","mani","map$(","map$(pow$(?,","margin","math","math.abs(piestim","math.abs(radius);","math.const","math.funct","math.pi","math.pi)","math.pi);","math.pow(point.x,","math.pow(point.y,","math.rang","math.sqrt","math/pi","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matter","maximum","means,","method","minimum","mit","modifi","mont","monte_carlo(10000000);","monte_carlo(samples)","montecarlo","montecarlo();","montecarlo(1000);","montecarlo(100000)","montecarlo.c","montecarlo.run(10000000);","montecarlointegr","montecarlopi","montecarlopi(100_000);","more","movsd","much","much,","mulsd","multipli","mut","n","n)","n);","n;","n_sampl","namespac","new","non","none","noprefix","not:","now,","nowadays,","number","object","objects.","obvious","on","one,","one:","otherwise.\"\"\"","output","over","p","p);","packag","percent","percent_error","percenterror","physic","pi","pi\"","pi)","pi))","pi))]","pi).abs()","pi);","pi:","pi;","pi_estim","pi_estimate)/math.pi","pi_estimate);","pi_estimate=monte_carlo(n)","pick","picount","piestim","piestimation);","place","point","point(doubl","point(random.uniform(0,","point(x,","point)","point,","point_i","point_x","point_y🤛","points,","point❗️","pos_i","pos_x,","pos_y,","possibl","pow($positionx,","pow($positiony,","power","premis","print","print(\"th","print(f\"us","printf,","println!(","println(\"estim","println(\"perc","privat","proc","produc","program","program.c","project","provid","public","pull","pv","pythagorean","quadrant","quarter","question","r","r)","r)))","r,","r]","r^2.","racket/bas","racket/local)","racket/math)","radiu","radius🤛","radius)","radius))","radius)))","radius),","radius.","radius:","radius=1)","rand","rand(2,","rand::random();","rand;","rand_max:","random","random();","random.","random.uniform(0,","randomgen","randomize()","randomli","random❗️","random❗️❗️","randx","randx:","randy:","ratio","rax","rax,","reading!","real","real(16),","repres","request","request,","requir","research,","rest","results,","ret","return","right","rough","row","run(int","same,","sampl","samples)","samples.\")","samples.\");","samples.🔤❗️","samples❗️","sampling.","save","schloss","scratch","see","seem","self.y)","set","set;","shape","shape?","shape?:","sharealik","shown","similar","simpl","simple,","simple:","simplicity,","simplicity.","slice","small","snippet","so,","someth","sort","squar","square,","square.","squares_array","srand,","start","static","std.math","std.stdio","std::f64::consts::pi;","straightforward","struct","submit","sum","sum(squares_array)","system.console.writeline(\"run","system.console.writeline($\"th","system.out.printf(\"perc","system.out.println(\"estim","system.random","system;","take","taken","technic","tell","term","test","text","thank","that'","them,","this.i","this.radiu","this.x","thm","time","time,","tool","topair","tri","trick.","true","tupl","tuple!(\"x\",","twist","two","under","uniform01))","unit","unsign","up","upper","us","used}}","using:","val","valu","value:","values?","var","vector","version","via","video","void","want","way","well,","whether","within","without","write","writeln(\"estim","writeln(\"perc","writeln;","written","x","x*x","x*x+y*i","x,","x;","x^2","x_pos^2","xam4lor","xmm0","xmm0,","xmm1","xmm1,","xor","xpo","xs","xy_array","xy_array.^2;","y","y)","y):","y*i","y*y)","y,","y:","y;","y^2","y_pos::float64)","y_pos^2","ypo","ypos)","ys","{","{:.3f}\".format(percent_error))","{:.3f}\".format(pi_estimate))","{:.3}%\",","{math.abs(piestim","{piestimate}\");","{samples:_}","|>","}","↩️","↪️","◀️","☝️","✖️","❗️","❗️🤛❗️","➕","➖","➗","➡️","⬅️"],"contents/bitlogic/bitlogic.html":["\"andgate\"","\"nandgate\"","\"norgate\"","\"notgate\"","\"orgate\"","\"roll","\"xorgate\"","(#560),","(>).","(found","(in","0","0'","0+127","0.5","0000","00000000000010100000000","00000101","00001010","0001","00010100","0010","00100100000000000000000","0011","0100","0101","01010000000000000000000","0110","0111","01111110","01111111","1","1'","1's.","1,","1.","1.00","1.00001","1.001001","10","10.25","1000","10000000","10000001","10000010","10001011","1001","1001.001","1010.01","1101:","126","127","127.","128","13,","13.","1:","1;","2","2,","2.","20","23","256","2;","2^0","2^1","2^2","2^3","2^{","2^{0}.","2^{126}","2^{130},","2^{3}","3","3+127=130,","32","3}","4","4,","4.","4.0","4096.625","5","5.25","6","7","754","8","8,","8.25","9","9.000","9.125","9.125,","=",">",">>","\\frac{1}{8}.","\\ldot","\\time","absolut","actual","ad","add","addit","alway","anoth","arises!","arithmet","attribut","available.","be","before:","bias","binari","binary,","binary:","bit","bit,","bit:","bitlogic.","bits,","bitshift","bitstr","bitstring.","bitstrings:","both","call","case","chapter","chapter:","code","code,","combin","common","compil","complic","complicated:","comput","computer.","computer?","consid","content","correspond","count","creat","creativ","cross","data","day!","deal","decim","describ","difficult","digit","digit.","discuss","divid","done","each","easiest","effect","end,","enough","essenti","exampl","example,","example:","exclus","explan","expon","exponent,","few","first","flip","float","float.","follow","gate","gate,","gate:","gates,","get","graphic","happens,","here","here'","high,","hold","however,","idea","ieee","imag","images/graph","imagin","implement","implies:","initi","input","integ","integer.","intern","interpret","it'","itself.","jame","keep","know","languag","largest","later.","lead","leav","left","left,","let'","licens","license.","license.md).","littl","logic","logic.","long,","make","mantissa","mantissa.","mathjax.hub.queue([\"typeset\",mathjax.hub]);","mean","method","mind:","mit","modifi","more","move","multipli","name","nand","natur","need","neg","negative.","new","next","none","nor:","normal","now","now,","number","number'","number.","numbers!","numbers,","numbers.","obviou","on","onto","oper","operations,","operators:","operators;","output","over\"","perform","play","point","point.","posit","power","precision)","profound","program","pull","purpos","read","realiz","reason,","redund","remov","repres","representations:","request","right,","said,","same","schloss","seem","seen","sens","sever","sharealik","shift","sign","similar","simpl","simpli","singl","smallest","so,","so:","someth","somewhat","standard.","start","still","store","straightforward","straightforward,","string","string,","structur","tabl","table:","take","talk","tell","text","that'","thing","things.","think","though","time","togeth","together.","tool!","transform","trick","truth","two","ultimately,","under","understand","understand.","us","us,","usual","valu","values:","video","way","we'll","well,","whenev","whether","whose","with.","without","work","write","written","xor"],"contents/box_muller/box_muller_rejection.html":["!=","\"","\",","\"re","#","((10,10)","(axis_num)","(found","(if","(like","(or","*","+",".+","/","0","0))","0.592m","0.618m","1","1)","1,","1.","1.273","1.9m","16","19.347","1:","1:axis_num","1]","1]^2","2","2))","2.64m","2.81m","21.46\\%","21.47\\%","256,","26.712","273.308","2]","2]^2","2d","2d,","32","32.","3700x","385.819","4)","4,","4.0","4096^2","433.644","78.54\\%,","970","=","==",">","@inbound","@index(global,","@kernel","@time","\\co","\\ell","\\ell\\tim","\\frac{1}{0.7853}","\\frac{\\pi","\\frac{pi}{4}","\\pi","\\pm","\\sim","\\sin","\\time","a[(i","abov","absolut","account","action","action,","action.","actual","again","again.","again:","allow","along","alreadi","altogether!","alway","anoth","anyon","anyway?","approach","array","array)","array,","ask","assum","at(zeros(n,","attribut","average!","aw","axi","axis_num","axis_num^2","back","bad","be","becom","befor","believ","below.","below:","benchmark","benchmarks,","benchmarktools,","best","better","between","bit","bit,","blue","both","box","box.","box—mul","bunch","calcul","call","carlo","cartesian","cartesian_box_muller!(input_pts,","cartesian_kernel!(cpu(),","cartesian_kernel!(cudadevice(),","cartesian_kernel!(input_pts,","cartesianindic","case","case,","cases,","cast","caus","ceil(int,","certain","certainli","chapter","chapter,","chosen","circl","circle,","circle.","code","code,","code:","column,","come","common","comparable.","complic","comput","computing.","configur","consid","consider:","continu","core","cos(theta)","cost","costli","cpu","cpu,","cpu.","create_grid(n,","create_rand_dist(4096^2,[0,1])","create_rand_dist(4096^2,[0,1],","create_rand_dist(n,","creativ","cuarray)","cuda","cuda.@sync.","cuda.@tim","cudakernel","dangerous!","deal","definit","depend","differ","difficult","dimens","dimension","dimensions!\")","discuss","distanc","distribut","distribution(s)","distribution,","diverg","divergence,","divid","do","don't","done","dx","each","easi","easy:","efficient.","element","elements.","else,","embed","end","endpoints;","endpoints[1]","endpoints[1])","endpoints[2]","essenti","essentially,","even","evenli","everyon","exactli","exactly.","exampl","execut","expect","expensive.","f","f(cpu(),","f(cudadevice(),","fact,","fair,","fall","fast,","fast.","faster,","few:","final","find","fine.","first","first,","firxt","for.","forev","found","full","function","fundament","gaussian","gener","given","go","gpu","gpu,","gpus)","grid","grid_ext","grid_extents/2","gtx","hand","hand,","hard","hardwar","hardware,","has_cuda_gpu()","here","here,","here:","hypothet","idea","idea,","ignor","imag","image,","imagin","implement","import","improperly,","inbuilt","includ","incred","initi","input","input_pt","input_pts[tid,","input_pts[tid,1]","insid","instead","instead?","interest","interested,","intern","is!","isa(input_pts,","issue.","it'","it.","j","j,","jame","julia","julia'","kernel","kernel!","kernel!(input_pts,","kernel,","kernel:","kernelabstract","kernelabstractions.jl,","kinda","know","larger","lead","learn","less","lesson","let'","licens","license.","license.md).","linear)","list","liter","littl","log(input_pts[tid,1]))","log(r_0)","long","look","loop","m","main()","make","mani","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matter","mean","method","method,","method:","minimum","mit","mont","more","mu","mu)","mu,","mu;","muller","multipli","n","n,","n=100)","na","nan","natur","ndrange=size(input_pts)[1])","nearest","need","new","note","now","number","numcor","numcores)","numthread","numthreads)","nvidia","odd","ok,","on","onc","onto","oper","operation,","operations.","optim","out","output","output_pt","output_pts,","output_pts[tid,1]","output_pts[tid,2]","outsid","overkill.","p1","p1^2","p2","p2^2","packag","pain","pair","parallel","parallel,","part","particl","perform","performed,","pi","pick","pink","place","platform","point","points,","points.","poison:","polar","polar_box_muller!(input_pts,","polar_muller_noreplacement!(input_pts,","polar_muller_noreplacement!)","polar_muller_replacement!(input_pts,","pre","println(\"cannot","probabl","problem","problem!","problem,","process","process,","process.","program","prohibit","provid","purpos","queu","queue","queued,","r","r^2}{(2r)^2}","r_0","r_0)","radic","ran","rand()","rand()*2","random","random?","randomli","re","read","realli","reasons.","reject","replac","replacement:","replacement?","requir","results!","results.","return","return(at(rand(n,2))","right,","right.","right?","roll\"","round","row","run","ryzen","same","sampl","sampling,","sampling?","say,","scenario","schloss","script","see","separ","set","sharealik","shouldn't","show","shown","sigma","sigma,","similar)","similar).","simulation,","sin(theta)","singl","slow","smallest","somehow","someon","someth","sometim","sometimes,","somewher","sort","specif","spend","sqrt(","sqrt(n)","sqrt(n))","squar","square.","start","statement","step","step.","step?","still","straightforward,","subsect","subsequ","subtract","such","suit","sure","sync","take","task","teach","text","there,","theta","thing","things!","things.","think","those","thread","threads,","threads.","tid","time","time,","time.","transform","transform.","tri","tricki","true","truth","tupl","type","under","unfortunately,","uniform","uniformli","unit","unlucky).","until","up","us","usual","valid","valu","values,","visual","wait(cartesian_box_muller!(input_pts,","wait(polar_box_muller!(input_pts,","want","warn","warp","warp.","way","well","well,","within","without","work","work!","worlds,","worth","write","written","||"],"contents/convolutions/2d/2d.html":["\"2d","\"8bit","\"circl","\"smeared\"","\"sobel","#","&","&=","(#560),","((i","((j","((x","(2*sigma^2))","(2d)","(a),","(array","(b),","(c)","(c),","(found","(j","(kernel_size,","(mat1.shape[0]","(normalized)","(one","(y","*","**","+","+=",".+","/","0","0.0","0.0,","0.5","1","1.0","1.0,","1.0]","1.0]*[","1.0]*[1.0","1.0],","1.0]])","1.canny,","10.","1986.","1:kernel_s","1]","2","2)","2))","2.0","2.0,","20","20\\time","2},","3","3\\time","3x3","4.0","50","50\\time","9","=","[","[0.0],","[1.0,","[1.0]],","[1].","[1~0~","[1~2~1]","[2.0],","[[","[[1.0,","\\\\","\\begin{align}","\\begin{bmatrix}","\\end{align}","\\end{bmatrix}","\\end{bmatrix}.","\\end{bmatrix}\\\\","\\frac{1}{2\\pi\\sigma^2}e^{","\\frac{1}{9}.","\\frac{x^2+y^2}{2\\sigma^2}},","\\left(","\\left(\\begin{bmatrix}","\\otim","\\right)","\\sigma","\\sigma_x","\\sigma_y.","\\sqrt{g_x^2","about,","abov","ad","add","addition,","again,","algorithm","allow","along","always,","anim","anoth","appli","approach","area","array","array.","associ","assum","attribut","axi","be.","befor","believ","below","between","bibliographi","black","blue","blur","blur\"","boundari","browser","canni","case,","center","center)^2","center)^2)","center+1)**2","center+1)**2)/(2*sigma**2))","chang","chapter","chapter,","chapter.","chapter:","circl","circle,","circle.","code","code,","color.","combin","common","complic","compon","compos","comput","compute_sobel(signal)","compute_sobel(signal):","condit","consequ","contextlib","convolut","convolution\"","convolution,","convolution:","convolutions.","convolv","convolve_linear(signal,","convolve_linear(signal::array{t,","correct","correspond","creat","create_circle(image_resolution,","create_gaussian_kernel(kernel_size)","create_gaussian_kernel(kernel_size):","create_sobel_operators()","create_sobel_operators():","creativ","cut","decid","def","definit","delimitedfil","derivatives.","detect","detection,","detector.","deviat","deviation,","diagram,","dimens","dimension","dimension)","dimensions,","direct","directions.","discuss","distribut","domain","each","edg","effect","effect,","element","elements.","ellipsoid","encourag","end","enforc","ensur","entir","essence,","essenti","essentially,","exampl","example,","examples,","exp(","expect","extens","factor","few","fill","filter","filter,","filter.","filter.shape[0]),","filter.shape[1]),","filter::array{t,","filter[i","filters\"","final","finally,","find","first","fit","float","focus","follow","formula","found","four","function","further","futur","fuzzier","g(x,y)","g_i","g_x","g_y^2}","g_{\\text{total}}","gaussian","gaussian,","gaussian.","gaussian;","gener","good","gradient","gradient.","gradient:","grant","graphic","green,","greyscal","grid.","grid_ext","grid_extents)","grid_extents,","gx","gy","gy.^2)","heart\"","here","here,","highlight","highlighted,","however,","i+1):","ieee,","imag","image,","image.","image:","image_resolution)","image_resolution))","images.","images/graph","import","independ","index","information.","initi","input","instead","integr","intern","introduc","involv","it.","iter","j","j+1):","j]","jame","john,","k","k,","kernel","kernel.","kernel[i,j]","kernel_function(x,","kernel_s","kernel_size)","kernel_size))","kernel_size*0.5","known","l","l]","larg","larger","licens","license.","license.md).","like,","linearalgebra","littl","longer","look","lot","made.","mani","mat1.shape[1]","mat2):","mat2.shape[0],","mat2.shape[1])","mathjax.hub.queue([\"typeset\",mathjax.hub]);","mean","measur","method","method:","mit","modifi","more","move","much","n","naïv","need","new","noise.","none","normalize(kernel)","note,","now","np","np.dot([[","np.dot([[1.0],","np.exp(","np.fromfunction(kernel_function,","np.linalg.norm(kernel)","np.power(gy,","np.sqrt(0.1*kernel_size)","np.sqrt(np.power(gx,","np.zeros((image_resolution,","np.zeros((kernel_size,","np.zeros(output_size)","numpi","obnoxi","off!","offset","on","onto","oper","operation.","operator.","operator:","operators,","origin","otherwis","out","out[i,","outlin","output","output_size)","output_size):","particular,","perform","place","play","point","possibl","practice:","previou","propos","pull","purpos","quadratur","radius):","random","range(image_resolution):","range(max(0,","range(output_size[0]):","range(output_size[1]):","red,","relat","rememb","reminder,","request","requir","return","right,","rule","s_i","s_x","s_x*a","s_y*a.","said,","same","sanderson","scale","schloss","section","section,","section.","sections;","see","separ","serv","set","sharealik","show","shown","sigma","signal[k,","signals,","significantli","similar","simpl","size(signal)","size(sx))","size(sy))","size,","size.","slightli","sobel","somewhat","sophist","specifi","sqrt(0.1*kernel_size)","sqrt.(gx.^2","squar","stage,","standard","start","stick","stop","such","sum","sum_matrix_dimensions(mat1,","sum_matrix_dimensions(signal,","support","suppress","suppress(indexerror):","sx","sx))","sx,","sy","sy))","sy,","tag.","talk","text","text.","that,","that:","this:","though","thought","through","thumb,","time","togeth","topic","total","tradit","two","ultim","under","us","user","valu","values).","variant","veri","video","visual","want!","way","white","whose","width","worth","write","written","x","x_posit","y","y):","y_posit","zeros(kernel_size,","{t"],"contents/cooley_tukey/cooley_tukey.html":["!","!(idx","!=","\"","\"%g\\n\"","\",","\"0.1.11\"]","\"calcul","\"combin","\"complet","\"difference:","\"dit","\"ftexample\"","\"perform","\"radix2\"","\"radix2positive\"","\"radix8\"","\"result","\"take","\"vx:\"","\"{}\",","#","#'","#'*","#'+","#(c/+","#(if","#(math/log","#c(0","#includ","#simpl","$","%","%))","%1","%1)","%2)","%2)))]","%3","%n))","&","&[complex])","'list","(","(#560),","((","((!))","((b","((dft","((fft","((stride","(*","(+","(/","(0","(0..((n","(0..n)","(0..n).step_by(strid","(1","(32","(:requir","(=","(\\cos(","(\\cos(2","(\\e","(a","(appli","(auto","(b","(bi","(c/*","(c/complex","(c/exp","(coeffici","(comp","(complex::new(0.0_f64,","(concat","(concaten","(count","(data)","(defn","(defun","(dft","(dft)","(dft),","(either","(elt","(even","(even?","(exp","(fft","(fft).","(fftw_complex*)x,","(fftw_complex*)y,","(for","(found","(i","(i.0","(if","(int","(into","(j","(k","(k)","(keep","(last","(length","(let","(let*","(like","(loop","(map","(mapcar","(mapv","(math/pow","(matrix","(mult","(n","(n)","(new_x[k","(odd","(odd?","(of","(or","(partial","(partit","(partition)","(println","(quot","(radix","(rang","(repeat","(size","(size)));","(size_t","(std::uint32_t","(stride","(time","(twiddl","*","**","*=","*x,","+","++","+=",",return",".",".*",".+","..]",".collect()",".doubl",".exp()",".extern",".fill(new",".filter(|i|",".global",".intel_syntax",".long",".map((temp,",".map(|i|",".map(|k|",".rodata",".section",".string",".sum()",".text","/","/)","//","0","0'","0)","0))","0));","0,","0..((stride","0..(n","0..64","0..n","0.0_f64));","0.0_f64);","0.0im","0:bnum","0:length(a)","0:n","0;","0s","0x00ff00ff)","0x0f0f0f0f)","0x33333333)","0x55555555)","1","1)","1)))","1)))))","1));","1)*pi*i*k/n)","1):","1,","1.","1..=((n","1.0","1.0);","1.0+0.0im","1.0+0.0im;","1.0+2.44929e","1.0_f64);","1.0im","1.0im]","1.22465e","1.83697e","1.cooley,","1105199103","16","16)","16+1.0im","16+1.0im;","16]","16im","16im;","17","1805","1965","1965.","1:digit","1:half","1:length(a)]","1:length(bit_indices)","1:length(indices)","1:length(x)]","1:length(y)","1:logn","1;","1]","1])","1e","1}","2","2)","2)))","2)));","2));","2):","2);","2**32","2*sqrt(","2,","2.","2.0","2.0_f64)","2.0j","2;","2]","2];","2^(j","2_u128.pow(i","2half","2im*pi*n*k/n)","2im*pi*n/n)","2pi","2pi*i*(k+n/2)/n=","2pi*i*k/n)","3.0","3.14159265358979323846264338327950288419716;","3.67394e","3]","4","4)","4.0","4290772992","5)","5.51091e","6.12323e","6.28318530718","8","8)","8]","8],",":+","::",":a",":depend",";;",";;els","=","=1:length(bit_indices)","=>",">",">());",">=",">>","[&","[&]","[(k","[0","[0,","[0]","[1.0+0.0im","[1].","[;;","[[w","[]","[complex","[complex(x[i])","[complex.cor","[first,","[float(i)","[i","[len","[m","[n","[r12","[r14","[r14]","[r14],","[r15","[r15]","[r15],","[rax","[rax]","[rax],","[rbx],","[rsp","[vx","[vx]","\\\\","\\cdot","\\co","\\cos(2","\\cos(\\omega","\\frac{1}{n}","\\infty}","\\int_{","\\log","\\mathcal{o}(n","\\omega","\\omega.","\\omega_2^0","\\omega_2^1","\\omega_2^1,","\\omega_n^k","\\pi","\\pm","\\rightarrow","\\sim","\\sin","\\sin(","\\sin(2","\\sin(\\omega","\\sum_{k=0}^{n","\\sum_{n=0}^{n","\\theta)","\\theta}","\\xi","\\xi)","\\xi))dx","\\xi}","])","^","^\\infti","__muldc3","__muldc3,","_i","`iterative_cooley_tukey`","a.add(b.mul(new","a[indices[i]]","a_0","a_1","abil","abov","above,","above?","accumul","accurate:","actual","add","addit","addsd","again","algorithm","algorithm.","algorithm:","allow","alreadi","alway","amaz","amount","anoth","appear","append","appli","applic","applications.","appropri","approx(y,","approx(z,","approxim","approximate.\\n\");","area","args]","arrang","array","array(n)","array(n).fill(null);","arrays.","ask","assum","attribut","auto","auto&","b","b,","b:","b[i]","b_0","b_1","back","bad","base","basically,","be","be.","be;","beauti","befor","before,","begin(initial),","behind","below","below.","better","between","bibliographi","binari","bit","bit.","bit_indic","bit_indices[i]","bit_indices[i][end","bit_reverse(x)","bit_reverse(x);","bit_reverse(x,","bit_reverse(x:","bit_reverse:","bit_reverse_entries:","bit_reverse_idxs(math.log2(n));","bit_reverse_return","bitreverse(a::array)","bitreverse(x)","bitstring(indices[i]))","bnum","bnum)","book.","both","both,","bottom","bottom;","bounc","built","butterfli","butterflies,","butterflies.","butterfly\"","butterfly(x)","butterfly(z[start_index:start_index","butterfly:","c","c/","c/*","c/+)","c/exp","c/stringifi","c]))","cabs,","calcul","calculation.","call","care","case!","case,","case.","certainli","cexp","cexp(","cexp()","cexp,","chang","chapter","chapter:","check","claim","clear,","clearli","cmath","cmp","code","code.","codebase.","coeffici","coefficients.","collect","column","column.","combin","come","common","complet","complex","complex(0,","complex(math.random(),","complex::new(1.0_f64,","complic","comput","concatenation,","console.log(\"cooley","console.log(\"it","const","constitu","convert(int,ceil(log2(length(a))))","convert(int,ceil(log2(length(x))))","cooler","cooley","cooley_tukey","cooley_tukey(&x);","cooley_tukey(&x.iter().skip(1).step_by(2).cloned().collect::>());","cooley_tukey(begin(recursive),","cooley_tukey(doubl","cooley_tukey(it","cooley_tukey(x)","cooley_tukey(x):","cooley_tukey(x);","cooley_tukey(x.filter((_,","cooley_tukey(x:","cooley_tukey(x[1:2:n])","cooley_tukey(x[2:2:n])","cooley_tukey:","cooley_tukey_end","cooley_tukey_end:","cooley_tukey_loop","cooley_tukey_loop:","cooley_tukey_mov","cooley_tukey_mov_data","cooley_tukey_mov_data:","cooley_tukey_moved:","cooley_tukey_return","cooley_tukey_return:","cooley_tukey_split","cooley_tukey_split:","cooley_tukey_spliting:","correct","correct;","correspond","course)","cover","crate","creat","creativ","cri","curv","cvtsi2sdq","cvttsd2si","cvx","cvx))","cvx)]","d\\xi","data","data)))","data.complex","data.list","data.map","data.ratio","def","defin","definit","dep","depict","describ","desire,","dft","dft(&x);","dft(doubl","dft(iter","dft(x)","dft(x):","dft(x);","dft(x:","dft.","dft:","dft:\"","dft_end_i","dft_end_i:","dft_end_j","dft_end_j:","dft_loop_i","dft_loop_i:","dft_loop_j","dft_loop_j:","dftmat","diagram","diagram:","diagrams.","didn't","differ","diffv","diffv))))","digit","digits:end]","directli","disciplin","discov","discret","distribution(0.0,","distribution(rng);","div(bnum,2)","div(n,","div(n,2)","divid","divsd","do?","does!","domain","dot","doubl","double]","during,","dx","e","e^(","e^(n*k*2*pi*(1/len)*(","e^{","e^{2","each","earli","easier","easiest","easili","effici","element","element.","elements,","elements.","end","end(initial),","end(iterative));","end(recursive));","end,","enforc","engin","entri","equal","equations:","equival","essenti","euler'","even","even[k]","evens)","everyon","exactli","exampl","example,","exist","exp","exp(","exp,","exp.(","explain","exponenti","expres","extern","f(\\xi)","f(x)","f64)","f64))","f64)).exp()","f64)).exp();","f64).log2()","f64).sqrt()).collect()","fact","factor","factor[1:half])","factor[1:half],","factors)))","far","fast","fast?","favored.","feasibl","feel","fewer","fft","fft'","fft(&x);","fft()","fft(doubl","fft(x)","fft(x:","fft)","fft))))))","fft.","fft.core","fft:\"","fft;","fftplanner::new(false);","ffts.","fftw","fftw)","fftw_destroy_plan(p);","fftw_estimate);","fftw_execute(p);","fftw_forward,","fftw_plan","fftw_plan_dft_1d((int)n,","figur","fill","find","first","first)","first,","first;","first[i]);","first[k","first[k];","firstly,","flip","fmt:","fn","follow","following:","formula:","formulas,","forth","fourier","frederick","free","freq","frequenc","friendlier,","fromintegr","front","fulli","function","function,","functions:","gathros,","gauss","glory!","go","goe","good","graphic","great","greater","half","half)","half,","half.","header","heart","help","here","here,","heroic","however,","https://github.com/alanforr/complex","i'll","i)","i))","i.1).norm()","idx","idx)","if(isapprox(y,","if(isapprox(z,","imag","images/graph","imagin","imaging,","implement","implement.","implementations.","import","imposs","imul","inclined).","independ","index","index'","index)","index))))))","indic","indices)","indices.","indices.\"","indices[i]","initi","initial;","instead","int","int(log2(n))","int)","int)time(null));","integ","integr","integrals:","intern","into:","introduc","intuit","is;","it'","it,","iter","iterative_cooley_tukey(&x);","iterative_cooley_tukey(begin(iterative),","iterative_cooley_tukey(doubl","iterative_cooley_tukey(it","iterative_cooley_tukey(x)","iterative_cooley_tukey(x):","iterative_cooley_tukey(x);","itself!","j","j*stride","j]","j]))","j]);","jame","jar","je","jle","jmp","john","jstor,","julia","julia;","k","k)","knew","know","known","landscap","languag","language,","larg","last","last)","last);","later","lay","lea","leftov","lein","len","len(x)","len)","len))))","len)]","length","length(x)","length)))","less","librari","licens","license.","license.md).","like","like:","limit","locat","log2","log_2(n)","logn","look","loop","m","m\"","m))","m.","m.fromlist","m_pi","machin","main","main()","mak","make","manag","mani","map","match","math","math,","math.floor(n","math.pi","math/ceil","math/pi","mathemat","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matmult","matrix","matrix!","matrix,","mazzuca.","mean","memcpi","memcpy,","memset(y,","memset,","mention","mentioned,","merg","mess","method","method,","method.\"","minu","miss","mit","modern","modifi","more","mov","movap","move","movq","movsd","much","much,","mulsd","mult","multipl","multipli","multiplications.","mut","n","n'","n)","n),","n).exp()));","n);","n,","n/2","n];","name","names,","necessari","necessary,","need","neg","new","new_x","new_x[k","next","nicol","non","none","noprefix","note","note,","note:","now","now,","null","number","n}","o","odd","odd[k];","odds)","odds)))","omega","on","on.","once,","one:","oper","operation.","operation:","operations.","order","order,","ordinari","oscillations.","out","output","outsider,","over","p","p;","package.\")","pad","paramet","parse(int,","particular,","particularli","parts:","peak","perfectli","perform","physic","pi","pictori","pieces.","planner","planner.plan_fft(n);","pleas","point","point,","pop","portal","posit","possible,","power","precis","preform","present","previou","primarili","principle,","print","print(all(abs([y[i]","printf(\"thi","printf,","println!(","println(\"it","println(\"recurs","problem","proce","processing.","product","prohibit","project.clj","provid","ptr","pull","push","push!(bit_indices,","put","put,","pxor","python","qualifi","quickli","qword","r12","r12,","r13","r13,","r13]","r14","r14,","r14]","r15","r15,","r15]","r15],","radic","rand(128)","rand,","rand::prelude::*;","rand;","rand_max:","random","rang","range(0,","range(1,","range(64):","range(64)][j])","range(n):","range(strid","range,","rare","rax","rax,","rbx","rbx,","rcx,","rdi","rdi,","rdx,","re","real","realli","reason","reason,","rec","recurs","recursion!","recursion,","recursion.","recursively,","reduc","relat","repl","replac","repres","request","requir","require(\"complex.js\");","research","resolut","respectively.","ret","return","return;","revers","reversal,","reverse(bit_indices[i])","right?","rng","rng.gen_range(0.0_f64,","row","row.","rsi","rsi,","rsp","rsp,","run","rustfft::fftplanner;","rustfft::num_complex::complex;","rustfft;","said,","same","save","saw","scheme,","schloss","scienc","scientif","second","section,","see","seem","seemingli","seen","sequenc","seri","series,","set","sharealik","shortcut:","show","shown","shr","shuffl","side","sign","signal","similar","simpl","simpli","singl","sinusoid","size","size_t","sizeof(y));","slow","slow,","small","snippet","so!","so,","someth","soon","sort","sort_by_bit_reverse(first,","sort_by_bit_reverse(it","soul","space","space\"","space,","space.","split","srand((unsign","srand,","stage","standard","start","start_index","static","std::array","std::begin;","std::complex;","std::cout","std::end;","std::f64::consts::pi;","std::generate(","std::size_t;","std::swap;","std::uint32_t(log2(static_cast(size))));","std::vector","std::vector(s","step,","still","straightforward","stride","stride)","stride):","string(bit_indices[i][end","strip","sub","subdivis","subdivision),","subsd","substitut","suggest","sum","summat","super","superfluid","surface,","swap","swap(first[b],","syntax,","systems;","t","t)","t)),","t));","take","tell","temp","temp[b]","temp[i]","temp[k","temp[k]","templat","term","term.","termin","terms)","terms))))","text","text,","that'","there!","thereafter.","thing","thing,","things,","this:","this_fft","this_fft.process(new_x.as_mut_slice(),","though","though,","thread_rng();","through","time","time,","time;","tmp","tmp(n);","tmp;","tmp[n];","today","together,","told,","toler","top","top;","transform","transform\"","transform,","transform.\"","transform?","transform_matrix","transform_matrix*x","transforms.","trick","truli","truth","tukey","tukey,","turn","twice.concat(twice.map(x","twiddl","two","two:","two_pi","two_pi:","u32);","ultim","ultimately,","under","understand","unnecessari","unport","until","us","used,","useful.","usiz","usize)","usize))","usize)]","usize)];","v","v))","v.iter().zip(y.iter()).all(|i|","v]","valid","valu","value:","values:","vcat(x_odd","vec![complex::new(0.0_f64,","vec::with_capacity(64);","vec>","vector","vector'","viren","void","vortex","vx","vx)","vx)))","vx)]","vx:\"","w","w))","w,","w0","w;","want","was:","wave","waveform,","way","way!","way,","well,","wikipedia)","wish","within","without","work!","work.","write","written","x","x)","x))","x);","x,","x.append(random())","x.len();","x.length;","x.map((_,","x.push(complex::new(real,","x.reduce((a,","x.to_vec();","x1","x2","x;","x[1]","x[2]","x[64],","x[b]","x[half+i]*factor[i]","x[i","x[i]","x[i];","x[indexes[i]]);","x[k","x[k]","x[n]","x[n];","x_even","x_k","x_n","x_odd","xmm0","xmm0,","xmm1","xmm1,","xmm2","xmm2,","xmm3","xmm3,","xmm6","xmm6,","xmm7","xmm7,","xmmword","xor","x}","y","y.as_mut_slice());","y.into_iter().map(|i|","y[64],","y[half+i]","y[i]","y[k]","y[n];","z","z[64];","z[i]","z[start_index+k","zero","zipwith3","{","|","}","})","});","},"],"contents/notation/notation.html":["\",","\"better\"","\"complex","\"on","#","(#560),","(a","(and","(becaus","(found","(length(a)","+","+=","0)","1","1!","1)","1.","1:length(a)","1:length(a)/2","1:size","2),","2,","2d","3","3)","3:","3d","4","4.0","4d!","8.","=",">",">=","\\log_2(8),","\\mathrm{size}\\times\\mathrm{size}","\\omega","\\omega(1)","\\omega(3)","\\omega(n)","\\omega,","\\theta","\\theta(1).","\\theta(2^n),","\\theta(3),","\\theta(\\frac{3n}{2}","\\theta(\\log(n))","\\theta(n).","\\theta(n^2)","\\theta(n^3),","\\theta.","a.","a[1])","a[2*i+1])","a[2*i]","a[2*i])","a[end])","about:","abov","acceptable,","access","access_image(img::array{float64},","action","actual","ad","addition,","advic","algorithm","algorithm.","algorithms.","alreadi","alway","anoth","answer","anyth","anything.","anyway.","arbitrari","are...\")","area","array","ask,","assum","assumption:","attribut","auxiliari","avoid","avoided,","awful,","b","b,","b::uint64)","back","bad","base","basically,","be","becom","befor","before,","below,","best","better","better:","big","book","both","breath","bunch","calcul","call","care","case","case,","case.","cases,","certain","certainli","chang","chapter","chapter:","clear","clear,","clearly,","code","come","common","compar","complet","complex","complexity.","complic","comput","concret","consid","constant","constant(a::array{float64})","constant(a::uint64,","constants!","constants,","constants.","consult","continu","convers","cover","crazi","creat","creativ","cutoff","cutoff)","cutoff::int64)","data.","decrement","definit","depend","describ","descript","descriptor","design","determin","differ","discuss","divid","doesn't","don't","done,","done.","due","each","each.","easi","easier","easili","element","element,","elements.","encourag","end","engin","entirely,","estim","even","exact,","exampl","example,","example:","examples!","examples,","exist","exist.","explain","explanation,","exponenti","exponential(value,","exponential(value::int64,","extra","fact,","factor","factors.","far","fast","fast!","faster","fastest","few","final","find","fine","finish.","first","first,","focu","follow","following:","forward","front","function","function,","function.","function:","functions,","gener","general,","geometr","go","go,","good","good!","grain","graphic","great,","great.","half","hand,","harm","haven't","here","here'","here,","histori","honest,","hour","however,","huge","hundr","i*siz","i=0:18446744073709551615","idea:","ideal","ideally,","if(a","if(n","ignor","ignored.","imag","images/graph","imagin","implement","imposs","increas","increases.","incred","index","inhibit","initi","inputs.","instead","interest","intern","intrins","intuitively,","is,","is:","issu","issue!","it!","it'","iter","j","jame","jimmi","job","keep","know","larg","larger","last","left","length","let'","librari","licens","license.","license.md).","life","like:","linear","linear(a::array{float64})","littl","logarithm","logarithmic(a::array{float64},","logarithmic(a[length(a)/2+1:end],","long","longer","look","loop","loop,","loops,","loops.","lot","love","machin","make","manag","mani","massiv","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matter","maximum","mean","mean?","measur","mind","miss","mit","modifi","more","most,","mostli","move","much","n","n)","n,","n::int64)","nearli","need","need.","nest","new","none","notat","notation","notation,","notation.","now","now,","number","o","o(1)","o(1).","o(3)","o(\\log","o(b),","o(log(n))?","o(n)","o(n),","o(n).","o(n^2)","o(n^2).","o,","obviou","obvious","obvious.","obviously,","of\"","old","older","on","on.","one,","one;","one?","ones.","oper","operation,","operation.","operations,","operations.","opposit","optim","order","others.","out","out,","outlin","over","p=np","pair","particular,","perfectli","plethora","plot","point","point,","point.","points.","polynomi","practic","practice.","pretti","print","print).","println","println(\"a","println(\"b","println(\"th","println(a[1])","println(a[2])","println(a[3])","println(a[i])","println(b)","println(img[index])","println(length(a))","println(value)","println,","probabl","problem","problem,","problem.","problems.","programming,","promis","provid","pull","put","question","question.","read","realiz","realli","reason,","reasons.","recurs","recursion.","regardless","repercussions,","request","requir","research","rid","roughli","run","run!","run,","run.","runtim","runtime,","runtime.","runtime:","rustl","said,","salt.","same,","same.","save","saw","say","scale","scaling\"","schloss","scientist","second","section","see","seem","sense,","set","sever","sharealik","should!","shouldn't","side","simpl","simpli","singl","situat","size","size.","size:","size::int64)","slowest","slowest.","small","smaller","so:","solv","solved.","someth","somewhat","space,","speaking,","speed","spend","split","square).","square,","start","statement","statements,","still","still,","stop","straightforward","strang","stupid!","sum","sure","system","system,","take","talk","task.","technic","tempt","term","territory!","text","that'","that.","that?","them,","them.","theme:","theori","theory.","there,","thing","thing:","think","thinking,","this,","those","thought","three","through","throughout","time","time,","time.","time:","time;","togeth","tool","total","total.","touch","tri","twice,","two","unclear.","under","understand","understand.","unfortunately,","unless","unlik","until","up","up,","us","useful)","useless.","vagu","vague.","valu","variabl","wait","want","warn","wasn't","wast","way","way,","way.","we'll","we'v","well","well,","whatev","whether","while,","while:","without","work","world","world;","worri","worse!","worst","worst,","write","written","wrong;","yet.","you'r","yourself"],"contents/thomas_algorithm/thomas_algorithm.html":["\"\"\"the","\"\",","\"[0.0","\"[1.0","\"[2.0","\"\\t\"))","\"divid","\"fmt\"","\"ha","\"return","\"the","\"|\",","\"~{~f","#","#(0","#(1","#(4","#(7","#a","#includ","$","$(join((\"\",","$(join((a[2],","$(join((b[1],","$a","$a,","$a[1],","$a[2],","$b","$b[0],","$b[1],","$b[2],","$c","$c,","$c[0],","$c[1],","$i","$i)","$solut","$x","$x,","$x;","$x[$i","$x[$i]","$x[0],","$x[1],","$x[2],","$y[$i]","%.1f,","%.1f][x]","%.1f][y]","%.1f][z]","%s,","%s][x]","%s][y]","%s][z]","&","&=","&[f64])","&[f64],","&b,","&c,","&x);","&x[0]);","&x[1]);","&x[2]);","'__main__':","'list))","(","(#560),","($i","((a","()","(*","(/","(0,","(0..(size","(1","(1+","(1...n).each","(a,","(a.siz","(b","(b[i]","(barely)","(c","(c',","(c,","(c_prime[i]","(coerc","(copi","(d","(d[i]","(decf","(defmacro","(defparamet","(defun","(diagon","(divf","(exclud","(format","(found","(helper","(i","(i)","(i)'","(i)^*","(in","(int","(length","(let","(loop","(n","(or","(place","(setf","(size","(size_t","(std::size_t","(svref","(thoma","(v1","(x[i]","(z[i]","(zip4)",")","*","*=","+",",divisor)))",",place",".",".266]",".5f]\".format(solution[i]))",".for_each(|i|","/","//","/=","0","0)","0))","0,","0..len(w)","0.0)","0.0);","0.0]","0.0];","0.0][x]","0.0}","0.0};","0.26666668","0.8666667","0.}","0;","0]","0][x]","0f,","1","1)","1)).rev()","1):","1,","1.","1..","1..n","1..size","1.0","1.5333333","1.upto(a.s","1:","1:1","1;","1]","1])","1]);","1]*a[i])","1];","1}","1}&","1}}","1}}{b_i","2","2)","2).downto(0)","2).downto(0).each","2,","2,0):","2.,","2.0,","2:n","3","3)","3))","3,","3.,","3.0","3.0)","3.0,","3.0]","3.0];","3.0}","3.0};","3.}","3]","4","4.0","5","5,","5.,","5.0,","5.0][y]","5][y]","6))","6.0)","6.0]","6.0];","6.0][z]","6.0}","6.0};","6.}","6]","6][z]",":","::",":=",";;",";;;;","=","==","=>",">","@[0.0,","@[1.0,","@[4.0,","@[7.0,","[","[\"\",","[%.1f]\".format(a[1],","[%.1f]\".format(b[0],","[%.1f]\\n\",","[%.1f]\\n\".format(0f,","[%s,","[%s]%s',","[.8666]","[0","[0,","[0.0,","[1","[1,","[1.0,","[1.533]","[2","[3.0]\"","[3.0]\")","[3.0]\");","[3]","[4,","[4.0,","[5.0]\"","[5.0]\")","[5.0]\");","[5]","[7,","[7.0,","[7.0]\"","[7.0]\")","[7.0]\");","[7]","[];","[]f32","[]f32)","[]f32,","[]float64","[]float64)","[]float64{0.,","[]float64{1.,","[]float64{4.,","[]float64{7.,","[a[1],","[a]","[b[0],","[double]","[double])","[double],","[i","[ratio","[{:?}]\",","\\\\","\\begin{align}","\\begin{array}{ccccccc|c}","\\begin{array}{ccccc|c}","\\ddot","\\end{align}","\\end{array}","\\frac{c_0}{b_0}","\\frac{c_i}{b_i","\\frac{d_0}{b_0}","\\frac{d_i","\\left[","\\left\\{","\\right.","\\right]","\\time","\\vdot","_,","__name__","`(setf","a'_i","a)","a))","a,","a.len();","a.length;","a.siz","a[0],","a[1],","a[2],","a[3],","a[i]","a[i])","a[i]))","a^*_i","a_0","a_0,","a_1","a_2","a_i","a_n","abov","algorithm","algorithm)","allow","allud","alreadi","analytically.","appli","args)","array)","assum","attribut","author:","auto","b","b'_i","b'_i=1","b))","b,","b:","b::vector{float64},","b[0]","b[0],","b[0];","b[1]","b[1],","b[1]}","b[2],","b[3],","b^*_i","b_0","b_0:","b_1","b_i","b_n","back","backtrack","brilliant!","c","c'","c'_0","c'_i","c'_{i","c))","c,","c.clone()","c.dup","c:","c::vector{float64},","c[0]","c[0],","c[1],","c[2],","c[i","c[i]","c[j]","c^*_i","c_0","c_1","c_i","c_in","c_in,","c_n","c_prime","c_prime[0]","c_prime[1]","c_prime[i","c_prime[i]","c_{n","calcul","call","case","cases!","certain","chapter","chapter,","chapter.","chapter:","class","code","column","column)","column)))","common","comput","console.log(\"[0.0","console.log(\"[1.0","console.log(\"[2.0","console.log(\"ha","console.log(\"th","const","const&","copi","copy(c)","copy(d)","correspond","cost","count($x));","countdown(n","course!).","course,","cprime","cprime[0]","cprime[i","cprime[i]","creat","creativ","cut","d","d')","d'_0","d'_0.","d'_i","d'_i.","d'_n.","d'_{i","d)","d))","d):","d,","d.clone()","d.count","d.dup","d.length","d:","d::vector{float64},","d[0]","d[0]].join(\"\\t\")","d[1])","d[1]),","d[1]].join(\"\\t\")","d[2])","d[2]),","d[2]].join(\"\\t\")","d[3])","d[3]),","d[i","d[i+1]","d[i]","d[j","d[j]","d^*_i","d_0","d_1","d_i","d_in","d_in:","d_n","d_{n","data.list","data.ratio","def","denomin","denominator)","denominator,","destruct","destructively\"","diagon","divf","divid","divisor\"","divisor)","don't","done","doubl","double[]","double[size];","doublearray","doublearray):","doublearray,","doublearrayof(0.0,","doublearrayof(1.0,","doublearrayof(4.0,","doublearrayof(7.0,","downto","easi","easier","echo","element","elimin","encode:","end","end.","ensur","equal","equat","equation:","equations,","even","exampl","exploit","express","factor","familiar","find","first","first,","firstly,","float","fmt.printf(\"[%f]\\n\",","fmt.println(\"[0.0","fmt.println(\"[1.0","fmt.println(\"[2.0","fmt.println(\"ha","fmt.println(\"th","fn","follow","format!(\"{:18}\",","format!(\"{:?}\",","formula,","forward","found","four","fraction","free!","fun","func","function","gammison","gaussian","goal","graphic","hand","helper","helps.","i)","i))","i))))","i)))))","i))));","implement","implementations,","import","importantly,","index","init","initi","inplac","input","instead","int","int]","intern","io","isn't","it'","it.","jame","know","last","len(d)","len(d_in)","let'","licens","license.","license.md).","lisp","local","look","main","main()","main():","main(args:","main(string[]","make","massiv","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matrix","matrix,","mayb","mechan","memset(y,","miss","mit","modifi","mut","n","n):","n:","n::int64)","neat?","need","new","new_c","new_c[0]","new_c[i]","new_d","new_d[0]","new_d[i+1]","new_d[i]","next","non","none","note","now,","number","o(n)","o(n)!","o(n^3)","obviou","on","one:","one?","overall,","packag","particular","particularli","pass","pass,","passes,","php_eol);","place","plu","print","print(\"\",","print(\"ha","print(\"th","print(a[2],","print(b[1],","print(soln)","print(table.unpack(solution))","printf('","printf('ha","printf('th","println!(\"[{:>19}]\",","println!(\"[{:?}","println!(\"ha","println!(\"th","println(","println(\"[$i]\")","println(\"[%","println(\"[%.1f,","println(\"[0.0","println(\"[1.0","println(\"[2.0","println(\"ha","println(\"solution:\")","println(\"system:\")","println(\"th","println(soln)","privat","proc","programm","project.","public","pull","put","quit","rang","range(1,","range(n","read","realli","regular","request","result","result[i","result[i]","return","right","row","row)","row)))))","rows.","same","scale","scale:","scale;","scanl","scanr","schloss","secondly,","see","separ","seq","seq[float]","seq[float]):","set","shape","sharealik","short","side","simpler:","simpli","singl","size","size)","size).","size];","size_t","sizeof(double));","soln","soln.join(\"\\t\")","soln:","soln[i]","solut","solution\");","solution.indices)","solution:\"","solution:\"\"\"","solution:\")","solution:%s',","solution:\\n\");","solution;","solution?","solution[0]","solution[i","solution[i]","solv","start","static","std::cout","std::vector","std::vector&","std::vector(a.size(),","step","steps.","substitut","system","system\"","system\")","system\");","system,\"","system,\")","system,\");","system,%s',","system,\\n\");","system.out.format(\"[%.1f,","system.out.format(\"ha","system.out.format(\"th","t","tabl","tail","tdma,","term","text","that'","this:","thoma","thomas(","thomas(&a,","thomas(a","thomas(a,","thomas(a:","thomas(a::vector{float64},","thomas(doubl","thomas_algorithm($a,","thomas_algorithm(a,","thomas_algorithm(x,","thomasalgorithm(a,","thomasalgorithm(double[]","those","time!","too,","transform","tri","two","two:","under","until","upto","v1","v2","v3","val","valu","var","vec","vec![0.0,","vec![0.0;","vec![1.0,","vec![4.0,","vec![7.0,","vec::from(x);","vector","void","w)","w:","way","we'll","well,","written","x","x)","x);","x,","x:","x[0]","x[0]))","x[0]);","x[1]","x[1]))","x[1]);","x[2]))","x[2]);","x[i","x[i+1])","x[i]","x_i","x_i.","x_n","x_{i+1}","y","y,","y.iter()","y:","y[0]","y[i","y[i]","y[size];","z","z,","z:","z[0]","z[i","z[i]","zero","zip4","{","{0.0,","{1.0,","{4.0,","{7.0,","{:?}","{:?}][x]","{c[1]","{d[1]","|i|","|j|","}","~}~%\""],"contents/IFS/IFS.html":["!)","\"$($_[0])`t$($_[1])\"","\"chao","\"if","\"out.dat\"","\"play","\"sierpinski.dat\"","\"w\")","\"yes,","\"~f~c~f\"","\"~{~a~%~}\"","#","#'format","#'make","#[derive(clone,","#\\tab","#includ","$(get","$i","$i++)","$n;","$outputpoint","$outputpoints.add($point)","$point","$shapepoint","$shapepoints)","$shapepoints.count)]","$shapepoints[$(get","$temp","$temp[0])","$temp[1])","%","&=","'list","'vector","($i","($point[0]","($point[1]","((!),","((double)","((format","()","(*","(+","(0..iters).into_iter().map(|_|","(0.0,","(0.5","(0.5,","(1","(1.0,","(1/2)","(:constructor","(appli","(auto","(auto&","(bound","(chao","(curpoint","(d,","(defparamet","(defstruct","(defun","(e)","(flet","(format","(found","(here,","(hutchinson","(ifss),","(ifss).","(int","(int)n];","(intercalate)","(iter","(lambda","(length","(loop","(make","(map","(one","(out","(p","(p)","(p.i","(p.x","(point","(rand_max));","(random","(shown","(size_t","(sqrt","(svref","(the","(with","(x","(x,","(y,",")","*","*array,","*in,","*out,","*shape","+","+=",",(sqrt",".+",".=","/","//","0)","0))))","0.,","0.0","0.0)","0.0),","0.0)]","0.0],","0.0]]","0.0},","0.0}};","0.5","0.5*(rand(shape_points)","0.5,","0.75)","0.75))","0.75_f64.sqrt()},","0.},","0;","1\"","1)","1)(rng());","1.,","1.0)","1.0)(rng());","1.0))","1.0),","1.wikipedia:","1000,","10000","1967.3.jampour,","1981.11.wikipedia:","1994.6.sanderson,","1:n","1]","2","2\"","20","200,000","2010.4.wikipedia:","2012.9.wikipedia:","2017.7.wikipedia:","2019.","2019.10.hutchinson,","2019.12.wolfram:","2019.2.mandelbrot,","2019.5.saupe,","2019.8.gneiting,","3","3\"","3blue1brown:","4","4\"","4.0","5","5\"",":","::",":direct",":if",":output",":supersede)",";",";;",";;;;","=","=>",">","@(","@($(get","@(0.0,","@(0.5,","@(1.0,","[(p","[0,","[0.5,","[1.0,","[11][12]..","[1],","[2],","[3],","[4][5].","[6][7][8].","[9][10],","[[0.0,","[math]::sqrt(0.75)),","[point(0.0,","[point]","[rand(),","[random(),","\\begin{align}","\\bigcup_{i=1}^3f_i(p)","\\bigcup_{i=1}^4f_i(p),","\\end{align}","\\frac{p","\\in","\\mathbb{r}^2","\\mathbb{r}^2)","\\mathbb{r}^n","];","_","__add__(self,","__rmul__(self,","`((0","a,","above,","accord","accordingly.","acm,","act","actual","add","addition,","advanc","again","al.,","algorithm","all,","allow","along","american","amount","anim","anoth","answer","appear","appears,","arbitrarili","archiv","aren't","array","array,","array[rand()","aspect","assess","associ","attention.","attract","attractor","attractors.","attribut","audience'","auto","avail","a}{2}\\\\","b","b,","back","backquot","becom","befor","before!","before,","before?","began","begin","below):","below:","benoit,","best","between","bewildering.","bibliographi","bit","bit.\"","blue","boggl","both","bounds,","branch","bring","britain","britain?","b}{2}\\\\","c","c,","c.","call","case","case!","catch","center","certain","chao","chaos_game(10000,","chaos_game(10_000,","chaos_game(iters:","chaos_game(n,","chaos_game(n::int,","chaos_game(struct","chaosgam","chaosgame($n,","chaosgame(10000,","chaosgame(int","chapter","chapter,","chapter.","child","children","children,","choic","choice(shape_points))","choice(shape_points))]","choice,","choos","choose(const","choose(inputpoints));","chosen,","circles?","class","clean,","clear","clearli","closer","coast","coastlin","code","collect","come","comma","common","compress","compression,","comput","computation","concept","concept,","const","constrict","context?","continu","continues.","conversation,","copy)]","costly.","count","creat","creativ","cur_point","curpoint","curpoint;","current","cut","c}{2}\\\\","d,","data","data,","data.array","data.list","day.","deal","decid","def","defin","definit","definitions,","delimitedfil","describ","detail","determin","determinist","develop","dietmar","differ","dimens","dimension","dimension,","dimension:","dimensions.","discuss","discussion.","distract","distribut","donald","dot","doubl","drand()","drand()};","draw","d}{2}\\\\","e","e))","e,","each","earlier,","easili","effici","embed","empti","end","engin","enter","entir","entirely:","equilater","escap","essenti","estim","et","evalu","everything,","exampl","example,","exist","explan","exploration,","exponenti","extend","extens","extern","f","f)","f.","f.write(\"{0}\\t{1}\\n\".format(*point))","f.write(\"{0}\\t{1}\\n\".format(p.x,","f64,","f:","f_1(p)","f_1,","f_2(p)","f_2,","f_3","f_3(p)","f_4(p)","fact,","famou","fashion,","fast","feasibl","few","file","fingerprint","first","first,","firstly,","fn","focu","follow","forego","form:","format!(\"{}\\t{}\\n\",","four","fractal","fractals,","fraction","function","function.","functions,","functions.","further","futur","future!","g","g'","g''","g'')","g')","g,","game","game\"","game,","games,","games.","gener","general,","get","glance,","go","green","h(p)","halfway","hamzaoui,","hana","happen","happens:","happili","hard","hausdorff","help","here","here,","here.","here:","hexagons?","hitch...","hutchinson","hutchinson)","idea","ident","identif","identifi","if","imag","images/graph","imagin","implement","import","in_n,","includ","incred","individu","initi","input","inputpoint","inputpoints)","inputpoints);","insert","instead","int","integ","interest","interested!","interested,","interesting?","intern","introduc","io","is!","isn't","it'","iter","iteration,","iteration.","iterations\"","iterations,","jame","java.io.filewriter;","java.util.random;","john","jstor,","k","k)","k,","keep","kinda","know","known","known:","land","languag","larg","larger","learn","let'","lhs,","lhs.i","licens","license.","license.md).","line","listarray)","literature,","load","locat","lone","long","longer","look","lower.","lt","magic","mahdi","main","main()","make","mani","math","mathemat","mathjax.hub.queue([\"typeset\",mathjax.hub]);","maximum","mean","mention","method","methodolog","methods,","midpoint","migrat","million","mind","minimum","miss","mit","modifi","more","move","movement","mut","n","n)","n,","natur","need","new","next","nil","non","none","not.","notat","note","noth","now","now,","null","number","numelem","numelems)","numoutputpoints,","object","object.","objects)","obviou","of","of!","ofs(\"sierpinski.dat\");","old_point","on","on,","onc","open","open(\"sierpinski.dat\",","oper","operator*(doubl","operator*(point","operator+(point","operator,","operator.","operators,","other)","other):","other,","other.x,","other.y)","out","out).unwrap();","out,","out_n)","outpoint","output","output_point","output_points)","output_points[i,:]","outputpoint","outputpoints(numoutputpoints);","outputpoints)","outputpoints;","outsid","overal","p","p)","p))))","p,","p.i","p.x","p.y))","p;","particular","particular.","path","pattern","pattern.","patterns,","peculiar","per","percival,","piec","plane","pleas","plenti","plot","plotter","plotter.","point","point(0.5,","point(1.0,","point(doubl","point(random(),","point(rng.nextdouble(),","point(self.x","point(x=0,","point)","point))","point)))","point))))","point,","point.x,","point.y).as_str();","point[]","point[n];","points)","points)))","points*","points*)))))","points,","points.","points:","points[randrange(points.size())];","pointvector","pointvector&","point{x:","posit","possibl","present","privat","process","provid","pseudo","pt","pt)","pt,","pt.x,","pt.y};","pt;","public","purpos","question","quick","quickli","rand","rand()","rand()]","rand::*;","rand::thread_rng();","randengine(std::random_device{}());","randengine;","random","random())","random();","random()]","random,","random_element(struct","randomgen","randomli","randomr","randrange(std::size_t","range(n):","raouf,","read","realli","red","rememb","repeat","requir","respectively.","restrict","result","retain","return","review","rhs)","rhs.x,","rhs.y};","right,","rigor","rng","rng()","rng.gen(),","rng.gen()};","rng.nextdouble());","rough","s","s)","said,","sampl","saw","scale","schloss","science,","scientific,","seconds.","section","see","seed","seem","select","self","self.i","sense,","separ","seri","set","set.","shape","shape,","shape_point","shape_points)","shape_points):","shapepoint","shapepoints)","shapes)","shapes.","shapes:","shapes[rng.gen_range(0..shapes.len())];","sharealik","show","shown","sierpinski","sierpinski.dat,","similar","similar,","similarity,","simpl","simplest","simul","simulation.","singl","size_t","slightli","so.","so:","someth","space","space,","space:","spaces;","spatial","spawn","specif","sqrt","sqrt(0.75))","sqrt(0.75)),","sqrt(0.75)],","squar","square,","square?","squares.","squares?","stage,","start","start,","start:","starts.","static","statist","std::default_random_engin","std::default_random_engine&","std::fs::write(\"./sierpinski.dat\",","std::ofstream","std::size_t","std::sqrt(0.75)},","std::uniform_int_distribution(0,","std::uniform_real_distribution(0.0,","std::vector;","step","still","still,","stori","string.","string::new();","struct","structur","structure,","structure.","structure?","subsect","subsequ","success","such","system","system.collections.arraylist","system.random","systems.","systems:","tab","take","techniqu","term","text","that:","them.","themselv","theory,","there'","therefore,","thing","this,","this.i","this.x","this:","those","though","thought,","thousand","three","through","tilmann","time","time.","tmp","tmp.x);","tmp.y);","topic","track","travers","tree","triangl","triangle,","triangle.","triangle:","triangular","tricki","truli","truth","turn","two","typic","under","underpinnings,","understand","union","until","updat","us","use)","usize,","usual","vec","vec![","vec)","vector","veri","vertic","via","video","view","visit.","visual","void","wander","wanderin","way","way.","we'll","well,","whether","why,","will","within","within.","wonder","word","world","write","writedlm(\"sierpinski.dat\",","written","x","x,","x:","x;","y","y)","y)))","y:","y;","y=0):","yield","zeros(n,2)","zip(point,","zipwith","{","{0.5,","{1.0,","{drand(),","{k","{lhs.x","{{0.0,","|","}","}).collect()","};","ševčíková,"],"contents/verlet_integration/verlet_integration.html":["!","\"[#]\\ntime","\"[#]\\nveloc","\"[#]~%time","\"[#]~%veloc","\"fmt\"","\"integr","\"~d~%\"","#","#includ","$","&=","&=x(t)","&vel,","'[#]'","'__main__':","'psetf',","'time","'veloc","(","(#560),","()","(*","(*vel)","(+","(5,","(>","(_,","(actual","(aold","(defun","(defvar","(f64,","(first","(float,","(format","(found","(incf","(list","(loop","(method","(po","(position,","(psetf","(return","(second","(show","(stormer","(tail","(time","(time,","(time:","(time:time,","(time_sv,","(time_vv,","(timesv,","(timevv,","(veloc","(verlet","(x'","(x',","(x,","(xold,","*","**","*time","*time,","*vel","*vel,","+","+=",".01)",".5*acc*dt*dt",".doubl",".extern",".global",".intel_syntax",".rodata",".section",".string",".text","/","//","0","0)","0,","0.0","0.0)","0.001","0.01","0.01)","0.01))","0.01);","0.01d0","0.0:","0.0;","0.5","0.5*acc","0.5d0","0:","0;","0d0","0d0)","1","10","10,","10.,","10.0","10.0,","10d0","2","2)","2.0","2d0","2v(t)\\delta","2x(t)","4.0","5","5.0","5.0,","5d0",":","::",":=",";;",";;;;","=","==",">","[particle]","\\\\","\\begin{align}","\\cdot","\\delta","\\end{align}","\\frac{1}{2}(a(t)","\\frac{1}{2}a(t)\\delta","\\frac{1}{2}a(t+\\delta","\\frac{1}{2}at^2","\\frac{1}{2}mv^2?","\\frac{1}{3}b(t)\\delta","\\frac{1}{6}b(t)","\\frac{1}{6}bt^3","\\frac{b(t)","\\frac{x(t+\\delta","\\mathcal{o}(\\delta","\\mathcal{o}(n\\log(n)).","\\mathcal{o}(n^2)","\\sim","^","_","_)","_,","__name__","_po","a'","a',","a(t)\\delta","a(t+\\delta","a)","a,","abov","above,","above.","aboveground","acc","acc*dt","acc*dt*dt","acc*dt;","acc,","acc:","acc::float64,","acceler","acceleration!","acceleration,","accuraci","actual","ad","add","addition,","addsd","again,","algorithm","algorithm,","algorithm.","allow","alreadi","anoth","aold,","appropriately.","approxim","approximation,","args)","array)","assum","attribut","b","ball","barn","be","befor","bodi","both","bring","calcul","calculations.\"","call","can't","case,","central","certainli","chang","chapter","chapter:","check","choice;","class","classic","close","code","code:","comisd","common","comparison","complex","console.log(`${stormer.time}`);","console.log(`${stormer.vel}`);","console.log(`${time}`);","console.log(`${velocity.time}`);","console.log(`${velocity.vel}`);","console.log(`[#]\\ntim","console.log(`[#]\\nveloc","const","constant,","creativ","current","cut","data","def","denomin","depend","describ","differ","done","doubl","double)","double):","double,","drop","dt","dt)","dt))","dt)))","dt),","dt):","dt,","dt:","dt::float64)","dt;","echo","end","energy,","equat","error","essenti","etc.","even","everyth","exampl","exit","expans","explan","f(x(t+\\delta","f64","f64)","f64,","few","final","find","first","float","float)","float):","float64)","fmt.println(\"[#]\\ntim","fmt.println(\"[#]\\nveloc","fmt.println(time)","fmt.println(vel)","fn","follow","following:","forc","forgotten","former,","freefal","fst","fun","func","function","further","get","given","go","graphic","graviti","great!","greater","ground","half","half:","handi","have.","height.","here","here'","higher","hit","hold","however,","hut","implement","implicit","import","increment","initi","instead","int","integr","integration.","integration.\"","integration:","integration:'","integration:~%\")","integrators.","intent(inout)","interfac","intern","io","is:\"","is:\")","is:\");","is:\\n\");","is:\\n%lf\\n\"","is:\\n%lf\\n[#]\\nveloc","is:`);","is:~%\")","ismainmodule:","it'","iter","ja","jame","jbe","jerk","jie","job","kinemat","kinet","know","knowledg","known","language.","last","latter","less","let'","licens","license.","license.md).","lisp","liter","look","m","magnitud","main","main()","main():","main(args:","main(string[]","main:","make","mani","mathjax.hub.queue([\"typeset\",mathjax.hub]);","mean","mention","method","method.","method.\"","mit","model","modifi","more","motion","mov","move","movsd","mulsd","mut","n","necessary!","need","new","newton'","newtonian","next","next_po","next_pos;","nextpo","none","noprefix","note","now,","object","object,","obvious","offset","old","on","order","out","output","over","p","p0","p0@(x,","p1","packag","paramet","particl","peopl","perform","physic","pinch.","play","po","poor,","pop","pos)","pos*2","pos,","pos,acc,","pos:","pos;","pos_in","pose","posist","posit","position,","prev","prev_po","prev_pos,","previou","prevpo","prevpos,","prevpos:","print","print(\"[#]\\ntim","print(\"[#]\\nveloc","print(\"\\(stormer.time)\")","print(\"\\(stormer.vel)\")","print(\"\\(velverlet.time)\")","print(\"\\(velverlet.vel)\")","print(\"\\(verlettime)\")","print(\"{:.10f}\".format(time))","print(\"{:.10f}\".format(vel))","printf","printf(\"%lf\\n\",","printf(\"[#]\\ntim","printf(\"[#]\\nveloc","println!(\"[#]\\ntim","println!(\"[#]\\nveloc","println!(\"{}\",","println(\"$(time)\")","println(\"$(vel)\")","println(\"$verlettime\")","println(\"${stormerverlet.time}\")","println(\"${stormerverlet.vel}\")","println(\"${velocityverlet.time}\")","println(\"${velocityverlet.vel}\")","println(\"[#]\\ntim","println(\"[#]\\nveloc","privat","problem;","program","public","pull","push","put","putstrln","pxor","quit","rax","rax,","rbp","rdi,","real(8)","real(8),","reference,","regist","request","requir","result","result))","ret","return","rid","said,","save","scale","schloss","sens","seri","set","sharealik","show","simpl","simpler","simpli","simul","simultan","snd","snippet","so,","solut","solv","solver","sometim","speed","speed,","split","start","static","std::cout","stormer","stormer_fmt","stormer_fmt:","stormer_verlet","stormer_verlet(&time,","stormer_verlet(5,","stormer_verlet(5.0,","stormer_verlet(doubl","stormer_verlet(mut","stormer_verlet(pos,","stormer_verlet(pos::float64,","stormer_verlet:","stormer_verlet_loop","stormer_verlet_loop:","stormer_verlet_return","stormer_verlet_return:","stormerverlet","stormerverlet(5,","stormerverlet(5.,","stormerverlet(5.0,","stormerverlet(_pos:","stormerverlet(pos,","stormerverlet(pos:","stormerverlet(pos_in,","straightforward","straightforwardli","struct","submit","subroutin","subsd","subtract","such","system.out.println(\"[#]\\ntim","system.out.println(\"[#]\\nveloc","system.out.println(stormerverlet.time);","system.out.println(stormerverlet.vel);","system.out.println(velocityverlet.time);","system.out.println(velocityverlet.vel);","system.out.println(verlettime);","t","t)","t))","t)),","t))\\delta","t),","t)\\delta","t)}{2\\delta","t,","t0","t0)","t^2","t^2)","t^2),","t^2).","t^3","t^3).","t^3.","t^3}{3","t^4)","t^4),","take","takewhil","taylor","temp","temp_po","temp_pos,","temp_pos;","temporari","temppo","temppos:","temppos;","term","term,","text","that,","there'","there.","this.tim","this.vel","this:","though","time","time)","time)))","time);","time,","time.","time:","time;","time_sv);","time_v","time_v);","time_vv);","timestep","timestep.","timesteps.","timesv","timev","timeveloc","timevv","togeth","traj","traj)","trajectori","trick","trick!","two","two:","type","typic","t}","t}.","under","unfortun","up","updat","us","v","v'","v',","v(t)","v(t),","v(t)\\delta","v(t+\\delta","v(t+\\frac{1}{2}\\delta","v)","v,","v=\\frac{\\delta","v_0t","val","valu","var","variabl","variable.","vel","vel)","vel))))","vel);","vel*dt","vel:","vel:vel)","vel;","vel_sv)","vel_sv);","vel_vv)","vel_vv);","veloc","velocity!","velocity,","velocity_fmt","velocity_fmt:","velocity_verlet","velocity_verlet(&time,","velocity_verlet(5,","velocity_verlet(5.0,","velocity_verlet(doubl","velocity_verlet(mut","velocity_verlet(pos,","velocity_verlet(pos::float64,","velocity_verlet:","velocity_verlet_loop","velocity_verlet_loop:","velocity_verlet_return","velocity_verlet_return:","velocityverlet","velocityverlet(5,","velocityverlet(5.,","velocityverlet(5.0,","velocityverlet(_pos:","velocityverlet(pos,","velocityverlet(pos:","velocityverlet(pos_in,","velsv","velsv)","velverlet","velvv","velvv)","verlet","verlet(&time,","verlet(5,","verlet(5.,","verlet(5.0,","verlet(_pos:","verlet(doubl","verlet(mut","verlet(pos,","verlet(pos:","verlet(pos::float64,","verlet(pos_in,","verlet:","verlet_fmt","verlet_fmt:","verlet_integr","verlet_loop","verlet_loop:","verlet_return","verlet_return:","verlettim","verletvalu","verletvalues(doubl","verletvalues(time,","verletvalues(v","video","void","want","ways,","well,","wide","work","worse.","write(*,*)","written","x","x'","x(t","x(t)","x(t)}{\\delta","x(t+","x(t+\\delta","x(t\\pm","x)","x,","x.","x_0","xmm0","xmm0,","xmm1","xmm1,","xmm2","xmm2,","xmm3","xmm3,","xmm4","xmm4,","xmm5","xmm5,","xmm6","xmm6,","xmm7","xmm7,","xold","xor","x}{\\delta","zero.","zero:","zipwith","{","}","};"],"contents/split-operator_method/split-operator_method.html":["!!","\"\"\"calcul","\"\"\"contain","\"\"\"initi","\",","\".dat\")","\".dat\",\"w\")","\"\\n\"","\"\\n\")","\"\\t\"","\"\\t\")","\"__main__\":","\"folder='../haskell'\"","\"imaginarysplitop\"","\"output00000.dat\"","\"output{}.dat\".format(str(i).rjust(5,","\"real","\"realsplitop\"","\"sloshing\"","\"split_op_method\"","\"w\")","\"{}\\t{}\\t{}\",","\"{}\\t{}\\t{}\\n\".format","#","#[derive(clone)]","#defin","#endif","#ifndef","#includ","$","%","&mut","&operators)","&opr)","&opr));","&par,","¶meters,","'0'","(","(\"output\"","(#560),","((/","((:+","((^","((double)i","((i","((par.x","((par.x[i]","()","(*","(*)","(+)","(.*),","(.+)","(0,","(2","(2.0","(5","(\\k","(\\mathbf{r})","(\\n","(\\x","(^","(albeit","(also","(complex","(cough","(dft,","(div","(double)i","(drop","(dt),","(dt^2)","(dx","(evol","(export","(factor","(fftw_complex*)x,","(fftw_complex*)y,","(format","(found","(granted,","(i","(i)","(i,","(intercal","(intercalate,","(invers","(inverse)","(k","(kineticop","(kstep","(like","(listarray","(map","(nlse):","(normal","(oper","(par.im_time)","(par.k","(par.timestep","(par.x","(par.x[i]","(pi","(re","(rstep","(show","(size_t","(so","(such","(t)","(the","(timestep","(wfc","(x","(x.0","(x.len()","(x.size()));","(x:xs)",")","))","));","*","*)","**","*=","*in","*k;","*ke;","*opr,","*out","*par,","*pe;","*v;","*wfc;","*x,","*x;","+","++","+=",",",".",".\"\"\"",".*",".*)",".+","..","../gnuplot/plot_output.plt","..]",".fold(0.0_f64,",".into_iter()",".zip(energy_r.into_iter())","/","//","/=","0","0)","0)))","0);","0,","0.","0..par.r","0..par.timestep","0..re","0..x.len()","0.0));","0.0,","0.01","0.05,","0.0_f64));","0.0_f64).powi(2);","0.0_f64);","0.0_f64,","0.5","0.5*opr.v*par.dt)","0.5*par.k.^2*par.dt)","0.5*wfc_c.*ifft((par.k.^2)","0.5_f64","0:","0;","1","1)","1)*pi/(xmax)),","1),","1,","1.","1.0);","1.00)","10","10.0","10.0),","10.0,","10.0/512","10.0/512,","100","100)","100,","1000","1000,","10^{","1:2","1:3","1:length(density)","1:length(energy_k)","1:length(opr.wfc)","1:par.timestep","1]","1j)","1}","1}\\left[\\hat{u}_k(dt)","2","2)","2))","2));","2),","2);","2*xmax/res,","2,","2.0","2.0);","2.0_f64","2.0_f64).exp(),","20.0/512","256,","3.14159265358979323846","35},","4","4.0","5,","5.272859","512","512,","512/2",":",":+","::","=","==","=>",">",">dk",">dt",">dx",">im_tim",">k",">k[i]",">ke",">ke[i]",">pe",">pe[i]",">re",">size",">timestep",">v",">v[i]",">v[i]);",">wfc",">wfc[i]",">x",">xmax","?","[","[0","[1","[operators]","[x","\\frac{1}{2}","\\frac{1}{2}\\hbar","\\frac{1}{2}\\hbar\\omega,","\\frac{[i\\hat{h}_r,","\\frac{\\hbar^2}{2m}\\nabla^2","\\frac{\\parti","\\frac{i(\\hat{h}_r","\\frac{i\\hat{h}_kdt}{\\hbar}},","\\frac{i\\hat{h}_kdt}{\\hbar}}e^{","\\frac{i\\hat{h}_rdt}{2\\hbar}}","\\frac{i\\hat{h}_rdt}{2\\hbar}}e^{","\\frac{i\\hat{h}_rdt}{\\hbar}},","\\frac{i\\hat{h}_rdt}{\\hbar}}e^{","\\frac{i\\hat{h}dt}{\\hbar}}\\right]\\psi(\\mathbf{r},t)","\\hat","\\hat{h}_k","\\hat{h}_k)dt}{\\hbar}}\\right]\\psi(\\mathbf{r},t)","\\hat{h}_r","\\hat{u}_k","\\hat{u}_r","\\hbar","\\hbar\\omega.","\\infty}^{+\\infty}\\psi^\\ast\\psi","\\int_{","\\left[","\\left[\\hat{u}_r\\left(\\frac{dt}{2}\\right)","\\left[\\hat{u}_r\\left(\\frac{dt}{2}\\right)\\mathcal{f}^{","\\left[e^{","\\left[v(\\mathbf{r})","\\mathcal{f}","\\mathcal{f}^{","\\mathcal{o}(dt^3)","\\nabla^2","\\omega","\\omega,","\\psi(\\mathbf{r},t","\\psi(\\mathbf{r},t)","\\psi(\\mathbf{r},t),","\\psi(\\mathbf{r},t)}{\\parti","\\psi(\\mathbf{r},t+dt)","\\psi(\\mathcal{r},","\\right]","\\right]\\psi(\\mathbf{r},t)","\\right]\\psi(\\mathbf{r},t).","\\tau","\\time","^","_","_)","__init__(self,","__name__","_dt,","_dt;","_res,","_res;","_timesteps,","_timesteps;","_xmax,","_xmax;","abov","above,","above.","above:","abs)","abs2.(opr.wfc)","acc","accru","actual","add","addition,","address","afterwards,","again","algorithm","allow","also,","ambiguous.","amount","anim","anoth","appropriately,","are;","area,","aside,","assum","atom","attribut","auto","b","back","bad","baker","base","basically,","befor","behave,","bit","bool","bool)","bool,","boolean","both","bottom","boundari","box","c","c++","calcul","calculate_energy(&par,","calculate_energy(par,","calculate_energy(par:","calculateenergi","call","campbel","carray","case","case,","cases.","center","cexp(","chang","chapter","chapter:","check","chunks,","class","close(outfile)","code","code,","coeffici","coefficients.\"\"\"","common","commonli","commut","complet","complex","complex)","complex::new(par.k[i],","complic","complicated).","compon","components,","concession,","conditions,","conj(wfc_r)","conjug","continue.","correct","cough)","cover","cpow(par.k[i],","cpow(par.x[i]","crate","creat","creativ","data","data.array.carray","data.complex","data.list","deal","decay","def","defaultparamet","definit","densiti","density,","density.iter().sum::()","density:","density[j],","density[j].real,","density[opr.size];","dependence,","describ","desir","dft","didn't","differ","differenti","dig","discontinu","display","display,","distribut","distribution.","div","div(par.timesteps,","divid","dk","dk,","dk:","dk::float64","dk;","do","do.","done","doubl","double)","doubt","dt","dt)","dt,","dt:","dt::float64","dt::float64,","dt;","dt^2","dt^3,","dtype=complex)","dure","dx","dx);","dx,","dx:","dx::float64","dx;","dynam","e","e^{","each","easier","easili","elem","element","elems)","else:","end","end).","energi","energy)","energy.","energy_fin","energy_final*par.dx","energy_k","energy_k,","energy_k[i]","energy_r","energy_r).r","energy_r[i]","energy_r[i])","enforc","enough","equat","err(why)","error","evol","evolution.","evolv","exactli","exampl","example,","exp","exp.(","expectation.","experimentalist","explan","exponenti","export","extern","f","f)","f64","f64)","f64))","f64).sqrt();","f64);","f64,","fact,","factor","false)","false);","fastest","feature!","few","fft","fft(&mut","fft(doubl","fft(opr.wfc)","fft(wfc_r)","fft(x:","fft.process(x.as_mut_slice(),","fftplanner::new(inverse);","ffts.","fftw","fftw3","fftw_backward","fftw_backward,","fftw_complex","fftw_destroy_plan(p);","fftw_estimate);","fftw_execute(p);","fftw_forward),","fftw_forward,","fftw_plan","fftw_plan_dft_1d((int)n,","fftw_plan_dft_1d(static_cast(x.size()),","fi","fi)","figur","file","file.","file.flush()","file::create(&path)","filenam","files,","final","find","fine","first","flip","float)","float,","float:","flowchart","flush","fn","follow","format","format!(\"output{}.dat\",","formula:","forth","forward","fourier","fraction","frequenc","fromintegr","front","full","function","future.","g","gaussian","gener","gif","give","gnuplot","gnuplot.","go","goe","good","good,","graphic","grid","ground","guess","g|\\psi(\\mathbf{r},t)|^2","h_r","half","hamiltonian","hamiltonian.","hamiltonians.","hard","harmon","heart,","here","here'","here,","higher","hold","honest,","hood","housdorff","however,","i'll","i)","i);","i\\hat{h}_k]dt^2}{2}}\\right]\\psi(\\mathbf{r},t)","id","ideal.","idft","idft)","ifft","ifft(opr.wfc)","im)","im*0.5*opr.v*par.dt)","im*0.5*par.k.^2*par.dt)","im;","im_tim","im_time,","im_time:","im_time::bool","im_time;","im_val","im_val::bool)","imag","images/graph","imaginari","impl","implement","implementations.","import","imtim","in,","includ","incred","index,","indic","individu","init(par,","init(par:","init(par::param,","init_operators(struct","init_params(struct","initi","instead","int","int)","int,","integr","interact","intercal","intern","interpret.","invers","inverse)","inverse:","involv","io","is:","issue,","it'","it.","it:","iter","iteration,","itself.","j","j,","jame","julian","k","k,","k.","k.push(((i","k.push((i","k.push_back((static_cast(i)","k.reserve(res);","k:","k::vector{complex{float64}}","k::vector{float64}","k;","k[i]","ke,","ke.push(complex::new(","ke.reserve(size);","ke:","kinetic","kineticop","kmax","know","known","ks","ks)","kstep","l","laplacian,","larg","left","length","let'","library.","licens","license.","license.md).","liftarray","liftarray2","line","linear","lines,","littl","locat","long","longer","look","loop","lose","lowest","luckily,","m_pi","main","main()","make","makeoper","makeparamet","malloc(sizeof(doubl","malloc(sizeof(double)","mani","map","mapm_","match","math","math.fft","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matter","mean","memset(y,","mention","method","method),","method:","mislead","mit","models)","modern","modifi","momentum","momentum,","momentum.","more","move","multipli","mut","mutabl","n","n)","n,","natur","need","new(","new(10.0,","new(par:","new(xmax:","new(zeros(res),","next","non","none","none:","nonlinear","norm","norm2","normal","notat","notation","note","note,","noth","np","np.abs(opr.wfc)","np.arange(","np.concatenate((np.arange(0,","np.conj(wfc_r)","np.empty(res,","np.exp(","np.fft.fft(opr.wfc)","np.fft.fft(wfc_r)","np.fft.ifft((par.k","np.fft.ifft(opr.wfc)","number","numbers.","numpi","o","odd","of:","offset","ok(good)","okay.","on","op","op@(oper","open(\"output\"","open(filename,","oper","operator.","operators(len(par.x))","operators(length(par.x))","operators(param","operators(res)","operators)","operators.","operators:","operators::new(&par,","opr","opr)","opr);","opr.k","opr.ke[j];","opr.pe[j];","opr.r","opr.v","opr.v[i]","opr.v[j].re)","opr.v[j].real)","opr.wfc","opr.wfc,","opr.wfc.clone();","opr.wfc.iter().map(|x|","opr.wfc[j]","opr:","opr::operators)","ops))","op}","order","oscillator,","other,","otherwis","out,","outfil","outfile.write(line)","outfile:","output","over","p","p)","p.plan_fft(x.len());","p;","pad","panic!(\"couldn't","par","par,","par.dt","par.dt)","par.dx","par.dx;","par.im_tim","par.im_time:","par.k[i].powi(2)).exp(),","par.res);","par.res;","par.res];","parallel","param","param()","param(5.0,","param(xmax::float64,","param)","param,","param:","paramet","parameter","parameters,","parameters.\"\"\"","parameters::new(5.0,","params(doubl","part","part,","particular","path","path.display();","path::new(&path_name);","path_nam","pe,","pe.push(complex::new((","pe.push(complex::new(0.0_f64,","pe.reserve(size);","pe:","perform","period","phd","phd.","physic","pi","pi/10.0),","pi/xmax,","play","plot","plot_output.plt","plotter","plotting:","posit","position),","potenti","potential","potential,","potential.","potential.\"\"\"","precis","pretti","primari","print","print(\"energi","print(\"output","printevolut","println!(\"th","println(\"energi","println(\"output","probabl","process","provid","pseudo","pub","public:","pull","purpos","quantum","quickli","quit","r","r::vector{complex{float64}}","range(len(density)):","range(par.timesteps):","re","real","real(energy_k[i]","real,","realli","realpart","realpart)","regardless,","reinterpret_cast(x.data());","reinterpret_cast(y.data());","rel","relat","renorm","renorm_factor","rep","repeat","replic","repres","request","res)","res));","res);","res,","res/2:","res:","res::int64","res::int64,","res;","res])","research","rest","results!","return","rng","rstep","run","rustfft::fftplanner;","rustfft::num_complex::complex;","rustfft;","said,","same","satisfied.","say,","scale","schacher","schloss","schrödinger","section,","see","self.dk","self.dt","self.dx","self.dx)","self.im_tim","self.k","self.r","self.timestep","self.v","self.wfc","self.x","self.xmax","seri","set","settl","sharealik","shift","shown","side","similar","simpl","simplest","simpli","simul","simulation,","simulation.","sit","size","size;","size_t","sizeof(y));","skip","slide","slight","slightli","small","smoothli","so:","solut","solv","solver...","someth","something).","somewhat","sort","space","space,","space:","spatial","specified.","spectral","split","split_op!(par,","split_op!(par::param,","split_op(&par,","split_op(par,","split_op(par:","split_op(param","split_op(struct","split_op.jl","splitop","sqrt","sqrt()","sqrt(renorm_factor)","standard","start","starting,","state","states,","states.","std::complex(0.0,","std::complex;","std::f64::consts::pi;","std::fs::file;","std::io::write;","std::path::path;","std::vector(opr.size,","std::vector;","step","step:","story.","str(0)))","straightforward","straightforward.","strang","string(0)))","string(density[j])","string(lpad(string(i","string(par.x[j])","string(real(opr.v[j]))","struct","studi","such,","sum","sum(density)","sum(energy_k","sum.sqrt();","sure","system","system!","system.","system:","systems,","t+dt)","t,","take","technic","templat","template(par.x[j],","term","term.","test","text","that'","think","this:","those","though.","through","throughout","time","time,","time.","timestep","timestep!","timestep,","timestep:","timesteps,","timesteps:","timesteps::int64","timesteps::int64,","timesteps;","too!","total","toward","transform.","transforms.","transpos","transpose)","trap","trap,","trap.","tri","trick","true","true)","true);","turbul","turn","two","type","typic","t}","u","under","understand","unit","units,","units.","unphysical,","unsign","until","us","usize,","v","v(\\mathbf{r})","v,","v.push(complex::new(","v.reserve(size);","v0","v0)","v:","v::vector{complex{float64}}","v[i]","v[i].re).exp()));","v[i].re).exp(),","v]","v_offset).powi(2),","v_offset:","valu","value.","vanish.","vec","vec![complex::new(0.0_f64,","vec,","vec::with_capacity(par.res);","vec::with_capacity(res);","vec;","vec>","vec>,","vector","vector_complex","vector_r","vector{float64}(","vector{float64}(vcat(0:512/2","vector{float64}(vcat(0:res/2","video","voffset)","voffset).^2","voffset,","voffset:","voffset::float64,","void","w","wave","wavefunct","wavefunctions.","wavevector","wavevectors,","way","way.","we'll","wfc","wfc'","wfc)","wfc.push(complex::new(","wfc.reserve(size);","wfc0","wfc0)","wfc:","wfc::vector{complex{float64}}","wfc_c","wfc_c.*opr.v","wfc_c[i]","wfc_c[i].scale(0.5_f64);","wfc_k","wfc_k)","wfc_k,","wfc_k[i]","wfc_offset).powi(2))","wfc_offset:","wfc_r","wfc_r[i].conj();","wfc_r[i];","wfcconj","wfcoffset)","wfcoffset).^2/2)","wfcoffset,","wfcoffset:","wfcoffset::float64)","whole","why)","why),","wide","work","world\"","write","write(outfile,","writefil","writeln!(file,","written","x","x))","x,","x.1).re);","x.len()];","x.norm().powi(2)).collect();","x.push(xmax","x.reserve(res);","x:","x::vector{float64}","x;","x[i]","x^2","xmax","xmax)","xmax),","xmax);","xmax+xmax/res:2*xmax/res:xmax),","xmax,","xmax:","xmax::float64","xmax;","xs)","x|","y","y(x.size(),","y.as_mut_slice());","y[i]","y[n];","zeros(res))","zeros(res),","zip","{","{wfc","{}\",","{}:","|","|\\psi(\\mathbf{r},t)|^2","|acc,","}","};"],"contents/domain_coloring/domain_coloring.html":["\"$2\\pi$\"])","\"$\\pi$\",","\"++\"","\"__main__\":","\"absz\"","\"hsv\"),","\"hsv1\"","\"hsv2\"","\"hsv3\"","\"hsv4\"","\"hsv5\"","\"im(z)\"","\"phase","\"plot","\"re(z)\"","\"rgb1\"","\"rgb2\"","\"shade\"","\"utf8\"","\"z2\"","#","&=","'++'","'2pi'","'domain.png'","'f(z)=z^2'","(","(\"0\"","(0,0)","(2*pi)","(2.0","(abs(sin(real_f(z(x,y))*pi)**thresh)","(clear)","(f(z)","(f_val_ab","(found","(hue,","(np.abs(np.sin(np.pi","(np.pi","(pi","(red).","(red,","(z","(z)",")","*","**","+","/","0","0,","0,0","0.1","0.1)","0.5","0.5*(abs(f(z(x,y)))","1","1)","1))","1,","1.","1.wikipedia:","1000","1000,","180","1:2:(color($1,$2))","1i","1j","2","2.","2.0","2.0)","2.0),","2.0,","2000","2000,","2004.","2008.4.wegert,","2012.5.poelke,","2019.3.pethick,","2020.2.schloss,","2:2]","2\\pi","2d","2i,","2pi","3.14159","3.14159)","3.14159,","4.0","4\\pi","500)","500x500","800",":","=","==","[","[1].","[2]","[3].","[4]","[5]","[6].","\\","\\&","\\\\","\\begin{align}","\\cdot","\\end{align}","\\frac12","\\frac{1}{2}","\\frac{1}{2}\\left(r","\\in","\\left(\\lfloor","\\left(f(z)=z^2\\right),","\\lfloor","\\mathbb{c}),","\\mathbb{c}.","\\mathbb{r}):","\\rfloor","\\rfloor.","\\right),","\\right).","\\sqrt{\\text{re}(z)^2","\\text{atan}\\left(\\frac{\\text{im}(z)}{\\text{re}(z)}\\right)","\\text{im}(z)^2}","\\theta","\\theta}","]","__name__","abs(sin(imaginary_f(z(x,y))*pi))**thresh)","accord","actual","ad","add","addition,","again,","along","also,","altern","alway","analyt","angle\"","angle\")","angle(x,y)","anoth","appropri","arbitrary.","around","array","aspect","aspect=\"equal\"","aspect=\"equal\")","assum","atan2","atan2(","atan2(y,x)","attribut","ax","ax=axes,","axes.get_xticklines():","axes.get_yticklines():","axes.imshow(","axes.set_title(\"$f(x)=z^2$\")","axes.set_xlabel(\"$re(z)$\")","axes.set_ylabel(\"$im(z)$\")","axi","axis,","back","bar","base","beauti","before,","below:","between","bibliographi","black","blue","blue),","border","bose","both","built.","busi","c,","calcul","cambridg","capabl","case","case,","cbar","cbar.set_ticklabels([\"$0.0$\",","cbar.set_ticks([0.0,","cblabel","cbrang","cbtic","center","certain","certainli","chang","chapter","chapter,","chapter:","choic","choos","chose","christoph","circl","clear","code","color","color(f_val,","color(x,y)","colorbar","coloring,","coloring:","colors,","common","compel","complet","complex","complic","compon","components,","components.","condens","consequ","constrain","contain","context","contour","contour.","contours.","convers","coord","coords)","corner","correspond","creat","creativ","crunching.","current","data","data.","datafil","dataset","def","defin","degre","degrees,","depend","describ","determin","diagon","differ","difficult","dilut","dimens","dimension","dimensionality,","dimensions,","directli","discontinu","distracting,","domain","draw","drop","each","easi","easier","easili","edg","edge.","einstein","elias,","ensur","equations,","essenti","essentially,","establish","exampl","example,","explan","extent=(","f(z)","f(z)!","f(z).","f(z):","f(z)=z^2.","f_val","f_val_ab","fact","feebl","feel","fig,","fig.colorbar(","fig.savefig(\"domain.png\")","figur","file","find","fix","floor","floor(abs(f(z(x,y)))))","fluctuat","fluids,","focu","follow","form","form,","form:","formula","fortran,","four","fourier","free","full","function","function'","function,","function.","function:","functions.","functions.6.lundmark,","functions:","further","g(r)","gases,","gener","gnuplot,","go","gradient,","graphic","green,","grid","gridlin","gridlines(f_val,","gridlines(x,y)","gridlines(x,y))","gridlines.","h(z)","hans,","happen","have","heat","heavili","henrik,","here","here,","hide","horizont","however,","hsl","hsv","hsv,","hsv2rgb(angle(real_f(z(x,y)),","hue","human","i\\sin(\\theta))","ideal,","imag","imag(f(z))","image.","image:","images!","images/graph","imagin","imaginari","imaginary_f(z(x,y))),","imaginary_f(z)","implement","import","improvise.","imput","incap","increas","increases.","independ","index","indic","inform","input","instead","integ","interest","intern","introduct","intuitive.","invert","inviscid","isosampl","isosamples\"","j","jame","james,","java","key","kind","konrad,","konstantin","label","label=\"phas","languag","last","lc","left","legend","let'","licens","license.","license.md).","line","line.","linearli","lines,","locat","long","look","lot","lower","magnitud","magnitude,","magnitude.","magnitude:","magnitude_shading(f_val)","magnitude_shading(f_val):","magnitude_shading(x,y)","magnitude_shading(x,y),","make","mani","map","maps,","massiv","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matplotlib.cm","matplotlib.color","matplotlib.colors.hsv_to_rgb(hsv)","matplotlib.pyplot","mean","means,","meant","media,","method","mind","mirror","mit","model","modifi","more","move","much","much,","necessari","need","new","next","nocontour","none","note","now","np","np.abs(f_val)","np.abs(np.sin(np.pi","np.angle(f_val))","np.floor(f_val_abs))","np.imag(f_val)))","np.linspace(","np.meshgrid(coords,","np.moveaxis((hue,","np.pi)","np.pi),","np.pi,","np.pi])","np.real(f_val)))","number","numpi","offset","on","onc","onto","oper","opposit","order","origin","origin,","origin.","origin;","origin=\"lower\"","origin=\"lower\",","other.","out!","outlin","output","output,","output.","overal","overall,","palett","parallel","pattern","peak","peopl","phase","phase.","pi","pi,","pixel","place","plane","play","plenti","plot","plot,","plot.","plot:","plotted:","plt","plt.subplots(1,","plug","pm3d","pngcairo","point,","polthier,","portraits,","possibl","precis","press,","problem.","process","produc","project","pull","pure","purpos","purposes,","put","quantum","r","r(\\cos(\\theta)","r(x,y)","r(x,y)*exp(theta(x,y)*sqrt(","r,","rang","rapidly,","ratio","re^{i","real","real(f(z))","real_f(z)","realli","reason,","red","remov","repres","request","requir","requires.","respectively.","return","rgb","rotat","round","sacrif","same","sampl","satur","saturation,","save","save_encod","saw","say,","scalarmapp","scalarmappable(matplotlib.colors.normalize(0.0,","scale","scheme","scheme,","schloss","scienc","script","see","seen","separ","set","shade","sharealik","sharpli","show","shown","similar","simpl","simpler","simplest","simpli","simul","singl","size","smaller","smith,","smooth","so,","so:","somewhat","sort","space","space,","space.","spatial","split","splot","springer","sqrt(x*x","squar","start","start,","step","subsequ","such","system","t","techniqu","termin","text","that,","theta(x,y)","this,","this:","those","thresh","threshold","threshold)","threshold):","through","throughout","thu","tic","tick","tick.set_visible(false)","titl","togeth","top","track","tupl","tuples,","twice,","two","types.","under","understand","unfortunately,","units,","univers","unset","us","user","valu","value)","value),","value).","value,","values,","values.","variabl","variable,","variou","vertic","video","view","visual","vortex","want","want!","wash","way","whatev","whenev","where,","wind","winding.","without","wrap","written","x","x)","x))","x,","xlabel","xrange[","xtic","xy","y","y*y)","y,","ylabel","yrange[","ytic","z","z(x,y)","z**2","z,","z.","z\\in\\mathbb{r}","z^2","z^2,","z^2.","z_imag","z_real","z_real,","zero","|\\sin(\\pi\\times\\text{re}(f(z)))^t|\\times|\\sin(\\pi\\times\\text{im}(f(z)))^t|,","|z|"],"contents/barnsley/barnsley.html":["!)","\"\\t\"","\"affin","\"fern","\"if","\"simpl","#","#[derive(clone,","#includ","$","&","&0","&0.04","&0.16","&0.22","&0.24","&0.28","&0.5","&0.85","&=","&[f64])","&[f64],","&[vec],","&barnsley_hutchinson,","&barnsley_probabilities,","'__main__':","(!))","(\"check","()","(+)","(0,","(0,0)).","(0..iters)","(0.0,","(a","(a,","(array,","(auto","(b","(double)rand()","(double,","(found","(i,","(int","(intercalate)","(name","(point","(rnd","(scale","(size_t","(step","(x","(x,","(xx,","(y,",")","*","*_","*hutchinson_op,","*probabilities,","+","++","+=","./barnsley.cpp",".collect()",".into_iter()",".map(|_|","/","//","0","0\"","0),","0.,","0.0","0.0),","0.0,","0.01","0.04","0.04,","0.07","0.07,","0.07]","0.07];","0.15","0.15,","0.16,","0.2","0.22,","0.23","0.24,","0.26","0.26,","0.28,","0.44","0.44),","0.44],","0.5","0.85","0.85,","0.],","0;","0u;","1\"","1\"));","1)","1,","1.","1.0)(rng());","1.0),","1.0,","1.6","1.60),","1.6],","1.],","1.barnsley,","10_000,","17","1994.","1:length(probabilities)","1])","1};","2\"","2014.2.wikipedia:","2019.3.saupe,","3","3\"","3d","4.0","4u;",":","::",":=","=","==","=>",">",">)","@","[","[0.,","[0.01,","[0.2,","[0.23,","[0.26,","[0.85,","[1]:","[2][3].","[point]","\\\\","\\begin{align}","\\begin{bmatrix}","\\end{align}","\\end{bmatrix}","\\end{bmatrix}p","\\frac{a}{2}","\\frac{b}{2}","\\frac{c}{2}","\\frac{p+a}{2}","\\frac{p+b}{2}","\\frac{p+c}{2}","\\frac{p+d}{2}","\\tau","]","]),","],","];","__name__","__rmatmul__(self,","a,","academ","account","acm,","act","ad","addit","advantag","affect","affin","again","align","all,","all.","along","anoth","answer","apparent.","appropri","around","array","attractor","attractor,","attractor.","attractor;","attractors,","attractors:","attribut","auto","b)","b,","back","barnsley","barnsley_hutchinson","barnsley_hutchinson,","barnsley_prob","barnsley_probabilities)","be","beauti","becom","bellow","below","between","bibliographi","big","biggest","bin","bin,","bit","bit...","both","bounds,","briefli","browser","bulk","c","c++","c,","call","case","cases,","cast","challeng","chang","chao","chaos_game(","chaos_game(initial_loc","chaos_game(point(0,","chaosgam","chapter","chapter,","check","choic","choices(hutchinson_op,","choos","chosen:","clang++","class","clear","code","code.","coeffici","come","common","common.","compil","compon","compress","compression,","const","constexpr","constitu","construct","construction,","continu","contractive.","contractivity,","convers","coordinates)","coordinates[0];","coordinates[1];","coordinates[2];","copy)]","correct.","correspond","creat","creativ","cumulprob","d","d_glibcxx_debug","data","data.array","data.list","def","definit","delimitedfil","derefer","describ","dietmar","differ","difficult","dimension","disect","distribut","don't","doubl","double)","double,","double[3];","double[]","drand();","drastic","draw","drawn.","dtor","due","e.g.:","each","easiest","effect","elem","element","elems,","end","end,","entir","essentially,","even","eventu","everyone'","everywhere,","exactli","exampl","example,","explain","explan","extend","f,","f64)","f64,","f_1","f_1(p)","f_1,","f_2","f_2(p)","f_2,","f_3","f_3(p)","f_3,","f_4","f_4(p)","f_4,","fact,","fashion","fashion,","features,","feel","fern","fern\"","fern,","fern.","fern:","few","fewer","final","find","first","flags,","fli","flip","fmap","fn","form:","format!(\"{}\\t{}\\n\",","forward.","fractal","fst","function","function.","functions,","functions:","functions?","g","g'","g''","g'')","g')","game","gdwarf","gener","general,","given","glance,","go","greater","half","halfway","hamzaoui,","hard","heart","here","here,","high","hop","hope","however,","hutchinson","hutchinson_op","hutchinson_op,","hutchinson_op[0];","idea","ident","imag","image.","images/graph","impl","implement","import","includ","incomprehens","individu","infin","initi","initial_loc","initial_location,","initial_location.x,","initial_location.y,","initial_location[1],","instead","int","interest","intern","introduc","involv","io","it'","iter","itself,","jame","java.io.filewriter;","java.io.ioexception;","java.util.random;","k","k)","k,","knob","knowledg","known","lead","leav","left","left.","length","less","let'","leverag","licens","license.","license.md).","likelihood","line.","linear","list","listarray,","literature,","location.","look","low","magic","main","main()","major","make","mani","map","mat,","mat.xi","mat.xx","mat.xz","mat.yi","mat.yx","mat.yz","mat.zi","mat.zx","mat.zz","mat:","mathematician","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matmul(struct","matrix","matrix)","matrix_mul(self,","matrixmultiplication(double[][]","me.","meant","meanwhile,","mention","mess","methods,","michael","mind","mit","modifi","more","move","mut","mystifying,","n","n,","natur","necessari","need","new","new(x:","next","no.","non","not,","notat","note","note:","now","np","np.array([","np.array([*output_gen$[:10000]])","np.array([self.x,","np.array):","np.savetxt(\"out.dat\",","num_op)","number","numpi","o3","obvious.","old_point","old_point.x,","old_point.y,","on","on,","op","op&","oper","operator*(const","operator*(doubl","operator*(std::array","operator+(std::array","operator.","opn","origin","others.","out","out).unwrap();","out;","output","output_gen","output_point","output_points)","over","p","p,","part","path","perform","pick","play","pluck","point","point(doubl","point(double[]","point(x,","point(x=0,","point)","point))","point,","point.i","point.matrix_mul(operation);","point.x","point.x,","point.y).as_str();","point.z","point.z,","point2","point2d","point3","point3::new(","point3::new(0.0,","point3::new(0.20,","point3::new(0.23,","point3::new(0.26,","point3::new(0.85,","point3d","point;","point_array","point_array))","points.","points:","posit","precis","predict","predict?","press,","privat","probabilities)","probabilities):","probabilities);","probabilities.iter().enumerate()","probabilities:","probability)","probabl","programm","promot","properti","provid","public","qualiti","question:","rand()","rand::prelude::*;","rand::thread_rng();","rand_max;","random","randomgen","randomli","randomr","raouf,","read","reconstruct","reflection,","reminder,","resolut","respectively.","result","result!","result,","ret","return","review","rhs:","rhs[0].i","rhs[0].x","rhs[0].z","rhs[1].i","rhs[1].x","rhs[1].z","rhs[2].i","rhs[2].x","rhs[2].z","right","right.","rnd","rng","rng.gen::();","rotat","row","rule,","said,","same","sampl","satisfi","scale","scanl1","schloss","see","seem","seemingli","select","select_array(","select_array(hutchinson_op,","select_array(hutchinson_op:","select_array(struct","self","self.i","self.x","self.y,","self.z;","self::new(x,","sens","sense,","sense.","separ","set","set.","shape","sharealik","shearing)","show","shown","showpoint","side","sierpinski","similar","simpl","simple,","simul","singl","size_t","slightli","smaller","snd","somewhat","soon,","space,","specif","squar","square,","stage,","start","static","std::array","std::array&","std::array;","std::fs::write(\"./out.dat\",","std::vector{};","std=c++17","stem","stem,","stem.","step","store","strategi","string","string::new();","struct","style","subtract","success","support","surpris","system","system.random","systems,","tag.","take","takewhil","templat","tend","text","them,","thing","this,","this.i","this.x","this.z","though","through","tilt","time","to_choic","toward","transform","transformation.","transforms,","translation.","triangl","triangle,","triangle.","true:","tuple(*(mat","turn","twiddl","two","under","understand","understandable.","uniform","unsettl","until","up","upon","us","v)","v,","v;","vari","variant","vec","vec![","vec![0.01,","vec)","vec2","vec3","vec3&","vec3{initial_location[0],","vec3{};","version","video","virtual","wall","want","way","wcast","wconvers","wdoubl","we'll","wextra","wformat=2","without","wnon","wnull","wold","work","works,","worry!","woverload","wpedant","written","wshadow","wsign","wunus","x","x,","x:","x;","xx","xx,","xy","xy,","xz,","y","y)","y,","y:","y;","y=0):","yield","yx","yx,","yy","yy)","yy,","yz,","z","z)","z:","z;","zipwith","zx,","zy,","zz;","{","}","})","},","};"],"contents/box_muller/box_muller.html":["!(isnan(input_x)","!=","\"affin","\"fern","\"if","\"simpl","#","&&","&=","(((x+mu[1])^2)/(2*sigma^2)","((y+mu[2])^2)/(2*sigma^2)))","(also","(axis_num)","(both","(found","(gaussian_valu","(input_i","(input_x","(j","(probabl","(to","(u_1","(yes,","(z_1","*","+","+1.","+=",".+",".=","/","0","0\"","0.1)","0.1,","0.5)","1","1\"","1)","1,","1,000","1,000,","1.","1.box,","10,000","100","1958","1958.2.wikipedia:","1:axis_num","1:size(histogram)[1]","1:size(histogram)[2]","1:size(input_pts)[1]","1;","1]","1],","2","2\"","2)","2022.","2022.3.wikipedia:","2\\ln(r_0)}\\left(\\frac{u_1}{\\sqrt{r_0}}\\right)","2\\ln(r_0)}\\left(\\frac{u_2}{\\sqrt{r_0}}\\right)","2\\ln(r_0)}{r_0}}","2\\ln(r_0)}{r_0}}.","2\\ln(u)}.","2\\ln(u_1)}","2\\pi","2\\pi,","2]","2d,","3\"","4.0",":]","=","==",">","[","[(i","[0,0],","[1].","[2].","[3].","[nan,","[sigma","\\\\","\\begin{align}","\\co","\\cos(\\theta)","\\end{align}","\\frac{r^2}{2}},","\\gt","\\mu","\\mu,","\\mu.","\\rightarrow","\\sigma","\\sigma,","\\sin","\\sin(\\theta)","\\sqrt{","\\sqrt{\\frac{","\\sqrt{u_1^2","\\theta","\\theta,","a[(i","actual","again,","all,","along","alreadi","amount","angl","angular","anyway,","applies,","are:","around","array,","as,","attribut","avoid","away","axi","axis_num","axis_num^2","backward","barnsley","basic","be.","between","bibliographi","bin","bin[1]","bin[2]","bodi","both","bottom.","bound","bounds[1,1]","bounds[1,1])","bounds[1,1])/dx),","bounds[2,1]","bounds[2,1])","bounds[2,1])/dx))","box","box—mul","bunch","calcul","call","cartesian","cartesian_box_muller(input_pts,","cartesianindex(ceil(int,","case","case,","case.","ceil(int,","ceil(int,(bounds[2,2]","chang","chapter","circl","circle,","cleanest","clear","code","code,","column,","come","common","complete,","compon","coordin","coordinates,","coordinates.","cos(theta)","costli","course,","creat","create_grid(n,","create_rand_dist(n,","creativ","debug","decent","decid","delimitedfiles,","determin","develop","deviates,","deviation,","differ","dimens","dimension","dimension:","dimensions,","discuss","distanc","distribut","distribution)","distribution,","distribution.","divid","dx","dx))","dx),","e^{","each","easiest","end","endpoints)","endpoints[1]","endpoints[1])","endpoints[1],","endpoints[1]]","endpoints[2]","entir","ep,","equat","equations,","essenti","exact","exampl","except","exp(","expect.","fairli","far","faster","fastest","fern","fern\"","few","final","finally,","first","follow","form","form,","full","function","gaussian","gaussian_valu","gener","general,","georg","given","good","grid","grid,","grid.","grid_ext","half","have,","heart","here","here,","here.","histogram","histogram[bin]","histogram[i,j])^2","hold","honest,","i*dx","idea","ident","imag","images/graph","implement","implementation,","individu","inher","initi","input","input.","input_i","input_pts[1]","input_pts[1]^2","input_pts[2]","input_pts[2]^2","input_pts[i,","input_x","instead","interest","intern","intuitive.","is_gaussian(input_pts;","isnan(input_y))","it!","it'","it.","it:","j","j*dx","j,","jame","know","larg","last","later):","let'","licens","license.","license.md).","like,","limit","linearalgebra","littl","log(input_pts[1]))","log(r_0)","logic","look","loop","main","mainli","make","marsaglia","mathjax.hub.queue([\"typeset\",mathjax.hub]);","mean","mean,","mention","mervin","messi","method","method,","mit","more","mu","mu)","mu[1],","mu[2]]","muller","multipli","n","n=100,","n=100:","name)","nan]","nearest","need","new","next","next!","nice","normal","normalize!(histogram)","note","now","number","numbers.","obviou","ok","ok,","on","onc","once.","one,","one.","oper","operations.","opt","order","origin","output","output:","outsid","over","pair","parallel,","particl","particular","particularli","peopl","percent","perform","physical,","pi","place","plot","point","points.","polar","polar_box_muller(input_pts,","practic","preform","process:","produc","purpos","question!","r","r,","r=\\sqrt{","r?","r\\cos(\\theta)","r\\sin(\\theta)","r\\sin(\\theta).","r_0","r_0)","r_0.","radial","rand()","random","random)","random,","rang","read","readi","real","redefin","reject","rel","relev","rememb","requir","research.","return","return(rand(n,2)","right,","rm","roughli","round","row","same","same,","sampl","sampling)","scale","schloss","see","seem","sense.","separ","set","shape","sharealik","shi","show","sigma","sigma,","simple.","simpli","simulation.","sin(theta)","singl","size","size,","smaller","so,","so:","solv","someth","somewhat","special","specifi","spin","sqrt(","sqrt(n)","sqrt(n))","sqrt(rms/n)","squar","stage,","standard","star","start","step","step.","straightforward:","subsections:","such","sum(histogram)","super","sure","take","techniqu","test","text","that'","theta","thing","this,","this:","threshold","transform","transform!","transform,","tri","triangl","trigonometr","turn","twiddl","two","typic","u","u_1","u_1/\\sqrt{r_0}","u_2","u_2),","u_2.","u_2/\\sqrt{r_0}.","u_2^2}.","ultim","under","uniform","uniform,","uniform.","uniform?","uniformli","unit","up","us","usual","valid","valu","value.","values,","values.","vari","version","video","walk","want","way","well,","within","without","work","works,","written","x","x,i","x\\sigma","y","y\\sigma","z_1","z_2","z_2).","zeros(ceil(int,(bounds[1,2]","zeros(n,","||"],"contents/computus/computus.html":["\"","\"#{a[i]}\\t#{servois_numbers[i]}\\t\\t#{easter_dates[i]}\"","\"$year`t$(calcul","\"%d\",(21","\"19","\"\\t\"","\"\\t\\t\"","\"a\"","\"april","\"calcul","\"full","\"march","\"meton","\"notation)","\"passover\"","\"patching\"","\"rel","\"servoi","\"synod","\"the","\"year","\"year\\tservoi","\"year`tservoi","\"you","\"{year}","\"{}\\t{:","\"~8a~18a~a~%\"","\"~{~a~%~}\"","#","#includ","$","$((21","$a","$b","$c","$d","$d)","$e","$e)","$k","$k)","$m","$m)","$n","$n)","$p","$q","$q)","$year","$year)\"","${22","${d","%","%d\",","&","&&","&e","&option","'(\"the","'april","'march","(","($d","((13","((2","((21","((22","((a","((d","()","(*","(+","(12","(13","(15","(19","(19a+m)~\\%~30","(2","(2020..2030).to_a","(21","(21+d)~\\%~31,","(22","(2b+4c+6d+n)~\\%~7.","(4","(4+k","(>","(a","(and","(b","(c","(computu","(computus)","(d","(date)","(defun","(e","(easter","(eql","(floor","(format","(found","(here","(if","(in","(int","(k","(let","(let'","(let*","(loop","(m","(mod","(modulo","(multipl","(n","(or","(orthodox)","(p","(q","(roughli","(servoi","(servois)","(setf","(solar)","(strawberry)","(such","(the","(to","(use","(valu","(var","(when","(where","(with","(within","(year",")",");","*","*/","*computus(int","*out,","+","++","..","/","/**","//","//shift","0","1","1))","1,","1.venerabilis,","10)","10))","10)))","10):","10)?","100","100)","100))","100).floor();","100).toint","100,","100.","100;","11","11~\\%~30","12","13","15","1777,","1800","1800,","1813.","1816.","1876.5.servois,","19","19)","19))","19.","1900.","1999.2.dictionary.com","19;","19a","19th","19th.","1:length(a)","1;","1st","1st,","2","2.","2000","2000,","2004.4.unknown,","2004.7.wikipedia:","2017","2018","2019","2020","2020,","2020.","2020..2030)","2020..2030:","2020..=2030;","2020.3.bien,","2020;","2021","2021;","2030","2030]","2031):","2039.","2099,","21","21st","21st).","21st,","21st.","22","22+d+e>31","22+d+e\\leq31","22nd","25","25)","25))","25).floor();","25).toint","2500","2500.","25;","25th","26","26th","27.5","28","28)","28).","29","29)","29.5","29th","2b+4c,","3","30","30)","30))","300","30;","30th","31","31)","31)))))","31).to_","31).to_string();","31).tostring()","31).tostring();","31);","31:","31}\"","354","365","365).","365.","365.2425","365.25","4","4)","4))","4).floor();","4).toint","4.0","400","400,","4200","45","4;","50%","52","52\\times7=364,","6","6)","6))","7","7)","7))","7)))","7;","8","84","9)","9))","9).to_","9);","96","97","9\\text{","9th.","9}\"","9}\".fmt","9}';","9}`;",":","::",";",";;",";;;;","=","==",">","?","@param","@return","[...]","[1]","[2020","[2],","[3].","[4].","[5].","[6].","[7].","[];","[int]","[math]::floor($k","[math]::floor($year","[math]::floor((13","[string]","[switch]$servois)","\\","\\%","\\%30","\\%~30","\\%~31","\\\\","\\begin{align}","\\end{align}","\\frac{\\pi}{4}","\\frac{\\pi}{4}).","\\left\\lfloor\\frac{13+8k}{25}\\right\\rfloor.","\\left\\lfloor\\frac{\\text{year}}{100}\\right\\rfloor,","\\left\\lfloor\\frac{k}{4}\\right\\rfloor.","\\left\\{","\\lfloor\\cdot\\rfloor","\\qquad","\\right.","\\text{","\\text{easter}","\\text{if","\\text{year}~\\%~19,","\\text{year}~\\%~4,","\\text{year}~\\%~7,","`april","`div`","`march","`mod`","a)","a,","a.each_index","a.map","a>10","abilities)","abov","above,","above.","accord","accordingly;","account","account.","accur","act","actual","ad:\"","ad:\")","ad:\");","ad:\",","ad:\\n\"","ad:\\n\");","ad:~%\"","add","addit","addition,","admittedly,","again","again,","ahead","algorithm","algorithm).","algorithm,","algorithm:","algorithm;","algorithms,","align","all,","allow","allud","along","alway","angl","annal","anoth","anyth","anything,","anywher","apparently,","appear","appliquées.6.standish,","approach","appropri","approxim","approximation,","april","april.","april}&","arbitrari","arc","arcan","archiv","archive,","arithmet","arithmetic)","arithmetic,","arithmetic.","around","array","array[string]):","ascens","astound","astrolog","astronom","attribut","auxiliari","away","axi","axis,","axis.","b","b)","b,","b:","back","background","bad","baffl","bamboozl","base","be","be,","becam","beda","bede,","befor","behind","behind.","below,","below:","best","better","between","beyond:","bibliographi","bind","birthday","bit","body.","bool","bool)","boolean","born","both","c","c)","c,","c.","calcul","calculation,","calculation.","calculator,","calendar","calendar,","calendar.","calendars.","calendrier,","call","cambridg","care","case","case;","cases,","celebr","center","center,","center.","centuri","centuries,","centuries.","century.","certain","certainli","chang","chapter","chapter.","char","chose","choseth","christendom.","christian","church","church'","circle.","clarity),","clergi","close","closer","code","code,","code.","collect(2020:2030)","color","combin","come","common","commun","compatriot","complain","complet","complex","complic","complicated.","comput","computation,","computer.","computu","computus([int]$year,","computus(int","computus(y)","computus(y,","computus(year","computus(year,","computus(year:","computus(year;","computus,","computus.(a)","computus.(a;","conc","concern","condit","conditionals,","conditions,","connect","consecut","consid","consider","console.log(","const","constrict","cooley","correct","correspond","counts,","cover","craft.","creat","creation.","creativ","current","cycl","cycle)","cycle,","d","d)","d+e","d+e+22\\text{","d+e.","d,","d,31))","d=28","d=28,","d=29","data","date","date.","dates.","day","day,","days),","days,","days.","de","decad","def","definit","delambre)","demand.","depend","describ","design","determin","devis","dictat","differ","dimension","discrep","discuss","div","divid","divis","doesn't","done","doubt","down","drama","drawn","duct","dumb","dure","e","e)","e)))","e).to_","e);","e,","e.","e=","e=6","e=6,","each","earli","earth","earth'","earth,","earth.","easili","easter","easter\"","easter\"))","easter)","easter)))","easter,","easter.","easter:","easter?","easter_d","easterd","eastern","echo","effect","electromagnetism,","element","elimination,","else:","em,","empir","encourag","end","engin","ensur","entir","eq","equinox","equival","era","era!","especi","essenti","essentially,","et","etc.","even","event","everyon","exampl","example,","except","exist","existed,","explain","explan","express","expressions.","e}\"","e}\".fmt","e}';","e}`;","f","f)","f,","fact","fact,","factor","fail","fall","false)","false):","false):6}\".fmt","false})","famou","fan","favorit","februari","feel","festival.","few","final","find","first","fld(13","fld(k,","fld(year,","fledgl","floor","fn","focu","follow","follow;","following,","for(","foreach($year","format!(\"april","format!(\"march","formula","found","found,","frederick","friday","full","fulli","func","function","funky,","further","gauss","gauss'","gauss,","gauss.","gausseast","gaussian","gem","gener","genius.\"","github)","give","given","glance,","go","go!","goe","good,","greater","greek","gregorian","grew,","grey","grumpili","gt","half","hand","happen","hard","heartili","held","here","here,","here;","hidden","higher","himself","histor","histori","history,","holiday","honest,","honestly,","horizont","host","hour","however,","hundr","hunter'","i'll","idea","if($servois)","if(($d","if(22","imag","images/graph","imagin","implement","import","includ","incorpor","increment","index","index,","indic","individually.","inform","information,","ingenu","initi","instead","instead,","int","int,","integ","integer.","interest","interestingly,","interfac","intermedi","intern","introduc","invent","investig","io","ioutputlin","ioutputline[]","is,","isiz","isize;","ismainmodule:","issu","it'","it.","itself,","itself.","jame","jan","januari","javascript/typescript","jean","jewish","johann","joseph","journal","julian","k","k)","k))","k,","keep","key","know","know!","known","lambert","languages,","larg","last","later","law","lead","leap","legend","length","less","let'","letter","licens","license.","license.md).","limit","line","liter","littl","liverpool","locat","longer","look","loop","loops,","lot","loves.","lunar","m","m)","m,","m.","made","magic,","main","main()","main(args:","make","mani","map","mapm_","march","march,","march.","march}&","mark","master","mathemat","mathjax.hub.queue([\"typeset\",mathjax.hub]);","mathématiqu","mayl","me,","mean","meaningful.","mediev","mentioned,","met","method","method'","meton","minut","missed.","mit","mod","mod(15","mod(19","mod(2","mod(4","mod(a,","mod(a:","mod(year,","mode","modern","modifi","modulo","modulu","monday","month","month)","month,","month.","months),","months:","moon","moon'","moon).","moon,","moon.","more","mother","move","much","multipl","n","n)","n,","name","namely:","names,","natur","near","nearest","necessari","need","neg","new","next","nil","nil))","nominally,","non","none","normal","notat","notation)","notation),","note,","note:","now","now,","nowadays,","number","number\"","number\":","number):","number,","number;","number\\teaster\"","number\\teaster\")","number\\teaster\");","number\\teaster\\n\")","number\\teaster\\n\");","number`teaster\"","numbers,","numbers.","object","observ","observation.","observed.","observed;","occur","off,","off.","offset","offset,","offsets,","old","on","one,","one.","ones.","onto","oper","operations,","option","orbit\"","orbits\"","origin","others,","others.","out","out;","out_size)","out_size,","outlin","outline,","output","over","p","p)","p+k","p,","partial","particular","particularli","parts:","paschal","past","paul","peopl","per","performance,","peter","phase","phase.","phases,","pictori","pink","place","place.","pleas","point","point,","point.","pope).","pope;","pose","posit","position,","positions,","possibl","power","precis","precise.","present","press,","presum","previou","print(","print(\"th","print(\"year\\tservoi","print(f\"{year}\\t{computus(year,","printf(\"th","printf(\"year\\tservoi","println!(","println!(\"year\\tservoi","println(\"$(a[i])\\t$(servois_numbers[i])\\t\\t$(easter_dates[i])\")","println(\"th","println(\"year\\tservoi","probabl","problem","problem,","programm","prolif","provid","public","publication,","publication.","pull","pure","put","put,","putstrln","q","q)","q))","q),","q)~\\%~30","q)~\\%~7.","q,","question","queues.","quot","range(2020,","re","read","real","realli","reason","reason,","reasons,","reckon","red","refer","regardless,","reinhold,","rel","relat","remark","rememb","remov","repli","replic","repres","represent","request","request.","requir","result","return","revolut","revolv","right.","roman","rotat","roughli","round","s","s\"${(21","s\"april","s\"march","said,","same","same,","saying,","schloss","scholars,","scientif","second","section,","sections,","see","seem","send","sens","sense!\"","separ","seri","servoi","servois\"","servois\",","servois'","servois)","servois)`t`t$(calcul","servois,","servois:","servois=false)","servois=false):","servois=true)","servois=true)}\\t\\t{computus(year)}\")","servois_numb","servoisnumb","servoisnumbers,","set","sever","shadows\"","sharealik","sheer","shift","shorter","show","shown","signifi","significantli","similar","simpli","simul","singl","size_t","slightli","small","snapshot","snow","snprintf(out,","so!","so,","softwar","solar","someth","sometim","somewhat","sort","space","special","split","spring","spring,","spring.","springer,","stacks,","standard","start","start,","state","static","std::cout","std::string","std::to_string((21","std::to_string(22","std::to_string(d","step","still","store","str((21","str(22","str(d","straightforward","straightforwardli","strformat","string","string(22","string(d","string(mod(21","string,","string;","student","students).","studi","subsequ","subtract","such","such,","suffic","sum","sun","sun,","sunday","support","sure,","surround","synchron","synchronized,","synod","system","systems,","systems.","t","t)","tab","tabl","table\"","table,","table:","take","tape","task","technic","techniques.","temp_","tempt","term","ters","text","text!","that'","then.","there,","thing","things:","think","this,","though","through","throughout","thus,","time","time,","time.","tittl","tmp1[9],","tmp2[9];","togeth","together,","told","track","transit","translat","tri","tricki","tricky.","trivial!","true","true)","true):14}","true,","truncat","truth","tuesday","tukey","tupl","twitch.","two","type","under","understand","understand,","understand.","undocu","unfortunately,","unit","univers","unlik","until","up","upon","us","used.","user","usize,","val","valu","values:","var","variabl","variable,","variables,","variou","video","void","wait","want","wave","way","way,","wednesday","week","week,","weekli","well","western","wish!","within","without","word","work","work,","worth","wrap","write","written","x","xadisten","y","year","year\"","year'","year,","year.","year:","years)","years,","years.","years.for_each(|year|","york","zipwith3","{","{22","{bool","{computus(year,","{d","{number}","{}\",","|","|i|","|y|","||","}","};","~a\""],"contents/gaussian_elimination/gaussian_elimination.html":["!","!=","!==","!singular","\",","\"\\n\")","\"\\t\"","\"__main__\":","\"current","\"echelon","\"fmt\"","\"game\"","\"gevis\"","\"math\"","\"origin","\"pivot\"","\"reduc","\"solut","#","#includ","$","&","&=","&[f64])","&eqns)","&f64","&matrix)","&mut","&self.data[row","&vec![2.0,","'eqns'","'rows'","(","(#560),","((1,","((i,","((r1,","()","(/)","(0);","(0..a.row","(3,","(a[(i,","(a[i","(a[i,","(a[i][col","(a[max_index,","(a[pivot","(a[pivot][col]","(a[pivot_i,","(a[r][col","(a[row,","(c,","(c1,","(col","(col+1):col","(compar","(curr_row),","(eqns[pivot][i]","(found","(fraction","(i","(i,","(i..a.rows).rev()","(instead","(int","(int,","(intercalate,","(k","(k,","(k..a.cols).rev()","(let","(no","(of","(on)","(r","(r,","(r1,","(r2,","(rn,","(row","(row+1):row","(row,","(similar","(size_t","(std::size_t","(target,","(tdma)","(the","(usize,","(v","(x,",")",");","*","*)a,","*a,","*x,","+","++row;","+=",".",".map(v","/","//","/=","0","0)","0,","0.","0..(a.col","0..min(a.cols,","0..row","0..self.col","0.0","0.0)","0.0,","0.0;","0:","0;","0x+0y+0z=1,","1","1)","1),","1)..a.col","1)..a.row","1).rev()","1):","1)]","1,","1.","1..a.row","1.0,","10","10.0],","10]","10]],","10},","10}};","11","11z","14","14.0}};","14}{11}","15","15.0},","18","1:(col","1:1","1:col","1:i","1:row","1;","1]","2","2)];","2,","2.","2.0,","2;","2x","2y","2z","3","3,","3.","3.0,","3.0},","3:","3\\\\","3d","3d,","3jane","3x","3y","3z","4","4))","4);","4,","4,],","4.","4.0","4.0,","4;","4\\\\","4y","4z","4}","4},","5","5,","5.","6","6,","6.0,","6;","6],","6},","7","8","9","::",":=",":]",":].copy()","=","==","===","=>",">",">=","[","[((r,","[(k,","[(m","[1,","[2,","[2.","[3,","[[((r2,","[];","[][]float64)","[][]float64{","[]float64","[]float64)","[ratio","[show","\\;,\\;","\\\\","\\begin{align}","\\begin{array}{ccccc}","\\begin{array}{ccc|c}","\\begin{array}{ccc}","\\begin{array}{cc}","\\begin{array}{c}","\\end{align}","\\end{array}","\\frac{","\\frac{18}{11}","\\frac{1}{3}","\\frac{1}{3}.","\\frac{1}{3}\\tim","\\left[","\\mathbf{","\\mathbf{0}","\\mathbf{10}","\\mathbf{1}","\\mathbf{2}","\\mathbf{3}","\\mathbf{4}","\\mathbf{6}","\\mathbf{\\frac{10}{3}}","\\mathbf{\\frac{2}{3}}","\\mathcal{o}(n^3).","\\quad","\\right]","\\rightarrow","\\sim","\\text{current_row}","\\text{pivot_row},","\\text{pivot}_{\\text{col}})","_),","_,","__name__","`on`","a(\\text{curr_row},","a(\\text{pivot}_{\\text{row}},","a)","a);","a,","a.col","a.length","a.length;","a.rows)","a.rows];","a.shape[0]):","a.shape[1]","a.shape[1])):","a.shape[1]:","a:","a[(a.row","a[(i,","a[(k,","a[(row,","a[0].length","a[0].length;","a[3][4]","a[col]","a[col];","a[i","a[i,","a[i,col]","a[i,col]*a[row,j]","a[i,col]/a[row,col]","a[i,j]","a[i][col]","a[i][i];","a[i][j]","a[i][j];","a[max_i,","a[max_index,","a[p]","a[p],","a[p][c]","a[pivot]","a[pivot];","a[pivot_i,","a[pivot_row,","a[r+1:]","a[r,","a[r:]","a[r]","a[r],","a[r][c]","a[r][j]","a[r][r]","a[row","a[row,","a[row,col]","a[row,i]","a[row,j]*fract","a[row][col];","a[row][i]","a[row][j];","a[rowa]","a[rowa];","a[rowb]","a[rowb];","ab","abov","above,","above.","above;","abysmal!","accum","actual","add","addition,","afterwards,","again,","algorithm","algorithm.","allow","along","alreadi","alway","ambigu","an","analog","analyt","anim","anoth","ans(rows);","ans;","answer","anything,","apply.","appropri","are:\")","argmax(abs.(a[row:end,col]))","args)","around","array","arrays.stream(a).foreach(x","assum","attribut","author","axes.","b","b:","back","back_substitution(&a);","back_substitution(a)","back_substitution(a):","back_substitution(a:","back_substitution(a::array{float64,2})","back_substitution(const","backsubs(const","backsubs(equations);","backsubstitut","backsubstitution(a","backsubstitution(a)","backsubstitution(double[][]","bases.","basic","basically,","becom","befor","before).","before,","before.","below","beneath","best.","better","beyond","boil","bottom","bound","break","browser","c","c)","c))","c)),","c))]","c),","c++","c,","c1)","c1),","call","can:","case","case,","case.","cell","cell)","chapter","chapter:","check","class","clear","clear:","clearli","cn","cn)","cn))","code","code,","code:","coeffici","col","col):","col);","col,","col]","col]))","col];","cols)","cols);","cols,","cols:","cols]","column","column,","column.","columns.","common","completeness.","complex","complic","comput","concat","conclus","conditions:","configuration:","confus","consid","consist","console.log(\"th","const","constrained,","context","continu","continue,","continue;","continuing,","contradiction.","convert","coordin","correct","correspond","course)","cover","creat","creativ","current","data.array","data.funct","data.list","data.ratio","data.to_vec(),","data:","deal","deduc","def","definit","demonstr","describ","desir","determin","diagon","differ","dimens","dimension","directli","divid","do","doesn't","done","doubl","double[]","double[][]","double[rows];","down","down.","downwards.","dtype=float)","due","dure","each","easi","easier","echelon","echelon)","either.","elem","element","element.","elimin","elimination\")","elimination,","elimination.","elimination:","elimination:\")","elimination:\");","elimination:\\n\");","encount","end","end,","enlighten","enough","ensur","entir","entri","eq","eqns.size(),","eqns.size();","eqns[0].size();","eqns[i]);","equat","equation.","equations,","equations.","equations;","equations?","equations{","essenti","evalu","even","everyth","exactli","exampl","example,","exist","exists,","exists.","exit","explan","f","f64","f64;","fabs(a[pivot","fabs(eqns[pivot][i]))","fact","fals","far","fashion.","faster","fastest","favorit","feel","find","first","first,","first.","float","fmt.print(\"[\")","fmt.printf(\"%9.4f","fmt.println(\"]\")","fmt.println(\"gauss","fmt.println(\"gaussian","fmt.println(\"origin","fmt.println(\"solut","fmt.println(\"thi","fmt.println()","fn","follow","following:","form","form\"","form,","form.","form:","found","frac","fraction","fraction,","fraction;","framework,","free","front","func","function","further","fuss!","game","game).","gauss","gauss_jordan(&mut","gauss_jordan(a:","gauss_jordan(doubl","gauss_jordan_elimination!(a)","gauss_jordan_elimination!(a::array{float64,2})","gauss_jordan_elimination(a)","gauss_jordan_elimination(a):","gaussian","gaussian_elimination!(a)","gaussian_elimination!(a::array{float64,2})","gaussian_elimination(&mut","gaussian_elimination((doubl","gaussian_elimination(a)","gaussian_elimination(a):","gaussian_elimination(a:","gaussian_elimination(doubl","gaussianelimin","gaussianelimination(a","gaussianelimination(a)","gaussianelimination(a);","gaussianelimination(double[][]","gaussianelimination(std::vector","gaussjordan","gaussjordan(a","gaussjordan(a)","gaussjordan(a);","gaussjordan(double[][]","gaussjordan(std::vector","gener","general,","give","glanc","go","goal","goe","good!","graphic","hand","happen","help","here","here'","here,","here?","higher","highest","hope","how?","however,","i)","i)]","i)];","i,","i;","i]","i];","idea","ideally,","ident","images/graph","imagin","immedi","impl","implement","implementation,","import","includ","inconsistent.","independ","index","index(&self,","index_mut(&mut","indexmut","indexmut};","inher","initi","instead","instead.","int","int)","int]","intend","intercal","intercept","interest","intern","interpret","interpretation!","intersect","introduc","invers","involv","io","is,","it'","it.","iter","itself.","j","j)","j),","j)]","j)];","j;","j]","j];","jame","java.util.arrays;","jess","jordan","jordan\")","jordan:\")","jordan:\");","k","k)]","k)].abs();","k)];","k;","keep","know","known","language.","larg","last","lead","leav","left","len(a)","len(a[0])","let'","licens","license.","license.md).","line","linearli","listarray","literature,","locat","look","loop","lower","m","m'","made","main","main()","main():","main(string[]","make","make([]float64,","mani","manipul","map","mat","math","math.abs(a[pivot][col]))","math.abs(row[c]);","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matric","matrix","matrix)","matrix,","matrix.","matrix:\"","matrix:\")","matrix::new(","matrix;","max_i","max_index","max_row","max_valu","maximum","maximumbi","maximumby)","maxval","mean","mess","method","mit","modif","modifi","moment","more","motiv","move","moves.","much","multipl","multipli","mut","name:","necessarili","necessary!","need","nevertheless,","new","new(rows:","next","next...","nice,","no.","non","none","nonzero","notat","note,","note:","now,","np","np.argmax(abs(a[pivot_row:,","np.array([[2,","np.zeros(a.shape[0]).t","number","numer","numpi","o(n)!","o(n^3),","obviou","obvious","on","opt","optim","otherwis","out","output","over","p","p,","packag","parallel","particular","particularli","parts.","perform","pivot","pivot)","pivot);","pivot,","pivot.","pivot_col","pivot_col]","pivot_col]))","pivot_i","pivot_i]","pivot_row","pivots.","plane","plane.","planes.","play","plenti","plot","plug","point","point,","possibl","precis","previou","print(\"back","print(\"gauss","print(\"gaussian","print(\"original\")","print(a,","print(back_substitution(a),","printf(\"gaussian","printf(\"th","println!(\"solution:","println(\"matrix","println(a)","println(soln)","printm","printmatrix(a","printmatrix(a)","printmatrix(const","printmatrixrow(row","printmatrixrow(row)","printmatrixrow(x)","printv","procedur","process","process,","program","properti","provid","pub","public","pull","put","putstrln","question:","quickli","r","r)","r++","r,","r1","r2","r;","random","rang","range(a.shape[0]","range(a.shape[0]):","range(min(a.shape[0],","range(pivot_i","range(pivot_row","range(row):","rank","ratio","re","reach","read","readers,","reason,","recreat","reduc","refer","remain","repeat","represent","request","resembl","reshap","respect","rest","rest.","return","right","right)","right,","rn)","roll","rounding)","row","row\"","row'","row++;","row,","row.","row:","row;","row[c]","row[j]","rowa,","rowb)","rows)","rows,","rows.","rows:","rule","s","s)","said,","same","satisfi","scale","scan","schloss","second","section","see","seem","seemingli","self,","self.col","self.data.swap(a","self.data[row","sens","separ","set","sever","sharealik","show","shown","side","sign","similar","similarly,","simpli","simplifi","simply:","singl","singular","singular!\")","singular\");","singular,","singular.\")","singular.\");","singular.\\n\");","size(a,1)","size(a,2)","size_t","skip","small","snd)","so:","sol","sol;","sol[col]","sol[i]","sol[j]","sol[pivot_i]","soln","soln);","soln[a.row","soln[i]","soln[j]","soln[j]*a[i,j]","solut","solution,","solution.","solution;","solution?","solution[i]","solution[j]","solutions.","solv","solvabl","solve,","solver","sometim","specif","split","start","start,","static","std::cmp::min;","std::cout","std::ops::{index,","std::size_t","std::swap(eqns[pivot],","std::vector","step","stop","straightforward","straightforward,","straightforward:","strategi","string","struct","submit","subrow","subsequ","subsitution\")","substitut","substitute,","substitution\"","substitution,","substitution.","substitution:","subtract","such","suggest","sum","sum'","sum)","support","sure","swap","swap_rows(&mut","swap_rows(a,","swap_rows(doubl","swaprow","swaprow(a,","swaprow(double[][]","switch","system","system.","system.err.println(\"th","system.out.println(\"\\ngauss","system.out.println(\"\\nsolutions:\");","system.out.println(\"gaussian","system.out.println(arrays.tostring(backsubstitution(a)));","system.out.println(arrays.tostring(x)));","systems,","systems.","t","t;","tag.","tediou","temp","temp;","temp_vector","term","text","that'","that,","that.","then,","there,","thing","think","this,","this:","thoma","through","thu","time,","time.","togeth","together,","top","transform","translat","treat!","tri","triangular","triangular.","tridiagon","trivial","true","two","two.","type","ultimately,","under","underneath","uniqu","unknowns,","unlin","until","up","upper","upward","us","usize)","usize))","usize,","valu","value,","value.","var","variabl","variable,","variable.","vec","vec![0.0;","vec,","vector","veri","via","video","visual","visualization,","void","want","way","way.","well,","well.","what'","what,","within","without","wobbl","words,","work","wouldn't","write","written","x","x,","x[c]","x[i]","x[j]","x[r]","y","y)","y,","y.","z","z)","z,","z.","zero","zero.","zeros(rows)","{","{1,","{2,","{2.0,","{3,","{5.0,","{:?}\",","{{3.0,","|","}","},","};","—"],"contents/quantum_systems/quantum_systems.html":["\"\"\"calcul","\"ftgaussian\"","\"the","\"wait.","#","$","&=","&opr)","&par,","(#560),","((/","(*","(\\psi_0);","(^","(found","(heat)","(inner","(k","(k_i)","(kineticop","(more","(or","(size_t","(wfc","(with","(x_i)","(|\\psi(x)|^2)","*","**","+","+=",".",".\"\"\"",".*",".+","0","0.5","0.5*wfc_c.*ifft((par.k.^2)","0;","1","1,","1.","1:length(energy_k)","1d","1}\\left(","2","2)","2))","2\\pi","4.0","::","=",">","\\\\","\\begin{align}","\\end{align}","\\frac{1}{2}\\omega","\\frac{2","\\frac{\\hbar^2}{2m}","\\frac{\\hbar}{2}","\\frac{\\parti","\\frac{\\partial\\phi(\\mathbf{r},t)}{\\parti","\\frac{h}{\\lambda}","\\frac{p^2}{2m}","\\geq","\\hat","\\hbar","\\infty}^{+\\infty}|\\psi(\\mathbf{r},t)|^2","\\int_{","\\lambda","\\lambda}","\\langl","\\left[","\\lvert","\\mathbf{r}","\\mathcal{f}\\left(","\\mathcal{f}^{","\\mu","\\mu)^2}.","\\nabla","\\nabla^2","\\omega","\\omega.","\\phi","\\phi(\\mathbf{r},t)","\\phi,","\\pi","\\psi","\\psi(\\mathbf{r},t)","\\psi(\\mathbf{r},t)^{*}\\psi(\\mathbf{r},t)","\\psi(\\mathbf{r},t)}{\\parti","\\psi(x)","\\psi(x).","\\psi(x)\\rangl","\\psi_i","\\rangl","\\rangle,","\\right)\\right)","\\right]","\\rvert","\\sigma","\\sigma_p","\\sigma_q","\\sigma_x","\\sqrt{\\frac{1}{n}\\sum_{i=1}^{n}(q_i","\\sum_i","\\textbf{k}","\\textbf{x},","abov","above.","absolut","accur","act","actual","add","advantage.","again,","again:","ahead","algorithm","algorithms.","all.","allow","alreadi","alway","always,","analog","analogu","angular","anim","anoth","answer,","area","areas.","argument","ascertain","associ","attribut","b","b.","back.","basic","basically,","be.","becom","befor","before.","behavior","behavior.","better","between","bit","blanketli","block","both","boundari","bra","braket","broader","brogli","build","c_i","c_i'","calcul","calculate_energy(par,","calculate_energy(par:","calculate_energy(param","calculate_energy(struct","calculateenergi","calculation:","call","can!","carlo,","carlo.","case","case,","cases!","cases.","certain","chang","change.","chapter","chapter.","chapter:","character","check","classic","cleaner","clear","clear,","clear:","clearli","code","collaps","column","come","common","complete.","complex","component,","comput","computation.","computations,","computer,","computers?","computers?\"","confin","conj(wfc_r)","conjug","conjugate.","consid","constant","constitu","contact","convers","convinc","cornerston","cours","course,","cover","creat","creativ","current","d","d\\mathbf{r}","de","deal","deeper","def","defin","definit","definitions:","densiti","densities.","density:","depend","depth","depth,","deriv","describ","descript","descriptions,","deserv","desired.","detail:","deviation,","devot","dft","diagonalization,","differ","difficult","diffus","discuss","distinct","distribut","distribution,","dive","dmrg,","do!","doesn't","don't","done","dot","doubl","dx","e","each","easi","easier","easiest","easili","effect","eigenst","elem","end","end,","energi","energy.","energy_fin","energy_final*par.dx","energy_k","energy_r","energy_r).r","energy_r[i])","enough","equat","equation,","equation:","essenti","even","eventu","everywher","exact","exactli","exampl","example,","exclus","exist","expect,","experi","experiment","explain:","explan","explicit","express","extra","f","fact","fact,","false);","features;","feel","fft(wfc_k,","fft(wfc_r)","find","find;","float:","focu","focus","follow","form","formal","formally):","formula:","formulations.","found","fourier","free","frequenc","full","function","function,","fundament","further","futur","f}{\\partial","gaussian","gener","general.","get","github","given","go","good","graphic","great","greatli","grid,","ground","grover'","h","hamiltonian","hamiltonian.","hamiltonians.","hand","hand,","hard","hardwar","hardware...","hardware;","harmon","have","heard,","heart","heisenberg","here","here'","here,","here.","here:","here;","hermitian","higher","however,","huge","human","h}{2","i,","i\\hbar","idea","idea.","idft","images/graph","imagin","imaginari","immedi","import","in,","includ","incred","indic","industry,","inform","inher","initi","inner","innov","instead","instead,","integr","interest","intern","interpret","interpretation,","intuit","intuitive,","invent","invers","involv","is!","isn't","issu","it!","it'","it,","itself,","jame","k","ket","kinetic","kineticop","know","know!","knowledg","knowledge;","known","laboratories,","lack","lagrangian","landscap","laplacian,","larg","larger","lead","left","less","let'","level.","licens","license.","license.md).","liftarray","literatur","locat","location,","location.","long","look","lot","lower","lowest","machines.","make","mani","map","mathemat","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matrix","me,","mean","meant","measur","mechan","mechanics!","mechanics,","mechanics.","memcpy(wfc_k,","memcpy(wfc_r,","mentioned,","method","method,","method.","methods,","methods.","miss","mit","modern","modifi","momentum","momentum,","momentum.","mont","more","more.","move","much","multipli","n","need","new","next","none","notat","notation,","notation.","note:","now","now,","np.conj(wfc_r)","np.fft.fft(wfc_r)","np.fft.ifft((par.k","number","numer","object","object,","observ","obviou","offer","on","onc","onto","op","oper","operations.","operator.","operators)","operators,","operators.","opposit","opr)","opr.size,","opr.v","opr.wfc","opr.wfc,","opr:","ops))","ourselves.","out","outer","over","p","p(\\mathbf{r},","p.","par,","par.dx","param","param)","param,","paramet","parameter","part","part,","particl","particle'","particle.","particles.","particular","particular,","particularli","parts;","perform","phenomenon.","physic","physically.","physics.","pictur","planck'","pleas","point","point,","posit","position,","possibl","potential","potential,","power","precis","pretti","principl","principle,","probability,","probabl","problem","proce","product","product)","product.","progress","properties.","provid","pull","purpos","push","put,","q","q_i","quantiti","quantum","qubit","qubits.","question","r","radic","re","readabl","real","real(energy_k[i]","real,","real.","realli","realpart","reason","reason.","reciproc","relat","replac","repres","request","research","restrict","results.","return","right","row","said,","same","sampled,","says:","scale","schloss","schrödinger","section","section,","section.","section;","see","sens","set","sever","sharealik","shor'","shown","side","side.","simpl","simpli","simplicity,","simplifi","simul","simulators.","singl","situation.","sizeof(wfc_k));","sizeof(wfc_r));","slightli","smaller","solv","someth","sometim","somewher","soon","sort","space","space,","space.","spatial","specif","specifically,","spectral","split","squar","stand","standard","start","state","state,","state.","statement","statist","steps)","sticky.","still","strengthen","struct","studi","sum","sum(energy_k","supercomput","sure","system","system'","system,","system.","systems,","systems.","t","t)","take","talk","taught","techniqu","temperature)","term","text","textbook","that!","that,","theori","theory.","thing","thinking,","thinner","this,","this:","those","though","thought","thought.","through","thu","time","time.","times,","total","transform","transform!","transform;","transformation,","transforms,","trap","trap,","tri","tricki","trivial","true:","truth","two","type","t}","t}.","ultim","ultimately,","uncertainti","under","understand","unfortunately,","unit","univers","universe.","up","updat","us","usual","v","v(\\mathbf{r},t)","valu","vector","vector.","vector_complex","want","wave","wavefunct","wavefunction,","wavefunction.","wavefunctions,","wavefunctions.","wavelength.","wavevector","wavey","way","way,","way.","we'll","weird.","well,","wfc","wfc_c","wfc_c(opr.size);","wfc_c.*opr.v","wfc_c[opr.size];","wfc_k","wfc_k(opr.wfc);","wfc_k)","wfc_k[opr.size];","wfc_r","wfc_r(opr.wfc);","wfc_r[opr.size];","wfcconj","wheel","without","words,","work","world","write:","written","x.","x^2","x}","{","|\\psi(\\mathbf{r},t)|^2"],"contents/affine_transformations/affine_transformations.html":["\"a11","\"a12","\"a13","\"a21","\"a22","\"a23","\"a31","\"a32","\"a33","\"coincidence\"","\"cosines\"","\"how","\"pseudo","\"rotat","\"scale\"","\"semi","\"shear\"","\"sines\"","\"stuff\"","&","&=","(a","(and","(at","(found","(note:","(x,y),","(yet","+","0","0!","0).","0,","0.","1","1)","1,","1.","1\\time","2","2,1],","2\\pi,","3","4","4.0","=","[","[0,0,1]","[0,0],","[1,2]","\\\\","\\begin{align}","\\begin{bmatrix}","\\cdot","\\cos(0)","\\cos(\\theta)","\\ell","\\ell.","\\end{align}","\\end{align},","\\end{array}\\right]","\\end{bmatrix}","\\end{bmatrix},\\\\","\\end{bmatrix}.","\\frac{\\vec{p_1","\\left[\\begin{array}{@{}ccc|c@{}}","\\left[\\begin{array}{@{}cc|c@{}}","\\mathbf{a}","\\mathbf{a}\\mathbf{v}_0","\\mathbf{a}\\mathbf{v}_0.","\\mathbf{a}_{\\text{rot}}","\\mathbf{v_0}","\\mathbf{v}","\\mathbf{v},","\\mathbf{v}_0","\\pi/2),","\\pi/2,","\\pi/2.","\\pm","\\rightarrow","\\sin(0)","\\sin(\\theta)","\\textbf{v}","\\theta","\\theta.","\\time","about,","about:","abov","above,","abruptli","accordingly.","act","actual","addit","affin","affine;","after.","again,","again...","ahead","algorithms.","all,","allow","along","alreadi","alway","always)","amount","angl","anim","animation:","anoth","answer","anyth","append","appli","applic","applications.","around","array,","array?","as,","assign","attribut","augment","away","back","balanc","barycent","barycenter.","basic","be:","befor","before,","before;","behaviors:","believ","between","beyond","bit","both","bottom","browser","button:","care","case,","case.","center","center),","certain","chang","chapter","circl","class","clearli","click","code","collect","collinear","combin","common","complet","complic","compon","component,","component.","components.","comput","computation:","concav","confus","confusing.","consid","continu","convex","correspond","cosin","course,","creat","creativ","cube","cube!","cube\"","cube,","cube:","decid","deeper","deepli","definit","definitions;","delv","describ","descript","dial","differ","dimens","dimension","direct","direction,","direction.","directions,","discuss","discuss.","distinct","dive","do","down","draw","dwell","each","easiest","effect,","effect.","element","emb","encompass","encourag","end","entir","equal","essenti","essentially,","even","everyon","exactly.","exampl","example.","example:","expected,","explan","extend","factor","feel","figur","finally,","find","first","flip","flip.","focus","follow","following:","formal","formalism.","found","fulli","fun","function","further","go","graphics.","grow","guarante","guess","hack:","hacki","happen","help","here","here,","hesit","honest,","hope","hopefulli","however,","hyper","ident","images/graph","imagin","implement","import","individu","initi","initially,","input","input,","instead,","interact","interest","intern","intro","intuit","is,","it).","it,","jame","keep","know","known","larg","larger","last","later","learn","leav","left.","length","less","licens","license.","license.md).","limit","line","linear","linear)","linear,","lines.","littl","locat","lot","loves:","magic","magnitud","make","manipul","mass","mathemat","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matric","matrices:","matrix","matrix,","matrix.","matter","me,","mean","meant","meanwhile,","mit","mix","modifi","more","more.","move","movements.","multipl","multipli","n","n+1","n\\time","namely,","necessarili","necessary.","need","need,","neg","never","new","next","nice","non","none","notat","note","now","now,","numer","object","ok,","on","on:","oper","opposit","origin","origin.","oscil","out","output","output,","overall,","p_1","p_2,","p_2}}{\\vec{p_3","p_3","p_4,","p_4}}","paint","parallel","parameter","particular","particularli","perform","perspective;","pictur","plane","plane.","plate.","play","point","point,","points,","points.","position,","position.","possibl","potenti","power","powerful,","practice.","practice:","preserv","previou","probabl","properti","provid","put","question","quick","quiet","ratio","ready,","realli","reason","reason,","regularli","regularly,","rel","relat","remain","represent","respectively.","result","right","right,","right?","rigor","rotat","rotate\"","rotation\"","rotation,","rotation.","rotation:","row","row?","same","same,","scale","scale?\"","scaling,","schloss","second","see","seem","seen","segments,","segments.","sens","set","sever","shape","shape.","sharealik","shear","shearing,","show","shown","side","similar","similarly,","simpli","sine","slice","slope","slowli","small","so,","someon","somewhat","space","space.","special","specifi","squar","square\"","square,","square.","stage,","start","start,","state","step","still","subsequ","such","suitabl","support","sure","surprising.","system,","tag.","take","talk","technic","terribl","text","that:","there,","thin)","think","this,","those","though","three","through","time,","time.","togeth","together.","took","top","topic,","touch","toward","transform","transformation,","transformation.","transformations,","transformations:","translat","translation,","translation.","treat","tug","turn","two","type","typic","under","underneath.","understand","unsatisfying!","us","varieti","variou","vector","vector,","vector.","vectors,","vectors.","vertic","video","video,","view","visible.","visual","visualizations,","want","watch","way","well,","well.","well...","whatev","whole","wide","within","work","worked.","works.","worth","wrap","written","x","y","y,","z","z.","z=1."],"contents/approximate_counting/approximate_counting.html":["\"!\"","\"a","\"approxim","\"count","\"delta","\"failed\"","\"finger","\"histogram","\"histograms\"","\"passed\"","#","#includ","&","&=","((1_f64","((avg","(0.4%).","(2^2","(2^{10}).","(4000)","(\\delta","(a","(a/(a+1))^j","(but","(chosen","(dot","(double)rand()","(drand()","(especi","(fingers),","(for","(found","(in","(items)","(left)","(left),","(like","(math.abs((avg","(math.pow(1","(math.random()","(maximum","(middle),","(n(v","(n)","(note:","(or","(pow((1","(pow(1","(sometim","(standard","(though","(unless","(v=2),","(variance)","(when","(which","(with","(without","*","*/","+",".average()",".getasdouble();",".limit(ntrials)",".sum::()",".take(n_trials)","/","/*","//","0","0.","0..n_item","0.025%","0.025\\%","0.037","0.053","0.25.","0.4%","0.4%).","0.42","0.42%","0.58),","00000000","00000001","00000010","00000100","00010000","01000000","0_f64;","0}","1","1)","1);","1)}","1)}{2a}.","1+1/a","1,","1,000,000","1,000,000\"","1,000,000)","1,000,000.","1.","1.0)(rng());","1.1\\time","1.71","1.85","1.sanderson,","1/(n(v","1/(n(v+1,","1/4000","1/a)**v","10","10,","10,000","10,000\"","10,000,","10,000.","100","1000","10000000","1023","1023,","1023?","10:","10^{110}.","10^{16}","10^{16},","10^{19}","10^{38}","10^{76}","10^{76}.","1110010101,","11111111","12,000,","128","130,000","130,000,","15","16","17,000).","1977","1978","1978.3.flajolet,","1985.4.bhayani,","1;","1=","1\\right).","1_f64","1_f64)","1_f64,","2","2).","2,","2.","20%","20.0","2015.2.morris,","2019.","2020.5.gundersen,","25","25%","250","255","255),","255,","255.","256","2^0","2^1","2^2","2^3","2^4","2^5","2^6","2^7","2^8","2^9","2^n","2^v","2^{10}","2^{255}","3","3.","3.36","3.40","3.84","35","35\"","3rd","3}","4","4,","4,000","4,000.","4.0","4000","4000*v.","4000,","4000.","4000:","4000th","483,200.0","499,813.2","4th","5.56","5.79","500,000","500,000\"","500,000,","511!","511,","512","512.","58%","6,","64","65535","8","8,000","8,000.0","8...","9,958.0","917","917:","961,600.0","999,466.0","=",">","[0,","[1,n]","[1]:","[2],","[2].","[3].","[4]","[5].","\\\\","\\approx","\\begin{align}","\\cdot","\\delta","\\delta,","\\delta_j","\\end{align}","\\frac{1}{(2^3","\\frac{1}{1.72","\\frac{1}{7","\\frac{1}{n_3","\\frac{1}{n_{v+1}","\\frac{\\log(1+n/a)}{\\log(1+1/a)}.","\\frac{\\log_e(n+1)}{\\log_e(2)}","\\frac{n(n","\\frac{n}{4000}","\\in","\\leq","\\log_2(1)","\\log_2(1+n),","\\log_e(1+e^v).","\\log_e(1+n).","\\neq","\\qquad","\\sigma","\\sigma(n,a)^2","\\sim","\\sum_{n=0}^9","\\text{if","\\time","_","a)","a))","a)))","a));","a),","a).powf(v)","a):","a);","a*((1","a*((1+1/a)^v","a,","a:","a=30","a=30,","a\\left(\\left(1+\\frac{1}{a}\\right)^v","abov","above:","abstract","abstractions.","access","account.","accur","acm","act","actions:","actual","ad","addit","addition,","advantage.","again,","algorithm","algorithm,","algorithm.","algorithm:","algorithm?","allow","along","also,","alway","analogy.","analysis,","anomaly:","anoth","answer","anyon","approach","appropri","approxim","approximate_count","approximatecount","approximatecount(nitems,","approximation).","arbitrari","arbitrarili","argument","around","ask","associ","attribut","auto","averag","avg","away","axi","back","bad,","bar.","base","base,","bases,","basic","be","be.","becom","befor","begin","bell","below:","better","better!","between","beyond","bibliographi","big","binari","bit","bits)","bits).","bits,","bits?","bitstr","bitstring.","black","blog","both","brought","bunch","by,","calcul","case","case,","cases,","catch","certain","certainli","chanc","chang","chapter","choos","chose","class","clear,","clearli","close","close?","closed,","closest","code","code,","come","common","comput","concret","configuration,","consequences:","consid","const","constant","constrictions.","convert","correct","correct,","correct.","correspond","count","count,","count.","counted,","counted.","counter","counter!","counter,","counter.","counting!","counting\"","counting,","counting:","counts,","counts.","counts:","cover","creat","creativ","deal","decid","decreas","def","definit","degre","delta","depend","describ","descript","detail","determin","determinist","deviation,","deviations.","differ","distanc","distinct","distribut","distribution,","distributions,","dive","do","don't","done","doubl","drand()","drawback","e","e)","e),","e,","e.","e^v","e^{255}","each","earli","effect","encount","end","engin","enough","ensur","equal","error","error,","error.","essenti","essentially,","estim","even","event","events,","events.","evid","exactli","exactly,","exampl","example,","excit","exp","expect","experi","experiment,","experiment.","experiment?","experiments,","experiments.","experiments:","explan","expon","exponentially.","express","f64","f64)","f64,","f64;","fact","fact,","factorial.)","feel","few","figur","final","finally,","find","finger","finger.","fingers?","first","fix","flajolet","flip","float","fn","follow","for)),","formula","found","fulli","function","further,","future.","g,","game","gaussian","gaussian,","gener","give","given","go","gone","good","good,","gotta","gray,","great!","guess","hairs.","half","hand","hand,","hand.","hands,","happen","hard","have,","have.","here","here,","here:","high","high!","high.","higher","higher)","higher,","highest","highlight","histogram","hold","honest,","hop","hope","however,","huge","ideal","imag","image,","images/graph","imagin","impact","implement","import","imposs","impressive!","in:","increas","increment","increment(doubl","increment(int","increment(v,","increment(v:","indic","individu","inform","initi","instead","integ","interest","intern","introduc","invent","issu","it!","it'","item","item,","item.","items,","items.","items;","items?","itself.","j","jame","java.lang.math;","java.util.stream.doublestream;","job","keep","kinda","know","known","lab","larg","largest","later","later,","learn","leav","left","less","let'","licens","license.","license.md).","lift","line","line),","line.","lines.","littl","logarithm","logarithm\"","logarithm):","logarithm,","logarithm.","logscale,","long","longer","look","loop","lot","low","lower","machin","main","make","mani","match","mathemat","mathjax.hub.queue([\"typeset\",mathjax.hub]);","maximum","mean","meaning","measur","mention","mentioned,","method","method!","method,","method.","mind","minimum","miss","mit","moder","modifi","more","morri","morris'","move","much","much,","multipl","mut","n","n(doubl","n(v,","n(v,a),","n(v:","n:","n=1","n=1.","n_2}","n_item","n_items:","n_items_float","n_items_float)","n_trial","n_trials:","n_v","n_v.","n_v:","n_{v+1}","n_{v}}","name","necessari","need","new","next","next.","nice","nitems)","non","none","not,","not.","note","note,","note:","notic","now","now,","number","number.","numbers,","numbers.","ny,","object","object,","obviou","obvious","occur","occurred.","occurs.","odd","on","on.","onlin","order","origin","out","out,","outputs.","overall,","p,","paper","paper,","paper.","paramet","parameters,","paus","peak","peopl","percent","perfect","perform","philipp","plot","plot,","point","possibl","possible,","potenti","power","practice,","pre","precis","precise)","precision.","predecessor","prefer","previou","primari","probability,","probabl","problem","problem,","problem:","process","proof","provid","pseudo","public","put,","put:","quantifi","question","question,","r","r,","rand()","rand::random::()","rand_max;","randengine(std::random_device{}());","randengine;","random","random()","random),","rang","read","real","realli","reason","reason,","regist","register,","register.","registers,","rel","rememb","reminder,","report","repres","resolut","resolution\"","resolution)","resolution,","resolv","resourc","result,","results.","return","right","right,","right.","right?","rigor","rng()","roughli","run","run,","said,","same","save","say,","scale","scale,","scale.","scales,","scheme","schloss","second","section,","section.","see","seed","seem","select","sens","sense,","separ","set","settl","sever","shade","sharealik","sheep","sheep,","sheep.","show","shown","signific","significantli","similar","similarly,","simpl","simpli","simul","situation?","size","skew","slightli","small","smaller","so)","solut","solution:","solv","some(approximate_count(n_items,","someon","someth","somewhat","space","specif","specifically:","split","springer,","stage,","standard","start","static","statistics.","std::default_random_engin","std::default_random_engine&","std::iter::from_fn(||","std::uniform_real_distribution(0.0,","step","still","stop","storage.","store","straight","straightforward","strategi","strategy:","stream","studi","such","system.","tabl","tackl","tak","take","talk","tell","term","terminolog","test","test_approximate_count(n_trials:","text","that'","that,","there'","there,","therebi","therefore,","thing","think","this,","this?","those","though","three","threshold:","thu","thumb","tick","time","time,","time.","times.","togeth","tool","top","total","track","traditionally,","trend","tri","trial","trials\"","trigger","trit","true","tune","twiddl","two","type","unaccept","under","understand","undoubtedli","unfortunately,","unpack","until","up","up,","up.","updat","updated.","upward","us","usa,","usize,","v","v\"","v(n)","v)","v,","v.","v:","v=1.","v=255.","valu","value,","value:","values.","values:","vari","variabl","varieti","veri","video","walk","want","way","way,","ways,","we'll","weight","well),","well,","what'","whether","win","wonder","work","world,","worthwhil","written","x.","y","y=x","y=x.","yes.","york,","yourself","{","}"],"contents/metropolis/metropolis.html":["\"\\n\".join(str(x)","\"__main__\":","\"adaptive\"","\"anim","\"barrier.\"","\"bins\"","\"multipl","\"plot","\"trained\"","\"w\")","\"walker\",","#","&","'''","'''iter","'''perform","'''random","'states'.","(","(#560),","(500,","(\\mathbf{x})","(a","(f(x_proposed)","(found","(n),","(np.sqrt(np.pi)","(there","(x","(x^2","(x_t","*","+","+1","+1,","+3].","+y^2",",",",x_n,",".","...","...)}.","/","/=","0","0)","0.2(x+1)^2}","0.2,","0.25","0:","1","1)","1).","1,","1,1)","1,1).","1.","1.,","1.]).reshape(3,","1.metropolis,nichola","10","10,","10^{41}","10^{50}","10d","10e^{","10}^{10}","1953.2.wikipedia:","1970.6.wikipedia:","1\\right).","1d","2","2(x","2.]).reshape(3,","2001.10.wikipedia:","2011.9.gareth","2021.","2021.3.wikipedia:","2021.4.wikipedia:","2021.5.hastings,","2021.7.wikipedia:","2021.8.rosenthal,","3","3,","3,3)","3.,","3e^{","3n","4(x+4)^2}","4.,","4.0","5)^2}.","5.]).reshape(3,","50","50_000","50_000))","50_000):","5_000,","=","==","[","[10].","[1]","[2]","[3]","[4]","[5]","[6],","[7],","[8]","[9].","\\dot","\\exp\\left[","\\exp\\left[\\frac{","\\exp\\left[{\\displaystyle\\frac{","\\frac{1}{\\sqrt{\\pi}}","\\frac{\\displaystyl","\\frac{e^{","\\frac{f(\\mathbf{x})}{\\displaystyle\\int_d","\\frac{f(x')}{f(x_t)}\\right).","\\frac{f(x)}{\\int_{","\\gt","\\infty}^{\\infty}","\\int_d","\\int_{x_1}","\\int_{x_{10}}","\\left(\\frac{f(x')}{f(x_t)},","\\leq","\\mathbf{x}","\\mathbf{x},","\\mathbf{x}.","\\min","\\min\\left(1,","\\right]","\\right].","\\right]}","\\rightarrow","_","__name__","a.","a=1","a])","abov","above,","accept","accur","achiev","act","actual","adapt","add","adjust","advanc","affect","ag","al.,","algorithm","algorithm!","algorithm,","algorithm.","algorithms,","algorithms.","allow","alreadi","although","altogeth","alway","always,","amin","analyt","anim","another,","another.","applic","applications,","approach","approxim","arbitrari","area","aris","assum","atoms,","attract","attribut","averag","away","b","bad","base","basi","be","befor","below","below.","between","between,","bibliographi","billion","bin","bin,","bin.","bin_width","bin_width)","bin_width/2,","bins=bins,","boca","boltzmann","boltzmann,","browser","built","bypass","calcul","calculate,","calculation,","call","carefulli","carlo","carlo,","case,","cases,","center","chain","chanc","chapman","chapter","chapter,","chapter:","charged,","choos","choose,","choose.","chosen","code","code!","coloss","combin","common","compar","complic","comput","computation","consid","constant,","continu","converg","coordin","coordinate,","count","coupl","creat","creativ","criterion","crucial","current","d","d\\mathbf{x}","d\\mathbf{x}.","data","data,","decis","def","defin","defined.","denomin","densiti","density=true)","depend","describ","deviat","deviation,","differ","difficult","dimens","dimension","dimension,","dimensions,","dimensions.","directly,","discov","discret","discrete,","discuss","distribut","distribution,","distribution.","distribution:","dive","divid","doesn't","domain","don't","done","dot","dramat","drastic","due","dx_1\\dot","dx_{10}.","dx}","e(\\mathbf{x})","e(\\mathbf{x})/t\\right],","e(\\mathbf{x})}{t}","e(x_1,","e(x_1,...,x_{10})","e(x_1,\\dot","e^{","each","easi","easier","effect","effici","else:","end","energi","energy,","ensur","equat","equilibrium","equival","error","error,","especi","estim","et","even","eventually,","everyth","exactly.","exampl","example,","exist","expens","explor","express","f(\\mathbf{x})","f(\\mathbf{x})d\\mathbf{x}},","f(centers,","f(x')","f(x)","f(x)).item())","f(x),","f(x).","f(x)},","f(x,","f(x_t),","f(x_t).","f=f,","fact","factor","factor,","far","fast","faster","fed","few","few.","field","figur","file","file,","finally,","first","fl,","fli","follow","footbal","form","frequenc","full","function","function,","function.","fundament","further","g","g()","g():","g,","g.","g=g):","game","gaussian","gaussian,","gaussians.","gener","give","given","global","goal","goal,","goe","good","graphic","hall/crc","hamiltonian","hand,","hast","height,","heights,","henc","high","higher","histogram","histograms\"","however,","i.","i.e.,","imag","images/graph","imagin","implement","implement.","impli","import","in!","incorpor","increas","increment","indeed.","iniit","initi","instead","instead,","institut","integ","integr","integral,","integrate,","integration.","intens","interact,","interactions.","intern","interv","intervals,","is,","is.","is:","it'","it.","iter","iterate.","iterations!","iterations,","itself.","jeffrey","k.","k.,","know","known","langevin","languag","larg","larger","later","learn","left,","length","let'","licens","license.","license.md).","line","list(metropolis_iterate(x0,","list,","locat","long","longer","look","lot","low","ludwig","machines,","made","magnitude!","make","mani","markov","mathemat","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matters!","mcmc,","mean","mean_valu","mean_value)","meter","method","method.","methods,","metric","metric.","metropoli","metropolis\"","metropolis_iterate()","metropolis_iterate(x0,","metropolis_step(x)","metropolis_step(x,","min(1,","min(true_values))","mit","modifi","molecules,","mont","more","more,","move","move,","much","multidimension","multidimensional,","multipl","n","n.","name","nanosecond","nearbi","necessarili","need","new","next","next,","nmsd","none","norm","normal","normalize:","normalize=false):","normalize=true)","note","note:","noth","now","np","np.arange(xmin","np.arange(xmin,","np.array([","np.array([10.,","np.average((height","np.exp(","np.histogram(x_dat,","np.mean(true_valu","np.random.choice([x_proposed,","np.random.uniform(","np.random.uniform(xmin,","np.sqrt(b))).sum()","np.sqrt(nmsd)","nrmsd","num_step","num_steps))","num_steps):","num_steps.","number","numer","numerically.","numpi","o.","obvious!","occur","occurr","on","one.","open(\"output.dat\",","optim","order","other","other.","others,","otherwise,","out.write(\"\\n\")","out.write(output_string)","out:","output_str","over","overlap","own,","own.","p(\\mathbf{x})","p(\\mathbf{x}),","p(x)","p(x)\"","p(x),","p(x).","p=[a,","parallel","parameters,","part","particl","particles\">","particles,","particles.","particularli","peak","peopl","perform","physic","physicist","plot","point","poor","popular","posit","position,","position.","position.'''","positions.","possibl","potenti","power","practice,","practice.","pretti","print(f\"test","print(f\"{'num_steps':>10s}","print(f\"{num_steps:10d}","probability,","probabl","process","processor","processor,","program","proport","propos","proposal,","pull","put","q","q,","q.","question","quickli","quickly.","quit","random","randomli","range(num_steps):","ratio","raton,","reach","read","readi","real","realli","reduc","ref.","region","region,","reject","repeat","repel","replic","repres","request","requir","research","resolut","resolution,","respectively:","rest","restrict","result","return","right.","robert","root","rosenthal,","run","s","s.","same","same.","sampl","scale","scheme.","second","see","segment","segment.","set","setup","shall","shape","sharealik","show","shown","shudipto","similar","simpli","simplifi","singl","size","size,","size.","slightli","slowly,","small","so,","solut","someth","sometim","spatial","sped","speed,","spheric","squar","star","start","state","statist","statistics,","step","step,","steps.","still","style=\"width:80%\">","such","sum","support","symmetr","symmetric,","system","systems!","systems,","t","t,","tag.","take","target","techniqu","temperatur","term,","test","test_metropolis_iter","test_metropolis_iterate(num_steps,","testing,","text","them),","there!","thing","third","this,","three","thus,","time","times,","times.","together,","took","total","toward","transit","trial","trillion","true","true,","true_valu","true_values)**2","two","u","under","understand","unfeas","unfeasible.","unity,","univers","up","us","using,","usual","valu","values.","vari","variou","vector.'''","veri","verifi","video","visit","w.","walk","walk\"","walk,","walk.","walker","walker'","walker,","wanna","want","watch","way","well.","what'","whatev","whether","whose","wide.","width","words,","work","work.","works,","world","world,","write","written","x","x'","x,","x.","x0","x0)","x0):","x=0.","x],","x^2}","x^2}.","x^2}}{\\displaystyle\\int_{","x_0","x_0'''","x_0.","x_2,","x_dat","x_dat)","x_i,","x_new","x_propos","x_t","x_{10})}{t}\\right]\\","x_{t+1}","xmax","xmax)","xmax,","xmin,","xs","xs)**2)).sum(axis=0)","y_1,","y_2,","y_i,","y_n,","yield","you'd","z_1,","z_2,","z_i","z_n),","{'nrmsd':10s}\")","{nrmsd:5.1%}\")","{q},","{x0:5.2f}\")","}","–"],"contents/probability_distributions/distributions.html":["\"frequenc","\"n","\"not","\"probabl","\"set","&;&","(#560),","(1","(a","(also","(bi","(denot","(for","(h)","(homework","(it","(or","(popularli","(such","(t)",")","+","0.","1","1).","1,","1.","1/6,","12","12,","15,","16","16.5.","1s.","2","2,","2;","3","36","36,","3;","4.0","5","50\\%","5\\%","6","=","[\\![1,6]\\!]","[\\![2,12]\\!].","\\begin{matrix}","\\displaystyl","\\displaystyle\\frac","\\end{matrix}","\\end{matrix}.","\\frac","\\frac{1}{2}.","\\frac{1}{\\sqrt{\\pi}}","\\frac{1}{n}","\\frac{\\displaystyle\\sum_{n}f(n)}{\\displaystyle\\sum_{n}","\\frac{f(\\mathbf{x})}{\\int_d","\\frac{f(n)}{\\displaystyle\\sum_{n}","\\geq","\\in","\\in\\left\\{h,t\\right\\},","\\infty}^{\\infty}","\\int_a^b","\\int_d","\\int_{","\\int_{d}","\\int_{s}f(\\mathbf{x})d\\mathbf{x}","\\left\\{h,t\\right\\}","\\left\\{h,t\\right\\}.","\\leq","\\mathbb{p}(a","\\mathbb{p}(x_0","\\sqrt{\\pi}.","\\sum_n","\\sum_{n=a}^{b}","\\time","abov","above.","actual","again","ahead","all,","allow","allowed\"","alreadi","also.","amin","analag","answer","approach","area","as,","ask","assum","attribut","away","b","b)","b).","b,","be","becom","belong","below.","between","boring,","both","brevity,","broadli","calcul","call","candid","case","case,","case.","categori","certain","chanc","chapter","chapter:","check","classifi","clearli","coin","common","consid","construct","contain","contin","continu","count","creat","creativ","crucial","curv","curve.","d","defin","defined.","definit","denot","densiti","density\"","depend","determin","dice","dice),","dice,","dice.","die","differ","discret","distribut","distribution,","distribution.","distribution:","distribution?","distributions),","distributions.","divid","do","doesn't","domain","doubl","dx","dx)","dx,","e^{","each","easi","edge!).","edge)","electron","entir","equal","equation,","essenti","etc.","exactli","exampl","example,","except","experi","express","f(2)=1.","f(3)=2.","f(\\mathbf{x})","f(\\mathbf{x}).","f(\\mathbf{x})d\\mathbf{x}.","f(\\mathbf{x})d\\mathbf{x}}.","f(n)","f(n),","f(n).","f(n)}","f(n)}.","f(x)","f(x),","f,","fact","featur","find","finite:","first","follow","formally,","frequenc","frequencies,","function","function,","function.","function:","function?","further","gambler!","gaussian","general,","get","get,","give","go","good","googl","graphic","great","green","h","half,","happen","head","hence,","here,","hold.","i.e.,","imag","images/graph","immedi","import","impossible,","includ","inclus","incred","infinit","infinitesim","information,","initi","instead","integ","integer,","integr","interest","intern","intuit","is.","isn't","it!","it'","it,","it.","itself","k.","know","know,","land","less","let'","licens","license.","lie","look","lowest","ly","make","mani","mathemat","mathjax.hub.queue([\"typeset\",mathjax.hub]);","maximum","mean","mean?","measur","measurement,","mention","modifi","n","n,","n.","n=2","n=2,","n=3,","n=4","n=7","n=7,","necessarili","neg","next,","non","none","noon","normal","notat","notation\",","note","now","now,","number","numbers,","object,","obtain","obviou","occur.","on","onc","out","outcom","outcome,","outcome.","outcome:","outcomes.","over","p(\\mathbf{x})","p(h)","p(n)","p(n),","p(n).","p(t)","p(x)","p(x),","p(x)dx","p(x)dx,","p(x)dx.","pair","particular","pattern","physic","plot","possibilities,","possibl","previou","probabilites.","probability,","probability.","probabl","procedure,","process","proport","prospect","pull","put","quantiti","quantity,","quick","rang","range,","range.","reader!).","real","realli","region","request","result","roll","roll\"","roll.","rule","s)","same","satisfi","say","search,","second","section:","see","sens","set","sharealik","show","shown","shudipto","similar","similarly,","simpli","singl","sixes,","sliver","small,","so,","sort","speaking,","spin","still","strictli","studi","style=\"width:100%\"/>","style=\"width:80%\"/>","subset","such","sum","sum:","suppos","sure.","system,","t\".","t.","tail","take","target","technic","tell","temperatur","text","things.","thu","thus,","tomorrow","toss","toss,","total","translat","tricky)","two","under","understand","unlikely,","up","up,","us","valu","values.","vari","variabl","varies.","veri","visual","vs","want","way","way,","weight?","well,","what'","wherea","whole","within","write","written","x","x,","x.","x^2}","x^2},","x^2}.","x_0","zero!","zero):","–"]},"length":49},"tokenStore":{"root":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"1":{"0":{"1":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"1":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"1":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"docs":{}},"1":{"0":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"1":{"0":{"1":{"0":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"1":{"0":{"0":{"0":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"docs":{}},"1":{"0":{"0":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"1":{"0":{"0":{"1":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}},"1":{"0":{"0":{"0":{"0":{"0":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"1":{"0":{"0":{"1":{"0":{"1":{"1":{"1":{"0":{"1":{"1":{"1":{"1":{"0":{"1":{"1":{"1":{"0":{"0":{"0":{"1":{"0":{"0":{"1":{"0":{"1":{"1":{"1":{"0":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"1":{"0":{"1":{"0":{"1":{"0":{"1":{"1":{"0":{"1":{"0":{"0":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"1":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"1":{"0":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"1":{"0":{"0":{"1":{"1":{"1":{"1":{"0":{"1":{"1":{"0":{"0":{"1":{"1":{"0":{"1":{"0":{"1":{"1":{"0":{"0":{"0":{"0":{"1":{"1":{"1":{"1":{"0":{"1":{"1":{"0":{"0":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"1":{"0":{"1":{"0":{"1":{"1":{"0":{"0":{"0":{"0":{"1":{"0":{"0":{"1":{"0":{"0":{"1":{"1":{"1":{"1":{"1":{"0":{"1":{"0":{"1":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"1":{"0":{"1":{"docs":{},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}}},"docs":{}},"1":{"1":{"0":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581}}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0035430431868237098},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.007045797684952189},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0037204358224820623},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.010638297872340425},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00821917808219178},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.00944206008583691},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.005635919594213789},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0028782894736842104},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.010225820195994887},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0018137847642079807},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.004419191919191919},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.014613778705636743},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.014251781472684086},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.016568047337278107},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004204625087596356},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.003638801110791918},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.005200469719845663},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.006391137622496805},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0022169437846397467},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"'":{"docs":{},".":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0016278847074595424},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0010629816635663034},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0031323414252153485},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0029655990510083037},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002843216896831844},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0024422318241593085},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003289473684210526},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.004402783695497799},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0028214429665457475},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.007759303246239113},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},",":{"0":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.005338078291814947},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0014251781472684087},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0015321267834913339},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"b":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},"[":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}},"}":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643}}},"}":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},"/":{"1":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"docs":{}},"a":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"x":{"0":{"0":{"docs":{},"f":{"docs":{},"f":{"0":{"0":{"docs":{},"f":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"docs":{}},"docs":{}}}},"docs":{},"f":{"0":{"docs":{},"f":{"0":{"docs":{},"f":{"0":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}}},"docs":{}}},"docs":{}}},"1":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"3":{"3":{"3":{"3":{"3":{"3":{"3":{"3":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"5":{"5":{"5":{"5":{"5":{"5":{"5":{"5":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{},"+":{"0":{"docs":{},"y":{"docs":{},"+":{"0":{"docs":{},"z":{"docs":{},"=":{"1":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"docs":{}}}},"docs":{}}}},"docs":{}}},".":{"0":{"0":{"1":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"docs":{}},"1":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0019883539269990058}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002272404487998864}}}},"d":{"0":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"docs":{}}},"2":{"5":{"docs":{},"%":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"\\":{"docs":{},"%":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"docs":{}},"3":{"7":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"4":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}}},"5":{"3":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767}}}},"7":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}},"]":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00695923874449652},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0031656700668308124},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},";":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0028405056099985795},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}},"_":{"docs":{},"f":{"6":{"4":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"i":{"docs":{},"(":{"2":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"docs":{}}}}}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}}}},"docs":{}},"docs":{}}},"i":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}},"[":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"}":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},"1":{"3":{"3":{"0":{"7":{"7":{"1":{"1":{"2":{"4":{"3":{"5":{"1":{"1":{"3":{"3":{"3":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"5":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}},"6":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}},"8":{"5":{"4":{"1":{"9":{"4":{"2":{"0":{"6":{"7":{"8":{"1":{"5":{"8":{"5":{"3":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}}}}}},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"2":{"2":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}},"3":{"6":{"4":{"8":{"9":{"1":{"6":{"1":{"8":{"7":{"4":{"3":{"9":{"4":{"0":{"6":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"8":{"4":{"2":{"1":{"6":{"2":{"6":{"7":{"8":{"3":{"2":{"7":{"3":{"2":{"8":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}},"4":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}},"5":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"6":{"6":{"6":{"6":{"6":{"6":{"8":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0041753653444676405}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}},"7":{"9":{"9":{"9":{"6":{"2":{"8":{"6":{"6":{"8":{"1":{"5":{"3":{"0":{"8":{"7":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"8":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}},"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}},"(":{"docs":{},"x":{"docs":{},"+":{"1":{"docs":{},")":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{}}}},"docs":{}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"3":{"0":{"6":{"9":{"9":{"0":{"9":{"1":{"6":{"9":{"1":{"8":{"9":{"6":{"2":{"6":{"3":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"5":{"4":{"8":{"4":{"0":{"5":{"5":{"5":{"3":{"7":{"5":{"4":{"3":{"1":{"9":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"5":{"8":{"9":{"6":{"2":{"5":{"5":{"9":{"4":{"0":{"0":{"5":{"6":{"4":{"7":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"6":{"1":{"3":{"0":{"7":{"9":{"2":{"6":{"0":{"4":{"6":{"0":{"2":{"7":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"9":{"2":{"1":{"0":{"2":{"4":{"2":{"9":{"8":{"0":{"4":{"3":{"8":{"9":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}},"4":{"0":{"6":{"1":{"0":{"8":{"6":{"1":{"8":{"5":{"7":{"7":{"0":{"1":{"5":{"9":{"7":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"2":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"%":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"4":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}},")":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"]":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}},"%":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},")":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"5":{"8":{"7":{"7":{"8":{"5":{"2":{"5":{"2":{"2":{"9":{"2":{"4":{"7":{"3":{"1":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"2":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"4":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{},")":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"9":{"2":{"docs":{},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"docs":{}},"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.007725321888412017},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.004924375659514597},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0034086067319982955},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0058444175735590485},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0029227557411273487},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"]":{"docs":{},")":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"*":{"docs":{},"(":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}},"a":{"docs":{},"c":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"v":{"docs":{},"*":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"d":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"k":{"docs":{},".":{"docs":{},"^":{"2":{"docs":{},"*":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"d":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}},"docs":{}}}}}}}},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},"_":{"docs":{},"c":{"docs":{},".":{"docs":{},"*":{"docs":{},"i":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"k":{"docs":{},".":{"docs":{},"^":{"2":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"d":{"0":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}},"docs":{}},"_":{"docs":{},"f":{"6":{"4":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534}}},"docs":{}},"docs":{}}},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}}},"6":{"0":{"7":{"5":{"6":{"8":{"8":{"5":{"3":{"4":{"4":{"0":{"9":{"0":{"2":{"7":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"1":{"8":{"docs":{},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"docs":{}},"3":{"3":{"8":{"9":{"4":{"3":{"7":{"2":{"4":{"1":{"8":{"8":{"0":{"9":{"1":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"5":{"1":{"1":{"2":{"6":{"0":{"2":{"7":{"8":{"5":{"0":{"4":{"5":{"8":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"7":{"5":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"_":{"docs":{},"f":{"6":{"4":{"docs":{},".":{"docs":{},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}},"docs":{}},"docs":{}}}},"6":{"0":{"5":{"7":{"5":{"2":{"6":{"0":{"8":{"7":{"4":{"5":{"5":{"0":{"6":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"7":{"9":{"6":{"7":{"8":{"4":{"9":{"0":{"2":{"8":{"6":{"2":{"8":{"0":{"3":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"8":{"9":{"5":{"5":{"4":{"5":{"5":{"5":{"8":{"0":{"6":{"7":{"3":{"5":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"9":{"7":{"2":{"0":{"0":{"9":{"7":{"3":{"7":{"6":{"2":{"3":{"8":{"4":{"6":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"8":{"5":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}}},"6":{"6":{"1":{"8":{"7":{"3":{"0":{"6":{"9":{"6":{"6":{"8":{"0":{"1":{"8":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"6":{"6":{"6":{"7":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"8":{"6":{"8":{"6":{"0":{"2":{"4":{"1":{"2":{"1":{"5":{"4":{"4":{"4":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"9":{"5":{"1":{"0":{"5":{"6":{"5":{"1":{"6":{"2":{"9":{"5":{"1":{"5":{"3":{"5":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},"6":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},".":{"6":{"4":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"docs":{}},"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},".":{"docs":{},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"(":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"a":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},"w":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.003022974607013301}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"x":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"a":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}},"]":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}}}},"s":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"'":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"+":{"1":{"2":{"7":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"f":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}},"d":{"0":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},"docs":{}},"\"":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407}}},"u":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}}},"!":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"_":{"docs":{},"f":{"6":{"4":{"docs":{},";":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}}}},"1":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603}}},"docs":{}},"1":{"0":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"1":{"0":{"1":{"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}},".":{"0":{"0":{"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002843216896831844},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"%":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},",":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},".":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"*":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},".":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}},".":{"0":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"_":{"0":{"0":{"0":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"docs":{}},"docs":{}},"docs":{}},"}":{"docs":{},"%":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}},"1":{"0":{"docs":{},".":{"0":{"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}}},"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"2":{"3":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"?":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"4":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"docs":{}},"4":{"0":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"docs":{}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0014251781472684087},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"❗":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"️":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001053337163650292}}}}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"3":{"6":{"docs":{},"a":{"docs":{},";":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"docs":{}},"docs":{}}},"docs":{}}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},",":{"0":{"0":{"0":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004905395935529082}},",":{"0":{"0":{"0":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"docs":{}},"docs":{}},"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}}},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}},"1":{"1":{"docs":{},")":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"docs":{}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002414429768498793},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},".":{"0":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0019883539269990058},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"/":{"5":{"1":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},"docs":{}},"docs":{}},"]":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"2":{"5":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}},"s":{"docs":{},",":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"c":{"docs":{},"m":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}},"d":{"0":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"^":{"docs":{},"{":{"1":{"1":{"0":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"docs":{}},"6":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"9":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"3":{"8":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"4":{"1":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{}},"5":{"0":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{}},"7":{"6":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"docs":{}},"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"_":{"0":{"0":{"0":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{}},"docs":{}},"docs":{}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"?":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"]":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"}":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"}":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"^":{"docs":{},"{":{"1":{"0":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{}},"docs":{}}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"e":{"docs":{},"^":{"docs":{},"{":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"1":{"0":{"1":{"docs":{},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"5":{"1":{"9":{"9":{"1":{"0":{"3":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"1":{"0":{"0":{"1":{"0":{"1":{"0":{"1":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"1":{"1":{"1":{"1":{"1":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"docs":{}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}},"a":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},".":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}},"docs":{}},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"~":{"docs":{},"\\":{"docs":{},"%":{"docs":{},"~":{"3":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}}}}},"z":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"2":{"3":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}},",":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"4":{"5":{"6":{"docs":{},"=":{"5":{"6":{"0":{"8":{"8":{"docs":{},",":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"docs":{}},"docs":{}}}}}}}},"6":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"7":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603}}}},"8":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.005200469719845663},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"*":{"7":{"7":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"docs":{}},"docs":{}},"/":{"1":{"9":{"2":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001053337163650292}},"#":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"9":{"1":{"docs":{},"b":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"docs":{}},"docs":{}}},"docs":{}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}}},",":{"0":{"0":{"0":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"b":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},".":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}},"docs":{}},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"c":{"docs":{},"m":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"3":{"0":{"docs":{},",":{"0":{"0":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"a":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"b":{"docs":{},"b":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"t":{"docs":{},"b":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604}}},".":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}},"}":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"docs":{}},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}},"{":{"1":{"1":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"docs":{}},"docs":{}}}},"5":{"3":{"6":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},".":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}},"}":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"docs":{}},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"6":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009301089556205156},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0035694157430020664},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0008618213157138753},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"#":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},":":{"9":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"docs":{}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"+":{"1":{"docs":{},".":{"0":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"docs":{}}},"docs":{}},"i":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},".":{"5":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"docs":{}}},"7":{"7":{"7":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},",":{"0":{"0":{"0":{"docs":{},")":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"docs":{}},"docs":{}},"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"8":{"0":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},"'":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"5":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}},"1":{"3":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"6":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"7":{"6":{"docs":{},".":{"5":{"docs":{},".":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}},"docs":{}}},"docs":{}},"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}},"\\":{"docs":{},"\\":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"]":{"docs":{},"=":{"docs":{},"[":{"4":{"docs":{},"+":{"1":{"docs":{},",":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"docs":{}}},"docs":{}}}}},"9":{"0":{"0":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"5":{"3":{"docs":{},".":{"2":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}},"docs":{}}},"8":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},".":{"2":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}}}},"docs":{}}},"docs":{}},"6":{"5":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"7":{"docs":{},".":{"3":{"docs":{},".":{"docs":{},"j":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"o":{"docs":{},"u":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}},"docs":{}}},"docs":{}},"7":{"0":{"docs":{},".":{"6":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}},"docs":{}}},"2":{"docs":{},".":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"3":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"7":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"8":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"3":{"docs":{},".":{"docs":{},"f":{"docs":{},"l":{"docs":{},"a":{"docs":{},"j":{"docs":{},"o":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}},"docs":{}}},"docs":{}},"8":{"1":{"docs":{},".":{"1":{"1":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}},"docs":{}},"docs":{}}},"5":{"docs":{},".":{"4":{"docs":{},".":{"docs":{},"b":{"docs":{},"h":{"docs":{},"a":{"docs":{},"y":{"docs":{},"a":{"docs":{},"n":{"docs":{},"i":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}},"docs":{}}},"6":{"docs":{},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"docs":{}},"9":{"4":{"docs":{},".":{"6":{"docs":{},".":{"docs":{},"s":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}},"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"9":{"docs":{},".":{"2":{"docs":{},".":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}}},"docs":{}}},"docs":{}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.004528985507246377}},".":{"3":{"4":{"7":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"docs":{}},"docs":{}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}},"a":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"t":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.005458201666187877},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0026574541589157587},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.008344923504867872},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00487408610885459},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.03287671232876712},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.010300429184549357},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0033815517565282736},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.007305194805194805},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004111842105263158},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.005681818181818182},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00870942201108472},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01952662721893491},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.010161177295024528},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.007415254237288136}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0018602179112410311},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.003355704697986577},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0020665038512117226},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0022168480451430876},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002058590657165479},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0019151584793641674},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"v":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}},"*":{"docs":{},"p":{"docs":{},"i":{"docs":{},"*":{"docs":{},"i":{"docs":{},"*":{"docs":{},"k":{"docs":{},"/":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}},"/":{"docs":{},"(":{"docs":{},"x":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}},"(":{"docs":{},"r":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{},"a":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}},"r":{"docs":{},"e":{"docs":{},"v":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"{":{"2":{"docs":{},"a":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"docs":{}}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0035087719298245615},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.005369127516778523},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.006334125098970704},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"]":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011958543715120914},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0028782894736842104},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0026845637583892616},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"^":{"2":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649}}},"docs":{}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004523026315789474},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"*":{"docs":{},"a":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}}}}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"9":{"1":{"docs":{},"b":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"docs":{}},"docs":{}}},"docs":{}}}},",":{"0":{"0":{"0":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},",":{"0":{"0":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003854239663629993}},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}},"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"docs":{}},"docs":{},".":{"5":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}}},"1":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.00800711743772242},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.003691275167785235},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0034837688044338875},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},".":{"0":{"0":{"0":{"0":{"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"1":{"0":{"0":{"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"(":{"docs":{},"r":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"f":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},"]":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}},"*":{"docs":{},"[":{"1":{"docs":{},".":{"0":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"docs":{}}},"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}},"]":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852}}}}},"+":{"0":{"docs":{},".":{"0":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"docs":{}}},"2":{"docs":{},".":{"4":{"4":{"9":{"2":{"9":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"_":{"docs":{},"f":{"6":{"4":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}},"docs":{}}},"i":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"1":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}}},"2":{"2":{"4":{"6":{"4":{"6":{"7":{"9":{"9":{"1":{"4":{"7":{"3":{"5":{"3":{"2":{"docs":{},"e":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"5":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"docs":{}},"docs":{}},"docs":{}},"7":{"3":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}},"docs":{}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"5":{"3":{"3":{"3":{"3":{"3":{"3":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"6":{"0":{"docs":{},")":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}},"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0041753653444676405}},"]":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}},"7":{"1":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"8":{"3":{"6":{"9":{"7":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"docs":{}},"docs":{}},"docs":{}},"5":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"9":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},".":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}},"=":{"docs":{},"(":{"docs":{},"(":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"a":{"docs":{},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}},"b":{"docs":{},"u":{"docs":{},"c":{"docs":{},"k":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"a":{"docs":{},"r":{"docs":{},"n":{"docs":{},"s":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"o":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},"j":{"docs":{},"a":{"docs":{},"r":{"docs":{},"v":{"docs":{},"i":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"h":{"docs":{},"a":{"docs":{},"m":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"l":{"docs":{},"l":{"docs":{},"i":{"docs":{},"a":{"docs":{},"m":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"n":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"u":{"docs":{},"p":{"docs":{},"t":{"docs":{},"o":{"docs":{},"(":{"docs":{},"a":{"docs":{},".":{"docs":{},"s":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"]":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}},")":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"(":{"3":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"docs":{}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"b":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},",":{"docs":{},"n":{"docs":{},"i":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"l":{"docs":{},"a":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}}}}}},":":{"1":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},":":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"(":{"docs":{},"$":{"1":{"docs":{},",":{"docs":{},"$":{"2":{"docs":{},")":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"docs":{}}}},"docs":{}}}}}}}}}}},"3":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001340610935554917},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},"n":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"a":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"/":{"2":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"docs":{}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}}}}}}}}},"x":{"docs":{},")":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"y":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"d":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{},"y":{"docs":{},"_":{"docs":{},"k":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"b":{"docs":{},"a":{"docs":{},"b":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"g":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"a":{"docs":{},"x":{"docs":{},"i":{"docs":{},"s":{"docs":{},"_":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}}}}}}}}},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"_":{"docs":{},"s":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}},"d":{"docs":{},"i":{"docs":{},"g":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"h":{"docs":{},"a":{"docs":{},"l":{"docs":{},"f":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}},"(":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},")":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"2":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"docs":{}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"docs":{}}}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}},"i":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},"/":{"0":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"4":{"0":{"0":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"docs":{}},"docs":{}},"6":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"docs":{},"(":{"docs":{},"n":{"docs":{},"(":{"docs":{},"v":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"+":{"1":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}}}}}},"a":{"docs":{},")":{"docs":{},"*":{"docs":{},"*":{"docs":{},"v":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"a":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"\"":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"}":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824}}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},"{":{"2":{"docs":{},"}":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"docs":{},"b":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"&":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"[":{"docs":{},"\\":{"docs":{},"h":{"docs":{},"a":{"docs":{},"t":{"docs":{},"{":{"docs":{},"u":{"docs":{},"}":{"docs":{},"_":{"docs":{},"k":{"docs":{},"(":{"docs":{},"d":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}},"(":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},"d":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":5.000555247084953},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}}},"s":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}},".":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}}}},"'":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}},"s":{"docs":{},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"j":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}},"i":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"+":{"1":{"docs":{},"/":{"docs":{},"a":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"docs":{}},"=":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"_":{"docs":{},"f":{"6":{"4":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}}}},"2":{"0":{"0":{"0":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"1":{"docs":{},".":{"1":{"0":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}},"docs":{}},"docs":{}}},"4":{"docs":{},".":{"4":{"docs":{},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"k":{"docs":{},"n":{"docs":{},"o":{"docs":{},"w":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}},"7":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}},"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"8":{"docs":{},".":{"4":{"docs":{},".":{"docs":{},"w":{"docs":{},"e":{"docs":{},"g":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}},"docs":{}}},"docs":{},",":{"0":{"0":{"0":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"docs":{}},"docs":{}},"docs":{}}},"1":{"0":{"docs":{},".":{"4":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}},"docs":{}}},"1":{"docs":{},".":{"9":{"docs":{},".":{"docs":{},"g":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"docs":{}}},"2":{"docs":{},".":{"5":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"e":{"docs":{},"l":{"docs":{},"k":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}},"9":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}},"docs":{}}},"4":{"docs":{},".":{"2":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}},"docs":{}}},"5":{"docs":{},".":{"2":{"docs":{},".":{"docs":{},"m":{"docs":{},"o":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}},"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"6":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"7":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"7":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}},"docs":{}}},"8":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"9":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"1":{"0":{"docs":{},".":{"docs":{},"h":{"docs":{},"u":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}}},"2":{"docs":{},".":{"docs":{},"w":{"docs":{},"o":{"docs":{},"l":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}},"docs":{}},"2":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"b":{"docs":{},"r":{"docs":{},"o":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}}},"3":{"docs":{},".":{"docs":{},"p":{"docs":{},"e":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"c":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"s":{"docs":{},"a":{"docs":{},"u":{"docs":{},"p":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"5":{"docs":{},".":{"docs":{},"s":{"docs":{},"a":{"docs":{},"u":{"docs":{},"p":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}},"8":{"docs":{},".":{"docs":{},"g":{"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}},"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"2":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.004347826086956522}},".":{"2":{"docs":{},".":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}},"s":{"docs":{},"c":{"docs":{},"h":{"docs":{},"l":{"docs":{},"o":{"docs":{},"s":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}},"3":{"docs":{},".":{"docs":{},"b":{"docs":{},"i":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"5":{"docs":{},".":{"docs":{},"g":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"2":{"0":{"3":{"0":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{},"=":{"2":{"0":{"3":{"0":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}}},"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"3":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}},"4":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}},"5":{"docs":{},".":{"docs":{},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}},"7":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}},"8":{"docs":{},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"h":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}},"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"2":{"docs":{},".":{"1":{"0":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}},"1":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}},"docs":{}},"2":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}},"3":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}}}},"4":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}},"5":{"docs":{},".":{"docs":{},"c":{"docs":{},"r":{"docs":{},"y":{"docs":{},"p":{"docs":{},"t":{"docs":{},"o":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}},"6":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}},"7":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}},"8":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}},"9":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}},"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"docs":{}},"3":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0038043478260869567}},"]":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"1":{"docs":{},")":{"docs":{},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"9":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"9":{"9":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}},".":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"/":{"5":{"1":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"%":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"1":{"4":{"7":{"4":{"8":{"3":{"6":{"4":{"7":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},".":{"4":{"6":{"docs":{},"\\":{"docs":{},"%":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}},"7":{"docs":{},"\\":{"docs":{},"%":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}},"docs":{}},"docs":{}},"s":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0034420289855072463}},")":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}},"+":{"docs":{},"d":{"docs":{},"+":{"docs":{},"e":{"docs":{},">":{"3":{"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"q":{"3":{"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}}}}}}}}},"n":{"docs":{},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"3":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"4":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"5":{"0":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"5":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}},")":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"6":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0030797101449275364},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}},"t":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"%":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"6":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261}},".":{"7":{"1":{"2":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"docs":{}},"docs":{}},"docs":{}},"t":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}},"7":{"3":{"docs":{},".":{"3":{"0":{"8":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835}},".":{"5":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}}},"8":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0019927536231884057}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"9":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0019927536231884057}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},".":{"5":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"t":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.003638801110791918},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.011126564673157162},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.006092607636068237},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00821917808219178},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.010526315789473684},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.006008583690987125},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0045087356753710315},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.007243289305496378},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0032245062474808546},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.006109979633401222},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.006017418844022169},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.00650887573964497},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002452697967764541},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.005280259951259139},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0035694157430020664},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.003022974607013301},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703054677774585},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"d":{"docs":{},"o":{"docs":{},"w":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},".":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}},"docs":{}}}}}}}}},"]":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},",":{"0":{"docs":{},")":{"docs":{},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.003371868978805395},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0026845637583892616},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},".":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004934210526315789},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.005050505050505051},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"_":{"docs":{},"f":{"6":{"4":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509}},".":{"docs":{},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}},"docs":{}},"docs":{}}},"j":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"4":{"4":{"9":{"2":{"9":{"3":{"5":{"9":{"8":{"2":{"9":{"4":{"7":{"0":{"6":{"4":{"docs":{},"e":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"6":{"4":{"docs":{},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"docs":{}},"7":{"docs":{},"+":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"8":{"1":{"docs":{},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"docs":{}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"]":{"docs":{},")":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"(":{"3":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"docs":{}}}}}}}}}}}}},":":{"2":{"docs":{},"]":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0014363688595231256}},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"b":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"+":{"4":{"docs":{},"c":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"docs":{}}},"d":{"0":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}},"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255}},"u":{"docs":{},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}},"\"":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407}}},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852}}}},"]":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004210526315789474},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465}}},"^":{"2":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649}}},"docs":{}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}},"s":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"^":{"0":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"2":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"3":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"4":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"5":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"6":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"7":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"8":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"9":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"docs":{},"{":{"0":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},"1":{"0":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}}}},"2":{"6":{"docs":{},"}":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"docs":{}},"3":{"0":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},"docs":{}},"docs":{}},"2":{"5":{"5":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}},"3":{"docs":{},"}":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"(":{"docs":{},"j":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"n":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"v":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"*":{"docs":{},"*":{"3":{"2":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"docs":{}},"docs":{}},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"x":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"/":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}},"_":{"docs":{},"u":{"1":{"2":{"8":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"(":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"docs":{}},"docs":{}},"docs":{}}},"h":{"docs":{},"a":{"docs":{},"l":{"docs":{},"f":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}}},"i":{"docs":{},"m":{"docs":{},"*":{"docs":{},"p":{"docs":{},"i":{"docs":{},"*":{"docs":{},"n":{"docs":{},"*":{"docs":{},"k":{"docs":{},"/":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"/":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}}}}}}}}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"p":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"*":{"docs":{},"i":{"docs":{},"*":{"docs":{},"(":{"docs":{},"k":{"docs":{},"+":{"docs":{},"n":{"docs":{},"/":{"2":{"docs":{},")":{"docs":{},"/":{"docs":{},"n":{"docs":{},"=":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"docs":{}}}}}},"k":{"docs":{},"/":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}}}}}}}},"v":{"docs":{},"(":{"docs":{},"t":{"docs":{},")":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}},"x":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"(":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"\\":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"l":{"docs":{},"n":{"docs":{},"(":{"docs":{},"r":{"docs":{},"_":{"0":{"docs":{},")":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"docs":{},"u":{"docs":{},"_":{"1":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"{":{"docs":{},"r":{"docs":{},"_":{"0":{"docs":{},"}":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}},"docs":{}}}}}}}}}}}},"2":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"{":{"docs":{},"r":{"docs":{},"_":{"0":{"docs":{},"}":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}},"docs":{}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}},"{":{"docs":{},"r":{"docs":{},"_":{"0":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},"docs":{}}}}}}},"docs":{}}},"u":{"docs":{},")":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"_":{"1":{"docs":{},")":{"docs":{},"}":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"docs":{}}}}}}},"y":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"z":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"(":{"docs":{},"x":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"3":{"0":{"0":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261}}},"1":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002898550724637681}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0014492753623188406}}},"t":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"1":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0019927536231884057}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},".":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"}":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"2":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002872737719046251},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"5":{"4":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"}":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"6":{"5":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},")":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},".":{"2":{"4":{"2":{"5":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"docs":{}},"docs":{}},"5":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"7":{"0":{"0":{"docs":{},"x":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"docs":{}},"docs":{}},"8":{"5":{"docs":{},".":{"8":{"1":{"9":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0014363688595231256},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.005681818181818182},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.006175771971496437},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004142011834319527},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703054677774585}}}},",":{"3":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002533650039588282},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"a":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"b":{"docs":{},"b":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"l":{"docs":{},"u":{"docs":{},"e":{"1":{"docs":{},"b":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"docs":{}}}}},"t":{"docs":{},"b":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"\"":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}},"+":{"1":{"2":{"7":{"docs":{},"=":{"1":{"3":{"0":{"docs":{},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"docs":{}},"2":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}},".":{"0":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003289473684210526}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004934210526315789},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004111842105263158}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946}}}},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"1":{"4":{"1":{"5":{"9":{"2":{"6":{"5":{"3":{"5":{"8":{"9":{"7":{"9":{"3":{"2":{"3":{"8":{"4":{"6":{"2":{"6":{"4":{"3":{"3":{"8":{"3":{"2":{"7":{"9":{"5":{"0":{"2":{"8":{"8":{"4":{"1":{"9":{"7":{"1":{"6":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"3":{"6":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"4":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"6":{"7":{"3":{"9":{"4":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"8":{"4":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"s":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"j":{"docs":{},"a":{"docs":{},"n":{"docs":{},"e":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"}":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}},"\\":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"x":{"3":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}},":":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"d":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"y":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"z":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"r":{"docs":{},"d":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"e":{"docs":{},"^":{"docs":{},"{":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},";":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"4":{"0":{"0":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004204625087596356}},"*":{"docs":{},"v":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"t":{"docs":{},"h":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"9":{"6":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},".":{"6":{"2":{"5":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"^":{"2":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"docs":{}}},"docs":{}},"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"2":{"0":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"8":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"9":{"0":{"7":{"7":{"2":{"9":{"9":{"2":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"4":{"9":{"6":{"7":{"2":{"9":{"5":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"3":{"3":{"docs":{},".":{"6":{"4":{"4":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"5":{"6":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"8":{"0":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},"3":{"docs":{},",":{"2":{"0":{"0":{"docs":{},".":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"9":{"9":{"docs":{},",":{"8":{"1":{"3":{"docs":{},".":{"2":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.004347826086956522},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.004908946951702296},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},".":{"0":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007773459189339256},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009468917249897077},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002843216896831844},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005627857896588111},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006944444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.010862186014935505},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01242603550295858},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"*":{"docs":{},"r":{"1":{"2":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"docs":{}},"8":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"docs":{},"a":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}},"d":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"\"":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},".":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"r":{"docs":{},"^":{"2":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"docs":{}}},",":{"0":{"0":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},"docs":{}},"docs":{}},"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"]":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"d":{"docs":{},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"\\":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}},"\\":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"u":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"y":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"z":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"t":{"docs":{},"h":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"(":{"docs":{},"x":{"docs":{},"+":{"4":{"docs":{},")":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{}}}},"docs":{}}}}},"5":{"0":{"0":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"x":{"5":{"0":{"0":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"docs":{}},"docs":{}},"docs":{}},",":{"0":{"0":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002803083391730904}},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"%":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"%":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"_":{"0":{"0":{"0":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},")":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"docs":{}},"docs":{}},"docs":{}}},"1":{"1":{"docs":{},"!":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"2":{"8":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"/":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"8":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"7":{"docs":{},"=":{"3":{"6":{"4":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}}}},"6":{"0":{"8":{"8":{"docs":{},".":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"docs":{}},"docs":{}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"8":{"docs":{},".":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"%":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},":":{"0":{"0":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"docs":{}},"docs":{}},".":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.009868421052631578},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"]":{"docs":{},"[":{"docs":{},"y":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}}}}}},"2":{"5":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"7":{"2":{"8":{"5":{"9":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"5":{"1":{"0":{"9":{"1":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}},"docs":{}},"docs":{}},"6":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"7":{"9":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},"docs":{}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},"]":{"docs":{},")":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"(":{"3":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"docs":{}}}}}}}}}}}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}},"^":{"2":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"docs":{}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"\"":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"x":{"5":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"docs":{}},",":{"2":{"docs":{},")":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.003371868978805395},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"+":{"1":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}},"]":{"docs":{},"[":{"docs":{},"y":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}},"d":{"0":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}},"docs":{}},"_":{"0":{"0":{"0":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{}},"docs":{}},"docs":{}},"\\":{"docs":{},"%":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"6":{"2":{"2":{"docs":{},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"docs":{}},"3":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"4":{"0":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.006542526421741319},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"*":{"8":{"1":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"docs":{}},"docs":{}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"5":{"5":{"3":{"5":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"docs":{}},"docs":{}},"7":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"9":{"1":{"docs":{},"b":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"docs":{}},"docs":{}}},"docs":{}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0018453279651065259}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224}}}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.004528985507246377},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002533650039588282},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"\"":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"1":{"5":{"docs":{},")":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"docs":{}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.009152215799614644},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.007046979865771812},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"0":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}},"[":{"docs":{},"z":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}}}}},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}},"1":{"2":{"3":{"2":{"3":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"2":{"8":{"3":{"1":{"8":{"5":{"3":{"0":{"7":{"1":{"8":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},":":{"9":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},"[":{"docs":{},"z":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"}":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"7":{"1":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"5":{"4":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"7":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"9":{"1":{"docs":{},"b":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"docs":{}},"docs":{}}},"docs":{}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844}},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}}}}},"8":{"docs":{},".":{"5":{"4":{"docs":{},"\\":{"docs":{},"%":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},"docs":{}},"docs":{}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},".":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}},"docs":{}},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}},"+":{"1":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0019927536231884057}}}},"8":{"0":{"0":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}},"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},"1":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"9":{"1":{"docs":{},"b":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"docs":{}},"docs":{}}},"docs":{}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}}}}},"4":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0014615997874036673},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.02127659574468085},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00821917808219178},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002717391304347826},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002803083391730904}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002585463947141626},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703054677774585},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438}}},"=":{"docs":{},"[":{"5":{"docs":{},",":{"8":{"docs":{},"]":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"docs":{}}},"docs":{}}}},"*":{"docs":{},"r":{"1":{"3":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}},"docs":{}},"docs":{},"a":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"c":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"d":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886}}}},".":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"2":{"5":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},".":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"}":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"+":{"2":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}},"\\":{"docs":{},"\\":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.010638297872340425}}}},"c":{"docs":{},"m":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},",":{"0":{"0":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}}},"docs":{}},"docs":{}},"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589}}}},"9":{"1":{"7":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"6":{"1":{"docs":{},",":{"6":{"0":{"0":{"docs":{},".":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"7":{"0":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"8":{"5":{"6":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"9":{"9":{"docs":{},",":{"4":{"6":{"6":{"docs":{},".":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.005150214592274678},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.004335260115606936},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0026845637583892616}}},".":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"9":{"5":{"8":{"docs":{},".":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}}},"docs":{}},"docs":{}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},".":{"0":{"0":{"0":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}},"1":{"2":{"5":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.005479452054794521}},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"docs":{}},"docs":{}},"docs":{}},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465}}},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"docs":{},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"'":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"`":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"t":{"docs":{},"h":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"docs":{},"(":{"0":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},".":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"4":{"docs":{},"%":{"docs":{},")":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"5":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}},"docs":{},".":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},".":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"_":{"docs":{},"b":{"docs":{},"y":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}},"(":{"docs":{},"(":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},".":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"|":{"docs":{},"_":{"docs":{},"|":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}},",":{"0":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},")":{"docs":{},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"1":{"0":{"0":{"docs":{},".":{"0":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"docs":{}}},"docs":{}},"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"3":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854}}},"5":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0019927536231884057}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"7":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"9":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507}},"a":{"docs":{},"+":{"docs":{},"m":{"docs":{},")":{"docs":{},"~":{"docs":{},"\\":{"docs":{},"%":{"docs":{},"~":{"3":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}}}}}}}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"0":{"docs":{},".":{"5":{"docs":{},")":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"docs":{}}},"docs":{}},"+":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},".":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}},"docs":{},".":{"docs":{},".":{"docs":{},"n":{"docs":{},")":{"docs":{},".":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}},"/":{"2":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"docs":{}}},"2":{"0":{"2":{"0":{"docs":{},".":{"docs":{},".":{"2":{"0":{"3":{"0":{"docs":{},")":{"docs":{},".":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"a":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}}},"docs":{}},"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"+":{"docs":{},"d":{"docs":{},")":{"docs":{},"~":{"docs":{},"\\":{"docs":{},"%":{"docs":{},"~":{"3":{"1":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"docs":{}}}}}}}}},"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"*":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{},"^":{"2":{"docs":{},")":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}},"docs":{}}}}}}},"p":{"docs":{},"i":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"d":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":3.333333333333333}}}},".":{"0":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"docs":{}},"b":{"docs":{},"+":{"4":{"docs":{},"c":{"docs":{},"+":{"6":{"docs":{},"d":{"docs":{},"+":{"docs":{},"n":{"docs":{},")":{"docs":{},"~":{"docs":{},"\\":{"docs":{},"%":{"docs":{},"~":{"7":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}}}}}}}}}},"docs":{}}}},"docs":{}}},"^":{"2":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{},"{":{"1":{"0":{"docs":{},"}":{"docs":{},")":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"docs":{}},"docs":{}}}},"3":{"2":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"4":{"0":{"0":{"0":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}},"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507}},"+":{"docs":{},"k":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"5":{"0":{"0":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{}},"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}},"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"7":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"9":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.010597302504816955},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.011073825503355705},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0036555645816409425},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0032245062474808546},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"f":{"6":{"4":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}},"docs":{}},"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002298190175237001},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}}}}},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{},".":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"i":{"docs":{},"f":{"docs":{},"o":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}},"l":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"[":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},".":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"a":{"docs":{},"i":{"docs":{},"l":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}},"o":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}}},"e":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}},"*":{"docs":{},"g":{"docs":{},")":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"[":{"docs":{},"n":{"docs":{},"]":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}},"f":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}},")":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"w":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},"*":{"docs":{},")":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"y":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},"(":{"docs":{},"z":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"x":{"docs":{},"_":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"i":{"docs":{},"o":{"docs":{},"s":{"docs":{},"o":{"docs":{},"s":{"docs":{},")":{"docs":{},":":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}}}},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},"(":{"docs":{},"n":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}}}}}}}}}}}},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},"/":{"2":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"docs":{}}}}}}}}},"a":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}}}}}}},"a":{"docs":{},"f":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}},"v":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002058590657165479}},"'":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"*":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"i":{"docs":{},"f":{"docs":{},"o":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"s":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}},"k":{"docs":{},"e":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"t":{"docs":{},"t":{"docs":{},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"o":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001053337163650292},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"docs":{}}},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},"f":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"m":{"docs":{},"b":{"docs":{},"d":{"docs":{},"a":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},"p":{"1":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},":":{"docs":{},"p":{"2":{"docs":{},":":{"docs":{},"p":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},"docs":{}}}},"2":{"docs":{},".":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"1":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"docs":{},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"1":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{}},":":{"docs":{},"p":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},"3":{"docs":{},".":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"1":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"docs":{},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"1":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{}}},"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"o":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.007669365146996165}},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},")":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"u":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"_":{"docs":{},"x":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.005780346820809248},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.005704697986577181},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0045726345409778405},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}},"o":{"docs":{},"n":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"l":{"docs":{},".":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"(":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}},")":{"docs":{},"o":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},".":{"docs":{},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},"w":{"docs":{},"(":{"1":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{},"(":{"1":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"l":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}}}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"d":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"b":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}},"a":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}}}},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},".":{"docs":{},"i":{"docs":{},"m":{"docs":{},"_":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}}}}}}}},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}},"t":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},".":{"docs":{},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"x":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}}},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"[":{"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"docs":{}},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"_":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}},"x":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"l":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"f":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}}}},"#":{"5":{"6":{"0":{"docs":{},")":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"docs":{}},"docs":{}},"docs":{}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.008387854386847844},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"n":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}}},"u":{"docs":{},"t":{"docs":{},"o":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}},"&":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004361684281160879},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}},"s":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{},"*":{"docs":{},"p":{"docs":{},"i":{"docs":{},")":{"docs":{},"*":{"docs":{},"*":{"docs":{},"t":{"docs":{},"h":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"h":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"d":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}}}}}}},"l":{"docs":{},"m":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}},"b":{"docs":{},"e":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"s":{"docs":{},"o":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"s":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"o":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},"u":{"docs":{},"m":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"p":{"docs":{},"p":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},".":{"docs":{},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"t":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"a":{"docs":{},"n":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}},"x":{"docs":{},"i":{"docs":{},"s":{"docs":{},"_":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}}}}},")":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"c":{"docs":{},"t":{"docs":{},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"o":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}},"[":{"docs":{},"(":{"docs":{},"i":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"i":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"]":{"docs":{},"[":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}}}}},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}}},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"]":{"docs":{},"[":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}}}}},"_":{"docs":{},"i":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}},"r":{"docs":{},"]":{"docs":{},"[":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}},"o":{"docs":{},"w":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}},"/":{"docs":{},"(":{"docs":{},"a":{"docs":{},"+":{"1":{"docs":{},")":{"docs":{},")":{"docs":{},"^":{"docs":{},"j":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"docs":{}}}}}},"o":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},"t":{"docs":{},"h":{"docs":{},"o":{"docs":{},"d":{"docs":{},"o":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"u":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},"e":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"l":{"docs":{},"d":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124}},"u":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}}}}}}}},"p":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"d":{"docs":{},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"?":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"f":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"w":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"i":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"(":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"!":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"i":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"f":{"docs":{},"c":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"c":{"1":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}},"(":{"docs":{},"$":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"s":{"docs":{},"[":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"g":{"docs":{},"h":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"n":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"e":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742}}}}},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"m":{"docs":{},"p":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"0":{"docs":{},".":{"0":{"docs":{},"_":{"docs":{},"f":{"6":{"4":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509}}}},"docs":{}},"docs":{}}}},"docs":{}}},"docs":{}}}}}}}}}},"a":{"docs":{},"r":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"u":{"docs":{},"t":{"docs":{},"u":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},"s":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"e":{"docs":{},"f":{"docs":{},"f":{"docs":{},"i":{"docs":{},"c":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}}}},"r":{"docs":{},"c":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"p":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}}},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}},"+":{"1":{"docs":{},")":{"docs":{},":":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}},"docs":{}}}},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364}}}}},"v":{"docs":{},"a":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}},"n":{"1":{"2":{"3":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"docs":{}},"docs":{}}},"a":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},")":{"docs":{},"i":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"?":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},"o":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}},"y":{"docs":{},"p":{"docs":{},"t":{"docs":{},"o":{"docs":{},"s":{"docs":{},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},")":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}}},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},")":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"j":{"docs":{},"u":{"docs":{},"r":{"docs":{},"e":{"docs":{},".":{"docs":{},"p":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"/":{"docs":{},"p":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"/":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},"[":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}}}}}}}}}}}}},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0030201342281879194}}},"x":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0030201342281879194}}}},"c":{"docs":{},"w":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},"[":{"docs":{},"m":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}},"i":{"docs":{},"p":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"/":{"docs":{},"*":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}}}}}},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}},"'":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}},"_":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}}}}}}}}},"i":{"6":{"4":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"docs":{}},"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"n":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002533650039588282}},"e":{"docs":{},"r":{"docs":{},"m":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"v":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},".":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"r":{"docs":{},"?":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"o":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},")":{"docs":{},"n":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001583531274742676}}}},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"f":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478}}}},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"t":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"b":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{},"s":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"e":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"x":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003355141754739138},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0026845637583892616},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754}},"s":{"docs":{},"s":{"docs":{},")":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"s":{"docs":{},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},"(":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"e":{"docs":{},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"m":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},".":{"0":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"docs":{},"e":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},".":{"docs":{},"a":{"docs":{},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},")":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"v":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}}}}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},"'":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"^":{"docs":{},"*":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}},"r":{"1":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114}}}},"2":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0014251781472684087}},"e":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}},"a":{"docs":{},"r":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},"d":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"e":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"d":{"docs":{},"u":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},")":{"docs":{},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}},"p":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"e":{"docs":{},"d":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"q":{"docs":{},"u":{"docs":{},"i":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}},"o":{"docs":{},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"+":{"1":{"docs":{},")":{"docs":{},":":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}},"docs":{}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"u":{"docs":{},"g":{"docs":{},"h":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00395882818685669}},"r":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"o":{"docs":{},"m":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542}},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"_":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}},"g":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}}}},"d":{"docs":{},"i":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}},"n":{"docs":{},"d":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}},"t":{"1":{"docs":{},":":{"docs":{},"t":{"2":{"docs":{},":":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"docs":{}}}},"2":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},"o":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"p":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276}},".":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"k":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},"r":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}},"i":{"docs":{},"l":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"h":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"s":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}},"e":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"r":{"docs":{},"e":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"u":{"docs":{},"g":{"docs":{},"h":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}}}}},"_":{"docs":{},"s":{"docs":{},"v":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"v":{"docs":{},"v":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"s":{"docs":{},"v":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"v":{"docs":{},"v":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}},"w":{"docs":{},"i":{"docs":{},"d":{"docs":{},"d":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"d":{"docs":{},"m":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"!":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"_":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},"&":{"docs":{},"q":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},"q":{"docs":{},")":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"_":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{},")":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"m":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}}},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"i":{"docs":{},"s":{"docs":{},"a":{"docs":{},"(":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},"$":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{},"(":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}},"g":{"docs":{},"i":{"docs":{},"r":{"docs":{},"l":{"docs":{},".":{"docs":{},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"f":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"i":{"docs":{},"s":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"(":{"docs":{},"o":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"$":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"o":{"docs":{},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669}}}}},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}},"h":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"e":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"1":{"docs":{},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"docs":{}}}}}}},"u":{"docs":{},"n":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"e":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742}}}}}}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"(":{"1":{"0":{"docs":{},",":{"1":{"0":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"docs":{}},"docs":{}}},"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"3":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"_":{"docs":{},"f":{"6":{"4":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"docs":{}}}},"2":{"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}},"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"b":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"x":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}},"n":{"docs":{},"d":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465}}}},"v":{"docs":{},"g":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},".":{"docs":{},"x":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},"e":{"docs":{},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}},"f":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"t":{"docs":{},"m":{"docs":{},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"docs":{}}}}}},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},">":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"x":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}},"$":{"1":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"docs":{}},"r":{"1":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0014251781472684087}}}},"docs":{},"e":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},"i":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"j":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"!":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}}}}}}},"/":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},":":{"docs":{},"+":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"^":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"(":{"docs":{},"x":{"docs":{},"+":{"docs":{},"m":{"docs":{},"u":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{},")":{"docs":{},"^":{"2":{"docs":{},")":{"docs":{},"/":{"docs":{},"(":{"2":{"docs":{},"*":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{},"^":{"2":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"docs":{}}}}}}}}},"docs":{}}}}},"docs":{}}}}},"docs":{}}}}}}},"y":{"docs":{},"+":{"docs":{},"m":{"docs":{},"u":{"docs":{},"[":{"2":{"docs":{},"]":{"docs":{},")":{"docs":{},"^":{"2":{"docs":{},")":{"docs":{},"/":{"docs":{},"(":{"2":{"docs":{},"*":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{},"^":{"2":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},"docs":{}}}}}}}}},"docs":{}}}}},"docs":{}}}}},"docs":{}}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},">":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},")":{"docs":{},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"s":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"n":{"docs":{},"(":{"docs":{},"$":{"1":{"docs":{},")":{"docs":{},")":{"docs":{},":":{"docs":{},"(":{"1":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"docs":{}}}}}},"docs":{}}}}},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},".":{"docs":{},"n":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},"o":{"docs":{},"y":{"docs":{},"f":{"docs":{},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},"t":{"docs":{},"h":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},".":{"docs":{},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.003691275167785235}}},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0030201342281879194}}}},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},")":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}},"e":{"docs":{},"c":{"docs":{},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003289473684210526}}}}},"u":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"d":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0036231884057971015}},"e":{"docs":{},"f":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"u":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001053337163650292},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"v":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}},"i":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}}},"a":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"m":{"docs":{},"a":{"docs":{},"c":{"docs":{},"r":{"docs":{},"o":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}},"p":{"docs":{},"t":{"docs":{},"h":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"c":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"f":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"n":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001340610935554917}},"s":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"i":{"docs":{},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},"l":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}},"a":{"docs":{},"g":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"v":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"f":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}}},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"e":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}},")":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}},"e":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"^":{"2":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"docs":{}}},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}},"e":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}},"n":{"docs":{},"s":{"docs":{},"[":{"docs":{},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"]":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}}}}}},"n":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"v":{"docs":{},"i":{"docs":{},"s":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004026170105686965}},"_":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}},"*":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}},"*":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"v":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"?":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"o":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"x":{"docs":{},"p":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"c":{"docs":{},"l":{"docs":{},"u":{"docs":{},"d":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"s":{"docs":{},"p":{"docs":{},"e":{"docs":{},"c":{"docs":{},"i":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"m":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"a":{"docs":{},"k":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}},"t":{"1":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}},"docs":{}}}}}}}}},"docs":{},"h":{"docs":{},".":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}},"(":{"docs":{},"a":{"docs":{},"v":{"docs":{},"g":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"(":{"1":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}},"/":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},".":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}}}},"[":{"docs":{},"c":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"c":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}}}}},"v":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"y":{"docs":{},"b":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"x":{"docs":{},"i":{"docs":{},"m":{"docs":{},"u":{"docs":{},"m":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"o":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0014492753623188406}},"u":{"docs":{},"l":{"docs":{},"o":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"r":{"docs":{},"e":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"t":{"docs":{},"h":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},"_":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},".":{"docs":{},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"m":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},"i":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"i":{"docs":{},"d":{"docs":{},"d":{"docs":{},"l":{"docs":{},"e":{"docs":{},")":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0026300958106331017},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},"o":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"d":{"docs":{},"e":{"2":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.005362443742219668},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837}}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}},"i":{"docs":{},"s":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"m":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"_":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}},"e":{"docs":{},"g":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"?":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}},"w":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}}},"_":{"docs":{},"x":{"docs":{},"[":{"docs":{},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"x":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},")":{"docs":{},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"p":{"docs":{},".":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"n":{"docs":{},"p":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"n":{"docs":{},"p":{"docs":{},".":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}},"p":{"docs":{},"i":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"n":{"docs":{},"p":{"docs":{},".":{"docs":{},"p":{"docs":{},"i":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}}}}}}}}},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"(":{"docs":{},"v":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}}}}},"q":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}},"_":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},"q":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}},"o":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"s":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}}}}}}}},"h":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"_":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0028214429665457475},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},")":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},"m":{"docs":{},"i":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}},"_":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}},"n":{"docs":{},"d":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"d":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"a":{"docs":{},"w":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"u":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"3":{"2":{"docs":{},"_":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}},"docs":{}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"_":{"docs":{},"t":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437}}}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"e":{"docs":{},"p":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"o":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"r":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}}}}}},"p":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}},":":{"docs":{},"p":{"1":{"docs":{},":":{"docs":{},"p":{"2":{"docs":{},":":{"docs":{},"p":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},"docs":{}}}},"docs":{}},"s":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465}}}}}},"u":{"docs":{},"m":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"c":{"docs":{},"h":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"v":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004934210526315789},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"e":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"v":{"1":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"a":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0031323414252153485},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"u":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"e":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"=":{"2":{"docs":{},")":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"docs":{}}},"%":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"*":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004193927193423922},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002272404487998864},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"c":{"docs":{},"b":{"docs":{},")":{"docs":{},"[":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}},"d":{"docs":{},"s":{"docs":{},"t":{"docs":{},")":{"docs":{},"[":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},")":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"'":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"=":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"_":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"g":{"docs":{},"c":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"e":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}},"i":{"docs":{},"r":{"docs":{},"l":{"docs":{},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"(":{"docs":{},"g":{"docs":{},"u":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}},"f":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},"[":{"docs":{},"x":{"docs":{},"]":{"docs":{},"[":{"docs":{},"y":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}}}}},"j":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}},"s":{"docs":{},"p":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}},"u":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"u":{"docs":{},"b":{"docs":{},"s":{"docs":{},"a":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}},"n":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"p":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}},"_":{"1":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"docs":{}},"s":{"docs":{},"e":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0036231884057971015}}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}},"x":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"y":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"a":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"b":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"c":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"*":{"docs":{},"x":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},":":{"docs":{},"y":{"docs":{},":":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}},"x":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}},"'":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0019883539269990058}}}},"o":{"docs":{},"l":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}},".":{"0":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}},"x":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"_":{"docs":{},"i":{"docs":{},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"^":{"2":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"docs":{}}},"z":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"e":{"docs":{},"r":{"docs":{},"o":{"docs":{},"?":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"i":{"docs":{},"p":{"4":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"_":{"1":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"docs":{}}},"~":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"'":{"docs":{},"_":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}},"i":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}},"o":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}},"t":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}},"y":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}},"#":{"docs":{},"f":{"docs":{},"f":{"0":{"0":{"0":{"0":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}}}},"+":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},";":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"(":{"docs":{},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}},"t":{"docs":{},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"l":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}}},"r":{"docs":{},"e":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"u":{"docs":{},"s":{"docs":{},"b":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"l":{"docs":{},"l":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}},"e":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}},"o":{"docs":{},"p":{"docs":{},"e":{"docs":{},"f":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"w":{"docs":{},"o":{"docs":{},"r":{"docs":{},"k":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}},")":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},"y":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}},"e":{"docs":{},"p":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},".":{"docs":{},".":{"docs":{},"a":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"s":{"docs":{},")":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"v":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}}}}}},"_":{"docs":{},"i":{"docs":{},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"{":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"\\":{"docs":{},"(":{"docs":{},"w":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"p":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"c":{"docs":{},"o":{"docs":{},"s":{"docs":{},"(":{"2":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"x":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}},"n":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"_":{"0":{"docs":{},")":{"docs":{},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"docs":{}}}}},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},":":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"i":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"/":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},"=":{"docs":{},"p":{"0":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{}}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"y":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}},"b":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"c":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"*":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"a":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}},"t":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"[":{"0":{"docs":{},".":{"5":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"docs":{}}},"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"]":{"docs":{},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"i":{"docs":{},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"o":{"docs":{},"w":{"docs":{},"(":{"docs":{},"$":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}}}}}}}}}},"\"":{"0":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{},"b":{"docs":{},"o":{"docs":{},"t":{"docs":{},"t":{"docs":{},"o":{"docs":{},"m":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}},".":{"docs":{},"*":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"+":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"^":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"|":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{},"|":{"docs":{},"^":{"2":{"docs":{},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"docs":{}}}}}}}}}}}},"/":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.005280259951259139},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.00631578947368421},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.00944206008583691},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.009768927296637234},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.013569078947368422},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.012696493349455865},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.005431093007467753},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.003260869565217391},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.004433887569279493},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004905395935529082},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891}},"*":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.005614035087719298},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"*":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.009824561403508772},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}},"/":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0077192982456140355},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002106674327300584},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.005871498070793491},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.005049162901939941},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.009005481597494126},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.005780346820809248},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.007046979865771812},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003886729594669628},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002843216896831844},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.005448055607739997},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.007386563489271896},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0025564550489987218},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0018137847642079807},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.01127348643006263},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.013768115942028985},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.009026128266033254},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.01296426068675543}},"s":{"docs":{},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},".":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"l":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"u":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}}}}}}}}},"h":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},".":{"docs":{},"d":{"docs":{},"f":{"docs":{},"s":{"docs":{},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"i":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"_":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}},"a":{"docs":{},"l":{"docs":{},"w":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"d":{"docs":{},"d":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"/":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}},"=":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003289473684210526},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"a":{"docs":{},"d":{"docs":{"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.03389830508474576},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}},"v":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"t":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"e":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"i":{"docs":{},"c":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"d":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.020833333333333332},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.017391304347826087},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002106674327300584},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0025245814509699707},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.005479452054794521},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.005448055607739997},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002717391304347826},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"(":{"docs":{},"$":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}},"l":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"p":{"docs":{},"a":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}}}}}}}},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"s":{"docs":{},"d":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0025564550489987218}}}}},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"m":{"docs":{},"i":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"d":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},":":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},")":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"~":{"docs":{},"%":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"a":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"j":{"docs":{},"u":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{"./":{"ref":"./","tf":5.045918367346939},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.007707129094412331},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.028169014084507043},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.03389830508474576},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.02608695652173913},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":5.013085052843483},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.02702702702702703},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0234375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.011029411764705883},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.008350730688935281},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.00699876492383697},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0020665038512117226},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.030844155844155844},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":5.002055921052632},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0038043478260869567},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":3.3347348750291985},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.01129305477131564}},";":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"s":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},",":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},":":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"?":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"!":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"d":{"docs":{},"\"":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},";":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364}}},"(":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},".":{"docs":{},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"!":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"u":{"docs":{},"d":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"o":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0047522063815342835},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.013609467455621301},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"!":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"c":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371}},"e":{"docs":{},"'":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},"a":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"s":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"p":{"docs":{},"h":{"docs":{},"a":{"docs":{},"b":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"s":{"docs":{},":":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"y":{"docs":{},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}}}}},"w":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"s":{"docs":{},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},")":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"t":{"docs":{},"o":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"!":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}},"n":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"h":{"docs":{},"o":{"docs":{},"u":{"docs":{},"g":{"docs":{},"h":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}},".":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"s":{"docs":{},"o":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"m":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}},"g":{"docs":{},"u":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"o":{"docs":{},"u":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}},"a":{"docs":{},"z":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"r":{"docs":{},"a":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}}}}}},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}}}},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"y":{"docs":{},"t":{"docs":{},"h":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"o":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},"w":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"?":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"m":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},".":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"e":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"m":{"docs":{},"a":{"docs":{},"l":{"docs":{},"y":{"docs":{},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"c":{"docs":{},"i":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"i":{"docs":{},"m":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"s":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}}},"s":{"docs":{},"w":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"_":{"docs":{},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}},"[":{"1":{"docs":{},":":{"3":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"docs":{}}},"docs":{}}}}}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"(":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"g":{"docs":{},"l":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.004335260115606936},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.005704697986577181},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},"e":{"docs":{},"(":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},".":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"u":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"a":{"docs":{},"l":{"docs":{},"y":{"docs":{},"z":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"t":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"i":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"o":{"docs":{},"g":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"u":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"y":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"a":{"docs":{},"g":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"r":{"docs":{},"c":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"a":{"docs":{},"n":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"h":{"docs":{},"i":{"docs":{},"v":{"docs":{"./":{"ref":"./","tf":5.01530612244898},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.016901408450704224},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"o":{"docs":{},"r":{"docs":{},"g":{"docs":{},"/":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}},"!":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},":":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409}}},",":{"docs":{"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"s":{"docs":{},"/":{"docs":{},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"\"":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}}},"x":{"docs":{},"i":{"docs":{},"v":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},".":{"docs":{},"o":{"docs":{},"r":{"docs":{},"g":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904}}}}}}}}},"g":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"(":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},".":{"docs":{},"(":{"docs":{},"a":{"docs":{},"[":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},":":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},",":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"a":{"docs":{},"y":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002585463947141626},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004997223764575236},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.007653061224489796},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00958106331016344},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.010551948051948052},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"<":{"docs":{},">":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}}}},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},".":{"docs":{},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"l":{"docs":{},"(":{"docs":{},"n":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}}}}}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{},"{":{"docs":{},"|":{"docs":{},"i":{"docs":{},"|":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},"$":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}},"s":{"docs":{},"h":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"$":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"[":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"]":{"docs":{},")":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"i":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"]":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"j":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"s":{"docs":{},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"m":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"x":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}}}}}}}}}}}},"?":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"n":{"docs":{},"g":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"[":{"docs":{},"#":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}},"e":{"docs":{},"a":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002843216896831844},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}},".":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"s":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"\"":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},".":{"docs":{},".":{"docs":{},".":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"i":{"docs":{},"c":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"s":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"s":{"docs":{},"!":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},".":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}},"i":{"docs":{},"c":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"l":{"docs":{},"i":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"y":{"docs":{},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}},"s":{"docs":{},"s":{"docs":{},"o":{"docs":{},"c":{"docs":{},"i":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}}}}}}}}}}},"s":{"docs":{},"s":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"u":{"docs":{},"m":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703054677774585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"p":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}}},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.018691588785046728},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"k":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},",":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"m":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}},"c":{"docs":{},"i":{"docs":{},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{},"e":{"docs":{},"r":{"docs":{},"c":{"docs":{},"a":{"docs":{},"s":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"e":{"docs":{},"[":{"docs":{},":":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"]":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"c":{"docs":{},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"[":{"docs":{},":":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"]":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"r":{"docs":{},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},"p":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"=":{"docs":{},"\"":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}},"y":{"docs":{},"m":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405}},"i":{"docs":{},"c":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}},"i":{"docs":{},"d":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"t":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"r":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"n":{"docs":{},"o":{"docs":{},"m":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"t":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"b":{"docs":{},"u":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.02040816326530612},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007773459189339256},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009057225195553726},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005627857896588111},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006944444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.010862186014935505},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01242603550295858},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}}}}},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"w":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"o":{"docs":{},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0029227557411273487}},"s":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"a":{"docs":{},"n":{"2":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"(":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"p":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"docs":{}}}}}}},"y":{"1":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"docs":{},",":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}},"(":{"docs":{},"z":{"docs":{},"e":{"docs":{},"r":{"docs":{},"o":{"docs":{},"s":{"docs":{},"(":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}}},"o":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0018137847642079807}},"s":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"v":{"docs":{},"a":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.007707129094412331},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},".":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}}}}},"o":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"e":{"docs":{},"!":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}},"g":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141}},"i":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"o":{"docs":{},"v":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002533650039588282},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"?":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"g":{"docs":{},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}},"u":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},":":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"s":{"2":{"docs":{},".":{"docs":{},"(":{"docs":{},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}},"docs":{},"(":{"docs":{},"$":{"docs":{},"a":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}},"b":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0020130850528434826}}}},":":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"b":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}},"b":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0020130850528434826}}}}},"i":{"docs":{},"n":{"1":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"2":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"docs":{}}},"p":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"i":{"docs":{},"_":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"_":{"docs":{},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{},"*":{"docs":{},"p":{"docs":{},"i":{"docs":{},")":{"docs":{},")":{"docs":{},"*":{"docs":{},"*":{"docs":{},"t":{"docs":{},"h":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"h":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}}},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}},"z":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001509813789632612}}},"c":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"c":{"docs":{},"c":{"docs":{},"c":{"docs":{},"d":{"docs":{},"d":{"docs":{},"d":{"docs":{},"d":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"v":{"docs":{},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"y":{"docs":{},"s":{"docs":{},"m":{"docs":{},"a":{"docs":{},"l":{"docs":{},"!":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"r":{"docs":{},"u":{"docs":{},"p":{"docs":{},"t":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}},"g":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},"n":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},".":{"docs":{},"\"":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}},"o":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},".":{"docs":{},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},":":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}}}},"h":{"docs":{},"e":{"docs":{},"m":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"a":{"docs":{},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},"i":{"docs":{},"x":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"(":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"[":{"docs":{},":":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"*":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}}}}}}}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}},"a":{"docs":{},"l":{"docs":{},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"s":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"r":{"docs":{},"o":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0019151584793641674},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}},"x":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"i":{"docs":{},"m":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.020242914979757085},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":3.347699135715954},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},")":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"e":{"docs":{},".":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"(":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}}}}}},"(":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"z":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"l":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"c":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"q":{"docs":{},"u":{"docs":{},"é":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"6":{"docs":{},".":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"h":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}},"docs":{}}}}}}}},"y":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"i":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409}},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"r":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002898550724637681}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"}":{"docs":{},"&":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"u":{"docs":{},"t":{"docs":{},"h":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"o":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002258836035078395},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.011862396204033215},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.004592901878914405},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904}}}}},"&":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}},"d":{"docs":{},"i":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"e":{"docs":{},"'":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"x":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"g":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}}}}}}}},"w":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"a":{"docs":{},"y":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"f":{"docs":{},"u":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"c":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.021729867916489135},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"e":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.005081874647092038}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}},"s":{"docs":{},"s":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"_":{"docs":{},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"m":{"docs":{},"g":{"docs":{},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"o":{"docs":{},"n":{"docs":{},"!":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"r":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"u":{"docs":{},"r":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"c":{"docs":{},"i":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}},"m":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},"u":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}},"*":{"docs":{},"d":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}},"*":{"docs":{},"d":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0097997443544951}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0031245561709984378}},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},"docs":{}},"docs":{}}}}}}}},"r":{"docs":{},"u":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"s":{"docs":{},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"v":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002452697967764541},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}}},"h":{"docs":{},"i":{"docs":{},"e":{"docs":{},"v":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"k":{"docs":{},"n":{"docs":{},"o":{"docs":{},"w":{"docs":{},"l":{"docs":{},"e":{"docs":{},"d":{"docs":{},"g":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}}}},"a":{"docs":{},"d":{"docs":{},"e":{"docs":{},"m":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"m":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.006374769334004362},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.003371868978805395},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0021303792074989347},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"{":{"docs":{},"b":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837}}}}}},"%":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001509813789632612}},",":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0014615997874036673},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004905395935529082}},"(":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"n":{"docs":{},"e":{"docs":{},"g":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"?":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},")":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},";":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},".":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"c":{"docs":{},"m":{"docs":{},"p":{"docs":{},"(":{"docs":{},"&":{"docs":{},"p":{"docs":{},"o":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{},"_":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"w":{"docs":{},"f":{"docs":{},"(":{"docs":{},"v":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}},"^":{"2":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},"docs":{},"n":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"e":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}}}}}}}}},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"b":{"docs":{},".":{"docs":{},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"(":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}}}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"(":{"docs":{},"b":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"x":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.00436241610738255}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"*":{"docs":{},"(":{"docs":{},"c":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886}}}}},"y":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.006040268456375839}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"*":{"docs":{},"(":{"docs":{},"c":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}},"1":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},")":{"docs":{},")":{"docs":{},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"docs":{}}}}}}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"]":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005956552207428171}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.007045797684952189},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"=":{"1":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"3":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{},"$":{"docs":{},"(":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"=":{"docs":{},"b":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},">":{"1":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{},"b":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141}}}}}}}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}},"2":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}}},"*":{"docs":{},"i":{"docs":{},"+":{"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}}},"docs":{}},"]":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"3":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},"[":{"4":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"docs":{}}}},"docs":{},"(":{"docs":{},"i":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0014251781472684087}}}},"a":{"docs":{},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}}}},"k":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}}}},"i":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141}},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004111842105263158}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"[":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}}},"i":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}},"j":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"*":{"docs":{},"a":{"docs":{},"[":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},",":{"docs":{},"j":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}},"/":{"docs":{},"a":{"docs":{},"[":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},",":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}}}}}}}},"j":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"_":{"docs":{},"i":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}}}}}}}}},"p":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"[":{"docs":{},"c":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"_":{"docs":{},"i":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0023752969121140144}}}}}}}}}}}},"r":{"docs":{},"+":{"1":{"docs":{},":":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}},"docs":{}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001583531274742676}}},":":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"[":{"docs":{},"c":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"j":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"r":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"i":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"j":{"docs":{},"]":{"docs":{},"*":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}},"]":{"docs":{},"[":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}}}},"i":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}},"j":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}}}},"a":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"b":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"i":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"f":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"f":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"i":{"docs":{},"n":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.005010438413361169},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":5.0094674556213015}},"e":{"docs":{},";":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"@":{"docs":{},"(":{"docs":{},"x":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"e":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731}},"s":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},"_":{"0":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"1":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"2":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{},"{":{"docs":{},"n":{"docs":{},"}":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003700657894736842}}},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"x":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"_":{"docs":{},"x":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"k":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}},"y":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"k":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"m":{"docs":{},"s":{"docs":{},"h":{"docs":{},"o":{"docs":{},"w":{"docs":{},"(":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"_":{"docs":{},"t":{"docs":{},"i":{"docs":{},"t":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"$":{"docs":{},"f":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{},"=":{"docs":{},"z":{"docs":{},"^":{"2":{"docs":{},"$":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"docs":{}}}}}}}}}}}}}}}},"x":{"docs":{},"l":{"docs":{},"a":{"docs":{},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"$":{"docs":{},"r":{"docs":{},"e":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},"$":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}},"y":{"docs":{},"l":{"docs":{},"a":{"docs":{},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"$":{"docs":{},"i":{"docs":{},"m":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},"$":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}}}}}}}}},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"_":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814}},"^":{"2":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"docs":{}}}}}}}},"=":{"docs":{},"a":{"docs":{},"x":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},"'":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}},"_":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},"^":{"docs":{},"*":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"\\":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}},"docs":{}}},"(":{"docs":{},"t":{"docs":{},")":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}},"+":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}}}}}},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"_":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"}":{"docs":{},"_":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"}":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"l":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}},"*":{"docs":{},"(":{"docs":{},"(":{"1":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"+":{"1":{"docs":{},"/":{"docs":{},"a":{"docs":{},")":{"docs":{},"^":{"docs":{},"v":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"docs":{}}},"docs":{}}}},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"1":{"docs":{},"+":{"docs":{},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"1":{"docs":{},"}":{"docs":{},"{":{"docs":{},"a":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{},"^":{"docs":{},"v":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}},"docs":{}}}}}}}}},"docs":{}}}}}}}}}}}}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.05569535312866969},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.011101973684210526},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.004166666666666667},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"s":{"docs":{},"!":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742}}}}},"a":{"docs":{},"m":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004142011834319527},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"!":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"?":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},")":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"(":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}},"i":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"a":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"t":{"docs":{},"w":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0033944331296673455},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.00421179302045728},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.007415254237288136}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},":":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"!":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},":":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.020833333333333332},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},")":{"docs":{},"!":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"n":{"docs":{},"g":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"t":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"i":{"docs":{},"e":{"docs":{},"v":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"l":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"o":{"docs":{},"w":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"n":{"docs":{},"e":{"docs":{},"f":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125}}}}},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"c":{"docs":{},"h":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"k":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737}},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}},"t":{"docs":{},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}}}}}},"o":{"docs":{},"i":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},".":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"a":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"f":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}}},"s":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.005681818181818182},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"y":{"docs":{},"o":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"a":{"docs":{},"v":{"docs":{},"i":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"s":{"docs":{},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"e":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"o":{"docs":{},"l":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"w":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}},"d":{"docs":{},"a":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"e":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"./":{"ref":"./","tf":0.015306122448979591},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.009633911368015413},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"s":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.003371868978805395},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.008529650690495532},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0024183796856106408},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"e":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"t":{"docs":{},"h":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"!":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"t":{"docs":{},"o":{"docs":{},"m":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"\"":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"b":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.009394572025052192}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"'":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"x":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":3.3380855397148674}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"—":{"docs":{},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.008825526137135099}}}}}}},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.009994447529150472},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"y":{"docs":{},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"s":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"[":{"1":{"docs":{},",":{"1":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"/":{"docs":{},"d":{"docs":{},"x":{"docs":{},")":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}},"docs":{}}},"2":{"docs":{},",":{"1":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"/":{"docs":{},"d":{"docs":{},"x":{"docs":{},")":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}},"docs":{}}},"docs":{}}}},"c":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}},"y":{"docs":{},"f":{"docs":{},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394}}}}},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"g":{"docs":{},"g":{"docs":{},"l":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"d":{"docs":{},"i":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"y":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"s":{"docs":{},"e":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"i":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"c":{"docs":{},"a":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"l":{"docs":{},"t":{"docs":{},"z":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.003952569169960474}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}},"c":{"docs":{},"k":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003289473684210526},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"g":{"docs":{},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":5.008695652173913},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"s":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"q":{"docs":{},"u":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"_":{"docs":{},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"&":{"docs":{},"a":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"a":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"2":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"docs":{}}},"docs":{}},"docs":{}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}},"t":{"docs":{},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"a":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"[":{"docs":{},"]":{"docs":{},"[":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}}}}}}}}}}}}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.003523884103367267}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"s":{"docs":{},".":{"docs":{},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"g":{"docs":{},"i":{"docs":{},"r":{"docs":{},"l":{"docs":{},".":{"docs":{},"f":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"h":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"[":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},"_":{"docs":{},"s":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}}},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"c":{"docs":{},"c":{"docs":{},"d":{"docs":{},"b":{"docs":{},"a":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}}},"s":{"docs":{},"i":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"s":{"docs":{},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"h":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0024897060231734176},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.009058882737795673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002898550724637681},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.010861948142957253},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"(":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"s":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"g":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}},"n":{"docs":{},"k":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}},"r":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"s":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":5.005010438413361},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"_":{"docs":{},"h":{"docs":{},"u":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"b":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"a":{"docs":{},"b":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}}}}}}},"y":{"docs":{},"c":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},"e":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}}},"d":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"f":{"docs":{},"f":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"m":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"z":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"i":{"docs":{},"g":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},")":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"g":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0008618213157138753},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.005580653733723093},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.013908205841446454},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":5.016438356164383},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0035502958579881655},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002803083391730904}},"s":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"_":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},"b":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0035875631145362743},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002452697967764541}},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},":":{"docs":{},":":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}},"_":{"docs":{},"b":{"docs":{},"u":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"e":{"docs":{},"r":{"docs":{},"*":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"?":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"s":{"docs":{},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}},"h":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.010958904109589041}}}}}},"?":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"m":{"docs":{},"a":{"docs":{},"s":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"?":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{},"i":{"docs":{},"c":{"docs":{},":":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"\"":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},".":{"docs":{},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"e":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"[":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}},"i":{"docs":{},"d":{"docs":{},"x":{"docs":{},"s":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},".":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"2":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"docs":{}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"a":{"docs":{},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"x":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044}}}}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{},"i":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125}}}}}}},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0037578288100208767},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.006511538829838169},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},"y":{"docs":{},"!":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"2":{"4":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"2":{"4":{"docs":{},";":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}},"_":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"_":{"docs":{},"i":{"docs":{},"d":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}}}},"w":{"docs":{},"i":{"docs":{},"d":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"/":{"2":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"docs":{}}}}}}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"[":{"1":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"2":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"docs":{}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"s":{"docs":{},"=":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"@":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"_":{"docs":{},"b":{"docs":{},"o":{"docs":{},"b":{"docs":{},"b":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"o":{"docs":{},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"h":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"(":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"a":{"docs":{},"s":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"r":{"docs":{},"t":{"docs":{},"h":{"docs":{},"d":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"l":{"docs":{},"l":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"s":{"docs":{},"f":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}}}}},"o":{"docs":{},"g":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"c":{"docs":{},"k":{"docs":{"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"w":{"docs":{},"f":{"docs":{},"i":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}},"u":{"docs":{},"r":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339}},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"\"":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"n":{"docs":{},"t":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}}}},"e":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},")":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"n":{"docs":{},"k":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}},"e":{"docs":{},"t":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}},"e":{"docs":{},"r":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004441976679622432},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.005010438413361169},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.011834319526627219},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}},"a":{"docs":{},"d":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"e":{"docs":{},"r":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"g":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"u":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"a":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0025245814509699707},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"1":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"}":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}},"k":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001053337163650292},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124}}}}},"k":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002872737719046251},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0030201342281879194}}}},"t":{"docs":{},"h":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"v":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"e":{"docs":{},"f":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}},"l":{"docs":{},"i":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"l":{"docs":{},"l":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{},"!":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"?":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"u":{"docs":{},"l":{"docs":{},"k":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"(":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}}}}}},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},"e":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"c":{"docs":{},"k":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}}},"s":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"f":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"y":{"docs":{},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"z":{"docs":{},"[":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},":":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"o":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.021976178493541353},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0024084778420038534},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"(":{"docs":{},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001677570877369569},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"(":{"docs":{},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},"{":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703054677774585}},"s":{"docs":{},"(":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},":":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"~":{"docs":{},"%":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"_":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"(":{"docs":{},"&":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"_":{"docs":{},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0008618213157138753}}}}}},"y":{"docs":{},"t":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0027903268668615466}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"p":{"docs":{},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0025163563160543532},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.009046052631578948},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"e":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}}}}}}}}}},"z":{"docs":{},"e":{"docs":{},"r":{"docs":{},"o":{"docs":{},"?":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"x":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"y":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004193927193423922},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"docs":{}},"docs":{}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}},"u":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"docs":{}},"docs":{}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.007045797684952189},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"=":{"0":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{},"$":{"docs":{},"(":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"b":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}},"b":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"c":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"x":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.006578947368421052}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004111842105263158}}}}},"1":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}},"2":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946}}}}},"3":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}},"docs":{},"i":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"@":{"docs":{},"(":{"docs":{},"x":{"docs":{},"b":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"|":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"!":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"_":{"0":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"1":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"'":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"=":{"1":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}}}},"^":{"docs":{},"*":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"\\":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}},"docs":{}}}},"c":{"1":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}}}},"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.009735744089012517},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.013980263157894737},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.003985507246376811},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00395882818685669}},"h":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.004528612597776863},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},",":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},"'":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"p":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.011267605633802818},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0026690391459074734},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.01020408163265306},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0024621878297572987},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},":":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0026574541589157587},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"*":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"c":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"*":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002258836035078395}},"*":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0025245814509699707},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.013908205841446454},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731}},"e":{"docs":{},"r":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936}}},"s":{"docs":{},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},":":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"s":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"u":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731}}}},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"g":{"docs":{},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"o":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00809004572634541},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}},"s":{"docs":{},"_":{"docs":{},"g":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"(":{"1":{"0":{"0":{"0":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}}}},"docs":{}},"docs":{}},"docs":{},"_":{"0":{"0":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}},"n":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}},":":{"docs":{},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{}}}}}}}}}}}}},"g":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"e":{"docs":{},"(":{"1":{"0":{"0":{"0":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{},"$":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"i":{"docs":{},"p":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"l":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.007469118069520253},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.009863066168725463},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0045726345409778405}},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0019151584793641674}},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"}":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}},"|":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"|":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"_":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}}}}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}},"}":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703054677774585}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}},"n":{"docs":{},"m":{"docs":{},"a":{"docs":{},"y":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0031323414252153485},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"e":{"docs":{},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"s":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},"[":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"+":{"docs":{},"+":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}}},"(":{"docs":{},"h":{"docs":{},"u":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},"_":{"docs":{},"o":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}}},"(":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"o":{"docs":{},"s":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0029227557411273487},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925}},"e":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"s":{"docs":{},"e":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"n":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"t":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"r":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"e":{"docs":{},"c":{"docs":{},"k":{"1":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"2":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0012448530115867088},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0018453279651065259},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0036555645816409425},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},".":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"a":{"docs":{},"t":{"docs":{},"s":{"docs":{},"h":{"docs":{},"e":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"m":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125}}}}}}}}}},"k":{"1":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"2":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"docs":{}},"u":{"docs":{},"n":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"s":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304}},"'":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"r":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"h":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{"./":{"ref":"./","tf":0.015306122448979591},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.009633911368015413},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.030985915492957747},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":5.010416666666667},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.03389830508474576},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.017391304347826087},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.023809523809523808},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.018018018018018018},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.018691588785046728},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.004251926654265214},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.011029411764705883},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004151838671411625},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.006954102920723227},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.007653061224489796},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.005479452054794521},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0068669527896995704},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.006493506493506494},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0028139289482940555},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0018137847642079807},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0047522063815342835},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.003952569169960474}},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.011267605633802818},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"/":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},"b":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0049162901939941534}},"'":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013287270794578793}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276}}}},"*":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"y":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"s":{"docs":{},"y":{"docs":{},"m":{"docs":{},"b":{"docs":{},"o":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"/":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276}},":":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},":":{"docs":{},":":{"docs":{},"~":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"[":{"0":{"docs":{},"]":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"docs":{}}}},"docs":{},"c":{"docs":{},"]":{"docs":{},")":{"docs":{},".":{"docs":{},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"i":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"n":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"]":{"docs":{},"=":{"docs":{},"\"":{"0":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"docs":{}}}}}}}}}},"]":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"_":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"p":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"!":{"docs":{},"(":{"docs":{},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},":":{"docs":{},":":{"docs":{},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},":":{"docs":{},":":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"n":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"e":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},".":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"1":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"docs":{}}}}}}}},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},"e":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}},"+":{"docs":{},"'":{"0":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"1":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"docs":{}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},":":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}},"=":{"docs":{},"'":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"s":{"docs":{},"(":{"docs":{},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"s":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},".":{"docs":{},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"[":{"2":{"5":{"6":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"docs":{}},"docs":{}},"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"w":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.011126564673157162}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"s":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}}}}}}},"!":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.016310372129849565}},"l":{"docs":{},"a":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{"./":{"ref":"./","tf":0.01020408163265306}}}}},"p":{"docs":{},"s":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"(":{"2":{"0":{"2":{"0":{"docs":{},":":{"2":{"0":{"3":{"0":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}}}},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},".":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}},"o":{"docs":{},"q":{"docs":{},"u":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"u":{"docs":{},"m":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.005067300079176564},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"s":{"docs":{},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},")":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},"o":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0050415183867141165},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.005351996706463565},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":5.015151515151516},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"(":{"docs":{},"f":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}}}}},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},":":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"s":{"docs":{},"s":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},")":{"docs":{},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0028503562945368173}},")":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"s":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"m":{"docs":{},"m":{"docs":{},"o":{"docs":{},"n":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703054677774585},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.012145748987854251},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.009439200444197668},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009468917249897077},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.005150214592274678},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005627857896588111},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006944444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.011541072640868975},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01301775147928994},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"l":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"u":{"docs":{},"n":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.011560693641618497},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},".":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"s":{"docs":{},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}},"a":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"n":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0037052284890901604}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557}}},"s":{"docs":{},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"e":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"d":{"docs":{},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"n":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"x":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":5.016233766233766},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0032245062474808546},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.015782828282828284},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0048134777376654635}},"(":{"0":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}}}},"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},".":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"1":{"docs":{},".":{"0":{"docs":{},"_":{"docs":{},"f":{"6":{"4":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}},"docs":{}}}},"docs":{}}},"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"k":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}}}}},"i":{"docs":{},"c":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},")":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"r":{"docs":{},"e":{"docs":{},"h":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}},"s":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":5.016689847009736},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"!":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"u":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.01348747591522158},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":5.0476190476190474},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":5.096045197740113},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.03676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.005479452054794521},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.00487012987012987},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.006618531889290012},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},"?":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"\"":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"?":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"_":{"docs":{},"s":{"docs":{},"o":{"docs":{},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"s":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"u":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":10.001268115942029}},"s":{"docs":{},"(":{"docs":{},"[":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"]":{"docs":{},"$":{"docs":{},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}},"y":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},".":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"a":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"t":{"docs":{},"o":{"docs":{},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"i":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"o":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339}},"i":{"docs":{},"t":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}},"n":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.007100591715976331}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"i":{"docs":{},"l":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}}}},"e":{"docs":{},"l":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.020833333333333332}}}}}},"e":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"i":{"docs":{},"s":{"docs":{},"d":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478}}}}}},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"d":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"x":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"l":{"docs":{},"i":{"docs":{},"b":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}},"?":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"r":{"docs":{},"i":{"docs":{},"b":{"docs":{},"u":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":10.011267605633803},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},"e":{"docs":{},",":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},".":{"docs":{},"m":{"docs":{},"d":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},":":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}}}}}}}},"o":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},".":{"docs":{},"m":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"d":{"docs":{},".":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"k":{"docs":{},",":{"docs":{},"v":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}}}}}}}}}}},"s":{"docs":{},"?":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"c":{"docs":{},"t":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"i":{"docs":{},"n":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"u":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0023752969121140144},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"e":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114}}},"s":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"s":{"docs":{},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}}}}},"c":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"s":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}},"p":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"a":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}},"(":{"docs":{},"&":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"*":{"docs":{},"*":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"*":{"docs":{},"*":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"v":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}}},"l":{"docs":{},"u":{"docs":{},"s":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"d":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"g":{"docs":{},"l":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}}},"s":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},":":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},"s":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"m":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"e":{"docs":{},"(":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},"o":{"docs":{},"l":{"docs":{},"e":{"docs":{},".":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{},"(":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},".":{"docs":{},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}}}}},"\"":{"docs":{},"[":{"0":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"1":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"2":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}},"\\":{"docs":{},"n":{"docs":{},"g":{"docs":{},"i":{"docs":{},"r":{"docs":{},"l":{"docs":{},"s":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"s":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"g":{"docs":{},"u":{"docs":{},"y":{"docs":{},"s":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"t":{"docs":{},"h":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"c":{"docs":{},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"h":{"docs":{},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}}}}}}}}}},"'":{"docs":{},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}}},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"(":{"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"(":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"docs":{}}}}}}}}}},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},".":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"`":{"docs":{},"$":{"docs":{},"{":{"docs":{},"g":{"docs":{},"i":{"docs":{},"r":{"docs":{},"l":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"u":{"docs":{},"y":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},"`":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"}":{"docs":{},"`":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},"`":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},"`":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"}":{"docs":{},"`":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}}}}}}}},"(":{"docs":{},"$":{"docs":{},"{":{"docs":{},"p":{"docs":{},".":{"docs":{},"x":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}}}}}}},"w":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},".":{"docs":{},"p":{"docs":{},"e":{"docs":{},"e":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},".":{"docs":{},"p":{"docs":{},"e":{"docs":{},"e":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}},"g":{"docs":{},"a":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"c":{"docs":{},"k":{"2":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"l":{"docs":{},"n":{"docs":{},"(":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.005614035087719298},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.005049162901939941},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.003915426781519186},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.010972716488730723},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0030201342281879194},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.005345394736842105},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00395882818685669},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"&":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001053337163650292},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011958543715120914},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0029655990510083037},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}},"o":{"docs":{},"r":{"docs":{},"(":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}},"*":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.00974025974025974},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815}},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"l":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"(":{"docs":{},"a":{"docs":{},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}}},"docs":{}},"docs":{}}}}}}}}}}}},"u":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"docs":{}},"docs":{}}}}}}}}},"s":{"docs":{},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}},"c":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"v":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"x":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.036036036036036036},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"l":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"p":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"docs":{}}}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"r":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{},"c":{"docs":{},"e":{"docs":{},"i":{"docs":{},"l":{"docs":{},"(":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"2":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"x":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}},"s":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"g":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}}},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":10.053333333333333},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":5.0210993892282065},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":5.00709219858156},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":5.028061224489796},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":3.3436337625178822}},"i":{"docs":{},"o":{"docs":{},"n":{"1":{"docs":{},"d":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}},"docs":{},"s":{"docs":{},",":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},".":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}},"?":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}},":":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}},"!":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003886729594669628},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003886729594669628},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653}}},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"e":{"docs":{},"d":{"docs":{},"!":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}}}},"v":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003886729594669628},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339}},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"y":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0068669527896995704}}},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}}}}}},"x":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216}}}}}}}}}}},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"1":{"docs":{},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"t":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653}}}}}}}}}}}}}},"docs":{}}}}}}},"x":{"docs":{},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}}}}},"c":{"docs":{},"y":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"(":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"[":{"docs":{},"]":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"(":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"[":{"docs":{},"]":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}}}},"x":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"n":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"f":{"docs":{},"u":{"docs":{},"s":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"i":{"docs":{},"g":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}},"n":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"d":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"s":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"o":{"docs":{},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"j":{"docs":{},"(":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},"_":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},"u":{"docs":{},"g":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001583531274742676},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"o":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"e":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"y":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0033815517565282736},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"_":{"docs":{},"t":{"docs":{},"u":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},"(":{"docs":{},"&":{"docs":{},"x":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},".":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"s":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"(":{"1":{"docs":{},")":{"docs":{},".":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"_":{"docs":{},"b":{"docs":{},"y":{"docs":{},"(":{"2":{"docs":{},")":{"docs":{},".":{"docs":{},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},":":{"docs":{},":":{"docs":{},">":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},")":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"x":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},".":{"docs":{},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"(":{"docs":{},"_":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}}}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"[":{"1":{"docs":{},":":{"2":{"docs":{},":":{"docs":{},"n":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"docs":{}}},"2":{"docs":{},":":{"2":{"docs":{},":":{"docs":{},"n":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"docs":{}}},"docs":{}}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"_":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},"e":{"docs":{},"d":{"docs":{},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"d":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"i":{"docs":{},"n":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"[":{"0":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"1":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"2":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"docs":{}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"s":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.008421052631578947},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0017273452032952432},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.004467912266450041},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":3.3729268862415323},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0026845637583892616},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.006657323055360897}},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"_":{"docs":{},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"k":{"docs":{},"w":{"docs":{},"i":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"1":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}}},"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"&":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"[":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}},"a":{"docs":{},":":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"[":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}}}}}}}}}}}}}}},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"k":{"docs":{},"w":{"docs":{},"i":{"docs":{},"s":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"(":{"docs":{},"p":{"1":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{}}}}}}}}}}}},"!":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"d":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"(":{"0":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}},"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"$":{"docs":{},"x":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815}}},"s":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"[":{"2":{"5":{"6":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"docs":{}},"docs":{}},"docs":{},"(":{"docs":{},"u":{"docs":{},"n":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"i":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"d":{"docs":{},"o":{"docs":{},"w":{"docs":{},"n":{"docs":{},"(":{"docs":{},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"!":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"r":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"!":{"docs":{},")":{"docs":{},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},"p":{"docs":{},"l":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"l":{"docs":{},"d":{"docs":{},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}}}}},"g":{"docs":{},"h":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}}}},"p":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"y":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"c":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"d":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},")":{"docs":{},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}}},"s":{"docs":{},"t":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"l":{"docs":{},"i":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":3.334035087719298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"y":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107}}}},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828}},"e":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.01322463768115942},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"s":{"docs":{},"p":{"docs":{},"o":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0029227557411273487},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"l":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},"e":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"e":{"docs":{},"f":{"docs":{},"f":{"docs":{},"i":{"docs":{},"c":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001340610935554917},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0023917087430241827},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004448398576512456},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00832870627429206},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.007653061224489796},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.015232606010703994},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.008441786844882167},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.012626262626262626},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.008350730688935281},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.01493550577053632},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.014792899408284023},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005255781359495445},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"i":{"docs":{},"v":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007773459189339256},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009057225195553726},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005627857896588111},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006944444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.010862186014935505},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01242603550295858},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}},"o":{"docs":{},"n":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"e":{"docs":{},"_":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}},"e":{"docs":{},"(":{"2":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}}}},"3":{"docs":{},",":{"2":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}},"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}},"l":{"docs":{},"e":{"docs":{},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"docs":{}},"docs":{}}}}}},"s":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}},"p":{"docs":{},"h":{"docs":{},"r":{"docs":{},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},":":{"docs":{},":":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"(":{"docs":{},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"n":{"docs":{},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}},"i":{"docs":{},"r":{"docs":{},"c":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}}}}}}}}}}}}}}}}}},"g":{"docs":{},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"p":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"i":{"docs":{},"d":{"docs":{},"(":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}}},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"(":{"docs":{},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"_":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"4":{"0":{"9":{"6":{"docs":{},"^":{"2":{"docs":{},",":{"docs":{},"[":{"0":{"docs":{},",":{"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}},"docs":{}}},"docs":{}}}},"docs":{}}},"docs":{}},"docs":{}},"docs":{}},"docs":{},"n":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}}}}}}}}},"s":{"docs":{},"o":{"docs":{},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{},"_":{"docs":{},"o":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852}},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}}},"d":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"e":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}},"e":{"docs":{},"(":{"2":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"3":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"s":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"s":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"p":{"docs":{},"h":{"docs":{},"r":{"docs":{},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"y":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"s":{"docs":{},"a":{"docs":{},"w":{"docs":{},"t":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}}}}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}},"p":{"docs":{},"t":{"docs":{},"o":{"docs":{},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"h":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551}},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":10.015657620041754}}},"y":{"docs":{},"\"":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731}}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}}}}}}}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001053337163650292},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"u":{"docs":{},"c":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"c":{"docs":{},"k":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}},"z":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"f":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"o":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"p":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0070860863736474195},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001509813789632612},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.004119053946319426},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.006263048016701462},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0035694157430020664},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0018463286464990769},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"o":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"(":{"0":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"1":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},"4":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"docs":{},"(":{"docs":{},"q":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"c":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011958543715120914},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0018463286464990769},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.010688405797101449},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.006211180124223602},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}},"u":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"s":{"docs":{},".":{"docs":{},"\"":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},":":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"e":{"docs":{},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{},"y":{"docs":{},"(":{"docs":{},"&":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"a":{"docs":{},"m":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"o":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0038043478260869567}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}},"s":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"n":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"'":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},"n":{"docs":{},"i":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"d":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0031323414252153485},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}}}}}}}},"v":{"docs":{},"a":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004151838671411625}},"s":{"docs":{},"[":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}},"u":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}},"p":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},"o":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"_":{"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}}}}}}}}}}}}}}}}},"x":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"2":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"docs":{}}}}}}}}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"!":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"s":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0035430431868237098},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0021808421405804393},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0018602179112410311},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.00974025974025974},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002803083391730904},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"s":{"docs":{},",":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"!":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"!":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0029585798816568047},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},":":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},")":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"p":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"a":{"docs":{},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}},"b":{"docs":{},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"c":{"docs":{},"a":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"m":{"docs":{},"p":{"docs":{},"\"":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"b":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},"g":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"f":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"r":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"a":{"docs":{},"y":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.006109979633401222}},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134}},"(":{"0":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}},"1":{"docs":{},",":{"1":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"c":{"docs":{},"e":{"docs":{},"i":{"docs":{},"l":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}},"{":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}},"i":{"docs":{},"c":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}},"_":{"docs":{},"b":{"docs":{},"o":{"docs":{},"x":{"docs":{},"_":{"docs":{},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"r":{"docs":{},"!":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}}}}}},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}}}}}}}}}}}}}}}}}},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"!":{"docs":{},"(":{"docs":{},"c":{"docs":{},"p":{"docs":{},"u":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}},"u":{"docs":{},"d":{"docs":{},"a":{"docs":{},"d":{"docs":{},"e":{"docs":{},"v":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":5.005686433793664},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"(":{"docs":{},"[":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"]":{"docs":{},"$":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"c":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"t":{"docs":{},"e":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428}}}}},"z":{"docs":{},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}},"c":{"docs":{},"h":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"v":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"s":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"e":{"docs":{},"s":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"e":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}}}},"u":{"docs":{},"s":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"i":{"docs":{},"r":{"docs":{},"o":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"b":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.007017543859649123},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0012448530115867088},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0017273452032952432},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.005873140172278779},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"i":{"docs":{},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0048134777376654635}}},"f":{"docs":{},"i":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"v":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}},"u":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"i":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"r":{"docs":{},"i":{"docs":{},"f":{"docs":{},"i":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{},")":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}}}}}}}}},"t":{"docs":{},"y":{"docs":{},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},")":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"n":{"docs":{},"g":{"docs":{},"+":{"docs":{},"+":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"l":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"y":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}},"n":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}},"l":{"docs":{},"i":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"u":{"docs":{},"p":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"e":{"docs":{},"r":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"s":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"r":{"docs":{},"g":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"u":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}}},"o":{"docs":{},"j":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}},"c":{"docs":{},"k":{"docs":{},"w":{"docs":{},"i":{"docs":{},"s":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604}},"e":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"?":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}},"b":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"s":{"docs":{},"e":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"s":{"docs":{},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"(":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}},"?":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"d":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"n":{"docs":{},"e":{"docs":{},")":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}}}},"c":{"docs":{},"k":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"+":{"docs":{},"+":{"1":{"4":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"docs":{}},"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0234375},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"l":{"docs":{},"i":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"y":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"t":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"y":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}}}}}}}}},"l":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837}},"(":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"s":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}}}}}}}}}}}}}}}}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"e":{"docs":{},"b":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}}}}}},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.006008583690987125},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},")":{"docs":{},"^":{"2":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"docs":{}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"+":{"1":{"docs":{},")":{"docs":{},"*":{"docs":{},"*":{"2":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}},")":{"docs":{},"/":{"docs":{},"(":{"2":{"docs":{},"*":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{},"*":{"docs":{},"*":{"2":{"docs":{},")":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}},"docs":{}}}}}}}}}},"docs":{}}}}},"docs":{}}}}},"docs":{}}}},"r":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"u":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.007608695652173913}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"y":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"a":{"docs":{},"s":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}}}},"i":{"docs":{},"l":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407}},"(":{"docs":{},"b":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{},"s":{"docs":{},"[":{"2":{"docs":{},",":{"2":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"docs":{}}},"docs":{}}}}}}}}}}}}}}}},"x":{"docs":{},"p":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},"(":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"p":{"docs":{},"p":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},"u":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}},"r":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}}}}},"o":{"docs":{},"w":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"k":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}},"x":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}}}}}},"u":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0014363688595231256},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0027903268668615466},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.011029411764705883},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00274079874706343},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}},".":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"_":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},"e":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0035587188612099642}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"e":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}},"r":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},".":{"docs":{},".":{"docs":{},".":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}},".":{"docs":{},"y":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}},"v":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"m":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}}}},"d":{"docs":{},"a":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},".":{"docs":{},"@":{"docs":{},"s":{"docs":{},"y":{"docs":{},"n":{"docs":{},"c":{"docs":{},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}}},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}},"t":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"o":{"docs":{},"f":{"docs":{},"f":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}},":":{"docs":{},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"docs":{}},"docs":{}}}}}}}}}},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"b":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}}}}}},"b":{"docs":{},"e":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},"!":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.005917159763313609}}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"#":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}},"i":{"docs":{},"c":{"docs":{},"c":{"docs":{},"o":{"docs":{},"t":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}}},"r":{"docs":{},"c":{"docs":{},"u":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588}},"s":{"docs":{},":":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}}}},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.01462225832656377},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.00631578947368421},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"e":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295}}},"(":{"1":{"docs":{},".":{"0":{"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"docs":{}}},"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"c":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"?":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}},"}":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"t":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}},"s":{"docs":{},"?":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"p":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}},"\"":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731}}},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}}}}}},"d":{"docs":{},"q":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}},"m":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002010916403332376},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0010629816635663034},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0024422318241593085}},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}},"o":{"docs":{},"v":{"docs":{},"n":{"docs":{},"z":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002533650039588282}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"b":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009301089556205156}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"[":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"b":{"docs":{},"b":{"docs":{},"c":{"docs":{},"!":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"a":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},".":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"_":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"k":{"docs":{},"l":{"docs":{},"a":{"docs":{},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{},"s":{"docs":{},"(":{"docs":{},"[":{"docs":{},"\"":{"docs":{},"$":{"0":{"docs":{},".":{"0":{"docs":{},"$":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"docs":{}}},"docs":{}}}}}}}}}}},"s":{"docs":{},"(":{"docs":{},"[":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}}},"docs":{}}}}}}}}}}}}}}},"l":{"docs":{},"a":{"docs":{},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}}},"f":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"|":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},"[":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}}}}}}}},"p":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},"u":{"docs":{},"p":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0026690391459074734}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.008634868421052632},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124}}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}},"=":{"docs":{},"=":{"docs":{},"b":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"@":{"docs":{},"(":{"docs":{},"x":{"docs":{},"c":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"c":{"docs":{},"w":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.003355704697986577}},"(":{"docs":{},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},"[":{"docs":{},"j":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}},"p":{"1":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},"a":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}},":":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}},":":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}},"?":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"_":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"1":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"'":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"n":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"1":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}}}}}}},"{":{"docs":{},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"y":{"docs":{},"p":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"c":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.003985507246376811}},"i":{"docs":{},"c":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653}}}},"e":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002898550724637681}}}}}}},"/":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}},"c":{"docs":{},"+":{"docs":{},"+":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"*":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}},"+":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}}}}}}}}}}},"v":{"docs":{},"t":{"docs":{},"s":{"docs":{},"i":{"2":{"docs":{},"s":{"docs":{},"d":{"docs":{},"q":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368}}}}}},"docs":{}}},"t":{"docs":{},"s":{"docs":{},"d":{"2":{"docs":{},"s":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}}}}},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"'":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"_":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579}}},"{":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.005756578947368421}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}}}},"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946}}}}},"2":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003289473684210526}}}},"j":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"^":{"docs":{},"*":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"\\":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}},"docs":{}}}},"d":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.006954102920723227},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.011513157894736841},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0125},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"i":{"docs":{},"f":{"docs":{},"f":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844}},"e":{"docs":{},"r":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.006493506493506494},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.006618531889290012},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003153468815697267},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"i":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"?":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}},"i":{"docs":{},"c":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}}}}},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}}},"v":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"u":{"docs":{},"s":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}},"s":{"docs":{},"c":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"v":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{},"u":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255}}}}}}}},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.017777777777777778},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.009533898305084746}},"e":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"p":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"i":{"docs":{},"p":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}}}}},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"b":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.018018018018018018},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.007017543859649123},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.009504412763068567},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.007905138339920948},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":5.008474576271187}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}}},"docs":{},"s":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"r":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"s":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},")":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"?":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"l":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"g":{"docs":{},"u":{"docs":{},"i":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}},"l":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"(":{"0":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}}},"g":{"docs":{},"u":{"docs":{},"i":{"docs":{},"s":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"s":{"docs":{},"i":{"docs":{},"m":{"docs":{},"i":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112}}},"y":{"docs":{},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"l":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"y":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"t":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"v":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},"i":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},"s":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"o":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"\"":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}}}}}},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}},"e":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"r":{"docs":{},"g":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}},"(":{"docs":{},"b":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},",":{"2":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}}}}}},"n":{"docs":{},",":{"2":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}}},"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},"f":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"a":{"docs":{},"g":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.006167763157894737},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"z":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"s":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"l":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0035502958579881655}}}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.005763688760806916},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0068669527896995704},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0053254437869822485},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"s":{"docs":{},",":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"!":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"a":{"docs":{},"l":{"docs":{},";":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},"(":{"docs":{},"(":{"docs":{},"v":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"[":{"docs":{},"(":{"docs":{},"v":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"w":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},":":{"docs":{},":":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"{":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"[":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0015944724953494552}}},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"[":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}},"{":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"}":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"}":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"e":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}},")":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"u":{"docs":{},"t":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"g":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"i":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"s":{"docs":{},":":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"d":{"docs":{},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"e":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}},"t":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}},"a":{"docs":{},"y":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.01956521739130435}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"!":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"s":{"docs":{},")":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0014492753623188406}}}}},"r":{"docs":{},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}},"t":{"docs":{},"a":{"docs":{"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":5.0508474576271185},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0035087719298245615},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0035430431868237098},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0015944724953494552},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":5.015299026425591},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.012350761630300536},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}},"e":{"docs":{},"t":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"s":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"f":{"docs":{},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},".":{"docs":{},"c":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"[":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}},"{":{"docs":{},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"e":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.010326086956521738}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"s":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"v":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"s":{"docs":{},"h":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"t":{"docs":{},"y":{"docs":{},"p":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}}}},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"s":{"docs":{},"!":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}}},"e":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},".":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"\"":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"l":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"m":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"l":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}},"v":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"e":{"docs":{},"t":{"docs":{},"e":{"docs":{},"!":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}},"i":{"docs":{},"m":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"d":{"docs":{},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}}}},"a":{"docs":{},"m":{"docs":{},"b":{"docs":{},"r":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"t":{"docs":{},"a":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.00350385423966363}}}}},"v":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}},"i":{"docs":{},"c":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"a":{"docs":{},"t":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"s":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}},"o":{"docs":{},"t":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"p":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}},"t":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.003638801110791918},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703054677774585}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"s":{"docs":{},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},",":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}},":":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"o":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}},"r":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002717391304347826},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}},"f":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.009824561403508772},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0037345590347601263},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0036906559302130517},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0029231995748073346},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00822239624119029},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004744958481613286},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.004026845637583893},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.004061738424045491},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.011158798283261802},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0028139289482940555},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0018463286464990769},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.004517221908526256}},"a":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.006954102920723227},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}},"i":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},":":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},"s":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},":":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},";":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}},"q":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"e":{"docs":{},"u":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"q":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},"!":{"docs":{},"(":{"docs":{},"q":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"docs":{}}}}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}},"(":{"docs":{},"[":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},".":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}},"r":{"docs":{},"i":{"docs":{},"v":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.020242914979757085},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}}},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"s":{"docs":{},"c":{"docs":{},"r":{"docs":{},"i":{"docs":{},"b":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0048134777376654635},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"e":{"docs":{},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}},"p":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"o":{"docs":{},"r":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}},"t":{"docs":{},"r":{"docs":{},"o":{"docs":{},"y":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"_":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},"\"":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"e":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"d":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"k":{"docs":{},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}}},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"i":{"docs":{},"s":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":5.02803738317757},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"m":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603}}}},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0035875631145362743},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731}},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},".":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"_":{"docs":{},"d":{"docs":{},"f":{"docs":{},"s":{"docs":{},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"o":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"e":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"_":{"docs":{},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"d":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"_":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276}},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},".":{"docs":{},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"_":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"[":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}},"r":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"y":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}},"a":{"docs":{},"y":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},"b":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"u":{"docs":{},"g":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"n":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0028214429665457475},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0048134777376654635},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.01059322033898305}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"y":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},".":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"s":{"docs":{},"u":{"docs":{},"m":{"docs":{},":":{"docs":{},":":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"[":{"docs":{},"j":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}},"=":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"\"":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"d":{"docs":{},"u":{"docs":{},"c":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"o":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"l":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0050335570469798654},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.008529650690495532},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0035174111853675696},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.01406050276949297},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.012293430068520758},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.004592901878914405},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005606166783461808},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"e":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0015622780854992189},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},"[":{"3":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"docs":{},"]":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004997223764575236},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004523026315789474},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}},"[":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.004061738424045491},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.004118733134497941},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}},".":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}},"o":{"docs":{},"f":{"docs":{},"(":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"1":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"4":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"7":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"docs":{}}}}}}}}}}}}},"c":{"docs":{},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}},"u":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}}}}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}},"e":{"docs":{},"s":{"docs":{},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"!":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"m":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0026690391459074734},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":5.005681818181818},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653}}},"s":{"docs":{},"\"":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},";":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}},"w":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"t":{"docs":{},"o":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}},"n":{"docs":{},"e":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"'":{"docs":{},"t":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"a":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"?":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"o":{"docs":{},"r":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},"s":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"!":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0032557694149190847}},"s":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},":":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011490950876185005}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011490950876185005}}}}},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}}},"~":{"docs":{},"%":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}}},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}},".":{"docs":{},".":{"docs":{},".":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"e":{"docs":{},"(":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},"_":{"docs":{},"b":{"docs":{},"t":{"docs":{},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"0":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"1":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"2":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"docs":{}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"_":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0012448530115867088}},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},"_":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"docs":{}},"{":{"1":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}},"2":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"docs":{}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"2":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"docs":{}}}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"e":{"docs":{},"(":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"docs":{}}}}}}}}}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},"_":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}},"b":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"&":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}}}}}}}}},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"e":{"docs":{},"(":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"(":{"docs":{},"&":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}},".":{"docs":{},".":{"docs":{},".":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"_":{"docs":{},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0016278847074595424}},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},"_":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},"docs":{}}}}}}}}}}}}}}}},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703054677774585}},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},"c":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"e":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}}}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"i":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"!":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"e":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}},"1":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},"docs":{}}}}}}}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0008618213157138753}}}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}},"e":{"docs":{},".":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},"c":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"e":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}}}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}},")":{"docs":{},"]":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.005635919594213789},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"(":{"docs":{},"&":{"docs":{},"x":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}},"x":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"j":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"p":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"j":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}}}},"w":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.004787896198410418},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002258836035078395}}}}},"e":{"docs":{},"l":{"docs":{},"l":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"a":{"docs":{},"w":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"m":{"docs":{},"a":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"}":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"u":{"docs":{},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"b":{"docs":{},"u":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"m":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"b":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"e":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"e":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"c":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}},"y":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"i":{"docs":{},"c":{"docs":{},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}}}}}}}}}}}}}}}}}}}}}}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004523026315789474},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"x":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0047522063815342835},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},")":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{}},"docs":{}}}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"_":{"1":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"docs":{},"{":{"1":{"0":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"docs":{}},"docs":{}}},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"\\":{"docs":{},"x":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"x":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}},"'":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},"_":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"n":{"docs":{},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"{":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}}},",":{"3":{"1":{"docs":{},")":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"docs":{}},"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}},".":{"docs":{},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"d":{"docs":{},"u":{"docs":{},"p":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003700657894736842}},"]":{"docs":{},".":{"docs":{},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"]":{"docs":{},".":{"docs":{},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}}}}},"2":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"]":{"docs":{},".":{"docs":{},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}}}}},"3":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}},"+":{"1":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"docs":{}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946}}}},"j":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"^":{"docs":{},"*":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"_":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"1":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"{":{"docs":{},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"g":{"docs":{},"l":{"docs":{},"i":{"docs":{},"b":{"docs":{},"c":{"docs":{},"x":{"docs":{},"x":{"docs":{},"_":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"u":{"docs":{},"g":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"\\":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"docs":{}}},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.036074421246981965},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0028214429665457475}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.008237466268995882},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0031245561709984378},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0039767078539980115},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},"docs":{}}}}}}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.011362022439994318},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}},"^":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"3":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"docs":{}},"y":{"docs":{},"p":{"docs":{},"e":{"docs":{},"=":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534}}}}}}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}},"o":{"docs":{},"r":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{}},"docs":{}}}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}},"+":{"docs":{},"e":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"+":{"2":{"2":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"docs":{}},"docs":{}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"=":{"2":{"8":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"9":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}},"m":{"docs":{},"r":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"e":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.011231884057971014},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"f":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}},"i":{"docs":{},"c":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},",":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"i":{"docs":{},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"v":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},")":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"m":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}},"e":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.018245614035087718},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0017236426314277506},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.005338078291814947},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004441976679622432},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0028782894736842104},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.004433887569279493},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},"s":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}}},"'":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"s":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"g":{"docs":{},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"c":{"docs":{},"t":{"docs":{},"r":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"n":{"docs":{},"e":{"docs":{},"t":{"docs":{},"i":{"docs":{},"s":{"docs":{},"m":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}},"n":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}},"i":{"docs":{},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":5.003008709422011}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"\"":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"\"":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}}}},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"a":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"l":{"docs":{},"i":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731}}},"s":{"docs":{},"o":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}},"n":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.009384276548884421},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.009058882737795673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0037204358224820623},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.009397024275646046},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.010083036773428233},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.004697986577181208},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.016842105263157894},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.005150214592274678},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.004320871688897238},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.011363636363636364},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.005756578947368421},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00710126402499645},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.004635227730753728},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.012219959266802444},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0019927536231884057},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.005067300079176564},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"h":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}}},"=":{"docs":{},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0024897060231734176}},"'":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}}}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"f":{"docs":{},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}}},"i":{"docs":{},"f":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"w":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}},"s":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0052986512524084775}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},")":{"docs":{},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},".":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{},"(":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"s":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"docs":{}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"s":{"docs":{},";":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}},"[":{"1":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}},"2":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}}},"docs":{}},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}}}}}}}}},"j":{"docs":{},"o":{"docs":{},"y":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}},"t":{"docs":{},"r":{"docs":{},"y":{"docs":{},".":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"i":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643}},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"q":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"!":{"docs":{},"(":{"docs":{},"q":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"_":{"docs":{},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428}}},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}},"a":{"docs":{},"g":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}}}},"c":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":5.005447781025778},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}},"e":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"b":{"docs":{},"i":{"docs":{},"b":{"docs":{},"b":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"_":{"docs":{},"b":{"docs":{},"o":{"docs":{},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},":":{"docs":{},":":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"{":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"p":{"docs":{},"h":{"docs":{},"r":{"docs":{},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"c":{"docs":{},"u":{"docs":{},"l":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"_":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"_":{"docs":{},"o":{"docs":{},"f":{"docs":{},"f":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"e":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"e":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"_":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"s":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"_":{"docs":{},"q":{"docs":{},"w":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"t":{"docs":{},"r":{"docs":{},"y":{"docs":{},"_":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},".":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"_":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397}},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}},"r":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"(":{"docs":{},"&":{"docs":{},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"b":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},"&":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}},"u":{"docs":{},"r":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"n":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"m":{"docs":{},"p":{"docs":{},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"l":{"docs":{},"o":{"docs":{},"s":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"r":{"docs":{},"y":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.015657620041753653}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"g":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"s":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"u":{"docs":{},"m":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},"_":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},")":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"c":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"_":{"docs":{},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}},"a":{"docs":{},"l":{"docs":{},"*":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"d":{"docs":{},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}}},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},")":{"docs":{},".":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.003022974607013301},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.006618531889290012},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}}}},"l":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}},"s":{"docs":{},"s":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"c":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}},"p":{"docs":{},"e":{"docs":{},"c":{"docs":{},"i":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703054677774585},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"b":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"_":{"docs":{},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"x":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.03389830508474576},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.017391304347826087},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.023809523809523808},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.018018018018018018},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.018691588785046728},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.01020408163265306},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.00487012987012987},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0028782894736842104},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0033944331296673455},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.006211180124223602},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"e":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002803083391730904},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.006355932203389831}}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"c":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"l":{"docs":{},"i":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},"y":{"docs":{},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"c":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"e":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"n":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}},"l":{"docs":{},"u":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"s":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}},"p":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"s":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},":":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"i":{"docs":{},"c":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"l":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"y":{"docs":{},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}},"o":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"s":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"c":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"?":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"c":{"docs":{},"t":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003854239663629993}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"n":{"docs":{},"s":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.012145748987854251},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},"s":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.024291497975708502},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},".":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}}}},"o":{"docs":{},"n":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00684931506849315},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.005681818181818182},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"a":{"docs":{},"l":{"docs":{},".":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},"s":{"docs":{},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},".":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}},"(":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}},":":{"docs":{},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"docs":{}},"docs":{}}}}}}}}}}}},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}},"r":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"(":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"x":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047}}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},".":{"docs":{},"(":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534}}}}},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.013333333333333334},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}},"=":{"docs":{},"(":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}}},"r":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"r":{"docs":{},"a":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"s":{"docs":{},"!":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"_":{"docs":{},"s":{"docs":{},"u":{"docs":{},"c":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649}}}}}}},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011958543715120914},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0023492560689115116},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0026690391459074734},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004441976679622432},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.004116920543433511},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0028139289482940555},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0041753653444676405},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0038043478260869567},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003167062549485352},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.00700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002010916403332376}}}},"r":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304}},"f":{"docs":{},"a":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"'":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}},"l":{"docs":{},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"s":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"l":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}},"e":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.01177536231884058}},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},")":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},")":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"?":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"_":{"docs":{},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}}}},"y":{"docs":{},":":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}},"v":{"docs":{},"e":{"docs":{},"s":{"docs":{},"d":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"p":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"e":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002298190175237001},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001677570877369569},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.006017418844022169}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}}},"c":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}},"r":{"docs":{},"a":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"!":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"r":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005956552207428171},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"2":{"4":{"docs":{},";":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}},"(":{"docs":{},"\"":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"s":{"docs":{},"!":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}},"_":{"docs":{},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"(":{"docs":{},"w":{"docs":{},"h":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}}}}}}},"v":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"e":{"docs":{},"r":{"docs":{},"y":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},"e":{"docs":{},"'":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"t":{"docs":{},"h":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"b":{"docs":{},"o":{"docs":{},"d":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"w":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.004696599661844825},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925}},"l":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"[":{"docs":{},"k":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}},"s":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003854239663629993}},"u":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"s":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"o":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"v":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904}}}}}},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"u":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}},"i":{"docs":{},"l":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"d":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"c":{"docs":{},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},")":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},")":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"m":{"docs":{},"o":{"docs":{},"j":{"docs":{},"i":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}}}},"p":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0008618213157138753},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}}},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}},"i":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"b":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"e":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"u":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.03125},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0019883539269990058},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0026920031670625497},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"?":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"{":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},",":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"!":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"s":{"docs":{},"(":{"docs":{},"o":{"docs":{},"b":{"docs":{},"j":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}},"i":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"l":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0024621878297572987}}}}}},"i":{"docs":{},"b":{"docs":{},"r":{"docs":{},"i":{"docs":{},"u":{"docs":{},"m":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"x":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"n":{"docs":{},"s":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}},"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}},"d":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"u":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},"g":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.005150214592274678},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},"e":{"docs":{},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"!":{"docs":{},")":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},")":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224}},"%":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}},"'":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"(":{"docs":{},"$":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"_":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001509813789632612}},"(":{"0":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844}}},"docs":{}},"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"docs":{}},"docs":{}}}}}}},"b":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}},"i":{"docs":{},"n":{"1":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}}}}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"_":{"docs":{},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"m":{"docs":{},"(":{"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}},"(":{"0":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}}},"docs":{}},"docs":{}},"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"docs":{}},"docs":{}}}}}}},"i":{"docs":{},"n":{"1":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}}}}},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"x":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"_":{"docs":{},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}},"e":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":5.011407481966113},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"o":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},".":{"docs":{},"c":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"(":{"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"(":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},"(":{"6":{"4":{"docs":{},"*":{"6":{"7":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"docs":{}},"docs":{}}},"docs":{}},"docs":{},"a":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}},"b":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844}},"(":{"1":{"2":{"8":{"docs":{},"*":{"1":{"2":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"docs":{}},"docs":{}}},"docs":{}},"docs":{}},"docs":{},"a":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}},"b":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"r":{"docs":{},"'":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"i":{"docs":{},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428}}}}}},"s":{"docs":{},"t":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}}}}}}},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},".":{"docs":{},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"y":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}},"e":{"docs":{},".":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}},"^":{"docs":{},"{":{"2":{"5":{"5":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}},"\\":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}},"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}}},"(":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}},"n":{"docs":{},"*":{"docs":{},"k":{"docs":{},"*":{"2":{"docs":{},"*":{"docs":{},"p":{"docs":{},"i":{"docs":{},"*":{"docs":{},"(":{"1":{"docs":{},"/":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},"*":{"docs":{},"(":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}},"docs":{}}}}}}},"docs":{}}}}}},"v":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"p":{"docs":{},"s":{"docs":{},"l":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},".":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"=":{"6":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"}":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"docs":{},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"'":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"`":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"x":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"/":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}},"}":{"docs":{},"{":{"docs":{},"t":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}}}}}}}}}}}}}}},"x":{"docs":{},"_":{"1":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{},".":{"docs":{},".":{"docs":{},",":{"docs":{},"x":{"docs":{},"_":{"docs":{},"{":{"1":{"0":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"docs":{}},"docs":{}}}}}}}},"\\":{"docs":{},"d":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"docs":{}}}}},"f":{"1":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"+":{"docs":{},"f":{"2":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"docs":{}}}},"2":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"6":{"4":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0028214429665457475},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0029227557411273487},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},".":{"docs":{},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}},".":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"2":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"docs":{}}}},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},"docs":{}},"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.013333333333333334},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"a":{"docs":{},"v":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"i":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},"o":{"docs":{},"r":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"[":{"1":{"docs":{},":":{"docs":{},"h":{"docs":{},"a":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}},"docs":{}},"s":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},".":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}},"e":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"t":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}}},"o":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}},"q":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},"r":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"l":{"docs":{},"s":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"e":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},":":{"6":{"docs":{},"}":{"docs":{},"\"":{"docs":{},".":{"docs":{},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"}":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"l":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"i":{"docs":{},"l":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"u":{"docs":{},"r":{"docs":{},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}},")":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}},"s":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},"r":{"docs":{},",":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"l":{"docs":{},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},"s":{"docs":{},"t":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.007653061224489796},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"?":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"h":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}},"b":{"docs":{},"s":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}},"(":{"docs":{},"a":{"docs":{},"[":{"docs":{},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}},"e":{"docs":{},"q":{"docs":{},"n":{"docs":{},"s":{"docs":{},"[":{"docs":{},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"]":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}}}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"u":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}},"e":{"docs":{},"e":{"docs":{},"l":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.007707129094412331},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"b":{"docs":{},"l":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"w":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00684931506849315},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},":":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"a":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"!":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"s":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},"s":{"docs":{},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"m":{"docs":{},"a":{"docs":{},"l":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"r":{"docs":{},"n":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":5.005845511482255},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}},"\"":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}},"b":{"docs":{},"r":{"docs":{},"u":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"d":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"i":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}},"n":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0029655990510083037},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002843216896831844},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.005150214592274678},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0034420289855072463},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.005384006334125099},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"f":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}},"_":{"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},"(":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"c":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518}}},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0035587188612099642}}}}}}}}},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518}}}}}}}}}}}}}}}}}}}}},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"a":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"_":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276}}}}},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},")":{"docs":{},".":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"g":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003854239663629993}},"t":{"docs":{},"i":{"docs":{},"p":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"s":{"docs":{},"?":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"i":{"docs":{},"s":{"docs":{},"h":{"docs":{},"e":{"docs":{},"d":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"e":{"docs":{},":":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"e":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}},"l":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":5.0094899169632265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}},"\"":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},"?":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}}}},"e":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009880609304240428},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0031656700668308124},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},")":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},"g":{"docs":{},"p":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"f":{"docs":{},"l":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"_":{"0":{"0":{"0":{"0":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"1":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"2":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},";":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},":":{"docs":{},":":{"docs":{},"c":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"p":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.012215435868961688},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852}},"$":{"docs":{},"(":{"docs":{},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},"i":{"docs":{},"n":{"docs":{},"_":{"docs":{},"c":{"docs":{},"i":{"docs":{},"r":{"docs":{},"c":{"docs":{},"l":{"docs":{},"e":{"docs":{},"$":{"docs":{},"(":{"docs":{},"?":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}}},"s":{"docs":{},":":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},"\"":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004441976679622432},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232}},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},")":{"docs":{},";":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412}}}}}}}}}},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}},"docs":{}}}}}}}},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}},"?":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},")":{"docs":{},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}}},"[":{"docs":{},"i":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.011228070175438596},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.005362443742219668},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0017273452032952432},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0050415183867141165},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00684931506849315},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0035174111853675696},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0019927536231884057},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"]":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},"x":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"u":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{},"(":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}},"s":{"docs":{},"a":{"docs":{},"v":{"docs":{},"e":{"docs":{},"f":{"docs":{},"i":{"docs":{},"g":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},".":{"docs":{},"p":{"docs":{},"n":{"docs":{},"g":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.022598870056497175},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"s":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},"e":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"i":{"docs":{},"e":{"docs":{},"v":{"docs":{},"e":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"a":{"docs":{},"l":{"docs":{},"(":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"o":{"docs":{},"c":{"docs":{},"u":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"s":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"r":{"docs":{},"t":{"docs":{},"u":{"docs":{},"n":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"h":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"_":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"[":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001340610935554917},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.005090054815974941},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"(":{"docs":{},"$":{"docs":{},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}},"v":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"g":{"docs":{},"o":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"m":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00332541567695962},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}}},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"a":{"docs":{},"l":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},"l":{"docs":{},"y":{"docs":{},")":{"docs":{},":":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"i":{"docs":{},"s":{"docs":{},"m":{"docs":{},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.004116920543433511},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"!":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"{":{"docs":{},":":{"1":{"8":{"docs":{},"}":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"docs":{}},"docs":{},"?":{"docs":{},"}":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"}":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"{":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"{":{"docs":{},"}":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}},"a":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}},"u":{"docs":{},"l":{"docs":{},"a":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"s":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}}},"\"":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"g":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"o":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}},"(":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00274079874706343},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.006175380815150268},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.005050505050505051},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0038043478260869567},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"a":{"docs":{},"t":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.025510204081632654},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00507232763479241},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976}}}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"o":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"t":{"docs":{},"b":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0012448530115867088},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"l":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657}}}},"(":{"docs":{},"q":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"_":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"e":{"docs":{},"(":{"docs":{},"q":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"e":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"_":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"k":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}},"g":{"docs":{},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"p":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"!":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"f":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0015944724953494552},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},".":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"_":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"1":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"docs":{}}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"[":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},".":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"+":{"docs":{},"+":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"u":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0026574541589157587},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.02295918367346939},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0026300958106331017},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},".":{"docs":{},"m":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"m":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}}}}}}}}},"y":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},".":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"r":{"docs":{},"y":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0035087719298245615}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004912280701754386}},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}},"e":{"docs":{},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"m":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"g":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"a":{"docs":{},"c":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114}},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0028503562945368173}},"s":{"docs":{},")":{"docs":{},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"a":{"docs":{},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.004924375659514597},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}},"s":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}}}}}}}},"m":{"docs":{},"e":{"docs":{},"w":{"docs":{},"o":{"docs":{},"r":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}},"i":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"l":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}},"d":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}},"u":{"docs":{},"n":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"d":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.011029411764705883},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0022024322512687925},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0021808421405804393},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.001993090619186819},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0028405056099985795},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141}},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.006032749209997127},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.006710283509478276},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002258836035078395},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.007047768206734534},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004448398576512456},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.004697986577181208},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.020242914979757085},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.013333333333333334},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004997223764575236},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.02040816326530612},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002881844380403458},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.006904955320877335},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.008421052631578947},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.005150214592274678},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0045087356753710315},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.012987012987012988},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":3.342126861296752},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0021303792074989347},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0022168480451430876},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.018308080808080808},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.013778705636743214},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.008146639511201629},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0014492753623188406},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002533650039588282},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005606166783461808},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.010163749294184076},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.013771186440677966}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"(":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}},")":{"docs":{},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},".":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"s":{"docs":{},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"?":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},";":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},".":{"6":{"docs":{},".":{"docs":{},"l":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}},"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},":":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"'":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"?":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"(":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"k":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},"!":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},".":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125}}}}}}},"r":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}},"i":{"docs":{},"o":{"docs":{},"u":{"docs":{},"s":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"l":{"docs":{},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004997223764575236},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.011231884057971014},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"_":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"_":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}}}}}},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"z":{"docs":{},"z":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}},"s":{"docs":{},"s":{"docs":{},"!":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}},"d":{"docs":{},"g":{"docs":{},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"p":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"a":{"docs":{},"t":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"v":{"docs":{},"o":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"g":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"j":{"docs":{},"o":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"u":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"s":{"docs":{},"h":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"c":{"docs":{},"t":{"docs":{},"u":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}}}}},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478}}}},"docs":{}},"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0050415183867141165},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.015068493150684932},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0036926572929981537},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"o":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":5.0056346381969155}}},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"(":{"docs":{},"x":{"docs":{},"/":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"_":{"docs":{},"w":{"docs":{},"i":{"docs":{},"d":{"docs":{},"t":{"docs":{},"h":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}}},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"w":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"d":{"docs":{},"(":{"1":{"3":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{},"k":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"n":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.008421052631578947},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011490950876185005},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0015944724953494552},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0014251781472684087},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},"m":{"docs":{},"t":{"docs":{},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"f":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"%":{"9":{"docs":{},".":{"4":{"docs":{},"f":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"docs":{}}},"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001340610935554917}}}},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"x":{"docs":{},"=":{"docs":{},"%":{"docs":{},"f":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"[":{"docs":{},"%":{"docs":{},"f":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}},"l":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}},"[":{"0":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"1":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"2":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}},"\\":{"docs":{},"n":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},":":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},":":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},":":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"h":{"docs":{},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"]":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"g":{"docs":{},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"c":{"docs":{},"k":{"1":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"2":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"docs":{}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},"r":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"(":{"docs":{},"\"":{"docs":{},"[":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001340610935554917}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"a":{"docs":{},"p":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"f":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"n":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"c":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"t":{"docs":{},"h":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"'":{"docs":{},"%":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011490950876185005}}}},"\\":{"docs":{},"n":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"b":{"docs":{},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"d":{"docs":{},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}}}}}}},"'":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},"(":{"docs":{},"{":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"{":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}},"{":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"(":{"docs":{},"{":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"x":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}},"(":{"2":{"docs":{},")":{"docs":{},"=":{"1":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"docs":{}}}},"3":{"docs":{},")":{"docs":{},"=":{"2":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"docs":{}}}},"docs":{},"a":{"docs":{},")":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}},"x":{"docs":{},")":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.016194331983805668},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},")":{"docs":{},".":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"}":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"(":{"docs":{},"t":{"docs":{},"+":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}},"'":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"_":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"\\":{"docs":{},"x":{"docs":{},"i":{"docs":{},")":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"x":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"d":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"x":{"docs":{},"}":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}},"c":{"docs":{},"p":{"docs":{},"u":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}},"u":{"docs":{},"d":{"docs":{},"a":{"docs":{},"d":{"docs":{},"e":{"docs":{},"v":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"z":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.008207070707070708}},"!":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255}}},":":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"=":{"docs":{},"z":{"docs":{},"^":{"2":{"docs":{},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}}}}}},"n":{"docs":{},")":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.006355932203389831}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},"}":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"^":{"docs":{},"{":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},"}":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}}}}}},"*":{"docs":{},"g":{"docs":{},"=":{"docs":{},"c":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}}},".":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"w":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"{":{"0":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"{":{"1":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"*":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}},"p":{"docs":{},".":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}}}}}}},"docs":{}}}}}},"docs":{}}}}}}}}}},"[":{"docs":{},"n":{"docs":{},"]":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"f":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":10.00638737554011},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},"_":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}}}}},"w":{"3":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"_":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"o":{"docs":{},"y":{"docs":{},"_":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{},"(":{"docs":{},"p":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}}}}}}}}}}},"x":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"_":{"docs":{},"d":{"docs":{},"f":{"docs":{},"t":{"docs":{},"_":{"1":{"docs":{},"d":{"docs":{},"(":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},"x":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}},"'":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"(":{"docs":{},"&":{"docs":{},"x":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"x":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},"_":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"k":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}}}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"c":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"(":{"docs":{},"x":{"docs":{},".":{"docs":{},"a":{"docs":{},"s":{"docs":{},"_":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"s":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}}}}}},":":{"docs":{},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},"f":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"_":{"1":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"(":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0037578288100208767}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}}},"2":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"(":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0037578288100208767}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}}},"3":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"(":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0037578288100208767}}}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}},"4":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"(":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845}}}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"_":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}},"=":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"g":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0031656700668308124},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.003952569169960474}},"i":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}},"h":{"docs":{},"u":{"docs":{},"b":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}},"v":{"docs":{},"e":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"_":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"r":{"docs":{},"a":{"docs":{},"d":{"docs":{},"i":{"docs":{},"u":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"s":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},".":{"docs":{},"t":{"docs":{},"o":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}},"f":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"t":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":5.027027027027027},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.004335260115606936},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.003355704697986577}},"\"":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},".":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0072254335260115606}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"docs":{}}}}},"r":{"docs":{},"e":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"1":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{}}}}}}}}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}},"docs":{},"j":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"u":{"docs":{},"r":{"docs":{},"a":{"docs":{},"k":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"r":{"docs":{},"l":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"f":{"docs":{},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}},"m":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"o":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0017236426314277506},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003642121931908155},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002452697967764541},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"a":{"docs":{},"l":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"a":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"o":{"docs":{},"d":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"g":{"docs":{},"l":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"n":{"docs":{},"e":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"b":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"d":{"docs":{},"y":{"docs":{},"g":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"!":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"h":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"i":{"docs":{},"c":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":5.03954802259887},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"s":{"docs":{},".":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"h":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":5.002013422818792}},"_":{"docs":{},"s":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"!":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},":":{"docs":{},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}}}}}}}}}},"(":{"docs":{},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{},":":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}}}}},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"&":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}},"s":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604}},"(":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"s":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}},"d":{"docs":{},"i":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.006008583690987125}},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"n":{"docs":{},"t":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"i":{"docs":{},"n":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"v":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"y":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001509813789632612}}}},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"l":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"!":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"e":{"docs":{},"c":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"n":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"k":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"y":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"s":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002717391304347826}}}}}}}},"w":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"o":{"docs":{},"w":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"s":{"docs":{},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"n":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"c":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"u":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"s":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"n":{"docs":{},"d":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"'":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"i":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.004419191919191919},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0026690391459074734},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}},"[":{"1":{"docs":{},":":{"2":{"docs":{},",":{"docs":{},":":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},"docs":{}}},"2":{"docs":{},",":{"docs":{},":":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"3":{"docs":{},",":{"docs":{},":":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},"_":{"docs":{},"x":{"docs":{},"]":{"docs":{},"[":{"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},"_":{"docs":{},"y":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}}}}}}}}}},"x":{"docs":{},"]":{"docs":{},"[":{"docs":{},"y":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643}}}}}}}},"{":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"_":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.005431093007467753}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},"/":{"2":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"docs":{}},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}}},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"f":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}}}}},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"u":{"docs":{},"m":{"docs":{},"p":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"u":{"docs":{},"i":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}},"e":{"docs":{},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}}},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}}}},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"r":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}},"y":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593}},".":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"o":{"docs":{},"(":{"docs":{},"g":{"docs":{},"i":{"docs":{},"r":{"docs":{},"l":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004210526315789474},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0045726345409778405},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.003952569169960474}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"e":{"docs":{},"(":{"2":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"3":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"_":{"docs":{},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"s":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"e":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"v":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"(":{"docs":{},"*":{"docs":{},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"_":{"docs":{},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},"e":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"_":{"docs":{},"d":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"e":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"(":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"l":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}},"u":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},":":{"docs":{},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"u":{"docs":{},"s":{"docs":{},".":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.006355932203389831}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0010629816635663034},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}},"_":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"_":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"o":{"docs":{},"f":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"_":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"o":{"docs":{},"f":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}},"l":{"docs":{},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},".":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"h":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}},"x":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},"i":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":5.011904761904762}}},"y":{"docs":{},".":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.023809523809523808}}}}}}}},"r":{"docs":{},"g":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}},"m":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"n":{"docs":{},"u":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.007822149032523672},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002881844380403458},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}},"c":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003355141754739138}},"_":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{},"u":{"docs":{},"s":{"docs":{},"(":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"docs":{},"a":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"(":{"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{},"a":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}}},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"x":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"r":{"docs":{},"o":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"s":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"e":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.005479452054794521}},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603}}},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"s":{"docs":{},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589}}}}}},"m":{"docs":{},"e":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005979599015124868},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}},"\"":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542}}},"s":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},")":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"m":{"docs":{},"i":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"r":{"docs":{},"!":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}},"l":{"docs":{},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},".":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"r":{"docs":{},"u":{"docs":{},"n":{"docs":{},"g":{"docs":{},"a":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{},"(":{"docs":{},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001583531274742676}},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004441976679622432},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.007725321888412017},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":5.002375296912114},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"?":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},";":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},"e":{"docs":{},"l":{"docs":{},"i":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"!":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"2":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"docs":{}}},"docs":{}},"docs":{}}}}}}}}}}}}}}}}},"(":{"docs":{},"&":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"(":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"a":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"l":{"docs":{},"i":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"a":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"[":{"docs":{},"]":{"docs":{},"[":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}},"'":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002536231884057971}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"_":{"docs":{},"j":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"a":{"docs":{},"n":{"docs":{},"(":{"docs":{},"&":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"a":{"docs":{},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}},"_":{"docs":{},"e":{"docs":{},"l":{"docs":{},"i":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"!":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"2":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"docs":{}}},"docs":{}},"docs":{}}}}}}}}}}}}}}}}},"(":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}}}}}}}}}}}}}},"j":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},"(":{"docs":{},"a":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"[":{"docs":{},"]":{"docs":{},"[":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"l":{"docs":{},"o":{"docs":{},"b":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"_":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"_":{"docs":{},"d":{"docs":{},"e":{"docs":{},"v":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},"g":{"docs":{},"l":{"docs":{},"o":{"docs":{},"b":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"_":{"docs":{},"d":{"docs":{},"e":{"docs":{},"v":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"r":{"docs":{},"y":{"docs":{},"!":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"e":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},",":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"\\":{"docs":{},"x":{"docs":{},"i":{"docs":{},")":{"docs":{},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}}},"r":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},".":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"[":{"docs":{},"n":{"docs":{},"]":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"p":{"docs":{},"u":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004210526315789474}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}},"s":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},"_":{"docs":{},"i":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"x":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"y":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"docs":{}}},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"t":{"docs":{},"o":{"docs":{},"t":{"docs":{},"a":{"docs":{},"l":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}}}}}}}}},"x":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339}}},"y":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339}},".":{"docs":{},"^":{"2":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"docs":{}}}},"'":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"'":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"|":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{},")":{"docs":{},"|":{"docs":{},"^":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"f":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"=":{"docs":{},"g":{"docs":{},")":{"docs":{},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"i":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"s":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"a":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"r":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"e":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},".":{"docs":{},".":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},"s":{"docs":{},"h":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},"m":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},"o":{"docs":{},"n":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"s":{"docs":{},"k":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},"l":{"docs":{},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002125963327132607},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"<":{"docs":{},">":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}},"}":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},"c":{"docs":{},"u":{"docs":{},"d":{"docs":{},"a":{"docs":{},"_":{"docs":{},"g":{"docs":{},"p":{"docs":{},"u":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}}}}}}}}},"f":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"v":{"docs":{},"e":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"i":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"r":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"s":{"docs":{},")":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"!":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"l":{"docs":{},"f":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0020665038512117226},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0018137847642079807},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"w":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"l":{"docs":{},"/":{"docs":{},"c":{"docs":{},"r":{"docs":{},"c":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"m":{"docs":{},"z":{"docs":{},"a":{"docs":{},"o":{"docs":{},"u":{"docs":{},"i":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}},"i":{"docs":{},"l":{"docs":{},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"s":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"d":{"docs":{},"o":{"docs":{},"r":{"docs":{},"f":{"docs":{},"f":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}},"c":{"docs":{},"k":{"docs":{},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"i":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"e":{"docs":{},"l":{"docs":{},"p":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},":":{"docs":{},":":{"docs":{},"m":{"docs":{},"a":{"docs":{},"k":{"docs":{},"e":{"docs":{},"_":{"docs":{},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"f":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"*":{"docs":{},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"d":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"r":{"docs":{},"e":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011490950876185005},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178}},"'":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002881844380403458},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.005681818181818182},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002536231884057971},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0035502958579881655},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002452697967764541},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},":":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"?":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"o":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}},"i":{"docs":{},"c":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"m":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}}}}},"a":{"docs":{},"v":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"t":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0030560722827531225}},"'":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"*":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},".":{"docs":{},"i":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"(":{"docs":{},"h":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},"h":{"docs":{},")":{"docs":{},".":{"docs":{},"(":{"docs":{},"*":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"h":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}},"_":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}},"(":{"docs":{},"&":{"docs":{},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"(":{"docs":{},"&":{"docs":{},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"_":{"docs":{},"d":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"s":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},"_":{"docs":{},"u":{"docs":{},"p":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"r":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"\"":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"d":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}},"d":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"n":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"r":{"docs":{},"i":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"x":{"docs":{},"a":{"docs":{},"g":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"?":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"s":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}}}}},"s":{"docs":{},"e":{"docs":{},"n":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488}}}}}}}}}}},"o":{"docs":{},"p":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"f":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"i":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"y":{"docs":{},",":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}}}}},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248}},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}}},"n":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"k":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}},"u":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"d":{"docs":{},"o":{"docs":{},"r":{"docs":{},"f":{"docs":{},"f":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"w":{"docs":{},"e":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.007707129094412331},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.005681818181818182},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.005415162454873646},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"?":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"l":{"docs":{},"d":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0031245561709984378},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"i":{"docs":{},"d":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}},"i":{"docs":{},"z":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}}},"m":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},"l":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"o":{"docs":{},"d":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"t":{"docs":{},"t":{"docs":{},"p":{"docs":{},"s":{"docs":{},":":{"docs":{},"/":{"docs":{},"/":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"c":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},".":{"docs":{},"g":{"docs":{},"g":{"docs":{},"/":{"docs":{},"p":{"docs":{},"r":{"2":{"docs":{},"e":{"9":{"docs":{},"s":{"6":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}},"docs":{}}},"docs":{}}},"docs":{}},"b":{"9":{"7":{"6":{"docs":{},"s":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}},"docs":{}},"docs":{}},"docs":{}}}}}}}}}}}}}},"g":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"u":{"docs":{},"b":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"/":{"docs":{},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}}}},"a":{"docs":{},"n":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"r":{"docs":{},"/":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"w":{"docs":{},"w":{"docs":{},"w":{"docs":{},".":{"docs":{},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}}}}}},"t":{"docs":{},"w":{"docs":{},"i":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},".":{"docs":{},"t":{"docs":{},"v":{"docs":{},"/":{"docs":{},"l":{"docs":{},"e":{"docs":{},"i":{"docs":{},"o":{"docs":{},"s":{"docs":{},"l":{"docs":{},"a":{"docs":{},"b":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}}}}}}}}}}}}}}},"y":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"u":{"docs":{},"b":{"docs":{},"e":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"/":{"docs":{},"u":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"/":{"docs":{},"l":{"docs":{},"e":{"docs":{},"i":{"docs":{},"o":{"docs":{},"s":{"docs":{},"o":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"m":{"docs":{},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003854239663629993},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"s":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.004908946951702296},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}},"l":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"!":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002717391304347826}},"i":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"y":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891}},"[":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},"i":{"docs":{},",":{"docs":{},"j":{"docs":{},"]":{"docs":{},")":{"docs":{},"^":{"2":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"docs":{}}}}}}}},"s":{"docs":{},"\"":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}}},"e":{"docs":{},"p":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"m":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"!":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"r":{"docs":{},"e":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"c":{"docs":{},"h":{"docs":{},".":{"docs":{},".":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"d":{"docs":{},"e":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"d":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"u":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"l":{"docs":{},"l":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.02702702702702703},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.014932562620423893},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.015771812080536914}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"o":{"docs":{},"n":{"docs":{},"_":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}}}}}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},"t":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},"i":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"m":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},"i":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"m":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{}}}}}},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{}}}}}}}}},"u":{"docs":{},"n":{"docs":{},"s":{"docs":{},"h":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0026845637583892616}},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"]":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}},"]":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"m":{"docs":{},"]":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828}},"s":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"1":{"5":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"docs":{}},"docs":{}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}},"s":{"docs":{},"[":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"n":{"docs":{},"g":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364}}}}}}}},"d":{"docs":{},"r":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"d":{"docs":{},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"'":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":5.003587563114536},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},":":{"docs":{},":":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},"_":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"b":{"docs":{},"e":{"docs":{},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"_":{"docs":{},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009301089556205156}},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},".":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"b":{"docs":{},"i":{"docs":{},"b":{"docs":{},"b":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0014615997874036673}},"e":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"b":{"docs":{},"i":{"docs":{},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"_":{"docs":{},"b":{"docs":{},"o":{"docs":{},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},".":{"docs":{},"c":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},":":{"docs":{},":":{"docs":{},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}}}}}}}}}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}},"s":{"docs":{},"b":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}},"g":{"docs":{},"e":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005627857896588111},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0041753653444676405}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"_":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}},"[":{"0":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"docs":{}}}}}}}}}}}}},"e":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255}}}},"s":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}},"l":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"v":{"2":{"docs":{},"r":{"docs":{},"g":{"docs":{},"b":{"docs":{},"(":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}}}}}}}}}}},"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.004419191919191919}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"(":{"docs":{},"*":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}},"y":{"docs":{},"p":{"docs":{},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"(":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"z":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}},"_":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"}":{"docs":{},"{":{"2":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"docs":{}}}},"i":{"3":{"2":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},"e":{"docs":{},".":{"docs":{},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"4":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"5":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"6":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"docs":{}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"4":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"5":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"6":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"docs":{}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},"docs":{}},"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}},"docs":{}},"docs":{},"m":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}},"p":{"docs":{},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.015306122448979591},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.005614035087719298},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"s":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"i":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},"c":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"'":{"docs":{},",":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004912280701754386},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0010629816635663034},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.004306969459671104},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0026690391459074734},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0030201342281879194},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.007653061224489796},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0037052284890901604},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00487408610885459},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0035174111853675696},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0041753653444676405},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0029585798816568047},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}},"s":{"docs":{},"s":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"v":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657}},"i":{"docs":{},"s":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"!":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"u":{"docs":{},"t":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"a":{"docs":{},"g":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.007653061224489796},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.015644298065047343},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00821917808219178},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":3.3496423462088694},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0045726345409778405},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.007575757575757576},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.003340292275574113},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004204625087596356},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"i":{"docs":{},"n":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"e":{"docs":{},"!":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}},"g":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0024183796856106408},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006313131313131313},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"y":{"docs":{},"_":{"docs":{},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}},"e":{"docs":{},"s":{"docs":{},"/":{"docs":{},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}},".":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"?":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"!":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},")":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394}}},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}}}}}}}},"(":{"docs":{},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"u":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}}},"*":{"0":{"docs":{},".":{"5":{"docs":{},"*":{"docs":{},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"v":{"docs":{},"*":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"d":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"k":{"docs":{},".":{"docs":{},"^":{"2":{"docs":{},"*":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"d":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}},"docs":{}}}}}}}}}},"docs":{}}},"docs":{}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"_":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},"e":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}},":":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},":":{"docs":{},":":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534}}}}}},"n":{"2":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276}},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"a":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.007708479327259986},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"(":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"v":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},")":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"u":{"docs":{},"d":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"d":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}},"s":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},"e":{"docs":{},"!":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}},"r":{"docs":{},"e":{"docs":{},"h":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"r":{"docs":{},"p":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"n":{"docs":{},"s":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}},"h":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"i":{"docs":{},"r":{"docs":{},"c":{"docs":{},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}},"e":{"docs":{},"(":{"docs":{},"$":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"a":{"docs":{},".":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}}}}}},"a":{"docs":{},"p":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"d":{"docs":{},"i":{"docs":{},"v":{"docs":{},"i":{"docs":{},"d":{"docs":{},"u":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0028179597971068945},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}}}}}}}},"e":{"docs":{},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0017273452032952432},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00507232763479241},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"r":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"'":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"_":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{},"(":{"docs":{},"&":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"}":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"u":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},"y":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"?":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}},"a":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409}}},"n":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"e":{"docs":{},"v":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}},"o":{"docs":{},"f":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"i":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737}}}}},"t":{"3":{"2":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"docs":{}},"6":{"4":{"docs":{},"}":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"docs":{}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.008421052631578947},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002298190175237001},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.013252809931219594},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0025245814509699707},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.00771055753262159},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0026845637583892616},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.004635227730753728},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.004710144927536232},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003800475059382423}},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007773459189339256},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009057225195553726},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.005150214592274678},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005979599015124868},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006944444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.010862186014935505},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01242603550295858},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"'":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"o":{"docs":{},"f":{"docs":{},"(":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"!":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"?":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"f":{"docs":{},"a":{"docs":{},"c":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"{":{"docs":{},"}":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"i":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"v":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"!":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"e":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"m":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"s":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"v":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"g":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.010638297872340425},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.01643835616438356},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.005681818181818182},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"(":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},">":{"docs":{},">":{"docs":{},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}}}}}},"s":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}}}},"r":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":5.010367845476495},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.003952569169960474},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"!":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"'":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449}}},"~":{"docs":{},"%":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"\"":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"e":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"l":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0012782275244993609}}}}}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}},"s":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}},"d":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"r":{"docs":{},"o":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"d":{"docs":{},"u":{"docs":{},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":10.001926782273603},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"u":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649}}},"_":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},".":{"docs":{},"e":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"4":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"5":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"9":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"docs":{}}}}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},".":{"docs":{},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"4":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"5":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"9":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"docs":{}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},"e":{"docs":{},".":{"docs":{},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"4":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}},"5":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}},"9":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}},"docs":{}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"4":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}},"5":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}},"9":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}},"docs":{}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0018453279651065259},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001583531274742676}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"(":{"docs":{},"n":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"(":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"2":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"docs":{}}}}},"o":{"docs":{},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"i":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003289473684210526},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.006683081252198382},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},"@":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"d":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"s":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"p":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},".":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"y":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"[":{"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"docs":{}}}}}}}}}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"(":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},":":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}},"_":{"docs":{},"o":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},"s":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"b":{"docs":{},"e":{"docs":{},"t":{"docs":{},"w":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{},"s":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124}}}}}}}}},"_":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}},"r":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},")":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}},"u":{"docs":{},"i":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002681221871109834}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"a":{"docs":{},"r":{"docs":{},"g":{"docs":{},"u":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"c":{"docs":{},"e":{"docs":{},"p":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"'":{"docs":{},"n":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},"_":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"[":{"docs":{},"'":{"docs":{},"'":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"n":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"g":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"o":{"docs":{},"l":{"docs":{},"v":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"i":{"docs":{},"s":{"docs":{},"c":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"(":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}}}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":5.014705882352941},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.015299026425591099},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},":":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"i":{"docs":{},"t":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003355141754739138},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"o":{"docs":{},"v":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.037383177570093455},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.005050505050505051},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.005431093007467753},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"l":{"docs":{},"d":{"docs":{},"(":{"docs":{},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"h":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"|":{"docs":{},"c":{"docs":{},"|":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"s":{"docs":{},".":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}},"s":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}},"^":{"2":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"docs":{}}}},"2":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}},"^":{"2":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"docs":{}}}},"docs":{},"t":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"1":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649}}}},"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.009122807017543859}}}}}},"i":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}}},"i":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"x":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"s":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}},"l":{"docs":{},"a":{"docs":{},"c":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}},"e":{"docs":{},"f":{"docs":{},"f":{"docs":{},"i":{"docs":{},"c":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}}},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"(":{"docs":{},"$":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}},"c":{"docs":{},"i":{"docs":{},"r":{"docs":{},"c":{"docs":{},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295}},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"p":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"o":{"docs":{},"s":{"docs":{},"_":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0036555645816409425}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},":":{"docs":{},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"docs":{}},"docs":{}}}}}}}}}}}}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}},"n":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},"h":{"docs":{},"i":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"e":{"docs":{},"r":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"u":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"!":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0035430431868237098},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"e":{"docs":{},"a":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.009633911368015413},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"l":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},":":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"n":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}},"i":{"docs":{},"f":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"i":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0008618213157138753}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0008618213157138753},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},"docs":{}},"docs":{}}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"i":{"docs":{},"v":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"f":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"g":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}},"s":{"docs":{},")":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0035087719298245615}}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}},"m":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.004061738424045491},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.00487012987012987},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"\"":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0021303792074989347}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.003550632012498225}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449}}}}},"%":{"docs":{},"l":{"docs":{},"f":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}}}}}}}}},"`":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449}}}}},"~":{"docs":{},"%":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}}}},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"g":{"docs":{},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},";":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"(":{"docs":{},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"n":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"f":{"docs":{},"t":{"docs":{},"o":{"docs":{},"f":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"a":{"docs":{},"n":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"m":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}},"u":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"e":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"i":{"docs":{},"n":{"docs":{},"m":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}}}},"z":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},"e":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"!":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"o":{"docs":{},"s":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},"e":{"docs":{},"s":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}},"t":{"docs":{},"!":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"'":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.008116883116883116},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0033944331296673455},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002803083391730904},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}},"e":{"docs":{},"m":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003153468815697267}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"x":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"y":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"s":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178}}},";":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"?":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0017273452032952432},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":3.3372024856372375},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.007098121085594989},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"t":{"docs":{},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{},"s":{"docs":{},":":{"docs":{},":":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{},"s":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},"_":{"docs":{},"t":{"docs":{},"u":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"(":{"docs":{},"&":{"docs":{},"x":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},")":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"x":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"s":{"docs":{},"\"":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"!":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"e":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"z":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"!":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"?":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},")":{"docs":{},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"'":{"docs":{},"l":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"m":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0035087719298245615}}}}}},"f":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},"e":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}},"f":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}},"t":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},"(":{"docs":{},"n":{"docs":{},"p":{"docs":{},".":{"docs":{},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},"i":{"docs":{},"p":{"docs":{},"l":{"docs":{},"y":{"docs":{},"(":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"1":{"docs":{},")":{"docs":{},",":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"2":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}},"docs":{}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}},"(":{"2":{"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"docs":{}},"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},".":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"1":{"docs":{},"(":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}},"docs":{}}}},"i":{"docs":{},"s":{"docs":{},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"x":{"docs":{},"(":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"z":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}},"a":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"n":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"$":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"(":{"docs":{},"$":{"docs":{},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"{":{"1":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669}}}}},"docs":{}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0028782894736842104},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"o":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"[":{"docs":{},"]":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}},"z":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0025163563160543532}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"1":{"docs":{},")":{"docs":{},".":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},".":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}}}}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"n":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"e":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"l":{"docs":{},"l":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}}}}},"+":{"1":{"docs":{},")":{"docs":{},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}},"docs":{},"+":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604}}}},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},"/":{"2":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"docs":{}}}}}}}}}}}}}}}}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002533650039588282}}},"e":{"docs":{},"e":{"docs":{},"e":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"*":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"d":{"docs":{},"x":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"=":{"0":{"docs":{},":":{"1":{"8":{"4":{"4":{"6":{"7":{"4":{"4":{"0":{"7":{"3":{"7":{"0":{"9":{"5":{"5":{"1":{"6":{"1":{"5":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"\\":{"docs":{},"h":{"docs":{},"a":{"docs":{},"t":{"docs":{},"{":{"docs":{},"h":{"docs":{},"}":{"docs":{},"_":{"docs":{},"k":{"docs":{},"]":{"docs":{},"d":{"docs":{},"t":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"docs":{}}}},"docs":{}}}}}}}}}}}},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"j":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.006107717934480844},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0068669527896995704},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0030058237835806877},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0032245062474808546},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.006809184481393508},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}},"m":{"docs":{},"e":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007773459189339256},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009057225195553726},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005627857896588111},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006944444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.010862186014935505},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01242603550295858},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719}},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"v":{"docs":{},"a":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"s":{"docs":{},"c":{"docs":{},"r":{"docs":{},"i":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"/":{"docs":{},"t":{"docs":{},"y":{"docs":{},"p":{"docs":{},"e":{"docs":{},"s":{"docs":{},"c":{"docs":{},"r":{"docs":{},"i":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}}}}}}}}}}}}}},".":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"l":{"docs":{},".":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},"s":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"n":{"docs":{},"k":{"docs":{},"e":{"docs":{},"d":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"m":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"m":{"docs":{},";":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}}}}}}}},"*":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"m":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}},"i":{"docs":{},"o":{"docs":{},".":{"docs":{},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"e":{"docs":{},"w":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}},"i":{"docs":{},"o":{"docs":{},"e":{"docs":{},"x":{"docs":{},"c":{"docs":{},"e":{"docs":{},"p":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},";":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"v":{"docs":{},"i":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":5.001926782273603},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}},"s":{"docs":{},"_":{"docs":{},"c":{"docs":{},"r":{"docs":{},"o":{"docs":{},"s":{"docs":{},"s":{"docs":{},"(":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"[":{"docs":{},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"1":{"docs":{},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"docs":{}}}},"s":{"docs":{},"(":{"0":{"docs":{},",":{"0":{"docs":{},")":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}},"docs":{}}},"docs":{}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"s":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},":":{"docs":{},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.003371868978805395}},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"s":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}},".":{"docs":{},"c":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"r":{"docs":{},"u":{"docs":{},"n":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"u":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754}}}}}}}},"o":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"a":{"docs":{},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"y":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904}}},"b":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"k":{"docs":{},"e":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}},"h":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"a":{"docs":{},"n":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"s":{"docs":{},"e":{"docs":{},"p":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"r":{"docs":{},"d":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001583531274742676}},"\"":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},":":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}},"r":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},"u":{"docs":{},"l":{"docs":{},"i":{"docs":{},"a":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"'":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"u":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001819400555395959},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0020665038512117226}},"s":{"docs":{},"s":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"r":{"docs":{},"k":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},"a":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"w":{"docs":{},"i":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"f":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}},"m":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002010916403332376},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0020130850528434826},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0014615997874036673},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298}}}},"n":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"z":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}}},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"z":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}},"z":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009301089556205156}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001677570877369569},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},"e":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"g":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"]":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},")":{"docs":{},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}},"+":{"1":{"docs":{},")":{"docs":{},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}},"docs":{}},"*":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"d":{"docs":{},"x":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"i":{"docs":{},"m":{"docs":{},"m":{"docs":{},"i":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"e":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"b":{"docs":{},"e":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"k":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.005823783580687582},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.007971014492753623},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"n":{"docs":{},"o":{"docs":{},"w":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"l":{"docs":{},"e":{"docs":{},"d":{"docs":{},"g":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488}},"e":{"docs":{},",":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044}}},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},":":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"!":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"b":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"e":{"docs":{},"w":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"e":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}}}},"y":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002125963327132607},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.012526096033402923},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"(":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},":":{"docs":{},":":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"w":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"s":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}},"=":{"docs":{},"(":{"docs":{},"p":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}},"l":{"docs":{},"a":{"docs":{},"m":{"docs":{},"b":{"docs":{},"d":{"docs":{},"a":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}}}}}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405}}}},"p":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"r":{"docs":{},"c":{"docs":{},"k":{"docs":{},"h":{"docs":{},"o":{"docs":{},"f":{"docs":{},"f":{"docs":{},"s":{"docs":{},"'":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004912280701754386},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.015450643776824034}},"!":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649}},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}}}}}}}}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737}}},":":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{},"j":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}},"[":{"docs":{},"i":{"docs":{},",":{"docs":{},"j":{"docs":{},"]":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}},"_":{"docs":{},"f":{"docs":{},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}},"s":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852}}}},"*":{"0":{"docs":{},".":{"5":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}},"docs":{}}},"docs":{}}}}}}}}}}},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},".":{"docs":{},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"t":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}}}},"o":{"docs":{},"t":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},".":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"e":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"r":{"docs":{},"a":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}},"t":{"docs":{},"h":{"docs":{},"x":{"docs":{},"b":{"docs":{},"y":{"docs":{},"e":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"i":{"docs":{},"c":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"o":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},"d":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"a":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"l":{"docs":{},"l":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},".":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"(":{"docs":{},"(":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"_":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},"i":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"s":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}}}}}}},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009301089556205156},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002881844380403458},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}},"u":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.01971830985915493},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002881844380403458},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},",":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"s":{"docs":{},".":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"'":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},":":{"docs":{},"\"":{"docs":{},"j":{"docs":{},"u":{"docs":{},"l":{"docs":{},"i":{"docs":{},"a":{"docs":{},"\"":{"docs":{},"]":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"/":{"docs":{},"j":{"docs":{},"u":{"docs":{},"l":{"docs":{},"i":{"docs":{},"a":{"docs":{},"/":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"v":{"docs":{},".":{"docs":{},"j":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"=":{"docs":{},"\"":{"docs":{},"j":{"docs":{},"l":{"docs":{},"\"":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}},"e":{"docs":{},"v":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}},"d":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"s":{"docs":{},"c":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}}}},"b":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"v":{"docs":{},"i":{"docs":{},"e":{"docs":{},"w":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}},"e":{"docs":{},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394}},"_":{"0":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"1":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"2":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"docs":{}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}},"=":{"docs":{},"\"":{"docs":{},"p":{"docs":{},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}},"c":{"docs":{},"k":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},")":{"docs":{},":":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"x":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002881844380403458}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"s":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004912280701754386},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0028782894736842104},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011958543715120914},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"y":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"r":{"docs":{},"g":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"r":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"y":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"e":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"c":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"w":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}},"e":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0012448530115867088},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.003986181238373638},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0026300958106331017}},"r":{"docs":{},"n":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.01348747591522158},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"!":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"i":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"s":{"docs":{},"'":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0010629816635663034}},"(":{"docs":{},"*":{"docs":{},"t":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"_":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"c":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"i":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"s":{"docs":{},"y":{"docs":{},"m":{"docs":{},"b":{"docs":{},"o":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"v":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"p":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.008333333333333333}}},"s":{"docs":{},"t":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"m":{"docs":{},"o":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"c":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"s":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}}}},"f":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0026574541589157587},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.003371868978805395},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"?":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009301089556205156},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"_":{"docs":{},"d":{"docs":{},"f":{"docs":{},"s":{"docs":{},"(":{"docs":{},"&":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"[":{"1":{"docs":{},".":{"docs":{},".":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"docs":{}}}}}}}}}}}}}}}}}},"f":{"docs":{},"s":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},":":{"docs":{},"u":{"docs":{},"n":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"{":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}},".":{"docs":{},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"_":{"docs":{},"m":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"s":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.003371868978805395},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},".":{"docs":{},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"s":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"v":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"m":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"s":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"r":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0030058237835806877}},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},".":{"docs":{},"_":{"docs":{},"_":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}},"n":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}}}}}}}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},"_":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"o":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}}}}}}},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412}}}}}}}}}}}}}}}}},"x":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"y":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"d":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"a":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}},"docs":{}}}},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0031889449906989105},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}}}},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"q":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"s":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}},")":{"docs":{},":":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}}}},"x":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"y":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"d":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125}}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0020665038512117226}},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"s":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"(":{"docs":{},"i":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"o":{"docs":{},"n":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"s":{"docs":{},":":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"'":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.009735744089012517},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.005479452054794521},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.00487012987012987},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}}}},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.004116920543433511},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{"./":{"ref":"./","tf":0.03571428571428571},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.009633911368015413},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.016901408450704224},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.0847457627118644},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0035087719298245615},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.043478260869565216},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0008618213157138753},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.044642857142857144},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.05952380952380952},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.04504504504504504},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.04672897196261682},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0390625},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.01838235294117647},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004151838671411625},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0024084778420038534},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.006954102920723227},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.024291497975708502},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.013333333333333334},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.009994447529150472},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.010638297872340425},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.015306122448979591},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009880609304240428},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002843216896831844},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.015068493150684932},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.007725321888412017},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.00487012987012987},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.006683081252198382},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.008838383838383838},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.007933194154488519},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.012898845892735914},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.014201183431952662},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005606166783461808},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.005081874647092038},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}},"e":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007773459189339256},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009057225195553726},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005627857896588111},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006944444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.010862186014935505},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01242603550295858},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"m":{"docs":{},"d":{"docs":{},")":{"docs":{},".":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},";":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},":":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}}}}},"n":{"docs":{},"k":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}},"s":{"docs":{},":":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}},"e":{"docs":{},"d":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.007410456978180321},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.005050505050505051},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004142011834319527},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"a":{"docs":{},"r":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004142011834319527}},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"e":{"docs":{},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"(":{"docs":{},"a":{"docs":{},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047}}}}}}},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},")":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"g":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"t":{"docs":{},"t":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},",":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}},"e":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"a":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"m":{"docs":{},":":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"r":{"docs":{},"p":{"docs":{},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002125963327132607},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.005090054815974941},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"$":{"docs":{},"b":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"a":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"b":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"c":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"f":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"x":{"0":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"docs":{}}}}}}}}}}}}}}}}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}},"x":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}},"y":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}}}}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004210526315789474}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},"[":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}},"p":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"f":{"docs":{},"e":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0024183796856106408},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}}}}},"k":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"l":{"docs":{},"i":{"docs":{},"h":{"docs":{},"o":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"m":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"s":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"y":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"e":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"i":{"docs":{},"k":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}}}},"o":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},"o":{"docs":{},"k":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011958543715120914},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.00699876492383697},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003153468815697267},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"s":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"s":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"s":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"v":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.007707129094412331},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},"s":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}},"a":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001677570877369569},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0010629816635663034},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002843216896831844},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003700657894736842}},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},".":{"docs":{},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0035587188612099642},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0024621878297572987},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"!":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},")":{"docs":{},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0035587188612099642}}},":":{"docs":{},":":{"docs":{},"c":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643}}}}}}}}}}}}}}}}}}},"[":{"1":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}},"}":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},"}":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}},"docs":{}}},"l":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"m":{"docs":{},"r":{"docs":{},"o":{"docs":{},"f":{"docs":{},"l":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"n":{"docs":{},"l":{"docs":{},"o":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"g":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},")":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"l":{"docs":{},"y":{"docs":{},"!":{"docs":{},"'":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"?":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"f":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"w":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"s":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}},"a":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0015944724953494552},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"g":{"2":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}},"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047}},"i":{"docs":{},"c":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":5.004109589041096},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},"s":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557}},"e":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}},"docs":{},"t":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"1":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},"docs":{}}}}}}}}}}}}}}},"r":{"docs":{},"_":{"0":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}}},"docs":{}}}},"_":{"2":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"docs":{}},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.005681818181818182},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.01051156271899089}},"i":{"docs":{},"c":{"docs":{},"(":{"docs":{},"a":{"docs":{},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}},"[":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},"/":{"2":{"docs":{},"+":{"1":{"docs":{},":":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}},"docs":{}}},"docs":{}}}}}}}}}}}}}}}},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},")":{"docs":{},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}},"u":{"docs":{},"a":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}},"c":{"docs":{},"k":{"docs":{},"i":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.003985507246376811}}}}},"d":{"docs":{},"w":{"docs":{},"i":{"docs":{},"g":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}},":":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003355141754739138}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003355141754739138}}},"c":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"s":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"l":{"docs":{},"h":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},".":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"i":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535}}},".":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"(":{"docs":{},"c":{"docs":{},"(":{"docs":{},"w":{"docs":{},")":{"docs":{},")":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}},"_":{"1":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"2":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}},"docs":{}},"c":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"]":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852}}},"y":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"m":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0018602179112410311},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.010738255033557046},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.009184481393507521}},"a":{"docs":{},"t":{"1":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}},"docs":{}}}}}}}}},"2":{"docs":{},")":{"docs":{},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}},"docs":{}}}}}}}}},"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0022169437846397467}},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593}},"r":{"docs":{},"i":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}},"a":{"docs":{},"l":{"docs":{},";":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742}},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"h":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"e":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":5.034782608695652},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.026785714285714284},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"i":{"docs":{},"c":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044}}},",":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364}}}},"a":{"docs":{},"l":{"docs":{},".":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}},".":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044}},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},"s":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001677570877369569}}}},"[":{"docs":{},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"]":{"docs":{},"[":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}}}}}}}}}}}}}},"b":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001677570877369569}}}}},"p":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"d":{"docs":{},"i":{"docs":{},"u":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}},"o":{"docs":{},"w":{"docs":{},"[":{"docs":{},"c":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"s":{"docs":{},"(":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"t":{"docs":{},"a":{"docs":{},"n":{"2":{"docs":{},"(":{"docs":{},"a":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}},"docs":{}},"docs":{}}}}}},"p":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},"docs":{}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},".":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"f":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"(":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"y":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}}}}}},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"j":{"docs":{},"a":{"docs":{},"x":{"docs":{},".":{"docs":{},"h":{"docs":{},"u":{"docs":{},"b":{"docs":{},".":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},"[":{"docs":{},"\"":{"docs":{},"t":{"docs":{},"y":{"docs":{},"p":{"docs":{},"e":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"j":{"docs":{},"a":{"docs":{},"x":{"docs":{},".":{"docs":{},"h":{"docs":{},"u":{"docs":{},"b":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"/":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}},"c":{"docs":{},"e":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"é":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"q":{"docs":{},"u":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"s":{"docs":{},"!":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"h":{"docs":{},"e":{"docs":{},"w":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"l":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"c":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0010629816635663034},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"r":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.026785714285714284},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428}}},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"x":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":5.017857142857143},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.01393507521773555},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.008284023668639054}},"!":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002533650039588282},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828}}},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}},"_":{"docs":{},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},"i":{"docs":{},"p":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"[":{"docs":{},"]":{"docs":{},"[":{"docs":{},"]":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}}}}}}}}}}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}}},":":{"docs":{},"\"":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{},"l":{"docs":{},"i":{"docs":{},"b":{"docs":{},".":{"docs":{},"c":{"docs":{},"m":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"s":{"docs":{},".":{"docs":{},"h":{"docs":{},"s":{"docs":{},"v":{"docs":{},"_":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"r":{"docs":{},"g":{"docs":{},"b":{"docs":{},"(":{"docs":{},"h":{"docs":{},"s":{"docs":{},"v":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"y":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},".":{"docs":{},"x":{"docs":{},"i":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"x":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"z":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"y":{"docs":{},"i":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"x":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"z":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"z":{"docs":{},"i":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"x":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"z":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"i":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.005614035087719298},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0018453279651065259},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0012782275244993609},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"[":{"docs":{},"]":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}},"a":{"docs":{},"r":{"docs":{},"g":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"l":{"docs":{},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"l":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"n":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.005873140172278779},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}},"a":{"docs":{},"g":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0234375},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.011029411764705883},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0037052284890901604},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"p":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.026785714285714284},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"(":{"docs":{},"\"":{"docs":{},"a":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"b":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"c":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"d":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"e":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"*":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"_":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"t":{"docs":{},"i":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"s":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"i":{"docs":{},"v":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"y":{"docs":{},"b":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"e":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},"(":{"docs":{},"'":{"docs":{},"?":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},"s":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},"e":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"(":{"docs":{},"[":{"docs":{},"]":{"docs":{},"r":{"docs":{},"u":{"docs":{},"n":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"docs":{}},"docs":{}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"[":{"docs":{},"r":{"docs":{},"u":{"docs":{},"n":{"docs":{},"e":{"docs":{},"]":{"docs":{},"*":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},"_":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"_":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767}}}}}}}},"r":{"docs":{},"k":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"d":{"docs":{},"o":{"docs":{},"w":{"docs":{},"n":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}},"e":{"docs":{},"t":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}},"o":{"docs":{},"v":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"c":{"docs":{},"h":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":5.0014450867052025},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.004166666666666667}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"}":{"docs":{},"&":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"i":{"docs":{},"u":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742}}}},"r":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}},"a":{"docs":{},"g":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":3.3348995040459406}},"e":{"docs":{},"s":{"docs":{},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{},"l":{"docs":{},"i":{"docs":{},"a":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}}}},"d":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},"(":{"4":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"o":{"docs":{},"f":{"docs":{},"(":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}},"e":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}}}}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"e":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0018602179112410311},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"$":{"docs":{},"(":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{},"_":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"[":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{},"_":{"docs":{},"_":{"docs":{},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"_":{"docs":{},"_":{"docs":{},")":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"_":{"docs":{},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"l":{"docs":{},"$":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"o":{"docs":{},"w":{"docs":{},"$":{"docs":{},"(":{"docs":{},"?":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"[":{"docs":{},"c":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}}},"r":{"docs":{},"u":{"docs":{},"n":{"docs":{},"e":{"docs":{},"]":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"m":{"docs":{},"_":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"h":{"docs":{},"e":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"d":{"docs":{},"i":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"x":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"_":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"y":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"i":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}}}},"i":{"docs":{},"m":{"docs":{},"u":{"docs":{},"m":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"b":{"docs":{},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"y":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"(":{"1":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}},"z":{"docs":{},"z":{"docs":{},"u":{"docs":{},"c":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"g":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{},"d":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006313131313131313},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},":":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"_":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"d":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},"f":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},":":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}},"!":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}},"i":{"docs":{},"c":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},":":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"j":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"e":{"docs":{},"a":{"docs":{},"n":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.009122807017543859},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.007305194805194805},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.00421179302045728},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.00350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.006211180124223602},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"f":{"docs":{},"u":{"docs":{},"l":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"w":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"s":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"?":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"s":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.004698512137823023}},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}}},"o":{"docs":{},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},")":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"[":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}}}}}}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"(":{"docs":{},"&":{"docs":{},":":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},"?":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"[":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"/":{"docs":{},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742}},"'":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"[":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"h":{"docs":{},"u":{"docs":{},"s":{"docs":{},"b":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},"s":{"docs":{},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}},"c":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"y":{"docs":{},"(":{"docs":{},"t":{"docs":{},"m":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}},"d":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},"_":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"r":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"y":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"(":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"h":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0008618213157138753},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":5.044642857142857},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0234375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004744958481613286},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.009824561403508772},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0021303792074989347},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":3.335147118097541},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.005431093007467753},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.00350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.003952569169960474}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},"s":{"docs":{},".":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"\"":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"'":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"!":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"o":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.006884057971014493}}}},"e":{"docs":{},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"r":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":10.010163749294184}},"s":{"docs":{},"\"":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"x":{"0":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"docs":{}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},"s":{"docs":{},"s":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.003986181238373638},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.021920668058455117}},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},":":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0010629816635663034}},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}}}},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405}},"e":{"docs":{},"r":{"docs":{},"'":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},")":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},";":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}},"i":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"e":{"docs":{},"v":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.005415162454873646}},"i":{"docs":{},"c":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},"!":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}}}}}},"r":{"docs":{},"g":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"v":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"i":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"n":{"docs":{},"d":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"e":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"s":{"docs":{},"w":{"docs":{},"e":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"i":{"docs":{},"m":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581}},"u":{"docs":{},"m":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"(":{"docs":{},"t":{"docs":{},"u":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},")":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}},"b":{"docs":{},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"y":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}},"(":{"1":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}},"p":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}}}},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"e":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}},"u":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"s":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"r":{"docs":{},"e":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"n":{"docs":{},"i":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"d":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"e":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}}}}}}}},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}},"o":{"docs":{},"d":{"1":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0055359838953195776},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507}},"e":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}},"r":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488}}}},"l":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"s":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"i":{"docs":{},"f":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0029585798816568047},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"(":{"1":{"5":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"9":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"4":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{},"a":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"b":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}}}}}},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}},"u":{"docs":{},"l":{"docs":{},"o":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754}},"(":{"docs":{},"a":{"docs":{},",":{"docs":{},"b":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"s":{"docs":{},".":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}},"r":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.03389830508474576},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.023809523809523808},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0010629816635663034},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003855278766310795},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0037052284890901604},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.005681818181818182},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.004220893422441084},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.005415162454873646},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0035502958579881655},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004204625087596356},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"r":{"docs":{},"i":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}},"s":{"docs":{},"'":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005956552207428171}}}}}}},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"o":{"docs":{},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029}}}}},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"'":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}}}}}},"v":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.020204921957291965},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004361684281160879},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.01222428913101249},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.007702423445425512},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0035502958579881655},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}},"s":{"docs":{},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"s":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157}}}},"u":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},"i":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}},"s":{"docs":{},"d":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0030058237835806877},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.005823036500497088}}}},"q":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0037572797294758596}}}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"u":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.004433696090286175},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.01263537906137184}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"l":{"docs":{},"i":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":5.006092607636068},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891}},"h":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.004166666666666667}},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},")":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"r":{"docs":{},"l":{"docs":{},"o":{"docs":{},"(":{"1":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{},"s":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"r":{"docs":{},"l":{"docs":{},"o":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}},"(":{"1":{"0":{"0":{"0":{"0":{"0":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},".":{"docs":{},"c":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"r":{"docs":{},"u":{"docs":{},"n":{"docs":{},"(":{"1":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"g":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}}}}}},"p":{"docs":{},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"(":{"1":{"0":{"0":{"docs":{},"_":{"0":{"0":{"0":{"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"docs":{}},"docs":{}}}}}}}}}}},"d":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"o":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.01213768115942029}},"'":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},")":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}},"u":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.007017543859649123},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"c":{"docs":{},"h":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},".":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"l":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}},"i":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":5.0177304964539005},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.007653061224489796},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002803083391730904},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}},".":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},":":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"s":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"y":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"m":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}}}},"d":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}},"s":{"docs":{},"d":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0028405056099985795}}}},"l":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":3.3374066530889337}}}}}},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0019883539269990058},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.004635227730753728},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}},";":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}},"[":{"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}}}},"2":{"docs":{},"]":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}}}},"docs":{}}},"y":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"t":{"docs":{},"i":{"docs":{},"f":{"docs":{},"y":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}},":":{"docs":{},":":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}},"k":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001677570877369569}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"!":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"m":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"w":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"e":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"o":{"docs":{},"p":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"(":{"docs":{},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"_":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"v":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"+":{"docs":{},"+":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465}}}}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"?":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"]":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"g":{"docs":{},"[":{"docs":{},"m":{"docs":{},"]":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"_":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0028214429665457475}}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}},"'":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}},"c":{"docs":{},"m":{"docs":{},"c":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.011482254697286013},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.007653061224489796},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.004061738424045491},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.00631578947368421},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.013150479053165508},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.008116883116883116},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0038691523039043265},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0047522063815342835},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0019927536231884057},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.025423728813559324}},"e":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},".":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"!":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"l":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}},"e":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.017391304347826087},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0010629816635663034},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.013333333333333334},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.004528612597776863},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00684931506849315},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0077192982456140355},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.005681818181818182},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0029585798816568047},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891}},"e":{"docs":{},"d":{"docs":{},"?":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}},".":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}},"a":{"docs":{},"r":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"l":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"b":{"docs":{},"i":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}},"t":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009}},"?":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"w":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.005614035087719298},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.017391304347826087},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0033515273388872928},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0038533085304278502},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.01096319498825372},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.011078998073217727},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.004924375659514597},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005606166783461808},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"(":{"1":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}}},"docs":{}},"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"}":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"x":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"z":{"docs":{},"e":{"docs":{},"r":{"docs":{},"o":{"docs":{},"s":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"_":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"e":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004744958481613286}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.009489916963226572}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518}}},"u":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004744958481613286}},"e":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0035587188612099642}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643}}}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643}}}}}}}},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}},"[":{"docs":{},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}}}}},"c":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"docs":{},"i":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"d":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"docs":{},"i":{"docs":{},"+":{"1":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},"f":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"s":{"docs":{},".":{"docs":{},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"f":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"e":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{},"'":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}},"x":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011958543715120914},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.005797101449275362},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},"_":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},"e":{"docs":{},"s":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0038346825734980826}},"s":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}}}},"(":{"docs":{},"(":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"p":{"docs":{},"o":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002272404487998864}}}},"!":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"g":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001509813789632612},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603}}}}}}}},"o":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.011269276393831554},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"_":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"_":{"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"_":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"_":{"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}},"[":{"4":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518}}}}},"docs":{}}},".":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"u":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935}}}}},"o":{"docs":{},"t":{"docs":{},"e":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"h":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"a":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":5.013798701298701},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854}}}},"\"":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}},"b":{"docs":{},"l":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}},"_":{"docs":{},"b":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"i":{"docs":{},"c":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"f":{"docs":{},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002898550724637681},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.023809523809523808},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"m":{"docs":{},"e":{"docs":{},"r":{"docs":{},"c":{"docs":{},"i":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},"z":{"docs":{},"e":{"docs":{},"r":{"docs":{},"o":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"w":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"a":{"docs":{},"d":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}},"s":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"d":{"docs":{},"e":{"1":{"0":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"1":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"2":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"}":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},".":{"docs":{},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}},"[":{"2":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"docs":{}}},"2":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},".":{"docs":{},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}},"[":{"1":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"2":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"docs":{}}},"3":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"}":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"4":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"}":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},"5":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"6":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"}":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"7":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"8":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"}":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"9":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"}":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.00631578947368421},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.01005458201666188},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.008105235184693063},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0050415183867141165}},"(":{"0":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}},"1":{"0":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"1":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"2":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"2":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"3":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"4":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"5":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"6":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"7":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"8":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"9":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}},"i":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"docs":{}},"docs":{}}}}}}},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"s":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},"(":{"docs":{},"o":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"y":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},".":{"docs":{},"t":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},"(":{"docs":{},"b":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002681221871109834},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}},"s":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"*":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"q":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"(":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0010629816635663034},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"!":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"docs":{}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}},".":{"docs":{},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"{":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}},"?":{"docs":{},".":{"docs":{},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}},"1":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"docs":{}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},"(":{"docs":{},"n":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}}}}}},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},">":{"docs":{},">":{"docs":{},"b":{"docs":{},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},"f":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}}}}}}}},"[":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"_":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},"(":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"{":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}},"p":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397}}}}}},"{":{"docs":{},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},")":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}}}},"'":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}}}}}}}}}}}}}}}}},"!":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"i":{"docs":{},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}},"b":{"docs":{},"o":{"docs":{},"d":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"r":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124}}},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"w":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"m":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"a":{"docs":{},"l":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.006355932203389831}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}},"!":{"docs":{},"(":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}}}},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"=":{"docs":{},"f":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},")":{"docs":{},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}},"i":{"docs":{},"s":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"e":{"docs":{},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"o":{"docs":{},"n":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"a":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}}},"m":{"docs":{},"e":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.004306969459671104},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"\"":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0023492560689115116},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742}}},"d":{"docs":{},"t":{"docs":{},"u":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"e":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}},"'":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},"s":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"n":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"d":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"i":{"docs":{},"v":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}},"ï":{"docs":{},"v":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339}}}}},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"o":{"docs":{},"l":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"m":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}}},"p":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"m":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409}}},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},".":{"docs":{},"z":{"docs":{},"e":{"docs":{},"r":{"docs":{},"o":{"docs":{},"s":{"docs":{},"(":{"docs":{},"(":{"5":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"docs":{},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}}}}}}}}}}},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}},"a":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},".":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}},"docs":{}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},".":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}},"y":{"docs":{},")":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}}}}}},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"l":{"docs":{},"(":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},"_":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},")":{"docs":{},")":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}}}}}}}}},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},"[":{"docs":{},"x":{"docs":{},"_":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"n":{"docs":{},"i":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"(":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"x":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"a":{"docs":{},"v":{"docs":{},"e":{"docs":{},"t":{"docs":{},"x":{"docs":{},"t":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}}}},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},".":{"1":{"docs":{},"*":{"docs":{},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}}}},"docs":{}}},"docs":{},"n":{"docs":{},"p":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"g":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}},"m":{"docs":{},"s":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"b":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},".":{"docs":{},"s":{"docs":{},"u":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"t":{"docs":{},"(":{"docs":{},"[":{"docs":{},"[":{"1":{"docs":{},".":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}},"docs":{}}},"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"(":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"m":{"docs":{},"f":{"docs":{},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"_":{"docs":{},"f":{"docs":{},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"f":{"docs":{},"t":{"docs":{},".":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},"_":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}},"i":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},"(":{"docs":{},"f":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"g":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}},"i":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"]":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"f":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"n":{"docs":{},"p":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"n":{"docs":{},"p":{"docs":{},".":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},"x":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"(":{"docs":{},"[":{"1":{"0":{"docs":{},".":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}},"docs":{}},"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"*":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"$":{"docs":{},"[":{"docs":{},":":{"1":{"0":{"0":{"0":{"0":{"docs":{},"]":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}}}}}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}},"[":{"2":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"docs":{}}}},")":{"docs":{},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"(":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"a":{"docs":{},"[":{"docs":{},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"_":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},":":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"f":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"docs":{},"(":{"docs":{},"h":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"(":{"docs":{},"n":{"docs":{},"p":{"docs":{},".":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}}}}}}}}}}}}}}}}}}}}},"j":{"docs":{},"(":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},"_":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"(":{"docs":{},"f":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"h":{"docs":{},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}},"a":{"docs":{},"n":{"docs":{},"(":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"e":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"a":{"docs":{},"x":{"docs":{},"i":{"docs":{},"s":{"docs":{},"(":{"docs":{},"(":{"docs":{},"h":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},"(":{"docs":{},"x":{"docs":{},"_":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011958543715120914},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},"p":{"docs":{},"t":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}},"m":{"1":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00536822680758262}}},"2":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004361684281160879}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844}},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001509813789632612},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.014184397163120567},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.005763688760806916},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.019178082191780823},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004210526315789474},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.006493506493506494},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.005845511482254697},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.005978260869565218},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.010161177295024528},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.009034443817052512},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00847457627118644}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},"e":{"docs":{},".":{"docs":{},"e":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"4":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"5":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"9":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"docs":{}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},".":{"docs":{},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"4":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"5":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"9":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"docs":{}}}}}}}}}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.005479452054794521},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},":":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"?":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"!":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603}}}},"_":{"docs":{},"o":{"docs":{},"f":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"'":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},")":{"docs":{},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}},"`":{"docs":{},"t":{"docs":{},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"docs":{}},"docs":{}}}}}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"s":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"{":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},".":{"docs":{},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},"}":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}}},"o":{"docs":{},"r":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}},"s":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"i":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},"s":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"p":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"t":{"docs":{},"h":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}},"s":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0015321267834913339},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},".":{"docs":{},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0008618213157138753}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"_":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"i":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669}}}}}}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},".":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"j":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},".":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"^":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"t":{"docs":{},"h":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}}}}}}}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.006355932203389831}}},"}":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"_":{"2":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{},"s":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"s":{"docs":{},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"_":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"s":{"docs":{},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"v":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"{":{"docs":{},"v":{"docs":{},"+":{"1":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"}":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"=":{"1":{"0":{"0":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},":":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}},"docs":{}},"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"2":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"3":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"4":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"7":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"docs":{}},"d":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"=":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}},"v":{"docs":{},"i":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}},"/":{"2":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}},"docs":{}},"]":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}},"docs":{}}}}}},"+":{"1":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"docs":{}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}}}}}},"(":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}}}}}},"v":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002803083391730904}},"a":{"docs":{},")":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}}}}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"y":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"m":{"docs":{},"s":{"docs":{},"d":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"r":{"docs":{},"m":{"docs":{},"s":{"docs":{},"d":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}}}}},"o":{"3":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"b":{"docs":{},"v":{"docs":{},"i":{"docs":{},"o":{"docs":{},"u":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"s":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"!":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"j":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"(":{"docs":{},"[":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002717391304347826},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"x":{"docs":{},"i":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011958543715120914},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.012145748987854251},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002717391304347826},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002452697967764541},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.006775832862789385},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}},"e":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"p":{"docs":{},")":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},";":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"?":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"s":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"g":{"docs":{},"o":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"c":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"e":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"t":{"docs":{},"o":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"u":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0022024322512687925},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.006954102920723227},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0024621878297572987},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"s":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"_":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"m":{"docs":{},"a":{"docs":{},"k":{"docs":{},"e":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{},"(":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"f":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"w":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.0138811771238201},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.013174145738987238},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.004924375659514597},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.003022974607013301},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.010732323232323232},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"s":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}},".":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394}}},"_":{"docs":{},"s":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}},"t":{"docs":{},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"p":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.011929824561403509}}},"[":{"docs":{},"t":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"1":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004912280701754386}}}},"2":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004912280701754386}}}},"docs":{}}}}}}}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"s":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"[":{"docs":{},"i":{"docs":{},",":{"docs":{},":":{"docs":{},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},":":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}},"s":{"docs":{},"(":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}}}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}}},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}}}}},"(":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}},"t":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"d":{"docs":{},"o":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}},"[":{"docs":{},"i":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}},"e":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"_":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}}}}}},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"e":{"docs":{},".":{"docs":{},"w":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}},"!":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"e":{"docs":{},"r":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.007415254237288136}},"e":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},":":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"s":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"v":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}},"f":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"n":{"docs":{},"d":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428}}}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0016278847074595424},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011958543715120914},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.006521739130434782}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"s":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"i":{"docs":{},"c":{"docs":{},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"!":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"\"":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"!":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"s":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"s":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{},"p":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"k":{"docs":{},"i":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"w":{"docs":{},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{},"m":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}},"a":{"docs":{},"l":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"l":{"docs":{},",":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"j":{"docs":{},"o":{"docs":{},"y":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"l":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"\"":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"k":{"docs":{},"i":{"docs":{},"l":{"docs":{},"l":{"docs":{},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"m":{"docs":{},"l":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}},"s":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0022168480451430876},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}},"t":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"[":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},">":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"m":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.013333333333333334},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.010300429184549357},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.008116883116883116},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0028139289482940555},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":3.3411930673115675},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.007933194154488519},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.00842358604091456},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004733727810650888}},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"!":{"docs":{},"=":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}},"=":{"docs":{},"=":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}},"&":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}}},".":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"s":{"docs":{},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767}},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},"&":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}},";":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"x":{"docs":{},")":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"x":{"docs":{},")":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"*":{"docs":{},"(":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}},"+":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}},"s":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"(":{"docs":{},"\"":{"docs":{},"s":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{},"p":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"k":{"docs":{},"i":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"i":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828}}}}}}},"a":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}},"@":{"docs":{},"(":{"docs":{},"o":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.007053607416364369}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},".":{"docs":{},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0026199113260781943}},"e":{"docs":{},"[":{"docs":{},"j":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"p":{"docs":{},"e":{"docs":{},"[":{"docs":{},"j":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0034260378879484078}}},"v":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0018137847642079807},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"j":{"docs":{},"]":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"a":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0068520757758968156},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},".":{"docs":{},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"|":{"docs":{},"x":{"docs":{},"|":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},"[":{"docs":{},"j":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},":":{"docs":{},"o":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"}":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"&":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"n":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"r":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"e":{"docs":{},"r":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001340610935554917},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"2":{"4":{"docs":{},";":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}},")":{"docs":{},".":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}},".":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"i":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"a":{"docs":{},"l":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},"x":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"y":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},";":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"=":{"docs":{},"\"":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}},"g":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"s":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"w":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"h":{"docs":{},"i":{"docs":{},"p":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"l":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"[":{"0":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.010676156583629894}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"u":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}},"e":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0071174377224199285}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},".":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"y":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},":":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},".":{"docs":{},"c":{"docs":{},"m":{"docs":{},"p":{"docs":{},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"c":{"docs":{},"m":{"docs":{},"p":{"docs":{},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"x":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"y":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},"w":{"docs":{},"i":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}},"e":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},".":{"docs":{},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}},"s":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}},"i":{"docs":{},"c":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"(":{"docs":{},"g":{"docs":{},"o":{"docs":{},"o":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"a":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"s":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"c":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"l":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"o":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}},"d":{"docs":{},"d":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0061995115536351685},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"[":{"docs":{},"k":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}}},"s":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},"m":{"docs":{},"e":{"docs":{},"g":{"docs":{},"a":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0020665038512117226}}}}}},"(":{"1":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"3":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}},"docs":{},"\\":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"b":{"docs":{},")":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},")":{"docs":{},"?":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}}},"n":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"!":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"^":{"2":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"3":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"docs":{}}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"p":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}},"@":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"1":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},")":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},")":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},".":{"0":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}},"1":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}},"docs":{},"x":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0024084778420038534},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465}}}},"y":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"*":{"docs":{},"(":{"docs":{},"p":{"2":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"3":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"docs":{}}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}},"docs":{}},"^":{"2":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}},"docs":{}}},"2":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}},"\"":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"^":{"2":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}},"docs":{}}},"3":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.004528612597776863},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0038691523039043265},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0015622780854992189},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0022168480451430876},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.004166666666666667},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.014084507042253521},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.020833333333333332},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"e":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},"u":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"t":{"docs":{},"h":{"docs":{},"o":{"docs":{},"r":{"docs":{},"a":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"n":{"docs":{},"b":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"e":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"s":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"a":{"docs":{},"r":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},".":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}},"c":{"docs":{},"k":{"docs":{},"'":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}},"y":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"t":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},"e":{"docs":{},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"u":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"g":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"i":{"docs":{},"n":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}},"c":{"docs":{},"k":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}},"o":{"docs":{},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":10.031700288184439},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0035174111853675696},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0018137847642079807},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.013257575757575758},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},";":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}},"t":{"docs":{},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},":":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"r":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"_":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},".":{"docs":{},"p":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}},"t":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},".":{"docs":{},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{},"s":{"docs":{},"(":{"1":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}}}}}}}}}}}}},"r":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"e":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}},"o":{"docs":{},"b":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.017391304347826087},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.011126564673157162},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.007220216606498195},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005606166783461808},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.009034443817052512},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":5.052966101694915}}},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},".":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"e":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}}},"y":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":5.046728971962617},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":3.335291046724093},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"!":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"s":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"c":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"e":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"s":{"docs":{},"s":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002058590657165479},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},".":{"docs":{},"w":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},":":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"o":{"docs":{},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"d":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"e":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.007707129094412331},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"m":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},",":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044}}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}},"j":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.02040816326530612},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},"s":{"docs":{},".":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}},"!":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"c":{"docs":{},"l":{"docs":{},"j":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}},"f":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}},"s":{"docs":{},"p":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"!":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}}},"v":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.006954102920723227},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"y":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"l":{"docs":{},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"o":{"docs":{},"s":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.004306969459671104},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}},"s":{"docs":{},"(":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"_":{"docs":{},"o":{"docs":{},"f":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"_":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"r":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}}},"d":{"docs":{},"u":{"docs":{},"k":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"c":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.003371868978805395},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"m":{"docs":{},"i":{"docs":{},"s":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"o":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"t":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}}}}},"h":{"docs":{},"i":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"l":{"docs":{},"i":{"docs":{},"f":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"o":{"docs":{},"f":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"f":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.008613938919342208},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"_":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"s":{"docs":{},".":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"o":{"docs":{},"f":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"docs":{}}}}}}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}},"s":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},":":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"i":{"docs":{},"x":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"[":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},"s":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"r":{"docs":{},"v":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"u":{"docs":{},"m":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"t":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"c":{"docs":{},"i":{"docs":{},"s":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"?":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"v":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478}},"a":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"i":{"docs":{},"o":{"docs":{},"u":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0015622780854992189},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.015054679732992472}},"s":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0026984803294986506}}}}}}},"p":{"docs":{},"o":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.005681011219997159}},"s":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}}}},"m":{"docs":{},"i":{"docs":{},"s":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.004596380350474002},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009301089556205156},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"(":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},".":{"docs":{},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}},"\"":{"docs":{},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"\\":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0008618213157138753}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}},"t":{"docs":{},"h":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"\"":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"h":{"docs":{},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"\\":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}}}},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}}}}},"{":{"docs":{},":":{"docs":{},".":{"1":{"0":{"docs":{},"f":{"docs":{},"}":{"docs":{},"\"":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}}}}}}}}},"docs":{}},"docs":{}}}},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}}}}}}}}},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"g":{"docs":{},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}},"'":{"docs":{},"i":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"\\":{"docs":{},"n":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}},"t":{"docs":{},"h":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},".":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}},"f":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0014363688595231256},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}}}}}}}}}}}}}},"f":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},"q":{"docs":{},")":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}},"'":{"docs":{},"{":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"\"":{"docs":{},"u":{"docs":{},"s":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"{":{"docs":{},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"{":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"u":{"docs":{},"s":{"docs":{},"(":{"docs":{},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}}}}}}}}},"'":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"s":{"docs":{},"'":{"docs":{},":":{"docs":{},">":{"1":{"0":{"docs":{},"s":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"s":{"docs":{},":":{"1":{"0":{"docs":{},"d":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"docs":{}},"docs":{}}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"n":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011490950876185005}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837}}}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},".":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},"s":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},"s":{"docs":{},")":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}}}}}}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837}}}}}}}},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"_":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"(":{"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"docs":{}},"docs":{}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"(":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"docs":{}},"docs":{}},"docs":{}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"(":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"(":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"(":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"[":{"docs":{},"y":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}},"[":{"2":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"b":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"_":{"docs":{},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},"l":{"docs":{},"n":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935}},"!":{"docs":{},"(":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"\"":{"docs":{},"{":{"docs":{},":":{"docs":{},"?":{"docs":{},"}":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004210526315789474}}}}}},"#":{"docs":{},"?":{"docs":{},"}":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"}":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449}}}}}},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}},"{":{"docs":{},":":{"docs":{},">":{"1":{"9":{"docs":{},"}":{"docs":{},"]":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"docs":{}},"docs":{}},"?":{"docs":{},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}}}},"h":{"docs":{},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"t":{"docs":{},"h":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}}}}}},"(":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"\"":{"docs":{},"[":{"0":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"1":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"2":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}}}}}}}},"$":{"docs":{},"i":{"docs":{},"]":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"%":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},".":{"1":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}},"docs":{}}}},"n":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"a":{"docs":{},"n":{"docs":{},"n":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"c":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"i":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"a":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"b":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"t":{"docs":{},"h":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"h":{"docs":{},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},":":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},":":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}},"$":{"docs":{},"(":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}},"a":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"$":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{},"s":{"docs":{},"_":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"$":{"docs":{},"(":{"docs":{},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"_":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}},"{":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}}}}}}}}}}}}},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}}},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"_":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"(":{"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"(":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"docs":{}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"(":{"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"(":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"docs":{}}}}}}}}}}},"i":{"docs":{},"s":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"m":{"docs":{},"g":{"docs":{},"[":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},"a":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}}},"2":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"3":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"b":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"!":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"{":{"docs":{},"}":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001340610935554917}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}}},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0016278847074595424},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}},"(":{"docs":{},"\"":{"docs":{},"%":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703054677774585}}},"l":{"docs":{},"f":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449}}}}}}}}},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}}}}}}},"t":{"docs":{},"h":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},":":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},":":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}}},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}},"g":{"docs":{},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}},"'":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"'":{"docs":{},".":{"docs":{},"p":{"docs":{},"h":{"docs":{},"p":{"docs":{},"_":{"docs":{},"e":{"docs":{},"o":{"docs":{},"l":{"docs":{},".":{"docs":{},"'":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}}}}}}}}}}},"%":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"s":{"docs":{},"\\":{"docs":{},"'":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}},"h":{"docs":{},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"t":{"docs":{},"h":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"f":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"e":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"i":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},")":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"e":{"docs":{},"v":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}}}}}}}},"m":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{},"(":{"docs":{},"a":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"(":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"x":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}},"v":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"c":{"docs":{},"i":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001340610935554917},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"e":{"docs":{},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"l":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"e":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"y":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},".":{"docs":{},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},"{":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}}}}}}}},"<":{"docs":{},">":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},"o":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"[":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"]":{"docs":{},"(":{"docs":{},")":{"docs":{},"(":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{},"b":{"docs":{},"y":{"docs":{},"(":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}},"{":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"}":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.03389830508474576},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.017391304347826087},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.023809523809523808},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.018018018018018018},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.018691588785046728},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.008344923504867872},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}},"r":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},".":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"s":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}},";":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"e":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"s":{"docs":{},"u":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}},"e":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"b":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.015438596491228071},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0046921382744422105},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0018453279651065259},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0035875631145362743},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.015661707126076743},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.008670520231213872},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.005280259951259139},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"s":{"docs":{},"h":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}}}},"s":{"docs":{},"h":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.006128507133965335},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004529441368897836},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.001993090619186819},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.004696599661844825},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"(":{"docs":{},"&":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"!":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}},"s":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}},"/":{"docs":{},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"z":{"docs":{},"z":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001340610935554917},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0028782894736842104},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"l":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141}}}}}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"a":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"g":{"docs":{},"e":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}},"s":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005255781359495445}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.004433696090286175}},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"c":{"docs":{},"u":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"l":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"l":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0012782275244993609},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.00421179302045728},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925}},"e":{"docs":{},"'":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"s":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"\"":{"docs":{},">":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"a":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"_":{"docs":{},"c":{"docs":{},"m":{"docs":{},"p":{"docs":{},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}},"e":{"docs":{},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"}":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.005873140172278779}},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},".":{"docs":{},"n":{"docs":{},"i":{"docs":{},"l":{"docs":{},"?":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"s":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"[":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},".":{"docs":{},"o":{"docs":{},"n":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"a":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.005441354292623942},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"e":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.004635227730753728},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"r":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},".":{"docs":{},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"5":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"docs":{}}},"docs":{}}}}}}}}}}}},"s":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"(":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}},"(":{"5":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}}},"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"x":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},":":{"docs":{},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},"docs":{}}}}}}}}}}}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0026199113260781943},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004210526315789474},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}},"_":{"docs":{},"c":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"l":{"docs":{},"{":{"1":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"docs":{}}}}}},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{},"d":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.004030632809351068}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"i":{"docs":{},"m":{"docs":{},"_":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},"e":{"docs":{},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}},"k":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"i":{"docs":{},"(":{"2":{"docs":{},")":{"docs":{},")":{"docs":{},".":{"docs":{},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}}}},"docs":{}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"]":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}}}}}}}}},"s":{"docs":{},"s":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}}}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.004710144927536232}}}}}}},"c":{"docs":{},"k":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"e":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},".":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"i":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0023492560689115116},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"s":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"n":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"n":{"docs":{},"i":{"docs":{},"c":{"docs":{},"!":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"u":{"docs":{},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"l":{"docs":{},"d":{"docs":{},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}}}}}}}}}}}}}},"t":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0010629816635663034},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},".":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},"&":{"docs":{},"p":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"_":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}}}}},"_":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"y":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394}}}}}},"u":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"s":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"e":{"docs":{},"o":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"f":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"l":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.01773049645390071},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004210526315789474},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0026300958106331017},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.014487079091620987}},"'":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}},"(":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"4":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}},"docs":{}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"{":{"docs":{},"f":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"p":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},";":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}}},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731}}}}},"i":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"i":{"docs":{},"c":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}},"c":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178}},"_":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}}}}}},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}},"i":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"e":{"docs":{},"k":{"docs":{},"(":{"docs":{},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},"[":{"2":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"docs":{}}}}}}}}}}}}},"a":{"docs":{},"k":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925}}}},"c":{"docs":{},"u":{"docs":{},"l":{"docs":{},"i":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},".":{"docs":{},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"0":{"docs":{},".":{"0":{"docs":{},"_":{"docs":{},"f":{"6":{"4":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},"docs":{}}}},"docs":{}}},"docs":{},"(":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"h":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"y":{"docs":{},"s":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":5.0625},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"s":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},"?":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}},"p":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},"_":{"docs":{},"e":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593}}},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},".":{"docs":{},"f":{"docs":{},"l":{"docs":{},"a":{"docs":{},"t":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},":":{"docs":{},":":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.00946969696969697},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"s":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"p":{"docs":{},"p":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.010154346060113728},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0033815517565282736},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0022168480451430876},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}},"e":{"docs":{},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"e":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"s":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}},"x":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}},"e":{"docs":{},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"c":{"docs":{},"k":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"_":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"u":{"docs":{},"r":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}}}}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"]":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},".":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.004697986577181208},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.010926365795724466}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0023752969121140144}},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"_":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0014251781472684087}},")":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}},"i":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"s":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"_":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},")":{"docs":{},"/":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},".":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"=":{"docs":{},"m":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"r":{"docs":{},"l":{"docs":{},"o":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"k":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"c":{"docs":{},"h":{"docs":{},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"/":{"1":{"0":{"docs":{},".":{"0":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"docs":{}}},"docs":{}},"docs":{},"x":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}},"o":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.038630876295980686}},"i":{"docs":{},"n":{"docs":{},"t":{"1":{"docs":{},".":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"y":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"2":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}},".":{"docs":{},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"x":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"y":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"d":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"3":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}},".":{"docs":{},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845}}}},"2":{"0":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"3":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"6":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{}},"8":{"5":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{}},"docs":{}}},"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}}}}},"d":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}}},"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.009786476868327402},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.03757225433526012},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.03959731543624161},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.012185215272136474},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0136986301369863},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.014035087719298246},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.037636299683432996},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.014196242171189978},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002355072463768116},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.00650887573964497},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"e":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0016278847074595424},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397}}}},"s":{"docs":{},".":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.018018018018018018},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},"a":{"docs":{},"g":{"docs":{},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"g":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"m":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0050335570469798654}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"u":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"m":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"|":{"docs":{},"a":{"docs":{},"|":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}},"i":{"docs":{},"s":{"docs":{},"_":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"1":{"docs":{},")":{"docs":{},".":{"docs":{},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"(":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}},"docs":{}}}}}},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"_":{"docs":{},"u":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"_":{"docs":{},"b":{"docs":{},"y":{"docs":{},"(":{"docs":{},"|":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}},"1":{"docs":{},":":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"m":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"]":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},".":{"docs":{},"x":{"docs":{},")":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"y":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"]":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"2":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},".":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{},"]":{"docs":{},".":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}}}}}}}}},"4":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"j":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"a":{"docs":{},"]":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"i":{"docs":{},"+":{"1":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{}},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"m":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}}}}}}}}}}}}}}}}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}},")":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},":":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"*":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"(":{"0":{"docs":{},",":{"1":{"4":{"docs":{},")":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"docs":{}},"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},".":{"5":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}}},"1":{"5":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},".":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}}},"2":{"docs":{},",":{"8":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"5":{"docs":{},",":{"7":{"docs":{},")":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"6":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"7":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"9":{"docs":{},",":{"9":{"docs":{},")":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.005369127516778523}},"p":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"+":{"1":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"docs":{}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}}}}}},"x":{"1":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"=":{"0":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{}}},"*":{"docs":{},"t":{"docs":{},")":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"p":{"docs":{},")":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}},"b":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"x":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}},"c":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"x":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"e":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}},"[":{"docs":{},"]":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"i":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}}}}}}}}}},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}},"n":{"docs":{},"g":{"docs":{},".":{"docs":{},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}}}}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0028139289482940555},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},":":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}}},"&":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"y":{"docs":{},")":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},".":{"docs":{},"a":{"docs":{},"s":{"docs":{},"_":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}},"x":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"i":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{},"_":{"docs":{},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"(":{"docs":{},"o":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}}}}}}}}},"z":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"docs":{},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"n":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}},"_":{"docs":{},"o":{"docs":{},"n":{"docs":{},"_":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624}}}}}}}},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}},"x":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}},"y":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"9":{"1":{"docs":{},"b":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},"docs":{}},"docs":{}}},"docs":{}}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},")":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"o":{"docs":{},"n":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657}},"l":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"*":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},":":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}},"t":{"docs":{},"y":{"docs":{},"p":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0024621878297572987}},"&":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}}}}}}}}},"{":{"docs":{},"x":{"docs":{},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848}}}}},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}},"o":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"r":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904}}},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"a":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"r":{"docs":{},"a":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002452697967764541},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.006355932203389831}},"e":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},"_":{"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.009489916963226572}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}},"s":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"{":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}},"u":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}}}}}}}}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}}}}}}}}}}}},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}},"s":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0017236426314277506}},"e":{"docs":{},"r":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002982530890498509},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0030797101449275364},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.009626955475330927},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.007340485601355167}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"'":{"docs":{},"'":{"docs":{},"'":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"v":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}},"(":{"1":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"2":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"3":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"2":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"3":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"docs":{}}}}}}},"_":{"docs":{},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"y":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}}}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}}},"*":{"2":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002272404487998864}}},"docs":{}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.004970884817497514}},"a":{"docs":{},"c":{"docs":{},"c":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0018463286464990769}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.005681011219997159}}},"e":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"w":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00684931506849315},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"s":{"docs":{},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}},"f":{"docs":{},"u":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"(":{"docs":{},"$":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"y":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}},"p":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.005458201666187877},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0023917087430241827},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0037572797294758596},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"(":{"docs":{},"&":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},"!":{"docs":{},"(":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},"e":{"docs":{},")":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"u":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0018137847642079807},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"a":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"l":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0077192982456140355},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0033944331296673455}},"_":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}},"s":{"docs":{},"_":{"docs":{},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"s":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}}}}}}}}},"b":{"docs":{},"o":{"docs":{},"x":{"docs":{},"_":{"docs":{},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"r":{"docs":{},"!":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}}}}}},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}}}}}}}}}}}}}}}}}},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"r":{"docs":{},"_":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"!":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}}}}}}}}},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"!":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}}},"b":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}}},"y":{"docs":{},"n":{"docs":{},"o":{"docs":{},"m":{"docs":{},"i":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247}}}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"s":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}},"e":{"docs":{},"u":{"docs":{},"d":{"docs":{},"o":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}}}}},"y":{"docs":{},"t":{"docs":{},"h":{"docs":{},"o":{"docs":{},"n":{"3":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"a":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}}}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.003691275167785235},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.010820645408407546},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.009433962264150943},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.010332519256058614}},"[":{"docs":{},"r":{"1":{"2":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"docs":{}},"docs":{}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},":":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},".":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"y":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"f":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},".":{"docs":{},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{},"}":{"docs":{},"`":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}}}}}},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"y":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"+":{"1":{"docs":{},")":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"docs":{}},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"}":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"x":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312}}}}}}}},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"x":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004151838671411625},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"m":{"3":{"docs":{},"d":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"docs":{}},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"b":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"k":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"d":{"docs":{},"f":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535}},"l":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}}}}}},"n":{"docs":{},"g":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"c":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{},"o":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},"v":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"x":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0019883539269990058}}}}},"=":{"docs":{},"n":{"docs":{},"p":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"[":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"+":{"docs":{},"k":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"x":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}},"x":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.006355932203389831}},"\"":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}},"d":{"docs":{},"x":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}}}},"h":{"docs":{},")":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"n":{"docs":{},")":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00847457627118644}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}}}}},"t":{"docs":{},")":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"_":{"1":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"2":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"}":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"{":{"docs":{},"p":{"docs":{},"_":{"3":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"docs":{}}}}}}}}}}}},"3":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"4":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"}":{"docs":{},"}":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"docs":{}}},"r":{"1":{"0":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009301089556205156}}},"b":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"1":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"2":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.006990328449679211},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0033218176986446984},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0031936877700544804}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002872737719046251},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011958543715120914},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"3":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.005362443742219668},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002258836035078395},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.004696599661844825}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0033515273388872928},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"4":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0032557694149190847},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011958543715120914},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.005260191621266203}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0015321267834913339},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0030058237835806877}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438}}},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}},"5":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0008618213157138753},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0028179597971068945}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0033815517565282736}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"d":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}},"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}},"2":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}},"8":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011958543715120914}}},"d":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"9":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013287270794578793}}},"b":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"d":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00268411340379131},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.004061738424045491},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.003787878787878788},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.005431093007467753},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003800475059382423},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"e":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.005239822652156389},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"a":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"r":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"'":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"s":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"!":{"docs":{},")":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"m":{"docs":{},"e":{"docs":{},".":{"docs":{},"m":{"docs":{},"d":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}},"o":{"docs":{},"n":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}},"i":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"l":{"docs":{},"i":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125}}}},"n":{"docs":{},"g":{"docs":{},"!":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"y":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0038291011688835145},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.007575757575757576},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"s":{"docs":{},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588}}}},"z":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}}}},"l":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"y":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},"o":{"docs":{},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"*":{"docs":{},"d":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"(":{"1":{"6":{"docs":{},")":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},"docs":{}},"8":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0012782275244993609}}}}},"docs":{},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{},"y":{"docs":{},"_":{"docs":{},"k":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"_":{"docs":{},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"s":{"docs":{},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"r":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737}},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}},"c":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412}}}}}}}},"g":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.006657323055360897}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}},"o":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"u":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"l":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"y":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}},"p":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"o":{"docs":{},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"y":{"docs":{},":":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"r":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00821917808219178},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.008838383838383838},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.011126564673157162},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}}}}}}}}}},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"r":{"docs":{},"c":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}}}}},"l":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"a":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},":":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737}}},"?":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}},"o":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.03389830508474576},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.017391304347826087},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.023809523809523808},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.018018018018018018},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.018691588785046728},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},".":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"i":{"docs":{},"r":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.034782608695652174},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"d":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"(":{"docs":{},"\"":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},".":{"docs":{},"j":{"docs":{},"s":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"o":{"docs":{},"u":{"docs":{},"r":{"docs":{},"c":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002803083391730904},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"v":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.03389830508474576},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},";":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}},"m":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"i":{"docs":{},"z":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"r":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"o":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}},"'":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},".":{"docs":{},"p":{"docs":{},"h":{"docs":{},"p":{"docs":{},"_":{"docs":{},"e":{"docs":{},"o":{"docs":{},"l":{"docs":{},".":{"docs":{},"'":{"docs":{},"%":{"docs":{},"s":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}}}}}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"$":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"c":{"docs":{},"k":{"1":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}},"2":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}},"docs":{}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}},"%":{"docs":{},"d":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}},"{":{"docs":{},"}":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}},"`":{"docs":{},"n":{"docs":{},"$":{"docs":{},"(":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}},"~":{"docs":{},"%":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}},"=":{"docs":{},"$":{"docs":{},"(":{"docs":{},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"_":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}},".":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}},"s":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"!":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"[":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}},"!":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"p":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}}}}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737}}},"/":{"2":{"docs":{},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},"docs":{}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534}}},"]":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"d":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},"u":{"docs":{},"c":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003167062549485352},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"n":{"docs":{},"d":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"m":{"docs":{},"e":{"docs":{},"m":{"docs":{},"b":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}},"o":{"docs":{},"v":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004210526315789474},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0026845637583892616},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"f":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}},"r":{"docs":{},"k":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"v":{"docs":{},"i":{"docs":{},"e":{"docs":{},"w":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":5.052083333333333},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"s":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}},"e":{"docs":{},"d":{"docs":{},"o":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},".":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"(":{"docs":{},"m":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}}}}}},"(":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}}}},"v":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}},"c":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"e":{"docs":{},"i":{"docs":{},"v":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.006263048016701462}},"e":{"docs":{},"o":{"docs":{},"p":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"(":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"a":{"docs":{},"l":{"docs":{},"(":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}},"r":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.003830316958728335},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0030058237835806877},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"!":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"v":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"\\":{"docs":{},"n":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"_":{"docs":{},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"l":{"docs":{},"!":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}}}}}},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},"$":{"docs":{},"(":{"docs":{},"?":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"(":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}}}}}},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"f":{"docs":{},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},")":{"docs":{},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"e":{"docs":{},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"o":{"docs":{},"m":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904}}}}}}},"g":{"docs":{},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"i":{"docs":{},"e":{"docs":{},"v":{"docs":{},"e":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"a":{"docs":{},"l":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"k":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"f":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}},"e":{"docs":{},"r":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},".":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"y":{"docs":{},")":{"docs":{},".":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},"n":{"2":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}},"docs":{}}}}}}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}},")":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"x":{"docs":{},")":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"y":{"docs":{},")":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"docs":{}},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002681221871109834},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0023917087430241827},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002414429768498793},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.037192982456140354},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0043091065785693765},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.011575239053850024},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.010098325803879883},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.011746280344557557},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.009489916963226572},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.012524084778420038},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.015436241610738255},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.015028432168968318},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.014592274678111588},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.004320871688897238},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003700657894736842},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00809004572634541},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.007811390427496095},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.003787878787878788},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.006109979633401222},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.006884057971014493},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.008759635599159075},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.004517221908526256}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"(":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"n":{"docs":{},",":{"2":{"docs":{},")":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}},"docs":{}}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"n":{"docs":{},",":{"2":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}},"docs":{}}}}}}}}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"=":{"docs":{},"$":{"1":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}}},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"v":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}}}}}},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"_":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"_":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},"p":{"docs":{},".":{"docs":{},"s":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}},"(":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"_":{"docs":{},"o":{"docs":{},"f":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}},"_":{"docs":{},"c":{"docs":{},"r":{"docs":{},"o":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"*":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"_":{"docs":{},"c":{"docs":{},"r":{"docs":{},"o":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"l":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"e":{"docs":{},"v":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}}}}},"a":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"x":{"docs":{},"!":{"docs":{},"\"":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"u":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588}}}}},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767}},"_":{"docs":{},"f":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}}}}},"j":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":3.340350877192982},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}}}},"i":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},"x":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}},"y":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}}},"h":{"docs":{},"o":{"docs":{},"l":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"^":{"docs":{},"{":{"docs":{},"i":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0031889449906989105},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"_":{"docs":{},"d":{"docs":{},"f":{"docs":{},"s":{"docs":{},"(":{"docs":{},"&":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"[":{"1":{"docs":{},".":{"docs":{},".":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"docs":{}}}}}}}}}}}}}}}}}},"f":{"docs":{},"s":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"u":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},"!":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},":":{"docs":{},"u":{"docs":{},"n":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"{":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"?":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}},"o":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"o":{"docs":{},"u":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"c":{"docs":{},"h":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009}}}},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"j":{"docs":{},"n":{"docs":{},"d":{"docs":{},"a":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}},"u":{"docs":{},"n":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.01461038961038961},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"g":{"docs":{},"a":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{},"(":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.00974025974025974}},"e":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},":":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"(":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935}}}},"b":{"docs":{},"i":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}},"s":{"docs":{},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},":":{"docs":{},":":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},":":{"docs":{},":":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"l":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"e":{"docs":{},")":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"l":{"docs":{},"e":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"/":{"docs":{},"b":{"docs":{},"a":{"docs":{},"s":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}},"n":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"g":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009301089556205156},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.007415254237288136}},"e":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"1":{"docs":{},",":{"1":{"0":{"1":{"docs":{},")":{"docs":{},"]":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653}}}}},"docs":{}},"docs":{}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"2":{"0":{"2":{"0":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"docs":{}},"docs":{}},"6":{"4":{"docs":{},")":{"docs":{},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"]":{"docs":{},"[":{"docs":{},"j":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"docs":{}},"docs":{},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"s":{"docs":{},")":{"docs":{},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}}}}}},")":{"docs":{},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}}},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852}}}},"docs":{}}}},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"a":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"docs":{}}}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824}}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}},"docs":{}}}}}}}}}}}}},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},"d":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"s":{"docs":{},")":{"docs":{},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}},"a":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},")":{"docs":{},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"docs":{}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},")":{"docs":{},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"d":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542}},"o":{"docs":{},"m":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0023492560689115116},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003886729594669628},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.006904955320877335},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.009145269081955681},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.008768267223382045},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.00350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.007340485601355167}},"(":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"4":{"2":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"docs":{}},"docs":{}}}}},"u":{"docs":{},"n":{"docs":{},"i":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}}}}}}}}}},"_":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"_":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"(":{"docs":{},")":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"?":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"(":{"1":{"2":{"8":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}},"docs":{}},"2":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"*":{"2":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649}}},"docs":{}},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},":":{"docs":{},":":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},":":{"docs":{},":":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"l":{"docs":{},"u":{"docs":{},"d":{"docs":{},"e":{"docs":{},":":{"docs":{},":":{"docs":{},"*":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}},"*":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"t":{"docs":{},"h":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{},"_":{"docs":{},"r":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"_":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"x":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"y":{"docs":{},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"_":{"docs":{},"d":{"docs":{},"e":{"docs":{},"v":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"{":{"docs":{},"}":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}}}}}}}}}}}}},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"_":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}}}}}}}},"k":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.003638801110791918},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0038584130179500084},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0033218176986446984},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.003926074882696543},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004193927193423922},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011958543715120914},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.004133007702423445},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"r":{"docs":{},"d":{"docs":{},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}}},"i":{"docs":{},"s":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"y":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"s":{"docs":{},"\"":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"l":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}},"u":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00934199837530463}},"s":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"9":{"1":{"docs":{},"b":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},"docs":{}},"docs":{}}},"docs":{}}}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0036555645816409425}}},"=":{"1":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"docs":{}}}},"c":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"s":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"r":{"docs":{},"e":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"o":{"docs":{},"u":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"p":{"docs":{},"i":{"docs":{},"d":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},"]":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"b":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0028179597971068945}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298}}}}},"c":{"docs":{},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011958543715120914}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.001993090619186819},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"d":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.003830316958728335},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00268411340379131},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0018602179112410311},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.006607296753806378},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.004119053946319426},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0017273452032952432},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001819400555395959},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0029231995748073346},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}},"_":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}},"b":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"y":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}},"\"":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"m":{"docs":{},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.030720506730007917},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"s":{"docs":{},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"}":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"\"":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"'":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"+":{"docs":{},"+":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"[":{"docs":{},"c":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}},"j":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}},"a":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"b":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"?":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"l":{"docs":{},"l":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}},"\"":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"t":{"1":{"3":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"docs":{}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},"a":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.007692307692307693}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},".":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"e":{"docs":{},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"u":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0033944331296673455},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}},"g":{"docs":{},"h":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"l":{"docs":{},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}}}}}}},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}},"m":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"a":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"s":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"h":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0030642535669826677},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002258836035078395},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.004213348654601168},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003355141754739138},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0033218176986446984},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438}}}},"a":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}}}}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}}},"?":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}}}}},"\"":{"docs":{},"(":{"docs":{},"b":{"docs":{},"i":{"docs":{},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"s":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"r":{"docs":{},"h":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},".":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"y":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"x":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"y":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"[":{"0":{"docs":{},"]":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"x":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"z":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"1":{"docs":{},"]":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"x":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"z":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"2":{"docs":{},"]":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"x":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"z":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"docs":{}}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}}},"n":{"docs":{},"g":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"_":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"0":{"docs":{},".":{"0":{"docs":{},"_":{"docs":{},"f":{"6":{"4":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}},"docs":{}}}},"docs":{}}},"docs":{}}}}}}}},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"}":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}},":":{"docs":{},":":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}},"(":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"d":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}}}},"g":{"docs":{},"b":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"^":{"2":{"docs":{},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"}":{"docs":{},"{":{"docs":{},"(":{"2":{"docs":{},"r":{"docs":{},")":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"docs":{}}}}},"docs":{}}}}},"docs":{}},"_":{"0":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.009824561403508772},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0047522063815342835}},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"docs":{}},"y":{"docs":{},"z":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},":":{"docs":{},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}}}}}}}}}},"(":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"s":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"*":{"docs":{},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"(":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{},"*":{"docs":{},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}}}}}}}}}}},"=":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"{":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}},"?":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"s":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}}}}},"m":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"+":{"docs":{},"+":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"a":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.006775832862789385}},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},".":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"2":{"4":{"docs":{},";":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"d":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"?":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":3.333333333333333}}},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}},"e":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0008618213157138753},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003886729594669628},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004733727810650888},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"v":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0019151584793641674},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0018602179112410311},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},"o":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"e":{"docs":{},"m":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}}},"f":{"docs":{},"e":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}}},"y":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}}}},"s":{"docs":{},":":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}},"w":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"t":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653}}}}}}}},"l":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"t":{"docs":{},"i":{"docs":{},"s":{"docs":{},"f":{"docs":{},"i":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"u":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.004419191919191919}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394}}}}}}}}}}},"c":{"docs":{},"r":{"docs":{},"i":{"docs":{},"f":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"c":{"docs":{},"h":{"docs":{},"l":{"docs":{},"o":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007773459189339256},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009057225195553726},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005627857896588111},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006944444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.010862186014935505},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01242603550295858},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719}},".":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}},".":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044}}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},"n":{"docs":{},"h":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}}}},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"s":{"docs":{},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"r":{"docs":{},"ö":{"docs":{},"d":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147}}}}}}}}}}},"i":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.007707129094412331},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.022598870056497175},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"e":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}},"t":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"f":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"i":{"docs":{},"c":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}},"p":{"docs":{},"y":{"docs":{},".":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}}}}},"a":{"docs":{},"l":{"docs":{},"a":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},".":{"docs":{},"{":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"_":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{},"l":{"docs":{},"i":{"docs":{},"b":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},".":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002881844380403458},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.01069078947368421},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.008284023668639054},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005956552207428171},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},"?":{"docs":{},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"\"":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"n":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":5.001677852348993},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"l":{"1":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"i":{"docs":{},"n":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"r":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094}}}}}}},"o":{"docs":{},"n":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}},"r":{"docs":{},"e":{"docs":{},"(":{"docs":{},"@":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}},"p":{"docs":{},"e":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"m":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},";":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"i":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.004528612597776863},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},".":{"docs":{},"g":{"docs":{},"p":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"e":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{},"o":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}},"e":{"docs":{},"e":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0022168480451430876},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004733727810650888},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.003952569169960474},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"m":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"n":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}}},"r":{"docs":{},"v":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},"e":{"docs":{},"r":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}},":":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}},"o":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.005253623188405797}},"s":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"'":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002355072463768116}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"`":{"docs":{},"t":{"docs":{},"`":{"docs":{},"t":{"docs":{},"$":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"c":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754}}},"=":{"docs":{},"f":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"}":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"{":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"u":{"docs":{},"s":{"docs":{},"(":{"docs":{},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},")":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"_":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}},"i":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":5.02834008097166},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"o":{"docs":{},"u":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.023809523809523808},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.018691588785046728},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}},".":{"docs":{"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"s":{"docs":{},".":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"!":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},";":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},":":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"o":{"docs":{},"r":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904}}}}},"o":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}}}}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"s":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"l":{"docs":{},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"u":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}},"l":{"docs":{},"f":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},"_":{"docs":{},"_":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},".":{"docs":{},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0023492560689115116}},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}}}}}}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},".":{"docs":{},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"l":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"_":{"docs":{},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"_":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},"?":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"c":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},".":{"docs":{},"s":{"docs":{},"w":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"a":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"[":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"_":{"docs":{},"d":{"docs":{},"f":{"docs":{},"s":{"docs":{},"(":{"docs":{},"&":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"[":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},".":{"docs":{},".":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}}}}}},"f":{"docs":{},"s":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},":":{"docs":{},":":{"docs":{},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"v":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},".":{"docs":{},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}},"e":{"docs":{},"r":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"c":{"docs":{},"m":{"docs":{},"p":{"docs":{},"(":{"docs":{},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},")":{"docs":{},"}":{"docs":{},"'":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"[":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}},"m":{"docs":{},"_":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},".":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"c":{"docs":{},"m":{"docs":{},"p":{"docs":{},"(":{"docs":{},"&":{"docs":{},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"y":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},".":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"c":{"docs":{},"m":{"docs":{},"p":{"docs":{},"(":{"docs":{},"&":{"docs":{},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}}}}}}}}}}}}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"z":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}}}},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"(":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"h":{"docs":{},"u":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},"_":{"docs":{},"o":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}}}},"a":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.003830316958728335},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"n":{"docs":{},"s":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"e":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},",":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"!":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}},"d":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.006263048016701462}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.003915426781519186},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.013908205841446454},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.02099629477151091},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003700657894736842},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0035174111853675696},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.021464646464646464},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0041753653444676405},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003167062549485352},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0035502958579881655},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0010629816635663034},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},".":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"e":{"docs":{},"(":{"docs":{},"m":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"$":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"p":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}},"u":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"c":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}}}}},"[":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003289473684210526}},")":{"docs":{},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}},"g":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"s":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405}},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"k":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007773459189339256},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009057225195553726},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005627857896588111},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006944444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.010862186014935505},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01242603550295858},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}}}}}},"p":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"l":{"docs":{},"i":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"m":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"p":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0045726345409778405},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"?":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}},"s":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"s":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}},"s":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"[":{"docs":{},"r":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"_":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"0":{"docs":{},".":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"n":{"docs":{},"n":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"e":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"k":{"docs":{},"e":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}},"d":{"docs":{},"e":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"l":{"docs":{},"l":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"o":{"docs":{},"w":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001053337163650292},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"n":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}}}},"c":{"docs":{},"a":{"docs":{},"s":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}}}}},"u":{"docs":{},"l":{"docs":{},"d":{"docs":{},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"r":{"docs":{},"'":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},"e":{"docs":{},"r":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},")":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"c":{"docs":{},"u":{"docs":{},"t":{"docs":{},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"i":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"f":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261}}}}},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"l":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"e":{"docs":{},"(":{"docs":{},"$":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},"g":{"docs":{},"i":{"docs":{},"r":{"docs":{},"l":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"u":{"docs":{},"y":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"_":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"i":{"docs":{},"p":{"docs":{},"t":{"docs":{},"o":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}}}}}}},"e":{"docs":{},"l":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"a":{"docs":{},"r":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.009467455621301775}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"p":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.00350385423966363}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"e":{"docs":{},":":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"u":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"?":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}},"z":{"docs":{},"e":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004912280701754386},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001340610935554917},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0037052284890901604},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0033815517565282736},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925}},",":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004210526315789474}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}},"x":{"docs":{},")":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}},"y":{"docs":{},")":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"a":{"docs":{},",":{"1":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}},"2":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}},"docs":{}}}},"_":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0015944724953494552},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.003915426781519186},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.003355704697986577},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0022169437846397467}},"(":{"0":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"docs":{}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"a":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"o":{"docs":{},"f":{"docs":{},"(":{"docs":{},"q":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}},"y":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},"_":{"docs":{},"k":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"r":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"docs":{}},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},":":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"docs":{}},"docs":{}}}}}},"]":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"g":{"docs":{},"n":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"i":{"docs":{},"f":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},"i":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"a":{"docs":{},"l":{"2":{"docs":{},")":{"docs":{},":":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"t":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653}}}}}}}}}}}}}},"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.012770682953914493},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.01020408163265306},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824}},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},"?":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},"s":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},";":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},"[":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}},"m":{"docs":{},"a":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.007017543859649123},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0033944331296673455}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.00631578947368421},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}}}}},"d":{"docs":{},"e":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}},"f":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.006954102920723227},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.006107717934480844},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815}},"i":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0037052284890901604},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0029585798816568047},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"c":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"f":{"docs":{},"i":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"s":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"_":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"_":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}}}}}}},"y":{"docs":{},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"u":{"docs":{},"l":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0035174111853675696},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0038291011688835145},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.009626955475330927},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"o":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},"s":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},"t":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"i":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"l":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"y":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"?":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"u":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114}},"!":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},".":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}}}},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094}}}},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}}}},"e":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828}}},"u":{"docs":{},"s":{"docs":{},"o":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"e":{"docs":{},"r":{"docs":{},"p":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"k":{"docs":{},"i":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005979599015124868},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848}}}}}}}}}}}}}}}},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"h":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004210526315789474},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{},".":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},")":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},"i":{"docs":{},"m":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}},"o":{"docs":{},"n":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"(":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"'":{"0":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"1":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"docs":{}},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"x":{"docs":{},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},"n":{"docs":{},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"w":{"docs":{},"h":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},"e":{"docs":{},"r":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}},"h":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}},"v":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.018018018018018018},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.046875},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0028503562945368173},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},";":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"r":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":5.0078125},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"s":{"docs":{},".":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125}}}},".":{"docs":{},".":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"d":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"u":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003700657894736842},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00332541567695962},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"'":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"\"":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},"\"":{"docs":{},"\"":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}},"%":{"docs":{},"s":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}}}},"_":{"docs":{},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}},"[":{"docs":{},":":{"3":{"docs":{},",":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"docs":{}}},"{":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"?":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"j":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"s":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"i":{"docs":{},"d":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0028782894736842104},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001583531274742676}},".":{"docs":{},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}},"a":{"docs":{},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}},"j":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"*":{"docs":{},"a":{"docs":{},"[":{"docs":{},"i":{"docs":{},",":{"docs":{},"j":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"a":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"[":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"i":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"j":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}},"r":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.004697986577181208},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"s":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"!":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},"[":{"2":{"docs":{},":":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}},"docs":{}}}}}}}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"s":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}},"e":{"docs":{},"d":{"docs":{},"(":{"docs":{},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}}}}},"p":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}},"o":{"docs":{},"n":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"_":{"docs":{},"b":{"docs":{},"y":{"docs":{},"_":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"f":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"r":{"docs":{},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"t":{"docs":{},"h":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"w":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"f":{"docs":{},"t":{"docs":{},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"o":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"!":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.008583690987124463}}}}},"p":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}},"!":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"p":{"docs":{},"e":{"docs":{},"c":{"docs":{},"i":{"docs":{},"f":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"i":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"r":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}},"a":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"t":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044}}}}}}}},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}}},"n":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},"a":{"docs":{},"k":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}}}}},"e":{"docs":{},"d":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"d":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.017857142857142856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.007255139056831923},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.010830324909747292},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.00421179302045728}}},"s":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},".":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.005415162454873646},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}},"w":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}}},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}},"n":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":3.3359532446594113},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"_":{"docs":{},"o":{"docs":{},"p":{"docs":{},"!":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}},"(":{"docs":{},"&":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}}},"a":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}},".":{"docs":{},"j":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},"o":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}},"o":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"e":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"u":{"docs":{},"c":{"docs":{},"e":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"y":{"docs":{},"?":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"o":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.005415162454873646},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"s":{"docs":{},":":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}},"i":{"docs":{},"c":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011490950876185005},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.003523884103367267},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.003371868978805395},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}},":":{"docs":{},":":{"docs":{},"d":{"docs":{},"f":{"docs":{},"s":{"docs":{},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"$":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"(":{"docs":{},"$":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"$":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},"docs":{}}}}}}}}}}}}},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}},"docs":{}}}}}},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}}},"docs":{}}}}},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},"docs":{}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"_":{"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"c":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"g":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"r":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011958543715120914},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004210526315789474},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0031656700668308124},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002898550724637681},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004142011834319527},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}},"{":{"1":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"docs":{}}}}},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}}}}}}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},".":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}},"s":{"docs":{},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"n":{"docs":{},"d":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557}}}}}}}},"c":{"docs":{},"k":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":5.016842105263158},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.008043665613329504},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003855278766310795}},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"c":{"docs":{},"[":{"docs":{},"t":{"docs":{},"]":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}},"\"":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},".":{"docs":{},".":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"?":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"x":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"&":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"_":{"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669}}}}},"l":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},"!":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"(":{"docs":{},"&":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},".":{"docs":{},".":{"docs":{},".":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}}}}}}},"c":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}},"<":{"docs":{},">":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"1":{"docs":{},":":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"s":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"2":{"4":{"docs":{},";":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},"\\":{"docs":{},"n":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"c":{"docs":{},"a":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"_":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"_":{"docs":{},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"f":{"docs":{},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},")":{"docs":{},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"l":{"docs":{},"!":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},"$":{"docs":{},"(":{"docs":{},"?":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"(":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}}}}}},"{":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"}":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"}":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}}}}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}}}}}},"y":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"b":{"docs":{},"l":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":3.337248760114852}},"e":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"_":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"docs":{},"$":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},"e":{"docs":{},"(":{"docs":{},"g":{"docs":{},"u":{"docs":{},"y":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},".":{"docs":{},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"a":{"docs":{},"d":{"docs":{},"a":{"docs":{},"m":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"m":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"x":{"docs":{},"e":{"docs":{},"n":{"docs":{},"a":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"y":{"docs":{},"e":{"docs":{},"v":{"docs":{},"a":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"z":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},"e":{"docs":{},"x":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742}}}}}}}}}}}}}}},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}},"i":{"docs":{},"l":{"docs":{},"l":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0029585798816568047},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"c":{"docs":{},"k":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},"y":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"y":{"docs":{},"t":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"e":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003854239663629993}}},"m":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"e":{"docs":{},"r":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.005965061780997018}},"_":{"docs":{},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}},"(":{"5":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},".":{"0":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}},"docs":{}}},"docs":{},"&":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}}},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}}},":":{"docs":{},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},"docs":{}},"docs":{}}}}}}}}}}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}},"(":{"5":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},".":{"0":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"g":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"e":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"p":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"?":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"l":{"docs":{},"i":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},":":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"y":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"?":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"s":{"docs":{},"s":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}}}},"n":{"docs":{},"g":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"e":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}}},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0027769797950780426},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.005846399149614669},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.010379596678529062},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0063758389261744965},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0028139289482940555},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0036275695284159614},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0037578288100208767},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"u":{"docs":{},"r":{"docs":{"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":5.033898305084746},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"?":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"n":{"docs":{},"g":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}},"(":{"0":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"2":{"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"_":{"docs":{},"_":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"(":{"2":{"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"\"":{"docs":{},".":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"n":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0038533085304278502},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0023492560689115116},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0014492753623188406},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"(":{"0":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"2":{"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"s":{"docs":{},".":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"s":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"r":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}}}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}},"i":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},"[":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"[":{"docs":{},"j":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}},"l":{"docs":{},"p":{"docs":{},"a":{"docs":{},"d":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"x":{"docs":{},"[":{"docs":{},"j":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"l":{"docs":{},"(":{"docs":{},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"v":{"docs":{},"[":{"docs":{},"j":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"(":{"2":{"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},":":{"docs":{},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},")":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"b":{"docs":{},"u":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}},"}":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"p":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"v":{"docs":{},"e":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}},"d":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"[":{"2":{"5":{"7":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"docs":{}},"docs":{}},"docs":{}},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"*":{"docs":{},"d":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},"*":{"docs":{},"d":{"docs":{},"s":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}},"s":{"docs":{},"r":{"docs":{},"c":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}},"o":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}},"e":{"docs":{},"r":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"u":{"docs":{},"d":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"o":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"s":{"docs":{},")":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"f":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"p":{"docs":{},"i":{"docs":{},"d":{"docs":{},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"y":{"docs":{},"l":{"docs":{},"e":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},":":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},"=":{"docs":{},"\"":{"docs":{},"w":{"docs":{},"i":{"docs":{},"d":{"docs":{},"t":{"docs":{},"h":{"docs":{},":":{"1":{"0":{"0":{"docs":{},"%":{"docs":{},"\"":{"docs":{},"/":{"docs":{},">":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"docs":{}},"docs":{}},"8":{"0":{"docs":{},"%":{"docs":{},"\"":{"docs":{},">":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"/":{"docs":{},">":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"docs":{}},"docs":{}}}}}}}}}}}},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},":":{"docs":{},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}},"{":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0008618213157138753},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"p":{"docs":{},"y":{"docs":{},"(":{"docs":{},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"(":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"docs":{}}},"docs":{}}}}}}}},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"m":{"docs":{},"p":{"docs":{},":":{"docs":{},":":{"docs":{},"{":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"k":{"docs":{},"e":{"docs":{},"_":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},">":{"docs":{},"(":{"docs":{},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}},"(":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"u":{"docs":{},"n":{"docs":{},"i":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},">":{"docs":{},"(":{"docs":{},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}},"(":{"docs":{},"l":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"l":{"docs":{},"h":{"docs":{},"s":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"l":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"_":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},"}":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},".":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}}},"h":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"t":{"1":{"9":{"9":{"3":{"7":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"i":{"docs":{},"n":{"docs":{},"_":{"docs":{},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},".":{"docs":{},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},">":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737}}}}}}}}}}},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"_":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"{":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}},"w":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}},"e":{"docs":{},"q":{"docs":{},"n":{"docs":{},"s":{"docs":{},"[":{"docs":{},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}}}}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},".":{"7":{"5":{"docs":{},")":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"docs":{}},"docs":{}}},"docs":{}}}}}},"u":{"docs":{},"n":{"docs":{},"i":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"r":{"docs":{},">":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"b":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"b":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"3":{"2":{"docs":{},"_":{"docs":{},"t":{"docs":{},"(":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"2":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}},"docs":{}},"docs":{}}}}},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"_":{"docs":{},"n":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},")":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"(":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"{":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},".":{"docs":{},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}},"s":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"a":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},">":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"&":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}}},"&":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"{":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}},"b":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}}}},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}},"&":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}}}}}}},"e":{"docs":{},"x":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"docs":{},"b":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}}}},"n":{"docs":{},"d":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"f":{"6":{"4":{"docs":{},":":{"docs":{},":":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},"s":{"docs":{},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"i":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}},"docs":{}},"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"_":{"docs":{},"i":{"docs":{},"f":{"docs":{},"(":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"_":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"f":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}}}}}},"s":{"docs":{},":":{"docs":{},":":{"docs":{},"w":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"\"":{"docs":{},".":{"docs":{},"/":{"docs":{},"s":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{},"p":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"k":{"docs":{},"i":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}}}}},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"g":{"docs":{},"u":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"\"":{"docs":{},"a":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"t":{"docs":{},"a":{"docs":{},"(":{"docs":{},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},":":{"docs":{},":":{"docs":{},"w":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},":":{"docs":{},":":{"docs":{},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"m":{"docs":{},"_":{"docs":{},"f":{"docs":{},"n":{"docs":{},"(":{"docs":{},"|":{"docs":{},"|":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"t":{"docs":{},"h":{"docs":{},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"s":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"(":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"o":{"docs":{},"_":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"2":{"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{},"(":{"2":{"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"s":{"docs":{},":":{"docs":{},":":{"docs":{},"{":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"m":{"docs":{},"&":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}},"f":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"_":{"docs":{},"d":{"docs":{},"e":{"docs":{},"v":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"f":{"docs":{},"a":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},"_":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"&":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}}}}}}}}}}}},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},"i":{"docs":{},"o":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}},"=":{"docs":{},"c":{"docs":{},"+":{"docs":{},"+":{"1":{"7":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"docs":{}},"docs":{}}}}}},"e":{"docs":{},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0034260378879484078},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.010163749294184076}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"s":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"?":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"r":{"docs":{},"e":{"docs":{},"o":{"docs":{},"t":{"docs":{},"y":{"docs":{},"p":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}}}}},"m":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0008618213157138753},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0026690391459074734}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},".":{"docs":{},"c":{"docs":{},"a":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"u":{"docs":{},"b":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0050327126321087065},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438}},"m":{"docs":{},"i":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},"s":{"docs":{},";":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}}}}}},"j":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"c":{"docs":{},"l":{"docs":{},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0021808421405804393},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0022169437846397467}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}}}}}}}},"(":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"*":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}}},"s":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}},"q":{"docs":{},"u":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"t":{"docs":{},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}},"e":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}},"d":{"docs":{},"i":{"docs":{},"v":{"docs":{},"i":{"docs":{},"s":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0025564550489987218}}}}}},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141}}}}}},"m":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004441976679622432},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.00944206008583691},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.004117181314330958},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.009533898305084746}},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"y":{"docs":{},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"e":{"docs":{},"r":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}}}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"(":{"docs":{},"s":{"docs":{},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{},"y":{"docs":{},"_":{"docs":{},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}}},"_":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{},"_":{"docs":{},"d":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"1":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}},"docs":{}}}},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852}}}}}}}}}}}}}}}}}}}}}}}}}}}},"'":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114}}},":":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"p":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"d":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"r":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004441976679622432},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.005010438413361169},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.011834319526627219},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},".":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"(":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}},"f":{"docs":{},"l":{"docs":{},"u":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"i":{"docs":{},"m":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"s":{"docs":{},"e":{"docs":{},"d":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.018691588785046728},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"s":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}},"f":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}}},"c":{"docs":{},"h":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.004517221908526256},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}}}},"d":{"docs":{},"d":{"docs":{},"e":{"docs":{},"n":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"o":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"s":{"docs":{},".":{"docs":{},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"s":{"docs":{},"u":{"docs":{},"i":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"(":{"docs":{},"m":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"s":{"docs":{},"p":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754}},"n":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"d":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.005978260869565218}}}}}},"g":{"docs":{},"g":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"f":{"docs":{},"f":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"l":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"y":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"e":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"s":{"docs":{},"t":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"p":{"docs":{},"e":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"l":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"p":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"c":{"docs":{},"e":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"d":{"docs":{},"e":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}}}},"m":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"t":{"docs":{},"a":{"docs":{},"s":{"docs":{},"k":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"l":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"y":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.007725321888412017}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0234375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.014705882352941176},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":3.335092038926017},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003642121931908155},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":5.007220216606498},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.003952569169960474}},"s":{"docs":{},";":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},".":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"!":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"l":{"docs":{},"n":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},".":{"docs":{},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}},"\"":{"docs":{},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}},"\"":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},":":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},":":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}},"\\":{"docs":{},"n":{"docs":{},"g":{"docs":{},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},":":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}}}}}},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"(":{"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"(":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"docs":{}}}}}}}}}}},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"w":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"s":{"docs":{},".":{"docs":{},"t":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}}}}}}}}}}}},"x":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}}}}}}}}}}}}}}},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},".":{"docs":{},"p":{"docs":{},"e":{"docs":{},"e":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},".":{"docs":{},"p":{"docs":{},"e":{"docs":{},"e":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}},"f":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"%":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"c":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"[":{"docs":{},"%":{"docs":{},".":{"1":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}},"docs":{}}}},"h":{"docs":{},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"t":{"docs":{},"h":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"c":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"n":{"docs":{},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"e":{"docs":{},".":{"docs":{},"w":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"(":{"docs":{},"$":{"docs":{},"\"":{"docs":{},"{":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"r":{"docs":{},"y":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"}":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},".":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"}":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"x":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}},"t":{"docs":{},"h":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}},"\"":{"docs":{},"j":{"docs":{},"a":{"docs":{},"r":{"docs":{},"v":{"docs":{},"i":{"docs":{},"s":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}},"r":{"docs":{},"u":{"docs":{},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"l":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"n":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"t":{"docs":{},"h":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"q":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"i":{"docs":{},"o":{"docs":{},";":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"\"":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"%":{"docs":{},"s":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},"\"":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"!":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"'":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"m":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"i":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"n":{"docs":{},"c":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"h":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"o":{"docs":{},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261}}}}},")":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339}}}},"n":{"docs":{},"i":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}},"d":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"a":{"docs":{},"p":{"docs":{},"s":{"docs":{},"h":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"o":{"docs":{},"w":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"f":{"docs":{},"(":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}}}}}}}}}}}},"w":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001053337163650292},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"a":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0030087094220110845}},"(":{"docs":{},"&":{"docs":{},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}}},"i":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"f":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{},"[":{"docs":{},"b":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}},"_":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},"(":{"docs":{},"&":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"a":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}},"(":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"[":{"docs":{},"]":{"docs":{},"[":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}}}}}}},":":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"c":{"docs":{},"k":{"docs":{},"_":{"1":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"2":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"docs":{}}}}}}},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"_":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"(":{"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{},"a":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"(":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"docs":{},"a":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}}}}}}}},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"$":{"docs":{},"{":{"docs":{},"(":{"2":{"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}}}},"a":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"l":{"docs":{},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"e":{"docs":{},"w":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"r":{"docs":{},"c":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"(":{"docs":{},"(":{"docs":{},"u":{"docs":{},"n":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}},"1":{"docs":{},"]":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}},"2":{"docs":{},":":{"docs":{},"]":{"docs":{},":":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}}},"docs":{}},"s":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003886729594669628},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.004220893422441084},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0033944331296673455},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"e":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"s":{"docs":{},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"?":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},")":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"?":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004142011834319527}}}}}}},"r":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"(":{"0":{"docs":{},".":{"1":{"docs":{},"*":{"docs":{},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}}}}}}}},"7":{"5":{"docs":{},")":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"]":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}},"docs":{}},"docs":{}}},"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.00631578947368421},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814}},"n":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"_":{"docs":{},"f":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}}}}}}},"m":{"docs":{},"s":{"docs":{},"/":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}},"x":{"docs":{},"*":{"docs":{},"x":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},".":{"docs":{},"(":{"docs":{},"g":{"docs":{},"x":{"docs":{},".":{"docs":{},"^":{"2":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"docs":{}}}}}}}}}},"_":{"docs":{},"i":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}},"x":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}},"*":{"docs":{},"a":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}},"y":{"docs":{},"*":{"docs":{},"a":{"docs":{},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}},"x":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339}},")":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.007725321888412017}}}}},"t":{"0":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"1":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"2":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.009824561403508772},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0024897060231734176},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.004402783695497799},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"e":{"docs":{},"x":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535}},"t":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.007707129094412331},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.014084507042253521},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.05084745762711865},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.02608695652173913},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.026785714285714284},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.03571428571428571},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.02702702702702703},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.028037383177570093},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0234375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0014615997874036673},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.011029411764705883},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.012145748987854251},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.013333333333333334},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.010638297872340425},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.007653061224489796},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}},"!":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}},"n":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"s":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002106674327300584},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0014615997874036673},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"s":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}}}}},"(":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"_":{"docs":{},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}},"(":{"docs":{},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}}}},"i":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"x":{"docs":{},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},"n":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}},"m":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.003160011490950876},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0036906559302130517},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0026300958106331017},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}},"l":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"x":{"docs":{},"[":{"docs":{},"j":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},".":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},"!":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},".":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"{":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"_":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0014492753623188406}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},".":{"docs":{},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"p":{"docs":{},"o":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0051129100979974435}},"s":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002272404487998864}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}}}}}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0020130850528434826},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"o":{"docs":{},"r":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},"l":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"[":{"docs":{},"b":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"i":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}}}},"t":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"p":{"docs":{},"o":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478}},"s":{"docs":{},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}}}}}},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"e":{"docs":{},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}},"r":{"docs":{},"m":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"i":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},":":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001340610935554917}}}}}}},"l":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"s":{"docs":{},".":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"y":{"docs":{},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"b":{"docs":{},"l":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"s":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"l":{"docs":{},"l":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"c":{"docs":{},"h":{"docs":{},"n":{"docs":{},"i":{"docs":{},"q":{"docs":{},"u":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"c":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"y":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}},"d":{"docs":{},"i":{"docs":{},"o":{"docs":{},"u":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"h":{"docs":{},"a":{"docs":{},"n":{"docs":{},"k":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"t":{"docs":{},"'":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"?":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"!":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"'":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"e":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"!":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"a":{"docs":{},"f":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"b":{"docs":{},"i":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"m":{"docs":{},"e":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},":":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"v":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},")":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"y":{"docs":{},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"e":{"docs":{},"m":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":5.017857142857143}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}},"t":{"docs":{},"a":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}},"(":{"docs":{},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},"n":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"i":{"docs":{},"n":{"docs":{},"k":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004142011834319527},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}},"!":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"s":{"docs":{},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"!":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},":":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},")":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"s":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}},".":{"docs":{},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"h":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"t":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"o":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"f":{"docs":{},"s":{"docs":{},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},".":{"docs":{},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"(":{"docs":{},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"s":{"docs":{},"h":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"a":{"docs":{},"d":{"docs":{},"i":{"docs":{},"u":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"s":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"a":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"i":{"docs":{},"m":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"e":{"docs":{},".":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"o":{"docs":{},"f":{"docs":{},"(":{"docs":{},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}}},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"y":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"z":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.005763688760806916},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001583531274742676},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"_":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"(":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"_":{"docs":{},"x":{"docs":{},".":{"docs":{},"a":{"docs":{},"s":{"docs":{},"_":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"s":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"?":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"r":{"docs":{},"d":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}}},"u":{"docs":{},"g":{"docs":{},"h":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"s":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"m":{"docs":{},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":5.003289473684211},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"s":{"docs":{},"(":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"&":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.006167763157894737}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},"_":{"docs":{},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{},"(":{"docs":{},"$":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"a":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"x":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}}}},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{},"(":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"[":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"g":{"docs":{},"h":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703054677774585},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0024621878297572987},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.003340292275574113},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001583531274742676},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"w":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"e":{"docs":{},"e":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.018018018018018018},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0031656700668308124},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"a":{"docs":{},"d":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0077192982456140355}},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}},"r":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},"s":{"docs":{},"h":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"o":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},":":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}}}}},"u":{"docs":{"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"m":{"docs":{},"b":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}},"s":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"o":{"docs":{},"p":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001819400555395959},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004210526315789474}},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0035087719298245615}},"e":{"docs":{},"r":{"docs":{},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}},"e":{"docs":{},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"i":{"docs":{},"c":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"s":{"docs":{},".":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}},":":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}}},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"r":{"docs":{},":":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"!":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}},"o":{"docs":{},"l":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}}},"s":{"docs":{},",":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044}}}},"!":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"!":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"k":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},"d":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"?":{"docs":{},"\"":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"u":{"docs":{},"r":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428}}},"c":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"_":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"b":{"docs":{},"e":{"docs":{},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}}}}},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"e":{"docs":{},"d":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"s":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"t":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"l":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"e":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}},"m":{"docs":{},"o":{"docs":{},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}},"r":{"docs":{},"i":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"c":{"docs":{},"k":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"y":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},")":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"!":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"g":{"docs":{},"o":{"docs":{},"n":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003886729594669628},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.010903974674639466},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"e":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848}}}}},"u":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"l":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"s":{"docs":{},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"v":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"!":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},"g":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"l":{"docs":{},"l":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"c":{"docs":{},"k":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"n":{"docs":{},"s":{"docs":{},"c":{"docs":{},"r":{"docs":{},"i":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001053337163650292},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}},"b":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"l":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.005917159763313609},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.02040816326530612},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0045087356753710315},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003700657894736842},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.007933194154488519},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":3.35234215885947},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.00421179302045728},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":5.021893491124261}},"s":{"docs":{},".":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"!":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},".":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"?":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}},"_":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"*":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"s":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}}}}}}}},"!":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"e":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":5.000861821315714},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004448398576512456},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"a":{"docs":{},"l":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"2":{"4":{"docs":{},";":{"docs":{},"️":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"e":{"docs":{},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}},"d":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}},"j":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}}}}},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}},"e":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"p":{"docs":{},"e":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"u":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}},"e":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.004061738424045491},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002452697967764541},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},":":{"1":{"4":{"docs":{},"}":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"docs":{}}},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},"*":{"docs":{},"*":{"2":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"docs":{}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.011029411764705883},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"t":{"docs":{},"h":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"!":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}},"n":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"!":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":5.008330939385234},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.008902471432367791},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"!":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}},"'":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"(":{"2":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"3":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"docs":{},"$":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"o":{"docs":{},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0017273452032952432}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276}},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}},"\"":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}},"b":{"docs":{},"f":{"docs":{},"s":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"d":{"docs":{},"f":{"docs":{},"s":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"f":{"docs":{},"s":{"docs":{},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"i":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}},"j":{"docs":{},"a":{"docs":{},"v":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{},"o":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"k":{"docs":{},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397}},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"~":{"docs":{},"%":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"\\":{"docs":{},"n":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}}}}}}}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"a":{"docs":{},"l":{"docs":{},".":{"docs":{},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"_":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}}}}}},"s":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},".":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"docs":{}}},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}},"a":{"docs":{},"l":{"docs":{},":":{"docs":{},":":{"docs":{},"d":{"docs":{},"f":{"docs":{},"s":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},"$":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"$":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"(":{"docs":{},"$":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"$":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},"$":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"*":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0026574541589157587}},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"*":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}},"?":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"[":{"1":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"docs":{}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009301089556205156}},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},".":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"m":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"}":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"n":{"docs":{},"d":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"y":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"w":{"docs":{},"i":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"c":{"docs":{},"e":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"t":{"docs":{},"w":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"d":{"docs":{},"d":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"o":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0021808421405804393},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.018018018018018018},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0017273452032952432},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0024084778420038534},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.017777777777777778},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004441976679622432},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.015306122448979591},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0068669527896995704},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0014251781472684087},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.008875739644970414},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.01059322033898305}},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{},"_":{"docs":{},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"b":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"i":{"docs":{},"b":{"docs":{},"b":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"p":{"docs":{},"h":{"docs":{},"r":{"docs":{},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{},":":{"docs":{},":":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"b":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"l":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0030797101449275364},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}},"e":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}},"k":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.008116883116883116},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005255781359495445},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"s":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"w":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}},"s":{"docs":{},"k":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},".":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"s":{"docs":{},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"l":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},"r":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.003952569169960474},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"g":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004441976679622432},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.005010438413361169},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.011834319526627219},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"y":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":5.0242914979757085},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"i":{"docs":{},"l":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"p":{"docs":{},"e":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"u":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.00974025974025974},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.029967334185485018},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0024183796856106408},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.006493506493506494},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.008095440988495952},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0019883539269990058},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0032245062474808546}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}},"s":{"docs":{},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},"docs":{}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}},"!":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"v":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},":":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0012782275244993609}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0015622780854992189}}},"!":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449}},")":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}},"_":{"docs":{},"s":{"docs":{},"v":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"v":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"v":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"v":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}},"v":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"t":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0037052284890901604},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394}},"e":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"t":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"p":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"c":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}},"k":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"_":{"docs":{},"v":{"docs":{},"i":{"docs":{},"s":{"docs":{},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"f":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615}}},"l":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"y":{"docs":{},"p":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0012782275244993609},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"s":{"docs":{},"c":{"docs":{},"r":{"docs":{},"i":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"e":{"docs":{},"t":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"r":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"t":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}},"i":{"docs":{},"c":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"&":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004210526315789474}}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004210526315789474},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0039767078539980115},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}},"}":{"docs":{},"{":{"2":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}},"docs":{}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"m":{"docs":{},"p":{"1":{"docs":{},"[":{"9":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"docs":{}}},"2":{"docs":{},"[":{"9":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"docs":{}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0024422318241593085},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}},"x":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},"y":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},")":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"s":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{},"i":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"m":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"e":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}},"[":{"docs":{},"n":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837}}},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"u":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}}}}}}},"*":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}},"!":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"x":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"r":{"docs":{},"n":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"_":{"docs":{},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"k":{"docs":{},"w":{"docs":{},"i":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"1":{"docs":{},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"docs":{}}}}}}}}}}}}}}}}}}}}},".":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"b":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0035694157430020664},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"e":{"docs":{},"s":{"docs":{},"d":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"g":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"n":{"docs":{},"e":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"b":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"f":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}},"d":{"docs":{},"m":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"^":{"2":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"3":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},")":{"docs":{},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"}":{"docs":{},"{":{"3":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"docs":{}}}},"4":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"docs":{}},"}":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"+":{"docs":{},"d":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"\"":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"u":{"3":{"2":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}},"6":{"4":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}},"docs":{}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"i":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{"./":{"ref":"./","tf":0.015306122448979591},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.011267605633802818},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.03389830508474576},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.017391304347826087},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.023809523809523808},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.018018018018018018},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.018691588785046728},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003855278766310795},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.012145748987854251},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00832870627429206},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.007653061224489796},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009468917249897077},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.010958904109589041},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.005150214592274678},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005979599015124868},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.007575757575757576},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.007098121085594989},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.011541072640868975},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0014492753623188406},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01301775147928994},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004905395935529082},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.007707129094412331},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.017391304347826087},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.006618531889290012},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"o":{"docs":{},"o":{"docs":{},"d":{"docs":{},"!":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}}},"l":{"docs":{},"y":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"_":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"g":{"docs":{},"o":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"p":{"docs":{},"i":{"docs":{},"n":{"docs":{},"n":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"e":{"docs":{},"d":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"c":{"docs":{},"u":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"u":{"docs":{},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}},"a":{"docs":{},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}},"c":{"docs":{},"c":{"docs":{},"e":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"i":{"docs":{},"q":{"docs":{},"u":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0234375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}}},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.005280259951259139},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"y":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},"o":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"{":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"0":{"1":{"docs":{},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"docs":{}},"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004912280701754386},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0047522063815342835}},"l":{"docs":{},"i":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"?":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"m":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428}}}}}}},"h":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},"t":{"docs":{},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"i":{"docs":{},"k":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"u":{"docs":{},"c":{"docs":{},"k":{"docs":{},"y":{"docs":{},")":{"docs":{},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}},"t":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002717391304347826},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"r":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}}}},"w":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"y":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}},"s":{"docs":{},"c":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}},"u":{"docs":{},"r":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}},"e":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"t":{"docs":{},"l":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0028214429665457475}}}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"s":{"docs":{},"f":{"docs":{},"y":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"!":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"u":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}},"b":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216}}}}}}},"p":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"h":{"docs":{},"y":{"docs":{},"s":{"docs":{},"i":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"k":{"docs":{},"n":{"docs":{},"o":{"docs":{},"w":{"docs":{},"n":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}},"s":{"docs":{"./":{"ref":"./","tf":0.015306122448979591},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0035087719298245615},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0022024322512687925},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00268411340379131},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0234375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.004119053946319426},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.005090054815974941},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004744958481613286},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.006263048016701462},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.013333333333333334},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007218212104386452},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.02040816326530612},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.018526142445450804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.005280259951259139},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.005479452054794521},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0068669527896995704},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.012175324675324676},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0024621878297572987},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002414429768498793},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0068520757758968156},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.010732323232323232},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0041753653444676405},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.010862186014935505},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.007821901323706379},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004733727810650888},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005956552207428171},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.010163749294184076},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}},"e":{"docs":{},"r":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0019927536231884057}}},"f":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"d":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"}":{"docs":{},"}":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},"z":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"e":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"p":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003153468815697267},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"!":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"o":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"t":{"docs":{},"o":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}},"r":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"t":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},".":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"_":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"k":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}},"s":{"docs":{},"u":{"docs":{},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}}}}}},"l":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}}}}}}}},"_":{"1":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}},"/":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"{":{"docs":{},"r":{"docs":{},"_":{"0":{"docs":{},"}":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"docs":{}}}}}}}}}}},"2":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}},")":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"/":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"{":{"docs":{},"r":{"docs":{},"_":{"0":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"docs":{}}}}}}}}}},"^":{"2":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"docs":{}}},"docs":{}}},"v":{"0":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"1":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"2":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},"3":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0026199113260781943},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.007358093903293623}},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"f":{"docs":{},"i":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"s":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"s":{"docs":{},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}},"a":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":5.016758983098992}},"(":{"5":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}},".":{"0":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"docs":{},"&":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}}},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},"docs":{}},"docs":{}}}}}}}},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}},"_":{"docs":{},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"g":{"docs":{},"r":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0015622780854992189}},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}}}}}}},"v":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0031656700668308124},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"c":{"1":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},".":{"docs":{},"x":{"docs":{},"*":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"2":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"docs":{}}}}}},"y":{"docs":{},"*":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"2":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"docs":{}}}}}}}},"2":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}},"3":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"&":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"{":{"docs":{},"i":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"docs":{}}}}}}}}}}}}}}}}}},"}":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}},"w":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"6":{"4":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}},"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}}}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},"e":{"docs":{},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}},"!":{"docs":{},"[":{"0":{"docs":{},".":{"0":{"1":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"docs":{}}},"1":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"4":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"7":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}},"]":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"n":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"0":{"docs":{},".":{"0":{"docs":{},"_":{"docs":{},"f":{"6":{"4":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}},"docs":{}},"docs":{}}}},"docs":{}}},"docs":{}}}}}}}}}}}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0036275695284159614},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0053254437869822485}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"'":{"docs":{},"'":{"docs":{},"'":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}},"(":{"0":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"1":{"5":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"docs":{}},"2":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"5":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"6":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"7":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"9":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"{":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"}":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},"(":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},"v":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},":":{"5":{"1":{"2":{"docs":{},"/":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{}}},"docs":{}},"docs":{}},"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"/":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{}}}}}}},"docs":{}}}}}}}}},"docs":{}},"docs":{}}}}}}},"'":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488}}}}}}}}},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}},"s":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}}}}}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},">":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0018137847642079807}}}}},"t":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.02371822184348814}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002982530890498509}},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},"*":{"docs":{},"d":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}}}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0015622780854992189}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}}},"_":{"docs":{},"s":{"docs":{},"v":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"v":{"docs":{},"v":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0097997443544951}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"!":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}},"_":{"docs":{},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}},"(":{"5":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},".":{"0":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}},"docs":{}}},"docs":{},"&":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}}},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}}},":":{"docs":{},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},"docs":{}},"docs":{}}}}}}}}}}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}},"(":{"5":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},".":{"0":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"v":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"v":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"i":{"docs":{},"a":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"l":{"docs":{},"l":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}},"d":{"docs":{},"e":{"docs":{},"o":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00832870627429206},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.004220893422441084},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.010855949895615866},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.008146639511201629},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.02485207100591716},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"e":{"docs":{},"w":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"s":{"docs":{},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"i":{"docs":{},"z":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"s":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"b":{"docs":{},"l":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},"e":{"docs":{},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"m":{"docs":{},"l":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}},"c":{"docs":{},"i":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"e":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"t":{"docs":{},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}}}}},"a":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0019151584793641674},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0038584130179500084},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0018602179112410311},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.003915426781519186},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0024084778420038534},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007218212104386452},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.005965061780997018},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"e":{"docs":{},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"s":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"n":{"docs":{},"t":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"o":{"docs":{},"u":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"e":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"s":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"_":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965}}}}},"l":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0023492560689115116},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003700657894736842},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}},"u":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0027769797950780426},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0023917087430241827},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002881844380403458},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0028179597971068945},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0019883539269990058},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.011363636363636364},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.005431093007467753},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.004908946951702296},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.019271198318149965},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.006355932203389831}},"e":{"docs":{},"(":{"docs":{},"v":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"|":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"_":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837}}}}}}}}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"s":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"?":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},")":{"docs":{},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}},"g":{"docs":{},"u":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}},"e":{"docs":{},",":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"n":{"docs":{},"i":{"docs":{},"s":{"docs":{},"h":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"o":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004210526315789474},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.005936991286028919},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002258836035078395},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00822239624119029},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003855278766310795},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0023752969121140144}}}},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"e":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}}},"f":{"docs":{},"f":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},".":{"docs":{},"^":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},"docs":{}}}}}}}}}}}}}},"}":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"y":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"z":{"docs":{},"i":{"docs":{},"p":{"docs":{},"(":{"docs":{},"y":{"docs":{},".":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},".":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"(":{"docs":{},"|":{"docs":{},"i":{"docs":{},"|":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},"(":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}}}}},"+":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}}},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"1":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}}}}}},"docs":{}}}},"docs":{}}}}}}}}},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},",":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488}}}}}}}}}}}}}}},"n":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"_":{"0":{"docs":{},"t":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"docs":{},"o":{"docs":{},"f":{"docs":{},"f":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"i":{"docs":{},"(":{"2":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"docs":{}}}}}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"x":{"docs":{},"_":{"docs":{},"o":{"docs":{},"d":{"docs":{},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}}},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368}},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}},":":{"docs":{},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"'":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0019883539269990058}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178}}},"=":{"1":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"2":{"5":{"5":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}},"docs":{},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719}},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}}}}}}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},")":{"docs":{},".":{"docs":{},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"s":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"w":{"0":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}},"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.005763688760806916},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0028179597971068945},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009301089556205156},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.008344923504867872},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.004528612597776863},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"s":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"!":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"i":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"n":{"docs":{},"a":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"i":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"b":{"docs":{},"o":{"docs":{},"x":{"docs":{},"_":{"docs":{},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"r":{"docs":{},"!":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{},"_":{"docs":{},"b":{"docs":{},"o":{"docs":{},"x":{"docs":{},"_":{"docs":{},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"r":{"docs":{},"!":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}},"y":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.004419191919191919},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002803083391730904},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}},"s":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},";":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}},"!":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"m":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}},"p":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}},"v":{"docs":{},"e":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004441976679622432},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.01020408163265306},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"y":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},",":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},";":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},".":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0032245062474808546},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.006016847172081829}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}},"l":{"docs":{},"k":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891}},"\"":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"e":{"docs":{},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891}},"'":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}}}},"l":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"s":{"docs":{},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"t":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"h":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"e":{"docs":{},"'":{"docs":{},"l":{"docs":{},"l":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00684931506849315},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"v":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"b":{"docs":{},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},":":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}}},"l":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},")":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0015944724953494552},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"f":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"docs":{}},"docs":{}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"]":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"s":{"docs":{},"[":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"_":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}}}}}},"?":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"r":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"s":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}}}}}},"x":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"d":{"docs":{},"n":{"docs":{},"e":{"docs":{},"s":{"docs":{},"d":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}}}},"e":{"docs":{},"k":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"l":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002355072463768116}}}}}}},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}},"s":{"docs":{},"h":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"!":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"e":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"t":{"docs":{},"h":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"i":{"docs":{},"n":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004210526315789474},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"_":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"_":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"(":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"r":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"s":{"docs":{},"c":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"t":{"docs":{},"h":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}}},"l":{"docs":{},"d":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},":":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}},"l":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"f":{"docs":{},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"n":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"d":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"k":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.011560693641618497},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"s":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"!":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"l":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},";":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"t":{"docs":{},"h":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828}},"w":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"s":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"r":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"y":{"docs":{},"!":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"s":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"t":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"u":{"docs":{},"l":{"docs":{},"d":{"docs":{},"'":{"docs":{},"v":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.005873140172278779}},"(":{"docs":{},"\"":{"docs":{},"f":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"g":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"h":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"i":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"j":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"f":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}},"p":{"docs":{},"i":{"docs":{},"c":{"docs":{},"k":{"docs":{},"_":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},"?":{"docs":{},".":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},":":{"docs":{},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.006656225528582615}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"/":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}},"'":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},":":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"[":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},"[":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"d":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"d":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}},"b":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.005479452054794521},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"(":{"docs":{},"*":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},"'":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}}}},"*":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0021303792074989347}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}},"l":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"c":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"!":{"docs":{},"(":{"docs":{},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"d":{"docs":{},"l":{"docs":{},"m":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"s":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{},"p":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"k":{"docs":{},"i":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}}}}}}}}}}},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},":":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}}}}},"o":{"docs":{},"n":{"docs":{},"g":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}},";":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}}}},"a":{"docs":{},"p":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":5.027027027027027},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.003371868978805395},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.004697986577181208},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}},"h":{"docs":{},"a":{"docs":{},"t":{"docs":{},"'":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"e":{"docs":{},"v":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339}},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"v":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},"q":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"s":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"*":{"docs":{},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}},"f":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},":":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"e":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"r":{"docs":{},"e":{"docs":{},"v":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"'":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"a":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"n":{"docs":{},"e":{"docs":{},"v":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"e":{"docs":{},"l":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"o":{"docs":{},"l":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"s":{"docs":{},"e":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"y":{"docs":{},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"f":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"n":{"docs":{},"o":{"docs":{},"b":{"docs":{},"o":{"docs":{},"d":{"docs":{},"y":{"docs":{},"\"":{"docs":{},")":{"docs":{},")":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"e":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"o":{"docs":{},"p":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"o":{"docs":{},"n":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"_":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"f":{"docs":{},"c":{"0":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0026199113260781943},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"'":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}}},".":{"docs":{},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}}}}}}}}}},"_":{"docs":{},"c":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}},".":{"docs":{},"*":{"docs":{},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"v":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},".":{"docs":{},"s":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"0":{"docs":{},".":{"5":{"docs":{},"_":{"docs":{},"f":{"6":{"4":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"docs":{}},"docs":{}}}},"docs":{}}},"docs":{}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}},"(":{"docs":{},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}}},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}},"(":{"docs":{},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},")":{"docs":{},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}},"o":{"docs":{},"f":{"docs":{},"f":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"i":{"docs":{},"(":{"2":{"docs":{},")":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"docs":{}}}}}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"j":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}},"(":{"docs":{},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},")":{"docs":{},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"j":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488}}}}}},"o":{"docs":{},"f":{"docs":{},"f":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}},".":{"docs":{},"^":{"2":{"docs":{},"/":{"2":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}}},"docs":{}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"=":{"2":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"docs":{}}}}}}}},"c":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"o":{"docs":{},"n":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"d":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"u":{"docs":{},"n":{"docs":{},"u":{"docs":{},"s":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"y":{"1":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.004335260115606936},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0063758389261744965},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.007410456978180321},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.01868399675060926},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0028139289482940555},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0033944331296673455},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.005917159763313609},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"u":{"docs":{},"b":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}},"e":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657}}}}}}},"!":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.020833333333333332},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"'":{"docs":{},"r":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"d":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"r":{"docs":{},"k":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.020471014492753622}},"s":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"_":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"|":{"docs":{},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"|":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}}}},"!":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"'":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002355072463768116}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"t":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"s":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00934199837530463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0029227557411273487},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}},")":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"=":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0036555645816409425},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465}}}},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.005871498070793491}},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047}},"e":{"docs":{},"[":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}},"a":{"docs":{},"s":{"docs":{},"_":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"s":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"|":{"docs":{},"i":{"docs":{},"|":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}},"\"":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}},"i":{"docs":{},"e":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0072254335260115606},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.005369127516778523},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845}},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"docs":{}},"docs":{}}}}}}}},"=":{"0":{"docs":{},")":{"docs":{},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"docs":{},"%":{"docs":{},"f":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"x":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"b":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"c":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"*":{"docs":{},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"y":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"^":{"2":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"docs":{}},"_":{"1":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"2":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},":":{"docs":{},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"docs":{}},"docs":{}}}}}}}},"^":{"2":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"docs":{}},"i":{"docs":{},"t":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}},"i":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"n":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"p":{"docs":{},"o":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}},"s":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}},"s":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579}}}},"6":{"4":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}},"docs":{},"h":{"docs":{},"a":{"docs":{},"l":{"docs":{},"f":{"docs":{},"+":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"k":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"n":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}},"(":{"docs":{},"x":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}},"l":{"docs":{},"a":{"docs":{},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"x":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}},"y":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"z":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"\\":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}},"\"":{"0":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},".":{"1":{"docs":{},".":{"1":{"1":{"docs":{},"\"":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}},"docs":{}}},"docs":{}}},"1":{"9":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"2":{"docs":{},"d":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},"_":{"docs":{},"s":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}}}}}}}}}}}}},"8":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.006990328449679211},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0014615997874036673},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.003915426781519186},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0036231884057971015}},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"u":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}}},"e":{"docs":{},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"s":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"f":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},"\"":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"\"":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"h":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0014492753623188406},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"d":{"docs":{},"\"":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}},"a":{"docs":{},"k":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}}},"y":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}},"o":{"docs":{},"p":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"_":{"docs":{},"_":{"docs":{},"m":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},"_":{"docs":{},"_":{"docs":{},"\"":{"docs":{},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649}}},"c":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"e":{"docs":{},"s":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}},"e":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}},".":{"docs":{},"p":{"docs":{},"n":{"docs":{},"g":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535}}}}}}}}}},"a":{"docs":{},"o":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0035174111853675696}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"o":{"docs":{},"d":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{},".":{"docs":{},".":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"n":{"docs":{},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"/":{"docs":{},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"s":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535}}}}}},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"m":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"x":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"i":{"docs":{},"n":{"docs":{},"c":{"docs":{},"i":{"docs":{},"d":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}}}},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"\"":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"i":{"docs":{},"r":{"docs":{},"c":{"docs":{},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"y":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}}}},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"m":{"docs":{},"i":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}},"a":{"docs":{},"k":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"t":{"docs":{},"h":{"docs":{},"\"":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"/":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}}}}}},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"e":{"docs":{},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},"i":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}},"\"":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837}}},"c":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"n":{"docs":{},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}},"a":{"docs":{},"l":{"docs":{},"c":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},"d":{"docs":{},"e":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}},"p":{"docs":{},"i":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}}}}}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},":":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}},"}":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"#":{"docs":{},"{":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{},"}":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{},"}":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}}},"@":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},".":{"docs":{},"r":{"docs":{},"j":{"docs":{},"u":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"2":{"0":{"docs":{},")":{"docs":{},"}":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"docs":{}},"docs":{}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"i":{"docs":{},"x":{"docs":{},"}":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"a":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"#":{"docs":{},"{":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{},"s":{"docs":{},"_":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"#":{"docs":{},"{":{"docs":{},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"_":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},"}":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"%":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"\"":{"docs":{},",":{"docs":{},"(":{"2":{"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}}}}},"s":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}},"g":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002681221871109834}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0029684956430144596}}},"\"":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0033515273388872928},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"r":{"docs":{},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},"o":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"[":{"0":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"1":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"2":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}}}}},"~":{"docs":{},"%":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}},"`":{"docs":{},"n":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}},"a":{"1":{"1":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},"2":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},"3":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},"docs":{}},"2":{"1":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},"2":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},"3":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},"docs":{}},"3":{"1":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"2":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"3":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"docs":{}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011490950876185005},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"d":{"docs":{},"g":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}}},"i":{"docs":{},"m":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}},"p":{"docs":{},"p":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"r":{"docs":{},"o":{"docs":{},"x":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}}},"r":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}}}}}},"b":{"docs":{},"s":{"docs":{},"z":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"f":{"docs":{},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.003340292275574113},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.005431093007467753}}}}}},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"d":{"docs":{},"a":{"docs":{},"p":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}},"b":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"f":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"i":{"docs":{},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}},"y":{"docs":{},"_":{"docs":{},"b":{"docs":{},"o":{"docs":{},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}},"n":{"docs":{},"s":{"docs":{},"\"":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"u":{"docs":{},"c":{"docs":{},"k":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},".":{"docs":{},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}}}},"e":{"docs":{},"a":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"f":{"docs":{},"u":{"docs":{},"l":{"docs":{},".":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}},"o":{"docs":{},"t":{"docs":{},"t":{"docs":{},"o":{"docs":{},"m":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"\"":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}},"e":{"docs":{},"p":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"f":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}},"\"":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"i":{"docs":{},"f":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"v":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"g":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"l":{"docs":{},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"s":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}},"\"":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{},".":{"docs":{},"\"":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"i":{"docs":{},"l":{"docs":{},"e":{"docs":{},"d":{"docs":{},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}},"g":{"docs":{},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}},"o":{"docs":{},"l":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"=":{"docs":{},"'":{"docs":{},".":{"docs":{},".":{"docs":{},"/":{"docs":{},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"k":{"docs":{},"e":{"docs":{},"l":{"docs":{},"l":{"docs":{},"'":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}}}},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"t":{"docs":{},"e":{"docs":{},"g":{"docs":{},"r":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}}},"t":{"docs":{},"'":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}},"f":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0038691523039043265},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"n":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"o":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"g":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}}}}}}}}},"r":{"docs":{},"g":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}}}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"g":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}}}}}},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}},"a":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"d":{"docs":{},"u":{"docs":{},"c":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"t":{"1":{"3":{"docs":{},"\"":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"docs":{}},"docs":{},"a":{"docs":{},"t":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}}}},"l":{"docs":{},"l":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}},"j":{"docs":{},"n":{"docs":{},"d":{"docs":{},"a":{"docs":{},"e":{"docs":{},"l":{"docs":{},"\"":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216}}}},"d":{"docs":{},"i":{"docs":{},"x":{"2":{"docs":{},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}},"8":{"docs":{},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}}}}},"g":{"docs":{},"b":{"1":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"2":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}}}},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},".":{"docs":{},"h":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}},"f":{"8":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}}},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"~":{"8":{"docs":{},"a":{"docs":{},"~":{"1":{"8":{"docs":{},"a":{"docs":{},"~":{"docs":{},"a":{"docs":{},"~":{"docs":{},"%":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"docs":{}},"docs":{}}}},"docs":{},"%":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}}}}},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001340610935554917}}},"d":{"docs":{},"~":{"docs":{},"%":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449}}}}}},"{":{"docs":{},"~":{"docs":{},"f":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"a":{"docs":{},"~":{"docs":{},"%":{"docs":{},"~":{"docs":{},"}":{"docs":{},"\"":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"f":{"docs":{},"~":{"docs":{},"c":{"docs":{},"~":{"docs":{},"f":{"docs":{},"\"":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"$":{"1":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"2":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"\\":{"docs":{},"p":{"docs":{},"i":{"docs":{},"$":{"docs":{},"\"":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"docs":{},"a":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}},"(":{"docs":{},"$":{"docs":{},"_":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},"`":{"docs":{},"t":{"docs":{},"$":{"docs":{},"(":{"docs":{},"$":{"docs":{},"_":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{},")":{"docs":{},"\"":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"docs":{}}}}}}}}}}},"docs":{}}}}},"\\":{"docs":{},"p":{"docs":{},"i":{"docs":{},"$":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"`":{"docs":{},"t":{"docs":{},"$":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"c":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"e":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"d":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"x":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"p":{"docs":{},"_":{"docs":{},"f":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"r":{"docs":{},":":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009}}}}}}},"\"":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}}}},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}},"m":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"n":{"docs":{},"u":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}},"_":{"1":{"docs":{},"d":{"docs":{},"_":{"docs":{},"s":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}},"2":{"docs":{},"d":{"docs":{},"_":{"docs":{},"s":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}}}}}}}}}},"docs":{},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"_":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}},"s":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"u":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"m":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"s":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}},"l":{"docs":{},"a":{"docs":{},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"t":{"docs":{},"y":{"docs":{},"p":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}},"o":{"docs":{},"g":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"2":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"s":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}},"s":{"docs":{},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}},"t":{"docs":{},"i":{"docs":{},"t":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"w":{"docs":{},"a":{"docs":{},"v":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"_":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}}}}}}}}},"w":{"docs":{},"a":{"docs":{},"v":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}}},"e":{"docs":{},"v":{"docs":{},"i":{"docs":{},"s":{"docs":{},"\"":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"(":{"docs":{},"b":{"docs":{},"i":{"docs":{},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"\"":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"?":{"docs":{},"\"":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"\\":{"docs":{},"\"":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{},".":{"docs":{},".":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},".":{"docs":{},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}},"t":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}},"\\":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"\"":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"o":{"docs":{},"w":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},"s":{"docs":{},"v":{"1":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"2":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"3":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"4":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"5":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178}},"s":{"docs":{},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"g":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}}},"u":{"docs":{},"t":{"docs":{},".":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"p":{"docs":{},"u":{"docs":{},"t":{"0":{"0":{"0":{"0":{"0":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{},"{":{"docs":{},"}":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"(":{"docs":{},"i":{"docs":{},")":{"docs":{},".":{"docs":{},"r":{"docs":{},"j":{"docs":{},"u":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"5":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},".":{"docs":{},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"p":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},",":{"docs":{},"\"":{"docs":{},"w":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}},":":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"c":{"docs":{},"k":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"a":{"docs":{},"w":{"docs":{},"t":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"_":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}}}}}}}}}}}}}},"h":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"a":{"docs":{},"d":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"i":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"e":{"docs":{},"m":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"c":{"docs":{},"a":{"docs":{},"r":{"docs":{},"l":{"docs":{},"o":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}}},"n":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"e":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"_":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{},".":{"docs":{},"p":{"docs":{},"n":{"docs":{},"g":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"e":{"docs":{},"r":{"docs":{},"p":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"k":{"docs":{},"i":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"e":{"docs":{},"c":{"docs":{},"i":{"docs":{},"r":{"docs":{},"c":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{},"_":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"m":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"\"":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"s":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}},"p":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"_":{"docs":{},"o":{"docs":{},"p":{"docs":{},"_":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"h":{"docs":{},"o":{"docs":{},"d":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754}}}}}},"m":{"docs":{},"i":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"t":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"y":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"r":{"docs":{},"l":{"docs":{},"d":{"docs":{},"'":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"h":{"docs":{},"a":{"docs":{},"t":{"docs":{},"'":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}},"\"":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"a":{"docs":{},"i":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"l":{"docs":{},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"o":{"docs":{},"r":{"docs":{},"g":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}}}}},"]":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}},"p":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"r":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}}}}},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"c":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"a":{"docs":{},"g":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}}}}},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"o":{"docs":{},"t":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"e":{"docs":{},"d":{"docs":{},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"s":{"docs":{},"e":{"docs":{},"u":{"docs":{},"d":{"docs":{},"o":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"r":{"docs":{},"o":{"docs":{},"b":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}},"y":{"docs":{},"\"":{"docs":{},")":{"docs":{},"(":{"docs":{},"u":{"docs":{},"n":{"docs":{},"i":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"0":{"1":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"docs":{}}}}}}}}}}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"a":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"\\":{"docs":{},"t":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}}}}}}}},"`":{"docs":{},"t":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"v":{"docs":{},"x":{"docs":{},":":{"docs":{},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"{":{"docs":{},"}":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"\\":{"docs":{},"t":{"docs":{},"{":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"{":{"docs":{},"}":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"}":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"|":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003700657894736842}}}}},"+":{"docs":{},"+":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"z":{"2":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}},"!":{"docs":{},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"q":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002298190175237001},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.00741399762752076},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002898550724637681},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.003952569169960474}},"u":{"docs":{},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{},"u":{"docs":{},"m":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":5.084558823529412},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":5.038507821901324}}}},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"y":{"docs":{},":":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"f":{"docs":{},"i":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}}}}}},"l":{"docs":{},"i":{"docs":{},"f":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"t":{"docs":{},"i":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"d":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}},"r":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},":":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"s":{"docs":{},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"!":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}},"u":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"e":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":5.013333333333334},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.008618213157138753},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"c":{"docs":{},"[":{"docs":{},"t":{"docs":{},"]":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}},"<":{"docs":{},">":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"1":{"docs":{},":":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"]":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"s":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"{":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"}":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"}":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}}}}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"2":{"4":{"docs":{},";":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"c":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"u":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"?":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}},"x":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"&":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"p":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},".":{"docs":{},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"u":{"docs":{},"n":{"docs":{},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}}}},"_":{"docs":{},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"(":{"docs":{},"&":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},".":{"docs":{},".":{"docs":{},".":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}}}}}}},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},":":{"docs":{},":":{"docs":{},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}},"_":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"a":{"docs":{},"t":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}},"s":{"docs":{},"h":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},"\\":{"docs":{},"n":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"c":{"docs":{},"a":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"i":{"docs":{},"l":{"docs":{},"l":{"docs":{},"!":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},"$":{"docs":{},"(":{"docs":{},"?":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"(":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},"q":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"f":{"docs":{},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},")":{"docs":{},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"d":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}},"r":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}},"i":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"t":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"e":{"docs":{},"t":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"s":{"docs":{},"!":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"o":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.003260869565217391}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"~":{"docs":{},"\\":{"docs":{},"%":{"docs":{},"~":{"3":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"7":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}}}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"c":{"docs":{},"a":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}},"t":{"docs":{},"(":{"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}},"p":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},"w":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.004021832806664752},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0047834174860483655},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.006763103513056547}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"_":{"docs":{},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"%":{"0":{"docs":{},".":{"2":{"docs":{},"f":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"docs":{}}},"1":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"2":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"3":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00536822680758262},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0036555645816409425},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.011594202898550725}},"}":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112}}},"%":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"s":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}},"'":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}},"]":{"docs":{},"[":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"y":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"z":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"t":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"f":{"docs":{},"%":{"docs":{},"%":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"l":{"docs":{},"f":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"n":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}},".":{"1":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946}}},"]":{"docs":{},"[":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"y":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"z":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}}}},"docs":{}},"d":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}},">":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.02456140350877193},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0043091065785693765},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.012246267404797853},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.005979271857560457},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.005873140172278779},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.005780346820809248},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.012080536912751677},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002843216896831844},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.004320871688897238},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0035174111853675696},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.01562278085499219},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.010882708585247884},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.005010438413361169},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.005615942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.008076009501187649},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},">":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"=":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"+":{"docs":{},"+":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}},"v":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649}}},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"=":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}}},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"c":{"docs":{},"a":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703054677774585},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},"[":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},"i":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}}}}}},"o":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"docs":{},"(":{"docs":{},"u":{"docs":{},"n":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}}},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009301089556205156}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"q":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},"]":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},"y":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669}},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},"docs":{}}}}}}}}}}}},"i":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001340610935554917}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"+":{"docs":{},"+":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}},"]":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}},"m":{"docs":{},"_":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"+":{"docs":{},"+":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"]":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"\"":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"e":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"y":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"+":{"docs":{},"+":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"h":{"docs":{},"s":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"r":{"docs":{},"h":{"docs":{},"s":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"e":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"c":{"docs":{},"e":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"a":{"docs":{},"l":{"docs":{},"(":{"docs":{},"$":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"d":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"t":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"$":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"$":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"[":{"docs":{},"b":{"docs":{},"u":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}},"u":{"docs":{},"i":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"[":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"z":{"docs":{},"e":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00274079874706343}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0023492560689115116}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"s":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"[":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"e":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}},"u":{"docs":{},"n":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"y":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"[":{"0":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},",":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},",":{"1":{"docs":{},"]":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"docs":{}}},"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},":":{"1":{"0":{"docs":{},"]":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}},"docs":{},"]":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}},"docs":{},"]":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},".":{"0":{"1":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{},"]":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946}}}},"2":{"3":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"6":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"5":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"8":{"5":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{}},"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845}}}}},"1":{"0":{"docs":{},"]":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"1":{"docs":{},"]":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"[":{"1":{"2":{"docs":{},"]":{"docs":{},".":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"docs":{}},"docs":{}}}},"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"]":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},".":{"0":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"]":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852}}}}},"+":{"0":{"docs":{},".":{"0":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}}},"docs":{}}},"5":{"3":{"3":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"docs":{}},"docs":{}},"docs":{}},"~":{"0":{"docs":{},"~":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"2":{"docs":{},"~":{"1":{"docs":{},"]":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"docs":{}}},"docs":{}},",":{"2":{"docs":{},"]":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"n":{"docs":{},"]":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"2":{"0":{"2":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}},"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},"]":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"[":{"3":{"docs":{},"]":{"docs":{},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"docs":{}}},".":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}},"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"3":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},".":{"0":{"docs":{},"]":{"docs":{},"\"":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"docs":{}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"4":{"docs":{},"]":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"[":{"5":{"docs":{},"]":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"docs":{}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946}}}},"docs":{}}},"5":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},".":{"0":{"docs":{},"]":{"docs":{},"\"":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"docs":{}}},"6":{"4":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"docs":{},"]":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"[":{"7":{"docs":{},"]":{"docs":{},"[":{"8":{"docs":{},"]":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"docs":{}}}},"docs":{}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"7":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946}}},"]":{"docs":{},"\"":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"docs":{}}},"8":{"docs":{},"]":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},"9":{"docs":{},"]":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"[":{"1":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"docs":{}},"docs":{}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002106674327300584},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004361684281160879},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"m":{"docs":{},"p":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},":":{"1":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},"docs":{}}}}}}},"t":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"n":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"]":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0015321267834913339},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"*":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"{":{"docs":{},"n":{"docs":{},"}":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}}}},"(":{"docs":{},"a":{"docs":{},"u":{"docs":{},"t":{"docs":{},"o":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"r":{"docs":{},"u":{"docs":{},"n":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"{":{"docs":{},"{":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"f":{"3":{"2":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}},"docs":{}},"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"{":{"0":{"docs":{},".":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"1":{"docs":{},".":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"4":{"docs":{},".":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"7":{"docs":{},".":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}},"docs":{}},"docs":{}}}}}},"[":{"docs":{},"]":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}},"{":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"docs":{}},"docs":{}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004210526315789474}}}}}}}}}}}}},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}},"$":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"&":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"]":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},".":{"8":{"6":{"6":{"6":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{},".":{"docs":{},".":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},"]":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"]":{"docs":{},".":{"docs":{},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"(":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"]":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},".":{"docs":{},"s":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"docs":{}}}}}}}}}}}}}}}}},"\"":{"docs":{},"a":{"docs":{},"b":{"docs":{},"c":{"docs":{},"d":{"docs":{},"e":{"docs":{},"\"":{"docs":{},"]":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}},"f":{"docs":{},"g":{"docs":{},"h":{"docs":{},"i":{"docs":{},"j":{"docs":{},"\"":{"docs":{},"]":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},"]":{"docs":{},".":{"docs":{},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"(":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}},"]":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579}},")":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"j":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"[":{"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}},"l":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}}},"f":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}}}}}},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{},"[":{"docs":{},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{},"[":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{},"[":{"docs":{},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001340610935554917}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},"?":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"e":{"docs":{},"w":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"_":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"]":{"docs":{},"(":{"docs":{},"a":{"docs":{},"u":{"docs":{},"t":{"docs":{},"o":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}},":":{"docs":{},"m":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"a":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}},"r":{"1":{"0":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"1":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"2":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0045006224265057935},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009301089556205156},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001053337163650292},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}},"3":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0012448530115867088},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}}}},"4":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"5":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"docs":{}},"8":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"9":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}},"docs":{},"a":{"docs":{},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0015944724953494552},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}},"b":{"docs":{},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"]":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}}},"d":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009301089556205156}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0010629816635663034}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}},"c":{"docs":{},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"s":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.001993090619186819},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}},"]":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"]":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"r":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"]":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{},"[":{"docs":{},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}}}}}}}}}},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001509813789632612}}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"i":{"docs":{},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}}}}},"w":{"docs":{},"i":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"]":{"docs":{},"$":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}},"h":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"t":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{},"[":{"docs":{},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{},"[":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}}}}}}}}}}},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{},"[":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{},"[":{"docs":{},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}}}}}}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"]":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669}}}},"'":{"docs":{},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"b":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"t":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"(":{"docs":{},">":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"e":{"docs":{},"q":{"docs":{},"?":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"o":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"'":{"docs":{},"b":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}},"a":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742}}}},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"i":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"t":{"1":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"docs":{}},"b":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"p":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"(":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"m":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"e":{"docs":{},"l":{"docs":{},"s":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"c":{"docs":{},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"m":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"]":{"docs":{},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"$":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"b":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"p":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"(":{"docs":{},"$":{"docs":{},"r":{"docs":{},"a":{"docs":{},"d":{"docs":{},"i":{"docs":{},"u":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}},"y":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},".":{"7":{"5":{"docs":{},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"docs":{}},"docs":{}}},"docs":{}}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},"(":{"docs":{},"$":{"docs":{},"k":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"(":{"1":{"3":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}}}}}}}}}}}}}},"i":{"docs":{},"d":{"docs":{},"d":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"[":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"docs":{}}},"1":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}},"docs":{}}},"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}},"[":{"docs":{},"'":{"docs":{},"_":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{},"]":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"w":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"(":{"docs":{},"(":{"docs":{},"r":{"2":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"docs":{}}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}},"c":{"docs":{},"]":{"docs":{},"(":{"docs":{},"a":{"docs":{},"u":{"docs":{},"t":{"docs":{},"o":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438}},"(":{"docs":{},"x":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}},"\"":{"docs":{},"a":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"e":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"\"":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"p":{"0":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"_":{"docs":{},"o":{"docs":{},"n":{"docs":{},"_":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}}}}}},"(":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}}},"docs":{}}}}},"s":{"docs":{},"(":{"2":{"docs":{},",":{"1":{"docs":{},".":{"5":{"docs":{},")":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"docs":{}}},"docs":{}}},"docs":{}}}},"v":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"l":{"docs":{},"e":{"docs":{},"]":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"m":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"i":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"/":{"2":{"0":{"0":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653}}},"docs":{}},"docs":{}},"docs":{}}}}},"]":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},";":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"%":{"docs":{},".":{"1":{"docs":{},"f":{"docs":{},"]":{"docs":{},"\"":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"a":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}},"b":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}}}}}}}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}}}}}}}}}}}}}},"docs":{}},"s":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}},"]":{"docs":{},"%":{"docs":{},"s":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}}}}}}},"{":{"docs":{},":":{"docs":{},"?":{"docs":{},"}":{"docs":{},"]":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}}}}}}}}}}}},"\\":{"docs":{},"!":{"docs":{},"[":{"1":{"docs":{},",":{"6":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"!":{"docs":{},"]":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"docs":{}}},"2":{"docs":{},",":{"1":{"2":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"!":{"docs":{},"]":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}},"docs":{}},"docs":{}}},"docs":{}}}}},"{":{"0":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}},"5":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}}},"1":{"5":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}}},"2":{"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},".":{"0":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"docs":{}}},"3":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"4":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}},"docs":{}}},"5":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},".":{"0":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"docs":{}}},"6":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"7":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}},"docs":{}}},"9":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.05754385964912281},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.027195250406971176},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.02549907733601745},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.03228806803082647},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.04463586530931871},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.019572953736654804},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.05250481695568401},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.03791946308724832},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003886729594669628},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.01949634443541836},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.009205335337215856},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.010279605263157895},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.012310939148786493},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.016332907257491834},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.017331721080209594},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.013361169102296452},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.008514492753623188},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.024228028503562947},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005255781359495445}},"%":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112}}},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"_":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},"{":{"docs":{},":":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"1":{"0":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},"[":{"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"docs":{}}},"2":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"5":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"6":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"docs":{},"_":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"{":{"docs":{},":":{"docs":{},"}":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"}":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}}}}}},"}":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}},"r":{"docs":{},"m":{"docs":{},"s":{"docs":{},"d":{"docs":{},":":{"5":{"docs":{},".":{"1":{"docs":{},"%":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"docs":{}}},"docs":{}}}}}}},"{":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}}},"3":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"docs":{}}},"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"}":{"docs":{},"}":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0012448530115867088}}}}}}},"}":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011958543715120914},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},"\"":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}},"\"":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},":":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}},".":{"3":{"docs":{},"f":{"docs":{},"}":{"docs":{},"\"":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"c":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}},"i":{"docs":{},"_":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}}}}}}}}}}}},"}":{"docs":{},"%":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"docs":{}},"?":{"docs":{},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},"]":{"docs":{},"[":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}}},"\"":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"r":{"docs":{},"y":{"docs":{},".":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}},"k":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},".":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"n":{"docs":{},"}":{"docs":{},")":{"docs":{},"'":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"y":{"docs":{},"}":{"docs":{},")":{"docs":{},"'":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{},"}":{"docs":{},")":{"docs":{},"'":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},":":{"docs":{},"_":{"docs":{},"}":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},".":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"h":{"docs":{},".":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"p":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}},"docs":{}}}},"h":{"docs":{},"s":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"p":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"y":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}},"c":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"u":{"docs":{},"s":{"docs":{},"(":{"docs":{},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}}}}}}}}}}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"[":{"1":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}}}}}}}},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"'":{"docs":{},"n":{"docs":{},"r":{"docs":{},"m":{"docs":{},"s":{"docs":{},"d":{"docs":{},"'":{"docs":{},":":{"1":{"0":{"docs":{},"s":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"docs":{}},"docs":{}}}}}}}}},"q":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"x":{"0":{"docs":{},":":{"5":{"docs":{},".":{"2":{"docs":{},"f":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"docs":{}}},"docs":{}}},"docs":{}}},"@":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"a":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.020833333333333332}},"s":{"docs":{},",":{"docs":{},"@":{"docs":{},"p":{"docs":{},"e":{"docs":{},"a":{"docs":{},"n":{"docs":{},"u":{"docs":{},"t":{"docs":{},"b":{"docs":{},"u":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"i":{"docs":{},"o":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.052083333333333336}}}}}},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"l":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.020833333333333332}},"e":{"docs":{},",":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.020833333333333332}},"@":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"d":{"docs":{},"o":{"docs":{},"w":{"docs":{},"m":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},",":{"docs":{},"@":{"docs":{},"a":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{},"@":{"docs":{},"p":{"docs":{},"e":{"docs":{},"a":{"docs":{},"n":{"docs":{},"u":{"docs":{},"t":{"docs":{},"b":{"docs":{},"u":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"d":{"docs":{},"o":{"docs":{},"w":{"docs":{},"m":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.041666666666666664}},",":{"docs":{},"@":{"docs":{},"p":{"docs":{},"e":{"docs":{},"a":{"docs":{},"n":{"docs":{},"u":{"docs":{},"t":{"docs":{},"b":{"docs":{},"u":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"(":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"5":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}}},"1":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}}},"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}},"a":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837}}}},"k":{"docs":{},",":{"docs":{},"v":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}},"$":{"docs":{},"(":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}},"i":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"n":{"docs":{},"b":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.014035087719298246}}}}}}},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"(":{"docs":{},"g":{"docs":{},"l":{"docs":{},"o":{"docs":{},"b":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},"\"":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"i":{"docs":{},"l":{"docs":{},"?":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"a":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"s":{"docs":{},".":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"[":{"docs":{},"@":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615}}}}}}}},"[":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"1":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"4":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"7":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"docs":{}}},"x":{"0":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891}},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"1":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"2":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}},"6":{"4":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}},"docs":{}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002106674327300584},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004697198456634793},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.004697986577181208},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.006587072869493619},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.017871649065800164},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.004884463648318617},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.006167763157894737},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0031656700668308124},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0019883539269990058},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.003787878787878788},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0037578288100208767},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0033944331296673455},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.007100591715976331},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.007340485601355167},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00847457627118644}},"m":{"docs":{},"m":{"0":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0035694157430020664},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0034086067319982955}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0024422318241593085},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.004970884817497514}}}},"1":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0028405056099985795}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0030058237835806877},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029}}}},"2":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0036926572929981537}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0033815517565282736},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}},"3":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002272404487998864}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002272404487998864}}}},"4":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}}}},"5":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002272404487998864}}}},"6":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0025564550489987218}}}},"7":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0025564550489987218}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},"docs":{},"w":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157}}}}}}},"a":{"docs":{},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00826279725916969},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}},"+":{"docs":{},"x":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"/":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},":":{"2":{"docs":{},"*":{"docs":{},"x":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"/":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},":":{"docs":{},"x":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{}},"docs":{}}}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0032245062474808546}}}}},"i":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}}}}}},"o":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001819400555395959},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0021808421405804393},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0015944724953494552},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"l":{"docs":{},"d":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"a":{"docs":{},"m":{"4":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"docs":{}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},".":{"1":{"docs":{},")":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"(":{"docs":{},"*":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}},"x":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},")":{"docs":{},";":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}}}}}},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509}}},"]":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"(":{"docs":{},"_":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"u":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},"(":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"i":{"docs":{},"(":{"2":{"docs":{},")":{"docs":{},")":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.004467912266450041},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.003340292275574113},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"y":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"i":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0072254335260115606},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.005369127516778523},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"docs":{}},"docs":{}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"^":{"2":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"+":{"docs":{},"y":{"docs":{},"^":{"2":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"docs":{}}}},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"y":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\\":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"{":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"docs":{}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"(":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}},")":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}},"+":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}}}}},"\\":{"docs":{},"p":{"docs":{},"m":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"_":{"0":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"'":{"docs":{},"'":{"docs":{},"'":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"2":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"^":{"2":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"docs":{}},"i":{"docs":{},"t":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"e":{"docs":{},"v":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438}}}}}},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"e":{"docs":{},"w":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}},"o":{"docs":{},"d":{"docs":{},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}}}}},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"{":{"1":{"0":{"docs":{},"}":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"t":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"]":{"docs":{},"\\":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}},"docs":{}},"docs":{},"i":{"docs":{},"+":{"1":{"docs":{},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"docs":{}}},"t":{"docs":{},"+":{"1":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"docs":{}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}},"/":{"docs":{},"y":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535}},"e":{"docs":{},"[":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"*":{"docs":{},"x":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"+":{"docs":{},"y":{"docs":{},"*":{"docs":{},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}},"p":{"docs":{},"o":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}}},"s":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"*":{"docs":{},"*":{"2":{"docs":{},")":{"docs":{},")":{"docs":{},".":{"docs":{},"s":{"docs":{},"u":{"docs":{},"m":{"docs":{},"(":{"docs":{},"a":{"docs":{},"x":{"docs":{},"i":{"docs":{},"s":{"docs":{},"=":{"0":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"docs":{}}}}}}}}}}}}}},"docs":{}}}}},"y":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},".":{"docs":{},"^":{"2":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"docs":{}}}}}}}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004111842105263158}},")":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"1":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"2":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},")":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"6":{"4":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}},"docs":{},"b":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"h":{"docs":{},"a":{"docs":{},"l":{"docs":{},"f":{"docs":{},"+":{"docs":{},"i":{"docs":{},"]":{"docs":{},"*":{"docs":{},"f":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}}}}}}}}}}},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0020665038512117226},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0028782894736842104},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"e":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}},"+":{"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}}},"n":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"c":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"j":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"r":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"}":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"{":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}},"'":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}}},"|":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"l":{"docs":{},"a":{"docs":{},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"x":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"z":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"\\":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}},"=":{"0":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{}},"]":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"!":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003642121931908155}},"=":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001340610935554917},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.008387854386847844},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002533650039588282}},"=":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"[":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},".":{"docs":{},".":{"docs":{},"]":{"docs":{},".":{"docs":{},"i":{"docs":{},"s":{"docs":{},"_":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"!":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"f":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"(":{"docs":{},"*":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"a":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"i":{"docs":{},"d":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"s":{"docs":{},"n":{"docs":{},"a":{"docs":{},"n":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"k":{"docs":{},"w":{"docs":{},"i":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}}}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"u":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}},"#":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.016853394618404672},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.006542526421741319},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.02763752325272389},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.012137823022709476},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.00771055753262159},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.006262042389210019},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.008053691275167786},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.012755102040816327},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0037052284890901604},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.007311129163281885},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.009824561403508772},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.012962615066691715},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.013569078947368422},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.012310939148786493},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.013776452208493111},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.012898024989923419},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.025252525252525252},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.003340292275574113},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.01322463768115942},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.010292953285827395},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.00421179302045728},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005956552207428171},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"!":{"docs":{},"/":{"docs":{},"u":{"docs":{},"s":{"docs":{},"r":{"docs":{},"/":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"/":{"docs":{},"e":{"docs":{},"n":{"docs":{},"v":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"c":{"docs":{},"l":{"docs":{},"u":{"docs":{},"d":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004210526315789474},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0015321267834913339},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002125963327132607},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.005090054815974941},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0026690391459074734},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0030201342281879194},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0028179597971068945},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0028139289482940555},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0026199113260781943},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003153468815697267}}}}}}},"f":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},"[":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"u":{"docs":{},"g":{"docs":{},")":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}},")":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"(":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"1":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"4":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"7":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{},"+":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}},"*":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"c":{"docs":{},"/":{"docs":{},"+":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"i":{"docs":{},"f":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"/":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"{":{"docs":{},"i":{"docs":{},"}":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{},"}":{"docs":{},"\"":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},"?":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"'":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"*":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"+":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"m":{"docs":{},"a":{"docs":{},"k":{"docs":{},"e":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"c":{"docs":{},"(":{"0":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"docs":{}}},"s":{"docs":{},"i":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},"\\":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"&":{"0":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.003340292275574113}},".":{"0":{"4":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}},"docs":{}},"1":{"6":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}},"docs":{}},"2":{"2":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}},"4":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}},"8":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}},"docs":{}},"5":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}},"8":{"5":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}},"docs":{}},"docs":{}}},"1":{"docs":{},"&":{"2":{"docs":{},"&":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"3":{"docs":{},"&":{"docs":{},"&":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}}},"docs":{}}}}}}}}}}}}}}},"docs":{}}},"4":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}},"&":{"5":{"docs":{},"&":{"6":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835}}},"docs":{}}},"docs":{}}},"6":{"docs":{},"&":{"5":{"docs":{},"&":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"}":{"4":{"docs":{},"&":{"docs":{},"&":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}}},"docs":{}}}}}}}}}}}}}},"docs":{}}},"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.09929078014184398},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.010300429184549357},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.021792763157894735},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.029453681710213776},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.014201183431952662},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"&":{"1":{"docs":{},"&":{"2":{"docs":{},"&":{"3":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835}}},"docs":{}}},"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"2":{"docs":{},"&":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"3":{"docs":{},"&":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"docs":{}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}},"6":{"docs":{},"&":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"}":{"5":{"docs":{},"&":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"4":{"docs":{},"&":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"docs":{}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0010629816635663034},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0024084778420038534},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.003985507246376811}},"&":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"6":{"docs":{},"&":{"5":{"docs":{},"&":{"4":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}}},"docs":{}}},"docs":{}}}}}},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"6":{"docs":{},"&":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"5":{"docs":{},"&":{"4":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}}},"docs":{}}}}}}}}}}}}}}},"docs":{}}}}}}},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"}":{"1":{"docs":{},"&":{"2":{"docs":{},"&":{"3":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}}},"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"2":{"docs":{},"&":{"3":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"3":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}},"6":{"docs":{},"&":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"5":{"docs":{},"&":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"4":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"1":{"9":{"4":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}}}},"5":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"3":{"1":{"5":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"1":{"9":{"5":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}},"docs":{}},"3":{"2":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"1":{"9":{"5":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}},"⭐":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"docs":{}},"docs":{},"b":{"0":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"1":{"9":{"5":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}},"docs":{}}},"docs":{}}},"docs":{}}}},"⏩":{"docs":{},"⏩":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"⏹":{"docs":{},"⏫":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}},"☝":{"docs":{},"️":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"1":{"9":{"5":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}}}},"docs":{}},"docs":{}},"3":{"0":{"0":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}},"docs":{},"c":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"4":{"1":{"5":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}}},"1":{"5":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"3":{"2":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"docs":{}},"4":{"6":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}},"7":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.004021832806664752},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.005280259951259139}}}},"9":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.003830316958728335},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.005280259951259139}}}},"docs":{}},"6":{"5":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}},"8":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"3":{"4":{"6":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"docs":{}},"docs":{}},"4":{"1":{"docs":{},"a":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"3":{"3":{"2":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"3":{"4":{"6":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}}},"docs":{}},"docs":{}}},"docs":{}}}}}},"docs":{},"c":{"docs":{},";":{"docs":{},"⏹":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"d":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"4":{"3":{"docs":{},"d":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}},"docs":{}},"docs":{}}},"docs":{}}}},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}},"a":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"2":{"4":{"docs":{},";":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}}},"7":{"docs":{},"c":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},"docs":{},"c":{"1":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"3":{"docs":{},";":{"docs":{},"‍":{"docs":{},"♀":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"4":{"0":{"7":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"9":{"2":{"1":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}}}}},"docs":{}},"e":{"2":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}},"7":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}},"docs":{}}},"4":{"0":{"7":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}}},"docs":{}},"1":{"4":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837}}}},"5":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}}}},"docs":{}},"2":{"8":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}},"docs":{}},"3":{"docs":{},"b":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}},"d":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}},"4":{"docs":{},"c":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},"docs":{},"a":{"docs":{},"d":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"f":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00487408610885459}},"s":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}},"d":{"7":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0019151584793641674}}}},"docs":{}},"e":{"5":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}},"docs":{},"a":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}},"b":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}}}},"5":{"0":{"1":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"2":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"1":{"0":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"8":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"docs":{}},"2":{"1":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0012448530115867088},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{},"❗":{"docs":{},"❗":{"docs":{},"️":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}},"2":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0020130850528434826},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"4":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"3":{"0":{"0":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"docs":{}},"6":{"5":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"docs":{},"d":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"docs":{},"e":{"2":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"docs":{}}},"5":{"2":{"4":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"docs":{}},"docs":{}},"9":{"5":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}},"docs":{}},"docs":{}}},"docs":{}}}},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"%":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"2":{"4":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"3":{"6":{"docs":{},"a":{"docs":{},";":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"docs":{}},"docs":{}}},"docs":{}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}},"r":{"docs":{},"u":{"docs":{},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"docs":{}},"3":{"docs":{},"c":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"8":{"docs":{},"d":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"1":{"9":{"5":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}},"v":{"docs":{},"a":{"docs":{},"r":{"docs":{},"_":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"v":{"docs":{},"a":{"docs":{},"r":{"docs":{},"_":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}},"r":{"docs":{},"a":{"docs":{},"d":{"docs":{},"i":{"docs":{},"u":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}},"docs":{}},"6":{"0":{"0":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0019151584793641674},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}},"docs":{}},"4":{"5":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"docs":{},"c":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}},"docs":{},"a":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}},"9":{"1":{"docs":{},"c":{"docs":{},";":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"docs":{}},"docs":{}},"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"docs":{}},"docs":{},"d":{"docs":{},"e":{"docs":{},"p":{"docs":{},"t":{"docs":{},"h":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"p":{"docs":{},"i":{"docs":{},"_":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"x":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"d":{"docs":{},"i":{"docs":{},"u":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}}},"2":{"1":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"3":{"7":{"docs":{},";":{"docs":{},"‍":{"docs":{},"♀":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"docs":{}},"5":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}},"6":{"7":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"4":{"docs":{},"a":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"4":{"docs":{},"a":{"docs":{},"f":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}},"docs":{}}},"docs":{}}}}}}},"docs":{}},"docs":{}}},"docs":{}}}}}},"docs":{}},"8":{"3":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"docs":{}},"docs":{},"d":{"2":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186}}}},"docs":{}}},"docs":{}}},"docs":{}}},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},"[":{"docs":{},".":{"docs":{},".":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837}}},"{":{"docs":{},"i":{"docs":{},"d":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}},"t":{"docs":{},"m":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"b":{"docs":{},"u":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"a":{"docs":{},"r":{"docs":{},"n":{"docs":{},"s":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},"_":{"docs":{},"h":{"docs":{},"u":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"b":{"docs":{},"a":{"docs":{},"b":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}}}}}}}}}},"c":{"docs":{},"b":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},"|":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"e":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"]":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},"q":{"docs":{},"n":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}}}},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"[":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}}},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"[":{"docs":{},"&":{"docs":{},"c":{"docs":{},"]":{"docs":{},")":{"docs":{},".":{"docs":{},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},"[":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"[":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"[":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}}}}}}}}}}},"f":{"6":{"4":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"docs":{}},"docs":{}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}}}}}},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}}}}},"=":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004111842105263158},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0024621878297572987},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.007098121085594989},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.008146639511201629},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0029585798816568047},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}},"x":{"docs":{},"(":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835}}}}}}},"x":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"2":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"docs":{}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},"c":{"docs":{},"!":{"docs":{},"[":{"2":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"docs":{}}},"docs":{}}}}}},"o":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}},"r":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"f":{"6":{"4":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"docs":{}},"docs":{}},";":{"docs":{},"&":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}},"'":{"0":{"docs":{},"'":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"1":{"0":{"0":{"0":{"docs":{},"'":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"1":{"docs":{},"'":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"docs":{},"'":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"1":{"docs":{},"'":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}},"docs":{}},"1":{"0":{"0":{"docs":{},"'":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"1":{"docs":{},"'":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"docs":{},"'":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"1":{"docs":{},"'":{"docs":{},")":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}},"docs":{}},"docs":{},"'":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"2":{"docs":{},"p":{"docs":{},"i":{"docs":{},"'":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001340610935554917},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"'":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},"'":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}}},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},".":{"docs":{},"p":{"docs":{},"n":{"docs":{},"g":{"docs":{},"'":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"'":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"q":{"docs":{},"n":{"docs":{},"s":{"docs":{},"'":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"'":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},"=":{"docs":{},"z":{"docs":{},"^":{"2":{"docs":{},"'":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"'":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"'":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"f":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"'":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"'":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"'":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"h":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276}},".":{"docs":{},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},"_":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"'":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0024897060231734176}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011490950876185005}},"n":{"docs":{},"u":{"docs":{},"m":{"2":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"(":{"docs":{},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"(":{"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"(":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"docs":{}}}}}}}}}}}}}}}},"docs":{}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001340610935554917}}},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449}}}}}},"_":{"docs":{},"_":{"docs":{},"m":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},"_":{"docs":{},"_":{"docs":{},"'":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}},"i":{"docs":{},"d":{"docs":{},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"'":{"docs":{},"]":{"docs":{},"]":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}}},"d":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},"'":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}}}},"(":{"docs":{},"g":{"0":{"docs":{},")":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}},"docs":{}},"(":{"docs":{},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"1":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"docs":{}}}}}}},"\"":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}},"a":{"docs":{},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"\\":{"0":{"docs":{},"'":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}},"docs":{}},"a":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"b":{"docs":{},"i":{"docs":{},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"_":{"docs":{},"b":{"docs":{},"o":{"docs":{},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"'":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}}}}}}}}}},"o":{"docs":{},"'":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"y":{"docs":{},"'":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"%":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"#":{"0":{"0":{"0":{"0":{"docs":{},"f":{"docs":{},"f":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"docs":{}},"docs":{},"f":{"docs":{},"f":{"0":{"0":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"docs":{}},"docs":{}}}},"docs":{}},"docs":{}},".":{"docs":{},".":{"docs":{},"/":{"docs":{},".":{"docs":{},".":{"docs":{},"/":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},"/":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"'":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},")":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"+":{"docs":{},"+":{"docs":{},"'":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"*":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.021052631578947368},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703054677774585},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.015433652071800034},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0015944724953494552},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003855278766310795},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.008188824662813102},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.010738255033557046},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.023558082859463852},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.02526315789473684},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.006008583690987125},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.015029118917903438},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.018092105263157895},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.006683081252198382},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.04033517966197983},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.03184199919387344},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.005681818181818182},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.009603340292275574},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.02308214528173795},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0125},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.009026128266033254},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004204625087596356},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925}},"/":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.015438596491228071},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"*":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0022168480451430876},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}},"t":{"docs":{},"m":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"=":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0026199113260781943}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"m":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"u":{"docs":{},"s":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}}}},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}}}}},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}},"q":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},".":{"docs":{},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"s":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},".":{"docs":{},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}}},"k":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}}}}},"o":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"*":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}},"t":{"docs":{},"m":{"docs":{},"p":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}}},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"a":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},"_":{"docs":{},"o":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},"l":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"s":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},".":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"r":{"docs":{},"y":{"docs":{},"(":{"docs":{},"c":{"docs":{},")":{"docs":{},".":{"docs":{},"o":{"docs":{},"r":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}},"g":{"docs":{},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"o":{"docs":{},"b":{"docs":{},"a":{"docs":{},"b":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}},".":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"f":{"docs":{},"c":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"f":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}},"b":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},".":{"docs":{},"a":{"docs":{},"u":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"e":{"docs":{},"p":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"x":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"p":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"k":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"e":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"_":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"+":{"1":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}},"3":{"docs":{},"]":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.010724887484439337},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.01793781557268137},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0074393108848864525},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.009489916963226572},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.005780346820809248},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0050335570469798654},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.008344923504867872},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.016194331983805668},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007218212104386452},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.018277822908204712},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.014035087719298246},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.01201716738197425},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.015216982904377232},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004111842105263158},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.009497010200492437},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.019883539269990057},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.004635227730753728},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.005681818181818182},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0162839248434238},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.016293279022403257},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.030253623188405798},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.01330166270783848},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.008409250175192713},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.004517221908526256},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"+":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011490950876185005},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304}},"i":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"=":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}},"=":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002125963327132607},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0026845637583892616},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.020451640391989774},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003800475059382423},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"y":{"docs":{},"^":{"2":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"docs":{}}}},".":{"0":{"1":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}},"docs":{}},"1":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}},"2":{"6":{"6":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"docs":{}},"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}},"3":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}},"4":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}},"5":{"docs":{},"f":{"docs":{},"]":{"docs":{},"\"":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}}}}}}}}}}}}}}},"*":{"docs":{},"a":{"docs":{},"c":{"docs":{},"c":{"docs":{},"*":{"docs":{},"d":{"docs":{},"t":{"docs":{},"*":{"docs":{},"d":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002872737719046251},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.006045949214026602},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009301089556205156},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},".":{"docs":{},"s":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}}}}}}}}}}},")":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"/":{"docs":{},"g":{"docs":{},"n":{"docs":{},"u":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{},"/":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{},"_":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},".":{"docs":{},"p":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},".":{"docs":{},"t":{"docs":{},"o":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}}}}}}}},":":{"docs":{},":":{"docs":{},">":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"!":{"docs":{},"(":{"docs":{},"a":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}},"s":{"docs":{},"v":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0016278847074595424},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0018602179112410311}}}},"x":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"p":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"g":{"docs":{},"l":{"docs":{},"o":{"docs":{},"b":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"p":{"docs":{},"b":{"docs":{},"y":{"docs":{},"(":{"docs":{},"i":{"docs":{},"d":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},"s":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"l":{"docs":{},"_":{"docs":{},"s":{"docs":{},"y":{"docs":{},"n":{"docs":{},"t":{"docs":{},"a":{"docs":{},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}},"o":{"docs":{},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"|":{"docs":{},"_":{"docs":{},"|":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"(":{"docs":{},"&":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"i":{"docs":{},"|":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}}},"k":{"docs":{},"|":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"(":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},"v":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"_":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}}}}}}}},"{":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"r":{"docs":{},"o":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}},"s":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"(":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}}},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"e":{"docs":{},"d":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},":":{"docs":{},":":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"o":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}},"s":{"docs":{},"v":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"a":{"docs":{},"k":{"docs":{},"e":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}},"f":{"docs":{},"l":{"docs":{},"a":{"docs":{},"t":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"i":{"docs":{},"l":{"docs":{},"l":{"docs":{},"(":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"|":{"docs":{},"i":{"docs":{},"|":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"_":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"|":{"docs":{},"i":{"docs":{},"|":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}},"l":{"docs":{},"d":{"docs":{},"(":{"0":{"docs":{},".":{"0":{"docs":{},"_":{"docs":{},"f":{"6":{"4":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"docs":{}},"docs":{}}}},"docs":{}}},"docs":{}}}}}},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}}},"=":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{},"c":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}},"a":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}}},"p":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"i":{"docs":{},"m":{"docs":{},"i":{"docs":{},"t":{"docs":{},"(":{"docs":{},"n":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}},"+":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"*":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0026199113260781943},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"z":{"docs":{},"i":{"docs":{},"p":{"docs":{},"(":{"docs":{},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{},"y":{"docs":{},"_":{"docs":{},"r":{"docs":{},".":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}}}}},"/":{"docs":{},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{},"n":{"docs":{},"s":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},".":{"docs":{},"c":{"docs":{},"p":{"docs":{},"p":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}},"a":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002106674327300584},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0018602179112410311},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.004306969459671104},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0026690391459074734},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0014363688595231256},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0018453279651065259},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006643635397289397},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002843216896831844},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.003550632012498225},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.007859733978234583},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"=":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002585463947141626},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003355141754739138},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0030560722827531225},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.00674373795761079},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.006167763157894737},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.006017418844022169}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"e":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"i":{"docs":{},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"e":{"docs":{},"l":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638}},"e":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"f":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.005225653206650831}},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"p":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}},"+":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737}}},"a":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"s":{"docs":{},"u":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}},"=":{"1":{"docs":{},":":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}}}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.025964912280701753},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.03179163075744518},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.06777386344573058},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.041589157587031626},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.056382145653876274},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.04833926453143535},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.038053949903660886},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.042953020134228186},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.023320377568017768},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.01020408163265306},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.030463038180341188},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.01643835616438356},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.041403508771929824},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.039484978540772535},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.041330077024234455},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.011363636363636364},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.07935855263157894},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.03447062961660218},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.06561567959096719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.06590084643288996},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.023989898989898988},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.030897703549060542},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.03054989816700611},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.030797101449275364},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.052256532066508314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.021660649819494584},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.008875739644970414},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.014716187806587245},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.028797289666854884},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.022245762711864406}},"=":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0035087719298245615},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0030642535669826677},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0020130850528434826},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.004251926654265214},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.003523884103367267},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.01571767497034401},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.008188824662813102},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.004697986577181208},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.007065217391304348},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.004592240696753761},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"'":{"docs":{},"_":{"docs":{},"_":{"docs":{},"m":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},"_":{"docs":{},"_":{"docs":{},"'":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}},"=":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},">":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001340610935554917},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0021808421405804393},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00451767207015679},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.004698512137823023},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"&":{"4":{"docs":{},"+":{"1":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}}},"5":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.010638297872340425}}},"docs":{}}},"_":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703054677774585},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0018602179112410311},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"_":{"docs":{},"a":{"docs":{},"u":{"docs":{},"t":{"docs":{},"h":{"docs":{},"o":{"docs":{},"r":{"docs":{},"_":{"docs":{},"_":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}},"d":{"docs":{},"d":{"docs":{},"_":{"docs":{},"_":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}},"b":{"docs":{},"s":{"docs":{},"_":{"docs":{},"_":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"_":{"docs":{},"_":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"_":{"docs":{},"_":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"_":{"docs":{},"_":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"=":{"docs":{},"=":{"docs":{},"\"":{"docs":{},"_":{"docs":{},"_":{"docs":{},"m":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},"_":{"docs":{},"_":{"docs":{},"\"":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"_":{"docs":{},"_":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}}}}},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"p":{"docs":{},"r":{"docs":{},"_":{"docs":{},"_":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585}}}}}}},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"_":{"docs":{},"_":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}},"a":{"docs":{},"t":{"docs":{},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"_":{"docs":{},"_":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"d":{"docs":{},"c":{"3":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314908317831517},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002414429768498793},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009301089556205156},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},".":{"docs":{},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}}}},"}":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"p":{"docs":{},"o":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},"d":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}},"x":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"`":{"docs":{},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"`":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"i":{"docs":{},"v":{"docs":{},"`":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}}}},"e":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"`":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"`":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{},"`":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"`":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"`":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},"`":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"_":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"`":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"`":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"d":{"docs":{},"`":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"`":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"`":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}},"b":{"docs":{},"`":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"`":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0014492753623188406}}}}},"a":{"docs":{},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"`":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}},"n":{"docs":{},"o":{"docs":{},"t":{"docs":{},"`":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"_":{"docs":{},"o":{"docs":{},"f":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"`":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"n":{"docs":{},"`":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},"_":{"docs":{},"t":{"docs":{},"u":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"`":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}}}}}},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"f":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"(":{"0":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"docs":{}}}},"}":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.05403508771929825},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.02537584985157522},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.024828048985069618},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.027504650544778103},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.04111198120595145},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.013938315539739028},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.02601156069364162},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.02919463087248322},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.008529650690495532},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0061995115536351685},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.008634868421052632},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.008793527963418923},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.014912654452492544},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.01713018943974204},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.008514492753623188},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.026286619160728424},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.00350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001053337163650292},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002258836035078395},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0024084778420038534},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0012782275244993609},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0003986181238373638},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0010629816635663034},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.02023121387283237},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0050335570469798654},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"~":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"i":{"docs":{},"s":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669}}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"{":{"1":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}},"docs":{}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"_":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}}}}}}}}}}}}},"=":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}}},"}":{"docs":{},"~":{"docs":{},"%":{"docs":{},"\"":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"a":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}},"$":{"1":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"2":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011490950876185005},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0022169437846397467},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"c":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502}}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}}}}}}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},"d":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}}}},"+":{"docs":{},"+":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}},"u":{"docs":{},"m":{"docs":{},"o":{"docs":{},"f":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}}}}}}}},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}},"[":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}}},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},"s":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}},"[":{"docs":{},"$":{"docs":{},"(":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},"docs":{}}}}},"h":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0012448530115867088},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00548159749412686}}}},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837}},")":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837}}}}}}},"m":{"docs":{},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}},"(":{"1":{"0":{"0":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"docs":{}},"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"docs":{}},"docs":{}},"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"docs":{}},"docs":{},"(":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"docs":{}},"docs":{}},"2":{"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"docs":{}},"docs":{}},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"a":{"docs":{},"[":{"2":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}},"b":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004193927193423922},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}}},"[":{"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"2":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0038584130179500084},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0018453279651065259}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"]":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"2":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}},"f":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}},"g":{"docs":{},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"m":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"e":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"p":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"s":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"e":{"docs":{},"r":{"docs":{},"c":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"r":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}},"i":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"+":{"docs":{},"+":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}},"o":{"docs":{},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"y":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}}}}},"u":{"docs":{},"n":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"e":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"{":{"2":{"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}},"docs":{}},"docs":{},"g":{"docs":{},"i":{"docs":{},"r":{"docs":{},"l":{"docs":{},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"p":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"y":{"docs":{},".":{"docs":{},"f":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},"`":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"p":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},".":{"docs":{},"y":{"docs":{},"}":{"docs":{},")":{"docs":{},"`":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}}},"r":{"docs":{},"a":{"docs":{},"d":{"docs":{},"i":{"docs":{},"u":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"s":{"docs":{},"=":{"1":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"docs":{}}}}}}}},"x":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"2":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{},"$":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"y":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"[":{"docs":{},"$":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}},")":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}},"s":{"docs":{},".":{"docs":{},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"$":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"e":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"k":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"q":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0026845637583892616},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0029231995748073346},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.005823783580687582},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}},";":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"e":{"docs":{},"l":{"docs":{},"s":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}}}},"o":{"docs":{},"f":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"r":{"docs":{},"e":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}}},"t":{"docs":{},"o":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}},"\\":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"n":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"a":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"^":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}}},"docs":{}}}}}},"e":{"docs":{},"q":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"\"":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"{":{"docs":{},"o":{"docs":{},"}":{"docs":{},"(":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"^":{"2":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"3":{"docs":{},")":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"docs":{}},"h":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"\\":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},".":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898}}}}}}}},"d":{"docs":{},"t":{"docs":{},"^":{"3":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}}}}}}},"f":{"docs":{},"}":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"(":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},"*":{"docs":{},"g":{"docs":{},")":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}},"g":{"docs":{},")":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}},"^":{"docs":{},"{":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}}},"r":{"docs":{},"m":{"docs":{},"{":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"r":{"docs":{},"m":{"docs":{},"{":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"}":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"b":{"docs":{},"b":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},"^":{"2":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},")":{"docs":{},":":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"c":{"docs":{},"}":{"docs":{},")":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"p":{"docs":{},"}":{"docs":{},"(":{"docs":{},"a":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}}},"x":{"docs":{},"_":{"0":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"docs":{}}}}}}}},"f":{"docs":{},"{":{"0":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"1":{"0":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"2":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"3":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}}}},"4":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"6":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"1":{"0":{"docs":{},"}":{"docs":{},"{":{"3":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"docs":{}}}},"docs":{}},"2":{"docs":{},"}":{"docs":{},"{":{"3":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"docs":{}}}},"docs":{}}}}}}},"r":{"docs":{},"}":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"a":{"docs":{},"}":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004142011834319527}},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"v":{"docs":{},"}":{"docs":{},"_":{"0":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"docs":{}}}}}}}}}}}},"_":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"r":{"docs":{},"o":{"docs":{},"t":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}}}}}}}}}}}}}}}},"v":{"docs":{},"_":{"0":{"docs":{},"}":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"docs":{}},"}":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"_":{"0":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},"docs":{}}}},"x":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}},"u":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},")":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"docs":{}}}},"i":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"1":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{}}}}}}}}}},"\\":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.04964539007092199},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.011158798283261802},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.005756578947368421},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.022964509394572025},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00855106888361045},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.022485207100591716},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"{":{"docs":{},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"}":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}}}}}},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"}":{"docs":{},"{":{"docs":{},"c":{"docs":{},"c":{"docs":{},"c":{"docs":{},"c":{"docs":{},"c":{"docs":{},"c":{"docs":{},"c":{"docs":{},"|":{"docs":{},"c":{"docs":{},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"|":{"docs":{},"c":{"docs":{},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"|":{"docs":{},"c":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0028503562945368173}}}}},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{},"}":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.028368794326241134},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"c":{"docs":{},"u":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"}":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}},"b":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{},"}":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.017954070981210855},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.009467455621301775}}}}}}}}}}}}}}},"i":{"docs":{},"g":{"docs":{},"c":{"docs":{},"u":{"docs":{},"p":{"docs":{},"_":{"docs":{},"{":{"docs":{},"i":{"docs":{},"=":{"1":{"docs":{},"}":{"docs":{},"^":{"3":{"docs":{},"f":{"docs":{},"_":{"docs":{},"i":{"docs":{},"(":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"4":{"docs":{},"f":{"docs":{},"_":{"docs":{},"i":{"docs":{},"(":{"docs":{},"p":{"docs":{},")":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}},"docs":{}}}},"docs":{}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"{":{"docs":{},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"}":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003800475059382423}},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{},"}":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.010638297872340425},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"\\":{"docs":{},"\\":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.01773049645390071}}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"c":{"docs":{},"u":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"}":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}},"b":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{},"}":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.008350730688935281},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.008284023668639054}},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"\\":{"docs":{},"\\":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"p":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.009603340292275574}}},",":{"docs":{},"\\":{"docs":{},"\\":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}}}}}}}},"l":{"docs":{},"l":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0035502958579881655}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"x":{"docs":{},"p":{"docs":{},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"[":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"{":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"y":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"{":{"docs":{},"i":{"docs":{},"=":{"0":{"docs":{},"}":{"docs":{},"^":{"docs":{},"{":{"docs":{},"n":{"docs":{},"}":{"docs":{},"w":{"docs":{},"_":{"docs":{},"i":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}}}}}}}}},"docs":{}}},"n":{"docs":{},"=":{"0":{"docs":{},"}":{"docs":{},"^":{"9":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{},"{":{"docs":{},"\\":{"docs":{},"i":{"docs":{},"n":{"docs":{},"f":{"docs":{},"t":{"docs":{},"y":{"docs":{},"}":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}}}},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"docs":{},"a":{"docs":{},"}":{"docs":{},"^":{"docs":{},"{":{"docs":{},"b":{"docs":{},"}":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}}}}}}},"m":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},"k":{"docs":{},"=":{"0":{"docs":{},"}":{"docs":{},"^":{"docs":{},"{":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"docs":{}}}},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"n":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}}}}},"i":{"docs":{},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"q":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.012145748987854251}}}}},"n":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407}},"(":{"0":{"docs":{},")":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"2":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"\\":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"g":{"docs":{},"a":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828}}}}}}}}}}},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"_":{"docs":{},"x":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"y":{"docs":{},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"p":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"q":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"(":{"docs":{},"n":{"docs":{},",":{"docs":{},"a":{"docs":{},")":{"docs":{},"^":{"2":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}}}}}}}}}}},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"{":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407}},"g":{"docs":{},"_":{"docs":{},"x":{"docs":{},"^":{"2":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"docs":{}}}}},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"r":{"docs":{},"e":{"docs":{},"}":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},"^":{"2":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"docs":{}}}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"1":{"docs":{},"}":{"docs":{},"{":{"docs":{},"n":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"{":{"docs":{},"i":{"docs":{},"=":{"1":{"docs":{},"}":{"docs":{},"^":{"docs":{},"{":{"docs":{},"n":{"docs":{},"}":{"docs":{},"(":{"docs":{},"q":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}},"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}},"p":{"docs":{},"i":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"u":{"docs":{},"_":{"1":{"docs":{},"^":{"2":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"docs":{}}},"docs":{}}}}}}}},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"}":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"(":{"docs":{},"c":{"docs":{},"_":{"docs":{},"i":{"docs":{},")":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"^":{"2":{"docs":{},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}}}}}}}}},"a":{"docs":{},"c":{"docs":{},"c":{"docs":{},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"}":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"}":{"docs":{},"_":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"c":{"docs":{},"i":{"docs":{},"r":{"docs":{},"c":{"docs":{},"l":{"docs":{},"e":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"=":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}},"s":{"docs":{},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"=":{"4":{"docs":{},"r":{"docs":{},"^":{"2":{"docs":{},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}}}},"docs":{}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"}":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"n":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"i":{"docs":{},"m":{"docs":{},"}":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"r":{"docs":{},"e":{"docs":{},"}":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"}":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"}":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}},"?":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}},"w":{"docs":{},"i":{"docs":{},"d":{"docs":{},"t":{"docs":{},"h":{"docs":{},"}":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}},"i":{"docs":{},"m":{"docs":{},"}":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}}}}}}},"f":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"}":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"}":{"docs":{},"~":{"docs":{},"\\":{"docs":{},"%":{"docs":{},"~":{"1":{"9":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"4":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"7":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}}}}}}}}}},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"_":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"}":{"docs":{},"_":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"}":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}}}}}}}}}}}},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"k":{"docs":{},"}":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}},"x":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"v":{"docs":{},"}":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.008344923504867872},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.02127659574468085},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.005479452054794521},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003289473684210526},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004142011834319527},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}}}}}}}}}}}}}},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0035502958579881655}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"}":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"(":{"1":{"docs":{},")":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"2":{"docs":{},"^":{"docs":{},"n":{"docs":{},")":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"3":{"docs":{},")":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"docs":{},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"3":{"docs":{},"n":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"docs":{}}}}},"docs":{}}}}}},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}}},"n":{"docs":{},")":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}},"^":{"2":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"3":{"docs":{},")":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"docs":{}}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}},"a":{"docs":{},"u":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}}}},"p":{"docs":{},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0026300958106331017},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"=":{"docs":{},"(":{"3":{"docs":{},",":{"1":{"docs":{},",":{"2":{"docs":{},",":{"4":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},"docs":{}}},"docs":{}}},"docs":{}}},"docs":{}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"/":{"2":{"docs":{},")":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828}}}},"docs":{}}},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828}}},"s":{"docs":{},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}}}}}}}}}},"^":{"docs":{},"{":{"docs":{},"*":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}}}}}}}}}}}}}},"+":{"docs":{},"d":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}},"x":{"docs":{},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"\\":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}},"_":{"docs":{},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"h":{"docs":{},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}}}}}}}}}}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"1":{"2":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"docs":{}},"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"{":{"1":{"8":{"docs":{},"}":{"docs":{},"{":{"1":{"1":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}},"docs":{}},"docs":{}}}},"docs":{},"}":{"docs":{},"{":{"0":{"docs":{},".":{"7":{"8":{"5":{"3":{"docs":{},"}":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}},"1":{"docs":{},".":{"7":{"2":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"docs":{}}},"2":{"docs":{},"}":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"docs":{},"d":{"docs":{},"^":{"2":{"docs":{},"f":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"d":{"docs":{},"x":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{},"(":{"docs":{},"x":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}},"docs":{}}}}}}}}}}},"docs":{}}}}}}}},"h":{"docs":{},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"\\":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"g":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"g":{"docs":{},"a":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},"a":{"docs":{},"t":{"docs":{},"^":{"2":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"docs":{}}},"(":{"docs":{},"t":{"docs":{},")":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}}}}}},"+":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}},"(":{"docs":{},"a":{"docs":{},"(":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"m":{"docs":{},"v":{"docs":{},"^":{"2":{"docs":{},"?":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"docs":{}}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}},"\\":{"docs":{},"p":{"docs":{},"i":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{},"e":{"docs":{},"^":{"docs":{},"{":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}},"docs":{}}}}}}}}}}}},"3":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"b":{"docs":{},"(":{"docs":{},"t":{"docs":{},")":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"6":{"docs":{},"}":{"docs":{},"b":{"docs":{},"(":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}},"t":{"docs":{},"^":{"3":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"docs":{}}}}}},"7":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"8":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},"9":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}},"docs":{},"n":{"docs":{},"}":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"_":{"3":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{},"{":{"docs":{},"v":{"docs":{},"+":{"1":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}}}}}},"(":{"2":{"docs":{},"^":{"3":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}}},"docs":{}},"\\":{"docs":{},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"i":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}}}},"2":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"d":{"docs":{},"^":{"2":{"docs":{},"x":{"docs":{},"(":{"docs":{},"t":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"d":{"docs":{},"t":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}},"docs":{}}}}}}}}}}},"docs":{}},"f":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"d":{"docs":{},"x":{"docs":{},"}":{"docs":{},"(":{"docs":{},"x":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}}}}}}}},"x":{"docs":{},"(":{"docs":{},"t":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"d":{"docs":{},"t":{"docs":{},"}":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}}}}}},"_":{"0":{"docs":{},"}":{"docs":{},"{":{"docs":{},"b":{"docs":{},"_":{"0":{"docs":{},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}}}}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"f":{"docs":{},"^":{"docs":{},"{":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},"}":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"n":{"docs":{},"!":{"docs":{},"}":{"docs":{},"(":{"docs":{},"x":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}}}}}}}}}}}}},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"x":{"docs":{},"}":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"y":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\\":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"d":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"d":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}}}}}}}}},"x":{"docs":{},"'":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"f":{"docs":{},"(":{"docs":{},"x":{"docs":{},"_":{"docs":{},"t":{"docs":{},")":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}}}}}},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"{":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}},"n":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"y":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"{":{"docs":{},"n":{"docs":{},"}":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"_":{"docs":{},"{":{"docs":{},"n":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"+":{"1":{"docs":{},"}":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"docs":{}}}}},"docs":{}}}}},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{}}}},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"}":{"docs":{},"_":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"c":{"docs":{},"i":{"docs":{},"r":{"docs":{},"c":{"docs":{},"l":{"docs":{},"e":{"docs":{},"}":{"docs":{},"}":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"}":{"docs":{},"_":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"s":{"docs":{},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"}":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}},"p":{"docs":{},"i":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"}":{"docs":{},"{":{"4":{"docs":{},"}":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},")":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"docs":{}}}},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147}},"a":{"docs":{},"l":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"h":{"docs":{},"i":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"h":{"docs":{},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"m":{"docs":{},"}":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"\\":{"docs":{},"n":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"a":{"docs":{},"^":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{}}}}}}}}}}},"docs":{}}}},"docs":{}},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"docs":{}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"{":{"docs":{},"p":{"docs":{},"_":{"1":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"docs":{}}}}}}},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{},"(":{"1":{"docs":{},"+":{"docs":{},"n":{"docs":{},"/":{"docs":{},"a":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{},"(":{"1":{"docs":{},"+":{"1":{"docs":{},"/":{"docs":{},"a":{"docs":{},")":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"docs":{}}},"docs":{}}}}}}}}}}}}}},"docs":{}},"_":{"docs":{},"e":{"docs":{},"(":{"docs":{},"n":{"docs":{},"+":{"1":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{},"_":{"docs":{},"e":{"docs":{},"(":{"2":{"docs":{},")":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"docs":{}}}}}}}}}}}},"docs":{}}}}}}}}},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"y":{"docs":{},"l":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"{":{"docs":{},"n":{"docs":{},"}":{"docs":{},"f":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"y":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"{":{"docs":{},"n":{"docs":{},"}":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0024621878297572987}},"i":{"docs":{},"}":{"docs":{},"{":{"4":{"docs":{},"}":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"docs":{}}}},"+":{"docs":{},"a":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}}},"docs":{}}}},"b":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}}},"docs":{}}}},"c":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}}},"docs":{}}}},"d":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{}}}}},"^":{"2":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"m":{"docs":{},"}":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"docs":{}}}},"docs":{}}},"x":{"docs":{},"^":{"2":{"docs":{},"+":{"docs":{},"y":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"docs":{}}}}}}}}},"docs":{}}}},"docs":{}}}}},"docs":{}},"(":{"docs":{},"t":{"docs":{},"+":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}}}}}}}},"c":{"docs":{},"_":{"0":{"docs":{},"}":{"docs":{},"{":{"docs":{},"b":{"docs":{},"_":{"0":{"docs":{},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}}}}},"docs":{},"i":{"docs":{},"}":{"docs":{},"{":{"docs":{},"b":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{}}}},"b":{"docs":{},"(":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{}}}},"[":{"docs":{},"i":{"docs":{},"\\":{"docs":{},"h":{"docs":{},"a":{"docs":{},"t":{"docs":{},"{":{"docs":{},"h":{"docs":{},"}":{"docs":{},"_":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}},"i":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"h":{"docs":{},"a":{"docs":{},"t":{"docs":{},"{":{"docs":{},"h":{"docs":{},"}":{"docs":{},"_":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}},"\\":{"docs":{},"h":{"docs":{},"a":{"docs":{},"t":{"docs":{},"{":{"docs":{},"h":{"docs":{},"}":{"docs":{},"_":{"docs":{},"k":{"docs":{},"d":{"docs":{},"t":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"h":{"docs":{},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{},"}":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"e":{"docs":{},"^":{"docs":{},"{":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},"r":{"docs":{},"d":{"docs":{},"t":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"\\":{"docs":{},"h":{"docs":{},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"e":{"docs":{},"^":{"docs":{},"{":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}},"docs":{},"\\":{"docs":{},"h":{"docs":{},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{},"}":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"e":{"docs":{},"^":{"docs":{},"{":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}},"d":{"docs":{},"t":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"h":{"docs":{},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{},"}":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},"docs":{}}}},"docs":{}}},"h":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"l":{"docs":{},"a":{"docs":{},"m":{"docs":{},"b":{"docs":{},"d":{"docs":{},"a":{"docs":{},"}":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}},"n":{"docs":{},"(":{"docs":{},"n":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"}":{"docs":{},"{":{"4":{"0":{"0":{"0":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}}},"e":{"docs":{},"^":{"docs":{},"{":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003800475059382423},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147}},"e":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}}}}}}},"c":{"docs":{},"i":{"docs":{},"r":{"docs":{},"c":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}},"o":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407}},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"3":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"6":{"docs":{},"=":{"1":{"8":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}},"docs":{}}},"docs":{}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"2":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"6":{"docs":{},"+":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"3":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"5":{"docs":{},"=":{"2":{"7":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}},"docs":{}}},"docs":{}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"}":{"1":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"}":{"5":{"docs":{},"+":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"2":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"4":{"docs":{},"=":{"1":{"3":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}},"docs":{}}},"docs":{}}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}},"6":{"docs":{},"+":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"2":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"5":{"docs":{},"+":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"3":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"4":{"docs":{},"=":{"2":{"8":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}},"docs":{}}},"docs":{}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}}}}},"docs":{},"{":{"1":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"}":{"docs":{},"{":{"4":{"docs":{},"}":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"docs":{}}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}},"s":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"2":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"docs":{},"\\":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"g":{"docs":{},"a":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828}}}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.00350385423966363}}}}}},"i":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"f":{"docs":{},"t":{"docs":{},"y":{"docs":{},"}":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},"^":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"i":{"docs":{},"n":{"docs":{},"f":{"docs":{},"t":{"docs":{},"y":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"f":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"x":{"docs":{},"i":{"docs":{},")":{"docs":{},"g":{"docs":{},"(":{"docs":{},"x":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}},"x":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"[":{"docs":{},"m":{"docs":{},"]":{"docs":{},"g":{"docs":{},"[":{"docs":{},"n":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}},"n":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}}}},"+":{"docs":{},"\\":{"docs":{},"i":{"docs":{},"n":{"docs":{},"f":{"docs":{},"t":{"docs":{},"y":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"^":{"docs":{},"\\":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}},"|":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{},")":{"docs":{},"|":{"docs":{},"^":{"2":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"_":{"docs":{},"{":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"x":{"docs":{},"_":{"1":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{},"{":{"1":{"0":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"docs":{}},"docs":{}}}},"d":{"docs":{},"}":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"s":{"docs":{},"}":{"docs":{},"f":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"x":{"docs":{},"}":{"docs":{},")":{"docs":{},"d":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"x":{"docs":{},"}":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"a":{"docs":{},"^":{"docs":{},"b":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"{":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"}":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"{":{"docs":{},"h":{"docs":{},",":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}}}}}}}}}}},"x":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"d":{"docs":{},"\\":{"docs":{},"x":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"g":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"x":{"docs":{},"i":{"docs":{},")":{"docs":{},"d":{"docs":{},"\\":{"docs":{},"x":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}}}},")":{"docs":{},"d":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"}":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"h":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.024822695035460994}}}}}},"a":{"docs":{},"t":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.006618531889290012}},"{":{"docs":{},"h":{"docs":{},"}":{"docs":{},"_":{"docs":{},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},")":{"docs":{},"d":{"docs":{},"t":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"h":{"docs":{},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{},"}":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"u":{"docs":{},"}":{"docs":{},"_":{"docs":{},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976}},"\\":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"g":{"docs":{},"a":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"c":{"docs":{},"u":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"c":{"docs":{},"l":{"docs":{},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{},"[":{"1":{"1":{"docs":{},"p":{"docs":{},"t":{"docs":{},"]":{"docs":{},"{":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"l":{"docs":{},"e":{"docs":{},"}":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}}}},"docs":{}},"docs":{}}}}}}}}}}}}},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"d":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"_":{"docs":{},"j":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"i":{"docs":{},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"y":{"docs":{},"l":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"e":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},"{":{"docs":{},"g":{"docs":{},"n":{"docs":{},"u":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"}":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"d":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},"\\":{"docs":{},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"{":{"docs":{},"b":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{},"}":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}}}}}}}},"l":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"docs":{},"f":{"docs":{},"(":{"docs":{},"x":{"docs":{},"'":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"f":{"docs":{},"(":{"docs":{},"x":{"docs":{},"_":{"docs":{},"t":{"docs":{},")":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}}}}}}}},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},"=":{"docs":{},"z":{"docs":{},"^":{"2":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}},"docs":{}}}}}}}}},"[":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003800475059382423},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"\\":{"docs":{},"h":{"docs":{},"a":{"docs":{},"t":{"docs":{},"{":{"docs":{},"u":{"docs":{},"}":{"docs":{},"_":{"docs":{},"r":{"docs":{},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"docs":{},"d":{"docs":{},"t":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"{":{"docs":{},"f":{"docs":{},"}":{"docs":{},"^":{"docs":{},"{":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}}},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"{":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"}":{"docs":{},"{":{"docs":{},"@":{"docs":{},"{":{"docs":{},"}":{"docs":{},"c":{"docs":{},"c":{"docs":{},"c":{"docs":{},"|":{"docs":{},"c":{"docs":{},"@":{"docs":{},"{":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}},"|":{"docs":{},"c":{"docs":{},"@":{"docs":{},"{":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"^":{"docs":{},"{":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}},"v":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}},"\\":{"docs":{},"{":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"h":{"docs":{},",":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"}":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}}},"l":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"1":{"3":{"docs":{},"+":{"8":{"docs":{},"k":{"docs":{},"}":{"docs":{},"{":{"2":{"5":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}}},"docs":{}},"docs":{}}}}},"docs":{}}},"docs":{}},"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"}":{"docs":{},"}":{"docs":{},"{":{"1":{"0":{"0":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}}},"docs":{}},"docs":{}},"docs":{}}}}}}}}}}}}}},"k":{"docs":{},"}":{"docs":{},"{":{"4":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}}}}},"q":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.011652542372881356}}}},"o":{"docs":{},"g":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"_":{"2":{"docs":{},"(":{"1":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"+":{"docs":{},"n":{"docs":{},")":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"8":{"docs":{},")":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"docs":{}}},"docs":{},"e":{"docs":{},"(":{"1":{"docs":{},"+":{"docs":{},"e":{"docs":{},"^":{"docs":{},"v":{"docs":{},")":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"n":{"docs":{},")":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"docs":{}}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},"\\":{"docs":{},"c":{"docs":{},"d":{"docs":{},"o":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"m":{"docs":{},"b":{"docs":{},"d":{"docs":{},"a":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"}":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976}}}}}}},"o":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}},"m":{"docs":{},"e":{"docs":{},"g":{"docs":{},"a":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"_":{"2":{"docs":{},"^":{"0":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}},"1":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}}},"docs":{},"n":{"docs":{},"^":{"docs":{},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"(":{"1":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}},"3":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"docs":{},"n":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},"v":{"docs":{},"d":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"&":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"g":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"e":{"docs":{},"q":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}},"%":{"3":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"~":{"3":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}}},"q":{"docs":{},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"u":{"docs":{},"a":{"docs":{},"d":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}}},";":{"docs":{},",":{"docs":{},"\\":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}}}}},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"x":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178}}}}}}}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003355141754739138},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001340610935554917},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}}},"^":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346}}}}}}},"a":{"docs":{},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"^":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}},"\\":{"docs":{},"i":{"docs":{},"n":{"docs":{},"f":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}}}}}},"z":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.003787878787878788},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0035502958579881655}},"e":{"docs":{},"r":{"docs":{},"o":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009301089556205156},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0022169437846397467}},"?":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"p":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}}}},"s":{"docs":{},"(":{"5":{"docs":{},",":{"5":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"docs":{}}},"docs":{},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}}}}}},"n":{"docs":{},",":{"2":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}},"c":{"docs":{},"e":{"docs":{},"i":{"docs":{},"l":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{},"(":{"docs":{},"b":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{},"s":{"docs":{},"[":{"1":{"docs":{},",":{"2":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"docs":{}}},"docs":{}}}}}}}}}}}}}}}}}}},".":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"!":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},")":{"docs":{},":":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"i":{"docs":{},"p":{"4":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"w":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"3":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"o":{"docs":{},"o":{"docs":{},"m":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"6":{"4":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"+":{"docs":{},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}},"(":{"docs":{},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"*":{"docs":{},"*":{"2":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}},"docs":{}}},"\\":{"docs":{},"i":{"docs":{},"n":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"b":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}}}}}}}}}}}},"^":{"2":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}},"_":{"1":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"2":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}},")":{"docs":{},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{},"i":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"n":{"docs":{},")":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}},"x":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"y":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"z":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"=":{"1":{"docs":{},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"docs":{}}},"|":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0019151584793641674},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00268411340379131},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.004592240696753761}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"|":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007660633917456669}}}}}}}},">":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007972362476747276},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0036555645816409425}}},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793}}}},"|":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"|":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0014492753623188406}}},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{},"|":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"i":{"docs":{},"|":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"j":{"docs":{},"|":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{},")":{"docs":{},"|":{"docs":{},"^":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"docs":{}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"i":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"r":{"docs":{},"e":{"docs":{},"}":{"docs":{},"(":{"docs":{},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},"^":{"docs":{},"t":{"docs":{},"|":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"|":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"i":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"i":{"docs":{},"m":{"docs":{},"}":{"docs":{},"(":{"docs":{},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},"^":{"docs":{},"t":{"docs":{},"|":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"c":{"docs":{},"c":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"z":{"docs":{},"|":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"y":{"docs":{},"|":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}},"↩":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0008618213157138753},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455}}}},"↪":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005745475438092502},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"⏫":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"⏹":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}},"▶":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00038303169587283346},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"◀":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"6":{"4":{"docs":{},"c":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}}},"docs":{}},"docs":{}}},"docs":{}}}}}},"✖":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393}}}},"❎":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002872737719046251},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0015321267834913339},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393}},"❗":{"docs":{},"️":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"9":{"1":{"docs":{},"b":{"docs":{},";":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"docs":{}},"docs":{}}},"docs":{}}}}}},"➕":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}},"➖":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00047878961984104186},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"➡":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002393948099205209},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.006498781478472786}}}},"⭐":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00009575792396820837}}}},"️":{"docs":{},"↪":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00019151584793641673}}}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"0":{"1":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"docs":{}},"3":{"docs":{},"c":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"4":{"0":{"7":{"docs":{},";":{"docs":{},"⬆":{"docs":{},"️":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}}},"docs":{}},"docs":{}}},"docs":{}}}},"⏫":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"4":{"0":{"7":{"docs":{},";":{"docs":{},"⬆":{"docs":{},"️":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00013287270794578793},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"≠":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"⬅":{"docs":{},"️":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"⬆":{"docs":{},"️":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"?":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00026574541589157585},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.004433696090286175},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"d":{"docs":{},"i":{"docs":{},"v":{"docs":{},"i":{"docs":{},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}}},"(":{"docs":{},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"x":{"docs":{},"_":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"☝":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}},"➗":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"š":{"docs":{},"e":{"docs":{},"v":{"docs":{},"č":{"docs":{},"í":{"docs":{},"k":{"docs":{},"o":{"docs":{},"v":{"docs":{},"á":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}},"—":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"–":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.004517221908526256},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}}},"length":30722},"corpusTokens":["!","!!","!!this.fiance;","!(*thi","!(a","!(idx","!(isnan(input_x)","!)","!=","!==","!counterclockwise(p,","!haskey(pairs,","!input[start..].is_empty()","!node.right)","!singular","!t","\"","\"!\"","\"\"","\"\"\"a","\"\"\"calcul","\"\"\"comput","\"\"\"contain","\"\"\"creat","\"\"\"determin","\"\"\"find","\"\"\"i","\"\"\"initi","\"\"\"pick","\"\"\"propos","\"\"\"return","\"\"\"set","\"\"\"the","\"\")","\"\"))","\"\",","\"\",:code","\"\";","\"\"}","\"#{@name.rjust(20)}:","\"#{a[i]}\\t#{servois_numbers[i]}\\t\\t#{easter_dates[i]}\"","\"#{node.id}","\"#{prefix}","\"#{temp.id}","\"$($_[0])`t$($_[1])\"","\"$1\")","\"$2\")","\"$2\\pi$\"])","\"$\\pi$\",","\"$a\"","\"$year`t$(calcul","\"%d","\"%d\",(21","\"%g\\n\"","\"%s\"","\"(\"","\"(bibbiti","\")","\")\";","\"),","\");","\"++\"","\",","\",error:","\",our","\".dat\")","\".dat\",\"w\")","\".join(p.nam","\"0\"","\"0\")","\"0\"),","\"0\",","\"0\":","\"0.1.11\"]","\"1\"","\"1\")","\"1\")))))","\"1\"),","\"1\",","\"1\":","\"19","\"2d","\"2d_sample_low_res.dat\"","\"8bit","\":\");","\"?\"))","\"[#]\\nmodulu","\"[#]\\nqueue","\"[#]\\nrecurs","\"[#]\\nstack","\"[#]\\nsubtract","\"[#]\\ntime","\"[#]\\nveloc","\"[#]`nmodulu","\"[#]`nsubtract","\"[#]~%modulu","\"[#]~%queue","\"[#]~%recurs","\"[#]~%stack","\"[#]~%subtract","\"[#]~%time","\"[#]~%veloc","\"[0.0","\"[1.0","\"[2.0","\"\\\":","\"\\n\"","\"\\n\")","\"\\n\".join(map(str,","\"\\n\".join(str(x)","\"\\ndecoding...\")","\"\\t\"","\"\\t\")","\"\\t\"))","\"\\t\\t\"","\"]\");","\"__main__\":","\"a","\"a\"","\"a11","\"a12","\"a13","\"a21","\"a22","\"a23","\"a31","\"a32","\"a33","\"absz\"","\"adaptive\"","\"affin","\"andgate\"","\"angle\"","\"anim","\"applic","\"approxim","\"april","\"b","\"b\"","\"b\",","\"barrier.\"","\"bbbbbbbb\"","\"beautiful.\"","\"better\"","\"bfssimple\"","\"bibbiti","\"bibbity_bobbity\"","\"bins\"","\"black\"","\"blend\"","\"blurred.\"","\"bottom\"","\"bucket","\"c\",","\"caesar","\"calcul","\"call","\"chao","\"check","\"check.png\"","\"check.png\".","\"check.tex\"","\"children","\"circl","\"coding...\")","\"coincidence\"","\"combin","\"complet","\"complex","\"container/heap\"","\"cos(x)\"","\"cosines\"","\"count","\"creat","\"current","\"cyclic\"","\"d\"]","\"data","\"decod","\"decoding:","\"delta","\"depth","\"determin","\"dfsinorder\"","\"dfspostorder\"","\"dfspreorder\"","\"difference:","\"dit","\"divid","\"doubl","\"echelon","\"encod","\"endod","\"error:\"","\"estim","\"euclidean","\"euclidmod\"","\"euclidsub\"","\"exampl","\"exp_fn\"","\"exp_fn_log\"","\"f\",","\"fact.\"","\"failed\"","\"fern","\"fill","\"fillsteps\"","\"find","\"finger","\"fmt\"","\"folder='../haskell'\"","\"frequenc","\"ftexample\"","\"ftgaussian\"","\"full","\"g\",","\"game\"","\"gaussian","\"gevis\"","\"gift\",","\"gnuplot","\"gnuplot_1d_sample\"","\"gnuplot_2d_sample\"","\"gnuplot_2d_sample_colorbar\"","\"gnuplot_exp_tex\"","\"gnuplot_histogram\"","\"gnuplot_scatterplot\"","\"gnuplot_sine_cosine_customtics\"","\"gnuplot_sine_cosine_label\"","\"gnuplot_sine_cosine_linetype\"","\"gnuplot_sine_cosine_log\"","\"gnuplot_sine_cosine_movekey\"","\"gnuplot_sine_cosine_movekey2\"","\"gnuplot_sine_cosine_nokey\"","\"gnuplot_sine_cosine_notics\"","\"gnuplot_sine_cosine_square\"","\"gnuplot_sine_cosine_title\"","\"gnuplot_sine_cosine_wave\"","\"gnuplot_sine_cosine_wave_range\"","\"gnuplot_sine_wave\"","\"gnuplot_test\"","\"grid","\"h\"]","\"ha","\"histogram","\"histograms\"","\"how","\"hsv\"),","\"hsv1\"","\"hsv2\"","\"hsv3\"","\"hsv4\"","\"hsv5\"","\"huffman_tree\"","\"if","\"im(z)\"","\"imaginarysplitop\"","\"integr","\"invalid","\"it'","\"languag","\"left\"","\"length:","\"levels\"","\"lonely\"","\"make","\"man\",","\"march","\"math\"","\"math/rand\"","\"meton","\"michael","\"mont","\"multipl","\"n","\"nandgate\"","\"norgate\"","\"not","\"notation)","\"notgate\"","\"on","\"orgate\"","\"origin","\"out.dat\"","\"out.tex\"","\"output00000.dat\"","\"output{}.dat\".format(str(i).rjust(5,","\"passed\"","\"passover\"","\"patching\"","\"percent","\"percentag","\"perform","\"period","\"phase","\"pivot\"","\"play","\"plot","\"probabl","\"pseudo","\"public","\"purple\"","\"queue","\"radix2\"","\"radix2positive\"","\"radix8\"","\"ramp","\"re","\"re(z)\"","\"real","\"realsplitop\"","\"recurs","\"reduc","\"rel","\"remov","\"result","\"return","\"rgb1\"","\"rgb2\"","\"right\"","\"rijndael\"","\"roll","\"rot13\"","\"rotat","\"round","\"sample_data.dat\"","\"sawtooth","\"scale\"","\"scatterplot_data.dat\"","\"semi","\"servoi","\"set","\"shade\"","\"shear\"","\"shift","\"sierpinski.dat\"","\"simpl","\"simplemontecarlo\"","\"sin(x)\"","\"sin(x)\",","\"sine","\"sine_cosine_plot.png\"","\"sines\"","\"sloshing\"","\"smeared\"","\"sobel","\"solut","\"sort\"","\"split_op_method\"","\"squar","\"squarecircle\"","\"stable\"","\"stack","\"stuff\"","\"synod","\"take","\"taylor","\"test\"","\"textbook\"","\"the","\"thi","\"time\"","\"top\"","\"trained\"","\"tree\"","\"triangl","\"unstable\")","\"utf8\"","\"utility.h\"","\"vx:\"","\"w\")","\"wait.","\"walker\",","\"what'","\"woman\",","\"world'","\"wrap","\"x","\"xorgate\"","\"y\")(uniform01,","\"year","\"year\\tservoi","\"year`tservoi","\"yes,","\"you","\"z2\"","\"{year}","\"{}\",","\"{}\\t{:","\"{}\\t{}\\t{}\",","\"{}\\t{}\\t{}\\n\".format","\"|\",","\"~%\")","\"~8a~18a~a~%\"","\"~a","\"~d~%\"","\"~f~c~f\"","\"~{~a~%~}\"","\"~{~f","#","#!/usr/bin/env","#'","#'*","#'+","#'format","#'make","#(*","#(+","#(0","#(1","#(4","#(7","#(appli","#(c/+","#(if","#(math/log","#(rand","#(str","#[derive(clone)]","#[derive(clone,","#[derive(debug)]","#[derive(debug,","#\\tab","#a","#c(0","#defin","#endif","#freq","#ifndef","#includ","#lang","#messag","#node","#simpl","#{i}\",","#{round}\"","#{self.lonely?","$","$((128","$((21","$((64","$(100","$(128","$(64","$(get","$(join((\"\",","$(join((a[2],","$(join((b[1],","$1","$2","$a","$a)","$a,","$a;","$a[1],","$a[2],","$b","$b)","$b):","$b,","$b;","$b[0],","$b[1],","$b[2],","$b];","$c","$c,","$c[0],","$c[1],","$child)","$child):","$child;","$children","$children;","$d","$d)","$e","$e)","$fianc","$groupsiz","$i","$i)","$i++)","$id,","$id;","$k","$k)","$m","$m)","$man","$man)","$man):","$man;","$match","$match)","$match):","$match;","$men","$men,","$men;","$n","$n)","$n;","$name;","$node","$node;","$numofchildren):","$numofrows,","$outputpoint","$outputpoints.add($point)","$p","$percenterror\")","$picount","$picount++","$piestim","$piestimate\"","$piestimate\")","$point","$positionx,","$positiony,","$prefer","$preference)","$preferences):","$preferences;","$q","$q)","$radiu","$radius=1)","$shapepoint","$shapepoints)","$shapepoints.count)]","$shapepoints[$(get","$solut","$stack","$stack[]","$temp","$temp[0])","$temp[1])","$thi","$tmp","$tree","$tree):","$unmarri","$woman","$woman)","$woman,","$women","$women):","$women);","$x","$x,","$x;","$x[$i","$x[$i]","$x[0],","$x[1],","$x[2],","$y","$y)","$y,","$y[$i]","$year","$year)\"","${22","${d","${girl.preferences.map(p","${guy.fiance.name}`);","${guy.preferences.map(p","${p.y})`));","%","%%","%))","%.1f,","%.1f][x]","%.1f][y]","%.1f][z]","%0.2f\\n\"","%1","%1)","%1))","%1)))]","%2)","%2))","%2)))]","%3","%d\",","%f%%\\n\",","%f\\n\",","%lf\\n\"","%n))","%s',","%s,","%s\\n\"","%s][x]","%s][y]","%s][z]","%t\\n\",","%}","&","🆔","🆕","🆕🌕🆕","🆕🌲🆕","🆕🌲⭐️","🆕🎰🆕","🆕⏩⏩","🆕⏹⏫❗️","🆕☝️🆕","🌀","🌀tree❗️","🌌","🌌🐕","🌕","🌲","🍆","🍇","🍉","🍥","🍥tree❗️","🍨","🍨🍆","🍨🐚🌲🍆","🍪🔤th","🍬⏹","🍭","🍭🐽","🍭binary_tree❗️","🍭tree❗️","🍼","🏁","🏃‍♀️","🏃‍♀️🐇🤡","🏢","🏢tree❗️","🏧","🏧a","🏧b","🐇","🐔","🐕","🐨","🐻","🐽","👌","💭","💯","💯samples❗️","📗","📥","📪","📫","🔁","🔂","🔐","🔘","🔡","🔡return❗❗️️","🔢","🔤","🔤%🔤🍪❗️","🔤🌀","🔤🍥","🔤🍭","🔤🏢","🔤🔤","🔤🥞","🔤run","🔤the","🔤tree","🔼","🖍🆕","🖍🆕var_a","🖍🆕var_b","🖍children","🖍id","🖍radiu","🖍var_a","🖍var_b","😀","🙅","🙌","🚮","🤜128","🤜64","🤜depth_count","🤜id","🤜pi_estim","🤜point_x","🤜radiu","🤡","🤷‍♀️","🥞","🥞tree❗️","🥧🕊💯","🦃","🧒","&&","&&&\\color{blue}6&5&4","&&&\\color{green}6&\\color{blue}5&4","&&&\\color{red}1&2&3","&&&\\color{red}1&\\color{green}2&3","&&&\\color{red}1&\\color{green}2&\\color{blue}3","&&&\\color{red}6&\\color{green}5&\\color{blue}4","&&1&2&3","&&1&\\color{green}2&\\color{blue}3&","&&6&\\color{red}5&\\color{green}4&","&0","&0.04","&0.16","&0.22","&0.24","&0.28","&0.5","&0.85","&1&2&\\color{blue}3&&","&4","&4&5&6","&6&5&\\color{red}4&&","&;&","&=","&=x(t)","&[complex])","&[f64])","&[f64],","&[point])","&[vec],","&\\time","&b,","&barnsley_hutchinson,","&barnsley_probabilities,","&builder,","&c,","&cb,","&codebook);","&count)|","&e","&encoder](char","&eqns)","&f64","&heap","&hull[hull.len()","&matrix)","&mut","&n);","&n.children","&n.children[..]","&node)","&node{id:","&operators)","&opr)","&opr));","&option","&par,","¶meters,","&point)","&point,","&result);","&self)","&self.codebook[&c]).join(\"\")","&self.data[row","&start);","&str)","&str,","&tmp","&tree,","&vec![2.0,","&vel,","&women[man","&x);","&x[0]);","&x[1]);","&x[2]);","'","'#0000ff',","'#00ff00')","'#00ff00',","'%","''","'''","'''iter","'''perform","'''random","''.join(decoded_message)","''.join(messag","'':","'(\"the","'(((node1","'(g0)')","')","'++'","',","',num2str(euclidmod(64","',num2str(euclidsub(128","'../../data/rand.dat'","'0'","'0')","'0'),","'0',","'0';","'1')","'1',","'1';","'100'),","'1000'),","'1001'),","'101'),","'110'),","'1100'),","'1101'),","'111')]","'2pi'","';","'[#]'","'\\0';","'__main__':","'a')","'a',","'a';","'april","'bibbity_bobbity'","'children","'children'","'data'","'dequeue'","'domain.png'","'enqueue'","'eqns'","'f(z)=z^2'","'front'","'i']]]","'id'","'list","'list))","'march","'modulu","'num","'num_child'","'num_rows'","'o'],","'pass","'pop'","'psetf',","'push'","'queue","'recurs","'red',","'rows'","'size'","'stack","'states'.","'subtract","'thi","'time","'top'","'vector","'veloc","'y'],","(","(!(o","(!))","(!empty($thi","(!equal(end_point,","(!girl.hasfiance)","(!heap","(!isa(current,","(!node.left","(!preferredmates.isempty())","(!prefers_partner(woman","(!queue_empty(&q))","(!queue_empty(q))","(!stack_empty(&stk))","(!stack_empty(stk))","(!tmp)","(!tree)","(!woman","(\"0\"","(\"bottom\"","(\"check","(\"output\"","(#560),","($a","($b","($d","($i","($man","($men","($numofrow","($point[0]","($point[1]","($prefer","($temp","($thi","($tree","($unmarried);","($woman","($women","(%","(%)","('#ff0000',","('_',","('i',","('o',","('t',","('y',","((","((!))","((!),","(($1","(((x+mu[1])^2)/(2*sigma^2)","((/","((1,","((10,10)","((128","((13","((1_f64","((2","((21","((22","((64","((:+","((>","((^","((a","((ab.getx()","((and","((avg","((b","((b.x","((d","((defin","((dft","((double)","((double)i","((fft","((format","((i","((i,","((j","((man,","((node","((par.x","((par.x[i]","((point(0,","((r1,","((ret","((stride","((tmp","((wrap","((x","((y+mu[2])^2)/(2*sigma^2)))","()","())","(),","();","(*","(*'","(*)","(*cb)[node.char]","(*dst)[len","(*dst)[len]","(*input","(*input);","(*it)","(*vel)","(+","(+)","(.*),","(.+)","(/","(/)","(/=p0)","(0","(0);","(0,","(0,0)","(0,0)).","(0..((n","(0..(size","(0..a.row","(0..iters)","(0..iters).into_iter().map(|_|","(0..n)","(0..n).step_by(strid","(0..num_child)","(0.0,","(0.4%).","(0.5","(0.5,","(1","(1+","(1,0.5),","(1...n).each","(1.0,","(1/2)","(100.0","(12","(128","(13","(15","(15,","(17","(19","(19a+m)~\\%~30","(2","(2*pi)","(2*sigma^2))","(2,","(2.0","(20","(2020..2030).to_a","(21","(21+d)~\\%~31,","(22","(2^2","(2^{10}).","(2b+4c+6d+n)~\\%~7.","(2d)","(3,","(32","(4","(4+k","(4000)","(5","(5,","(500,","(6,","(64","(7,","(9,","(:constructor","(:requir","(;","(;;)","(=","(>","(>).","([0.5,","([math]::pi))","([math]::pi))\"","([math]::pow($x,","(\\(px,","(\\(w,","(\\(x,y)","(\\cos(","(\\cos(2","(\\delta","(\\e","(\\k","(\\mathbf{r})","(\\mathbf{x})","(\\n","(\\psi_0);","(\\x","(^","(_,","(a","(a),","(a,","(a.i","(a.siz","(a/(a+1))^j","(a[(i,","(a[i","(a[i,","(a[i][col","(a[max_index,","(a[pivot","(a[pivot][col]","(a[pivot_i,","(a[r][col","(a[row,","(ab","(ab.gety()","(ab.magnitude()","(abs(sin(real_f(z(x,y))*pi)**thresh)","(actual","(ad)","(addition,","(albeit","(almost","(also","(and","(aold","(appli","(array","(array,","(assert","(assoc","(assum","(at","(atan","(auto","(auto&","(axis_num)","(b","(b),","(b.i","(b.x","(b[i]","(bachelors.nonempty)","(barely)","(becaus","(bf","(bfs)","(bi","(bin($1)):(1)","(bit","(blue,","(both","(bound","(boyfriend,","(but","(c","(c',","(c)","(c),","(c,","(c.data[cur_loc.x","(c.i","(c.x","(c/*","(c/complex","(c/exp","(c1,","(c_prime[i]","(candid","(canva","(case","(ccw(points[m","(chao","(char","(char)i;","(char,","(char?","(child","(children","(chin123)","(chosen","(cipher),","(clear)","(clojure.pprint/pprint","(clojure.set/map","(coder","(coeffici","(coerc","(col","(col+1):col","(comp","(compar","(complement","(complex","(complex::new(0.0_f64,","(computu","(computus)","(concat","(concaten","(concatmap","(cond","(const","(copi","(cough","(count","(count($tre","(counts[char]","(createtre","(cryptosystem),","(curpoint","(curr_point","(curr_row),","(current","(d","(d,","(d[i]","(data)","(date)","(dec","(decf","(decod","(def","(default","(defin","(defmacro","(defn","(defparamet","(defstruct","(defun","(defvar","(denot","(depend","(depthcount","(df","(dfs)","(dft","(dft)","(dft),","(dft,","(diagon","(display","(displayln","(div","(divf","(dot","(doubl","(double)i","(double)rand()","(double,","(dp","(drand()","(drop","(dt),","(dt^2)","(dx","(e","(e)","(easter","(either","(elemindex)","(elt","(end","(endpoint","(envis","(eq","(eql","(eqns[pivot][i]","(especi","(euclid","(euclid_mod","(euclid_mod*","(euclid_sub","(euclid_sub*","(even","(even?","(evol","(exclud","(exp","(export","(f(x_proposed)","(f(z)","(f*g)(x)","(f*g)[n]","(f64,","(f_val_ab","(factor","(fail)\");","(fft","(fft)","(fft).","(fftw_complex*)x,","(fftw_complex*)y,","(fifo),","(filter[i","(fingers),","(first","(flet","(float)","(float):","(float,","(floor","(fn","(follow.partn","(for","(format","(found","(fraction","(freq","(freq.empty())","(front","(front_pointer.get()","(func","(gaussian_valu","(gcd","(gcd)","(get","(gift)","(girl.prefers(guy))","(granted,","(grid[x][y]","(h)","(hash","(haskey(weights,","(heap","(heap.length","(heat)","(helper","(here","(here,","(homework","(hopefully)","(hue,","(hull[i]","(husband,","(hutchinson","(i","(i)","(i)'","(i)^*","(i,","(i..a.rows).rev()","(i.0","(i.e.","(i64,","(if","(ifss),","(ifss).","(in","(inbounds(canvas.shape,","(inbounds(size,","(inc","(incf","(index","(index)","(inner","(input_i","(input_x","(insert,","(instead","(int","(int)n];","(int,","(integer?","(intercal","(intercalate)","(intercalate,","(interest.partn","(interleav","(intermediat","(into","(invers","(inverse)","(is_leaf(tree))","(it","(it',","(items)","(iter","(j","(jspp)","(jspp),","(just","(k","(k)","(k,","(k..a.cols).rev()","(k_i)","(keep","(kernel_size,","(key","(kineticop","(kstep","(label","(lambda","(last","(leaf","(leav","(left","(left)","(left),","(leiosos):","(length","(length(a)","(length(filter)/2)","(length(n.children)","(let","(let'","(let*","(lifo),","(like","(list","(listarray","(littl","(loc[0]","(local","(lonelyfollows.count","(loop","(m","(m,","(m,_))","(m.fromlist","(make","(man,","(map","(map,","(map.entri","(map[c]","(mapcar","(mapv","(mat1.shape[0]","(mate","(math.abs((avg","(math.abs(a),","(math.pow(1","(math.random()","(math/ab","(math/pow","(matrix","(maximum","(mayb","(merg","(method","(middle),","(mod","(modulo","(mont","(more","(mostdesir","(mult","(multipl","(n","(n(v","(n)","(n),","(n.children)","(n.children.size())","(n.children_size)","(name","(nconc","(negative?","(new_x[k","(newline)","(next","(nlse):","(no","(node","(node)","(node.children.size())","(node.isleaf)","(node.left","(node.left)","(node.leftchild","(node.right","(node.right)","(node.rightchild","(node2","(nodeprioritylist.count","(normal","(normalized)","(note:","(np.abs(np.sin(np.pi","(np.pi","(np.sqrt(np.pi)","(null","(num","(num_row","(number","(numrow","(o","(odd","(odd?","(of","(old_val","(old_valu","(on","(on)","(one","(one:","(oper","(optional)","(or","(ord","(orthodox)","(out","(output","(p","(p)","(p.getx()","(p.i","(p.x","(p.x,","(p1","(p1:p2:ps)","(p2.0","(p2.1","(p2.i","(p2.x","(p2:ps)","(p2[0]","(p2[1]","(p3.0","(p3.1","(p3.i","(p3.x","(p3[0]","(p3[1]","(p[1],","(pa","(par.im_time)","(par.k","(par.timestep","(par.x","(par.x[i]","(partial","(partit","(partition)","(person","(pi","(pi_estim","(place","(po","(point","(point)o;","(point.i","(pointonhul","(pointonhull.equals(hull.get(0)))","(pop","(pop())","(popularli","(pos_x","(position,","(post","(potentially)","(potentialnextpointonhul","(pow((1","(pow(1","(print","(println","(priorityqueue.data.length","(priorityqueue.size()","(probabl","(product","(propos","(psetf","(ptr)","(push","(push())","(px","(q","(q.size()","(queue.count","(queue.length","(queue.size()","(queue_empty(q))","(quot","(r","(r,","(r,r)","(r1,","(r2,","(radix","(rand","(rand_max));","(random","(randomr","(rang","(re","(read,","(real","(rear","(receiver).","(recur","(red).","(red,","(reduc","(remov","(repeat","(repeatedli","(requir","(rest","(ret.size()","(return","(right","(rn,","(rnd","(roughli","(row","(row+1):row","(row,","(rowcount","(rstep","(s.size()","(s:p1:p2:ps)","(s:ss)","(scale","(second","(self.x,","(sender)","(servoi","(servois)","(set","(setf","(show","(show)","(show,","(shown","(similar","(size","(size)));","(size_t","(size_t)rand()","(so","(solar)","(sometim","(sort","(sort,","(sorton,","(split","(sqrt","(stack.count","(stack.length","(stack.size()","(stack_empty(stk))","(standard","(std::size_t","(std::uint32_t","(step","(stk","(stormer","(str","(strawberry)","(stride","(string","(string,","(struct","(such","(sum)","(svref","(t","(t)","(t,","(t1:t2:ts)","(t2,","(tabl","(tail","(take","(target","(target,","(tdma)","(temp","(the","(there","(thi","(this.mat","(thoma","(though","(time","(time,","(time:","(time:time,","(time_sv,","(time_vv,","(timestep","(timesv,","(timevv,","(to","(top","(top())","(top_pointer.get()","(tree","(tree,","(tree._children.count)","(tree.children.length)","(tree.siz","(twiddl","(u_1","(ubsan)","(uncurri","(unless","(unsign","(updat","(use","(usize,","(v","(v1","(v=2),","(val","(valu","(var","(variance)","(vec","(veloc","(verlet","(w,","(we","(wfc","(when","(where","(which","(with","(within","(without","(woman)","(woman.prefers(this))","(women!theone)","(x","(x'","(x',","(x*x","(x*x)","(x,","(x,y)","(x,y),","(x.0","(x.len()","(x.size()));","(x:xs)","(x:y:rest)","(x[i]","(x^2","(x_i)","(x_t","(xa,","(xb","(xb,","(xc","(xc,","(xold,","(xx,","(y","(y*y)","(y,","(yb","(yc","(year","(yes,","(yet","(z","(z)","(z[i]","(z_1","(zero:","(zero?","(zerop","(zip4)","({","(|\\psi(x)|^2)","(~",")","))","));",");","*","*)","*));","*)a,","**","**data;","**tmp","*.aux,","*.ep","*/","*/)","*=","*_","*a,","*array,","*b)","*children;","*codebook","*codebook,","*computus(int","*data;","*dequeue(struct","*dst","*element)","*first_point_it);","*group,","*huffman_tre","*hutchinson_op,","*in","*in,","*input));","*input;","*k;","*ke;","*lh","*lhs;","*man","*map.entry(c).or_insert(0)","*n","*neighbors)","*node","*node)","*node,","*nodeheap)","*opr,","*out","*out,","*par,","*partner;","*pe;","*points,","*points.iter().min().unwrap();","*prefers;","*probabilities,","*q)","*q,","*queue.front();","*ret","*rh","*rhs;","*self","*shape","*sooner*","*stack.top();","*stack_pop(struct","*stk)","*stk,","*str","*time","*time,","*tmp","*tmp;","*v;","*vel","*vel,","*wfc;","*woman","*x,","*x;","+","+))","++","++=","++i)","++input)","++it)","++row;","++str)","+1","+1,","+1.","+3].","+=","+y^2",",",",(sqrt",",divisor)))",",place",",return",",x_n,",".",".\"\"\"",".*",".*)",".+","..","...","...)}.","...this.data.slice(target)];","../gnuplot/plot_output.plt","..]","./barnsley.cpp",".01)",".1",".2",".266]",".3",".4",".5*acc*dt*dt",".5f]\".format(solution[i]))",".=",".average()",".code",".collect()",".collect();",".collect(collectors.tolist());",".collect::>();",".count!(a",".csv",".dat",".distinct()",".doubl",".equ",".exp()",".extern",".fill(new",".filter(|i|",".flatmap(bit",".fold(0.0_f64,",".for_each(|i|",".getasdouble();",".global",".groupby(identity)",".intel_syntax",".into_iter()",".iter()",".limit(ntrials)",".long",".map((temp,",".map(v",".map(|(&value,",".map(|_|",".map(|i|",".map(|k|",".mapvalues(_.length)",".map{",".next_index",".png",".rodata",".section",".select(n",".sorted(comparator.comparingdouble(point",".str",".string",".sum()",".sum::()",".take(n)",".take(n_trials)",".tex",".text",".tolist();",".tsv",".zip(energy_r.into_iter())","/","/)","/*","/**","//","///return","//add","//alway","//find","//found","//print","//shift","//system.out.println(\"us","//test","//tree.dfsrecursiveinorderbinary();","//utility_h","/=","0","0!","0\"","0'","0)","0)'.","0))","0)))","0))))","0));","0),","0).","0);","0)]","0+127","0,","0,0","0.","0.,","0..","0..((stride","0..(a.col","0..(n","0...n","0..64","0..len(w)","0..min(a.cols,","0..n","0..n_item","0..par.r","0..par.timestep","0..re","0..row","0..self.col","0..x.len()","0.0","0.0)","0.0));","0.0),","0.0);","0.0)]","0.0,","0.001","0.01","0.01)","0.01))","0.01);","0.01d0","0.025%","0.025\\%","0.037","0.04","0.04,","0.05,","0.053","0.07","0.07,","0.07]","0.07];","0.0:","0.0;","0.0]","0.0],","0.0];","0.0][x]","0.0]]","0.0_f64));","0.0_f64).powi(2);","0.0_f64);","0.0_f64,","0.0im","0.0}","0.0},","0.0};","0.0}};","0.1","0.1)","0.1,","0.13307711243511333","0.15","0.15,","0.16,","0.18541942067815853","0.1\\time","0.2","0.2(x+1)^2}","0.2,","0.22,","0.23","0.23648916187439406","0.23842162678327328","0.24,","0.25","0.25.","0.26","0.26,","0.26666668","0.27999628668153087","0.28,","0.3","0.30699091691896263","0.3548405553754319","0.35589625594005647","0.361307926046027","0.3692102429804389","0.4","0.4%","0.4%).","0.40610861857701597","0.42","0.42%","0.44","0.44),","0.44],","0.5","0.5)","0.5*(abs(f(z(x,y)))","0.5*(rand(shape_points)","0.5*acc","0.5*opr.v*par.dt)","0.5*par.k.^2*par.dt)","0.5*wfc_c.*ifft((par.k.^2)","0.5,","0.58),","0.587785252292473","0.5877852522924731","0.5877852522924732","0.5877852522924734","0.592m","0.5]),","0.5_f64","0.5d0","0.6075688534409027","0.618m","0.6338943724188091","0.6351126027850458","0.75)","0.75))","0.75.","0.75_f64.sqrt()},","0.7605752608745506","0.7796784902862803","0.789554555806735","0.7972009737623846","0.85","0.85,","0.8661873069668018","0.8666667","0.8686860241215444","0.9510565162951535","0.9510565162951536","0.],","0.}","0.},","0/1","0/1a","00","000","0000","00000000","00000000000010100000000","00000001","00000010","00000100","00000101","00001010","0001","00010000","00010100","001","0010","00100100000000000000000","0011","01","0100","01000000","01000010010111011110111000100101110.","0100101010110100","0101","01010000000000000000000","0110","0111","01110011110110011010110000111101100","01110011111010110000100100111110101","0111101,","01111110","01111111","0:","0:bnum","0:length(a)","0:n","0;","0]","0][x]","0_f64;","0aa","0d0","0d0)","0f,","0s","0u;","0x+0y+0z=1,","0x00ff00ff)","0x0f0f0f0f)","0x1","0x33333333)","0x55555555)","0}","0},","0};","0}};","0❗️","0❗️❗️","1","1!","1\"","1\"));","1🤛","1'","1's.","1)","1)(rng());","1))","1)))","1)))))","1)),","1)).rev()","1));","1)*pi*i*k/n)","1)*pi/(xmax)),","1),","1).","1)..a.col","1)..a.row","1).rev()","1):","1);","1)]","1)}","1)}{2a}.","1+1/a","1,","1,0.5","1,000","1,000,","1,000,000","1,000,000\"","1,000,000)","1,000,000.","1,1","1,1)","1,1).","1.","1.,","1..","1...numchildren","1..=((n","1..a.row","1..n","1..size","1.0","1.0)","1.0)(rng());","1.0))","1.0),","1.0);","1.0+0.0im","1.0+0.0im;","1.0+2.44929e","1.0,","1.0.","1.00","1.00)","1.00001","1.001001","1.0]","1.0]*[","1.0]*[1.0","1.0],","1.0]])","1.0_f64);","1.0f,","1.0f\\n\",","1.0im","1.0im]","1.1\\time","1.2","1.2246467991473532e","1.22465e","1.273","1.5333333","1.6","1.60),","1.6],","1.71","1.83697e","1.85","1.9","1.9m","1.]).reshape(3,","1.],","1.barnsley,","1.box,","1.bucket","1.canny,","1.cooley,","1.graham,","1.jarvis,","1.metropolis,nichola","1.sanderson,","1.step","1.upto(a.s","1.venerabilis,","1.wikipedia:","1.williams,","1/(n(v","1/(n(v+1,","1/0","1/4000","1/6,","1/a)**v","10","10)","10))","10)))","10):","10)?","10,","10,000","10,000\"","10,000,","10,000,000","10,000.","10,11),","10.","10.,","10.0","10.0),","10.0,","10.0/512","10.0/512,","10.0],","10.25","100","100%","100)","100))","100))))","100).floor();","100).toint","100*abs(math.pi","100,","100.","100.0","1000","1000,","10000","10000000","10000000❗️","10000001","10000010","10001011","1001","1001.001","100;","100_000","100}%\");","101","1010.01","1023","1023,","1023?","1024","1040","10:","10;","10]","10]],","10^{","10^{110}.","10^{16}","10^{16},","10^{19}","10^{38}","10^{41}","10^{50}","10^{76}","10^{76}.","10_000,","10cm","10cm,","10d","10d0","10e^{","10s,","10},","10}^{10}","10}};","10❗","10❗🍪❗️","10❗️❗️","11","11));","11),","11.0","110","1101:","1105199103","1110","1110010101,","1111","11111111","11aa","11z","11},","11~\\%~30","12","12🤛","12)","12))","12));","12),","12,","12,000,","12.0","123","123,","123\\times456=56088,","126","127","127.","128","128*77)","128/192","12]","12]#","12],","12ab","12ba","12cm,","12},","13","13,","13.","130,000","130,000,","13aab","13bba","13tba","14","14));","14),","14,","14.0","14.0,","14.0}};","14},","14}{11}","15","15));","15),","15);","15,","15.0","15.0,","15.0},","1536","15;","15},","16","16)","16+1.0im","16+1.0im;","16.5.","16:9)","16]","16]#","16],","16im","16im;","17","17,","17,000).","1777,","18","180","1800","1800's.","1800,","1805","1813.","1816.","1876.5.servois,","18\\\\","18]=[4+1,","19","19)","19))","19.","19.347","1900.","1953.2.wikipedia:","1958","1958.2.wikipedia:","1965","1965.","1967.3.jampour,","1970.6.wikipedia:","1972.","1973","1973.","1977","1978","1978.3.flajolet,","1981.11.wikipedia:","1985.4.bhayani,","1986.","1994.","1994.6.sanderson,","1999.2.dictionary.com","19;","19a","19th","19th.","1:","1:(col","1:1","1:2","1:2:(color($1,$2))","1:3","1:axis_num","1:col","1:digit","1:half","1:i","1:kernel_s","1:length(a)","1:length(a)/2","1:length(a)]","1:length(bit_indices)","1:length(density)","1:length(energy_k)","1:length(indices)","1:length(opr.wfc)","1:length(other_points)","1:length(probabilities)","1:length(x)]","1:length(y)","1:logn","1:n","1:num_child","1:par.timestep","1:row","1:size","1:size(histogram)[1]","1:size(histogram)[2]","1:size(input_pts)[1]","1;","1=","1\\right).","1\\time","1]","1])","1]);","1]*a[i])","1],","1];","1]^2","1_f64","1_f64)","1_f64,","1aa","1d","1e","1i","1j","1j)","1s","1s.","1st","1st,","1}","1}&","1})","1},","1};","1}\\left(","1}\\left[\\hat{u}_k(dt)","1}}","1}}{2}","1}}{b_i","1❗️","1❗️❗️","2","2\"","2(x","2)","2))","2)))","2)));","2)),","2));","2),","2).","2).downto(0)","2).downto(0).each","2):","2);","2)];","2**32","2*sqrt(","2*xmax/res,","2,","2,0):","2,1],","2.","2.,","2.0","2.0)","2.0),","2.0);","2.0,","2.0_f64","2.0_f64)","2.0_f64).exp(),","2.0j","2.4492935982947064e","2.64m","2.7+","2.81m","2.]).reshape(3,","20","20%","20.0","20.0/512","200,000","2000","2000,","2001.10.wikipedia:","2004.","2004.4.unknown,","2004.7.wikipedia:","2008.4.wegert,","2010.4.wikipedia:","2011.9.gareth","2012.5.poelke,","2012.9.wikipedia:","2014.2.wikipedia:","2015.","2015.2.morris,","2016.","2017","2017.7.wikipedia:","2018","2019","2019.","2019.10.hutchinson,","2019.12.wolfram:","2019.2.mandelbrot,","2019.3.pethick,","2019.3.saupe,","2019.5.saupe,","2019.8.gneiting,","2020","2020,","2020.","2020..2030)","2020..2030:","2020..=2030;","2020.2.schloss,","2020.2.torbert,","2020.3.bien,","2020.5.gundersen,","2020;","2021","2021.","2021.3.wikipedia:","2021.4.wikipedia:","2021.5.hastings,","2021.7.wikipedia:","2021.8.rosenthal,","2021;","2022.","2022.10.wikipedia:","2022.11.wikipedia:","2022.2.wikipedia:","2022.3.wikipedia:","2022.4.wikipedia:","2022.5.crypto","2022.6.wikipedia:","2022.7.wikipedia:","2022.8.wikipedia:","2022.9.wikipedia:","2030","2030]","2031):","2039.","2099,","20\\time","21","21.46\\%","21.47\\%","2147483647","21st","21st).","21st,","21st.","22","22+d+e>31","22+d+e\\leq31","22nd","23","24","24]","25","25%","25)","25))","25).floor();","25).toint","250","2500","2500.","255","255),","255,","255.","256","256,","25;","25th","26","26.712","26th","27","27.5","273.308","28","28)","28).","29","29)","29.5","29th","2:","2:2]","2:n","2;","2\\ln(r_0)}\\left(\\frac{u_1}{\\sqrt{r_0}}\\right)","2\\ln(r_0)}\\left(\\frac{u_2}{\\sqrt{r_0}}\\right)","2\\ln(r_0)}{r_0}}","2\\ln(r_0)}{r_0}}.","2\\ln(u)}.","2\\ln(u_1)}","2\\pi","2\\pi,","2]","2],","2];","2]^2","2^(j","2^0","2^1","2^2","2^3","2^4","2^5","2^6","2^7","2^8","2^9","2^n","2^v","2^{","2^{0}.","2^{10}","2^{126}","2^{130},","2^{255}","2^{3}","2_u128.pow(i","2ab","2b+4c,","2ba","2d","2d,","2d0","2dup","2half","2i,","2im*pi*n*k/n)","2im*pi*n/n)","2pi","2pi*i*(k+n/2)/n=","2pi*i*k/n)","2s","2v(t)\\delta","2x","2x(t)","2y","2z","2},","2❗️","3","3\"","3)","3))","3))))","3);","3+127=130,","3+2","3,","3,3)","3.","3.,","3.0","3.0)","3.0,","3.0]","3.0];","3.0}","3.0},","3.0};","3.14159","3.14159)","3.14159,","3.141592653589793","3.14159265358979323846","3.14159265358979323846264338327950288419716;","3.14159265358979323846264338;","3.36","3.40","3.67394e","3.84","3.}","30","30)","30))","300","301","30;","30th","31","31)","31)))))","31).to_","31).to_string();","31).tostring()","31).tostring();","31);","31:","31}\"","32","32.","32]","32],","35","35\"","354","35},","36","36,","365","365).","365.","365.2425","365.25","3700x","385.819","3:","3;","3\\\\","3\\time","3]","3aab","3bba","3blue1brown:","3d","3d,","3e^{","3jane","3n","3rd","3s","3tba","3x","3x3","3y","3z","3}","3❗️","4","4\"","4(x+4)^2}","4)","4))","4),","4).floor();","4).toint","4);","4*r12]","4*r8]","4*rax]","4*rdi]","4,","4,000","4,000.","4,],","4.","4.,","4.0","4.0,","40","400","400,","4000","4000*v.","4000,","4000.","4000:","4000th","4096","4096.625","4096^2","42","4200","4288","4290772992","4294967295","433.644","45","456","48","480","483,200.0","499,813.2","4;","4\\\\","4\\pi","4d!","4r^2","4s,","4th","4u;","4y","4z","4}","4},","5","5\"","5)","5))","5));","5),","5);","5)^2}.","5+1","5,","5,2),","5.","5.,","5.0","5.0,","5.0:","5.0][y]","5.25","5.272859","5.51091e","5.56","5.79","5.]).reshape(3,","50","50%","500)","500,000","500,000\"","500,000,","500x500","50\\%","50\\time","50_000","50_000))","50_000):","511!","511,","512","512,","512.","512/2","5128","5184","52","52\\times7=364,","56","56088.","58%","58.","5:00am","5;","5\\%","5][y]","5_000,","5d0","5x5","5},","6","6\"","6)","6))","6),","6,","6,15),","6.0","6.0)","6.0,","6.0]","6.0];","6.0][z]","6.0}","6.0};","6.12323e","6.28318530718","6.}","622:","63","64","64*81)","64,","640,","65535","67","67🤛","67)","67))","67,","6:9","6;","6]","6],","6][z]","6},","7","7)","7))","7)))","7));","7),","7+1","7,","7.0","7.0,","71)","754","77","77🤛","77)","77))","77))\"","77)))","77)).","77));","77))]","77);","78.54\\%,","7;","7]","7},","8","8)","8));","8),","8*r13],","8*rax]","8*rcx]","8*rcx],","8*rdx]","8+2","8,","8,000","8,000.0","8.","8...","8.0","8.25","80","800","81","81🤛","81)","81))","81))\"","81)))","81))))","81)).","81));","81))]","81);","84","8\\\\","8]","8],","8]=[5,8]","8cm","8},","8}};","9","9)","9))","9));","9),","9).to_","9);","9,","9,958.0","9.0","9.0,","9.000","9.125","9.125,","917","917:","96","961,600.0","97","970","9856","999,466.0","9:","9\\text{","9th.","9}\"","9}\".fmt","9}';","9},","9}`;",":",":+","::",":=",":]",":].copy()",":a",":child",":children",":code",":code)",":data",":depend",":direct",":els",":id,",":if",":messag",":message))",":name",":output",":partner",":supersede)",";",";;",";;;;",";;els",";add",";extract",";of",";remov",";to","=","=&4+1","=&5","=1:length(bit_indices)","==","=='__main__':","===","=>",">",">\",",">());",">)",">=",">>",">>=",">back",">back;",">back]",">capac",">capacity)",">capacity;",">children",">children,",">children;",">children[]",">children[i]);",">choosematch();",">codes)",">codes[(unsign",">codes[0]);",">count",">count)",">count;",">data",">data);",">data,",">data[",">data[0]));",">data[0]);",">data[0],",">data[0];",">data[heap",">data[index]);",">data[index],",">data[left]",">data[parent_index]",">data[parent_index],",">data[q",">data[right]",">data[stk",">data[target]);",">decoder.get();",">dk",">dt",">dx",">encoder;",">float",">frequenc",">frequency),",">frequency;",">front",">front)",">front,",">front];",">getchildren()",">getchildren()))",">getchildren()[0]);",">getchildren()[1]);",">getid()",">getmatch());",">getname(),",">getpreferences()));",">id",">id);",">id,",">id;",">im_tim",">index++;",">index]];",">issingle())",">k",">k[i]",">ke",">ke[i]",">key);",">key,",">left",">left);",">left,",">length",">length)",">length++]",">length]);",">lhs.get(),",">lhs.get();",">match",">match;",">name;",">next",">next);",">next;",">next_index",">next_index++]",">next_index]",">partner",">partner)",">partner;",">pe",">pe[i]",">prefer",">preferences))",">preferences);",">preferences;",">prefers,",">prefers[man",">propose();",">re",">receiveproposal($this);",">rhs.get(),",">rhs.get();",">right",">right);",">right,",">right;",">second;",">setmatch($preference);",">setmatch($this);",">setpreferences($preferences);",">singl",">size",">str);",">str[builder",">string",">suitor",">suitors))",">suitors[]",">timestep",">top",">top++]",">top];",">unmatch();",">v",">v[i]",">v[i]);",">value);",">value;",">value]",">wfc",">wfc[i]",">x",">xmax",">y",">y)","?","?,","?person","@","@(","@($(get","@(0.0,","@(0.5,","@(1.0,","@(a,","@(k,v)","@[0.0,","@[1.0,","@[4.0,","@[7.0,","@amara","@amaras,@peanutbutterwarrior","@children","@choic","@id","@inbound","@index(global,","@kernel","@leio","@name","@ntindl","@ntindle,","@ntindle,@shadowmitia","@ntindle,@shadowmitia,@amaras,@peanutbutterwarrior","@overrid","@param","@partner","@partner.name}\"","@partner.nil?","@partner.partn","@partner.sett","@pref","@prefs.index(partner.id)","@prefs.siz","@prefs[@choices]","@properti","@return","@shadowmitia","@shadowmitia,@peanutbutterwarrior","@test","@testset","@time","[","[\"\",","[\"a\",","[\"e\",","[$a","[$tree];","[%.1f]\".format(a[1],","[%.1f]\".format(b[0],","[%.1f]\\n\",","[%.1f]\\n\".format(0f,","[%s,","[%s]%s',","[&","[&]","[&freq](char","[&ret,","['[#]","['b',","['t',","[('b',","[((r,","[(>","[(a,","[(b,","[(char,","[(eq?","[(i","[(int,","[(k","[(k,","[(m","[(or","[(p","[(t1,","[(x,y)","[...\"abcde\"].map(nam","[...\"fghij\"].map(nam","[...]","[...array(children).keys()].map(()","[...bitstring])","[...iterable].sort((a,","[...iterable];","[...points].sort((a,","[...str].map(c","[...str];","[...this.data.slice(0,","[.8666]","[0","[0,","[0,0,1]","[0,0],","[0.,","[0.0,","[0.01,","[0.0],","[0.2,","[0.23,","[0.26,","[0.5,","[0.85,","[0:10]","[0:1]","[0:]","[0]","[1","[1,","[1,2]","[1,n]","[1.0+0.0im","[1.0,","[1.0]],","[1.533]","[10].","[11].","[11][12]..","[1]","[1],","[1].","[1]:","[1~0~","[1~2~1]","[2","[2,","[2.","[2.0],","[2020","[2]","[2],","[2].","[2][3].","[3,","[3.0]\"","[3.0]\")","[3.0]\");","[3]","[3],","[3].","[4,","[4.0,","[4]","[4].","[4][5].","[5.0]\"","[5.0]\")","[5.0]\");","[5]","[5].","[64","[6],","[6].","[6][7][8].","[7,","[7.0,","[7.0]\"","[7.0]\")","[7.0]\");","[7]","[7],","[7].","[8]","[8].","[9].","[9][10],","[;;","[[","[[((r2,","[[0.0,","[[1.0,","[[['_',","[[noreturn]]","[[w","[\\![1,6]\\!]","[\\![2,12]\\!].","[]","[](auto","[](const","[])","[]*node","[]*node{n}","[];","[][]float64)","[][]float64{","[]f32","[]f32)","[]f32,","[]float64","[]float64)","[]float64{0.,","[]float64{1.,","[]float64{4.,","[]float64{7.,","[]point","[]point)","[]point{{","[]rune)","[a","[a[1],","[a]","[a])]","[array[i],","[array[j],","[b[0],","[b]))","[b])]","[bit","[bit]","[bit])","[c](auto","[charact","[code","[codebook]","[complex","[complex(x[i])","[complex.cor","[constant","[double]","[double])","[double],","[ecx","[els","[first,","[float(i)","[float(i)/200","[float])","[hull[i],","[hull[m],","[hull_point]","[i","[import:1","[int]","[it',","[it,","[l,","[l])","[left","[left,","[left]","[len","[letter","[lf][lf][lf]","[lf][lf][lf][lf]","[lf][space][lf][lf]","[lf][space][space][lf]","[lf][space][space][tab][lf]","[lf][space][space][tab][space][lf]","[lf][tab][space][tab][lf]","[lf][tab][tab][tab][space][lf]","[loc","[location]","[m","[math]::abs($a)","[math]::abs($b)","[math]::abs($piestim","[math]::floor($k","[math]::floor($year","[math]::floor((13","[math]::pow($radius,","[math]::pow($y,","[math]::sqrt(0.75)),","[middl","[n","[n:m],","[nan,","[new","[new_freq](auto","[node]","[node])","[node]?","[operators]","[p0]","[p]","[particle]","[person(name)","[point(0.0,","[point]","[point_on_hull]","[pos(2,1.5),","[pv","[r10","[r10]","[r10],","[r11","[r12","[r12]","[r12],","[r13","[r13]","[r14","[r14]","[r14],","[r15","[r15]","[r15],","[r8","[r8]","[r9","[r9]","[r9],","[r]","[rand(),","[random(),","[ratio","[rax","[rax]","[rax],","[rbx","[rbx],","[rcx","[rcx]","[rdi","[rdi]","[rdx","[rdx]","[rdx],","[rsi","[rsp","[rsp],","[s","[s,","[show","[sigma","[space][lf][space]","[space][lf][tab]","[space][space][space][lf]","[space][space][space][tab][lf]","[st]","[stack","[start,","[string]","[switch]$servois)","[t]","[tab][lf][space][tab]","[tab][lf][tab][tab]","[tab][space][space][tab]","[tab][space][tab][tab]","[tab][tab][space]","[tab][tab][tab]","[top](it","[tree","[tree]","[tree];","[tree_left,","[value][next]","[vx","[vx]","[x","[x]","[{:?}]\",","\\","\\\"\"","\\%","\\%30","\\%~30","\\%~31","\\&","\\;,\\;","\\\\","\\approx","\\begin{align}","\\begin{array}{ccccccc|c}","\\begin{array}{ccccc|c}","\\begin{array}{ccccc}","\\begin{array}{ccc|c}","\\begin{array}{ccc}","\\begin{array}{cc}","\\begin{array}{c}","\\begin{bmatrix}","\\begin{document}","\\begin{matrix}","\\bigcup_{i=1}^3f_i(p)","\\bigcup_{i=1}^4f_i(p),","\\cdot","\\circ","\\co","\\color{blue}3\\times\\color{blue}6=18","\\color{green}2\\times\\color{green}6+\\color{blue}3\\times\\color{blue}5=27","\\color{red}1\\times\\color{red}5+\\color{green}2\\times\\color{green}4=13","\\color{red}1\\times\\color{red}6+\\color{green}2\\times\\color{green}5+\\color{blue}3\\times\\color{blue}4=28","\\color{red}{1}\\times\\color{red}{4}","\\cos(0)","\\cos(2","\\cos(\\omega","\\cos(\\theta)","\\ddot","\\delta","\\delta,","\\delta_j","\\displaystyl","\\displaystyle\\frac","\\documentclass[11pt]{article}","\\dot","\\ell","\\ell.","\\ell\\tim","\\end{align}","\\end{align},","\\end{array}","\\end{array}\\right]","\\end{bmatrix}","\\end{bmatrix},\\\\","\\end{bmatrix}.","\\end{bmatrix}\\\\","\\end{bmatrix}p","\\end{document}","\\end{matrix}","\\end{matrix}.","\\end{matrix}\\\\","\\exp\\left[","\\exp\\left[\\frac{","\\exp\\left[{\\displaystyle\\frac{","\\frac","\\frac12","\\frac{","\\frac{18}{11}","\\frac{1}{(2^3","\\frac{1}{0.7853}","\\frac{1}{1.72","\\frac{1}{2\\pi\\sigma^2}e^{","\\frac{1}{2}","\\frac{1}{2}(a(t)","\\frac{1}{2}.","\\frac{1}{2}\\frac{d^2f(a)}{dx^2}(x","\\frac{1}{2}\\hbar","\\frac{1}{2}\\hbar\\omega,","\\frac{1}{2}\\left(r","\\frac{1}{2}\\omega","\\frac{1}{2}a(t)\\delta","\\frac{1}{2}a(t+\\delta","\\frac{1}{2}at^2","\\frac{1}{2}mv^2?","\\frac{1}{3}","\\frac{1}{3}.","\\frac{1}{3}\\tim","\\frac{1}{3}b(t)\\delta","\\frac{1}{6}b(t)","\\frac{1}{6}bt^3","\\frac{1}{7","\\frac{1}{8}.","\\frac{1}{9}.","\\frac{1}{\\sqrt{\\pi}}","\\frac{1}{n_3","\\frac{1}{n_{v+1}","\\frac{1}{n}","\\frac{2","\\frac{[i\\hat{h}_r,","\\frac{\\displaystyl","\\frac{\\displaystyle\\sum_{n}f(n)}{\\displaystyle\\sum_{n}","\\frac{\\hbar^2}{2m}","\\frac{\\hbar^2}{2m}\\nabla^2","\\frac{\\hbar}{2}","\\frac{\\log(1+n/a)}{\\log(1+1/a)}.","\\frac{\\log_e(n+1)}{\\log_e(2)}","\\frac{\\parti","\\frac{\\partial\\phi(\\mathbf{r},t)}{\\parti","\\frac{\\pi","\\frac{\\pi}{4}","\\frac{\\pi}{4}).","\\frac{\\text{area}_{\\text{circle}}}{\\text{area}_{\\text{square}}}","\\frac{\\text{count","\\frac{\\vec{p_1","\\frac{a_{n","\\frac{a_{n+1}}{2},","\\frac{a}{2}","\\frac{b(t)","\\frac{b}{2}","\\frac{c_0}{b_0}","\\frac{c_i}{b_i","\\frac{c}{2}","\\frac{d^2x(t)}{dt^2}","\\frac{d_0}{b_0}","\\frac{d_i","\\frac{df(a)}{dx}(x","\\frac{dx(t)}{dt}","\\frac{e^{","\\frac{f(\\mathbf{x})}{\\displaystyle\\int_d","\\frac{f(\\mathbf{x})}{\\int_d","\\frac{f(n)}{\\displaystyle\\sum_{n}","\\frac{f(x')}{f(x_t)}\\right).","\\frac{f(x)}{\\int_{","\\frac{f^{(n)}(a)}{n!}(x","\\frac{h}{\\lambda}","\\frac{i(\\hat{h}_r","\\frac{i\\hat{h}_kdt}{\\hbar}},","\\frac{i\\hat{h}_kdt}{\\hbar}}e^{","\\frac{i\\hat{h}_rdt}{2\\hbar}}","\\frac{i\\hat{h}_rdt}{2\\hbar}}e^{","\\frac{i\\hat{h}_rdt}{\\hbar}},","\\frac{i\\hat{h}_rdt}{\\hbar}}e^{","\\frac{i\\hat{h}dt}{\\hbar}}\\right]\\psi(\\mathbf{r},t)","\\frac{n(n","\\frac{n}{4000}","\\frac{p","\\frac{p+a}{2}","\\frac{p+b}{2}","\\frac{p+c}{2}","\\frac{p+d}{2}","\\frac{p^2}{2m}","\\frac{pi}{4}","\\frac{r^2}{2}},","\\frac{x(t+\\delta","\\frac{x^2+y^2}{2\\sigma^2}},","\\geq","\\gt","\\hat","\\hat{h}_k","\\hat{h}_k)dt}{\\hbar}}\\right]\\psi(\\mathbf{r},t)","\\hat{h}_r","\\hat{u}_k","\\hat{u}_r","\\hbar","\\hbar\\omega.","\\hline","\\in","\\in\\left\\{h,t\\right\\},","\\infty}","\\infty}^{+\\infty}\\psi^\\ast\\psi","\\infty}^{+\\infty}|\\psi(\\mathbf{r},t)|^2","\\infty}^{\\infty}","\\infty}^{\\infty}f(\\xi)g(x","\\infty}^{\\infty}f(x","\\infty}^{\\infty}f[m]g[n","\\infty}^{\\infty}f[n","\\input{out}","\\int_a^b","\\int_d","\\int_{","\\int_{d}","\\int_{s}f(\\mathbf{x})d\\mathbf{x}","\\int_{x_1}","\\int_{x_{10}}","\\lambda","\\lambda}","\\langl","\\ldot","\\left(","\\left(\\begin{bmatrix}","\\left(\\frac{f(x')}{f(x_t)},","\\left(\\lfloor","\\left(f(z)=z^2\\right),","\\left[","\\left[\\begin{array}{@{}ccc|c@{}}","\\left[\\begin{array}{@{}cc|c@{}}","\\left[\\hat{u}_r\\left(\\frac{dt}{2}\\right)","\\left[\\hat{u}_r\\left(\\frac{dt}{2}\\right)\\mathcal{f}^{","\\left[e^{","\\left[v(\\mathbf{r})","\\left\\lfloor\\frac{13+8k}{25}\\right\\rfloor.","\\left\\lfloor\\frac{\\text{year}}{100}\\right\\rfloor,","\\left\\lfloor\\frac{k}{4}\\right\\rfloor.","\\left\\{","\\left\\{h,t\\right\\}","\\left\\{h,t\\right\\}.","\\leq","\\lfloor","\\lfloor\\cdot\\rfloor","\\log","\\log_2(1)","\\log_2(1+n),","\\log_2(8),","\\log_e(1+e^v).","\\log_e(1+n).","\\lvert","\\mathbb{c}),","\\mathbb{c}.","\\mathbb{p}(a","\\mathbb{p}(x_0","\\mathbb{r}):","\\mathbb{r}^2","\\mathbb{r}^2)","\\mathbb{r}^n","\\mathbf{","\\mathbf{0}","\\mathbf{10}","\\mathbf{1}","\\mathbf{2}","\\mathbf{3}","\\mathbf{4}","\\mathbf{6}","\\mathbf{\\frac{10}{3}}","\\mathbf{\\frac{2}{3}}","\\mathbf{a}","\\mathbf{a}\\mathbf{v}_0","\\mathbf{a}\\mathbf{v}_0.","\\mathbf{a}_{\\text{rot}}","\\mathbf{r}","\\mathbf{v_0}","\\mathbf{v}","\\mathbf{v},","\\mathbf{v}_0","\\mathbf{x}","\\mathbf{x},","\\mathbf{x}.","\\mathcal{f}","\\mathcal{f}(f)","\\mathcal{f}(f*g)","\\mathcal{f}(g)","\\mathcal{f}\\left(","\\mathcal{f}^{","\\mathcal{o}(\\delta","\\mathcal{o}(dt^3)","\\mathcal{o}(n","\\mathcal{o}(n\\log(n)),","\\mathcal{o}(n\\log(n)).","\\mathcal{o}(n^2)","\\mathcal{o}(n^3).","\\mathcal{o}(nh)","\\mathcal{o}(nh),","\\mathrm{size}\\times\\mathrm{size}","\\min","\\min\\left(1,","\\mu","\\mu)^2}.","\\mu,","\\mu.","\\n\"","\\nabla","\\nabla^2","\\neq","\\omega","\\omega(1)","\\omega(3)","\\omega(n)","\\omega,","\\omega.","\\omega_2^0","\\omega_2^1","\\omega_2^1,","\\omega_n^k","\\otim","\\phi","\\phi(\\mathbf{r},t)","\\phi,","\\pi","\\pi,","\\pi/2),","\\pi/2,","\\pi/2.","\\pi=(3,1,2,4))","\\pm","\\psi","\\psi(\\mathbf{r},t","\\psi(\\mathbf{r},t)","\\psi(\\mathbf{r},t),","\\psi(\\mathbf{r},t)^{*}\\psi(\\mathbf{r},t)","\\psi(\\mathbf{r},t)}{\\parti","\\psi(\\mathbf{r},t+dt)","\\psi(\\mathcal{r},","\\psi(x)","\\psi(x).","\\psi(x)\\rangl","\\psi_i","\\qquad","\\quad","\\rangl","\\rangle,","\\rfloor","\\rfloor.","\\right)","\\right),","\\right).","\\right)\\right)","\\right.","\\right]","\\right].","\\right]\\psi(\\mathbf{r},t)","\\right]\\psi(\\mathbf{r},t).","\\right]}","\\rightarrow","\\rvert","\\sigma","\\sigma(n,a)^2","\\sigma,","\\sigma_p","\\sigma_q","\\sigma_x","\\sigma_y.","\\sim","\\simeq","\\sin","\\sin(","\\sin(0)","\\sin(2","\\sin(\\omega","\\sin(\\theta)","\\sqrt{","\\sqrt{\\frac{","\\sqrt{\\frac{1}{n}\\sum_{i=1}^{n}(q_i","\\sqrt{\\pi}.","\\sqrt{\\text{re}(z)^2","\\sqrt{g_x^2","\\sqrt{u_1^2","\\sum_i","\\sum_n","\\sum_{i=0}^{n}w_i\\tim","\\sum_{k=0}^{n","\\sum_{m","\\sum_{n=0}^9","\\sum_{n=0}^{\\infty}","\\sum_{n=0}^{n","\\sum_{n=a}^{b}","\\tau","\\textbf{k}","\\textbf{v}","\\textbf{x},","\\text{","\\text{acceleration}","\\text{area}_{\\text{circle}}","\\text{area}_{\\text{circle}}.","\\text{area}_{\\text{circle}}=\\pi","\\text{area}_{\\text{square}}","\\text{area}_{\\text{square}}=4r^2.","\\text{area}_{\\text{square}}\\times\\text{ratio}","\\text{atan}\\left(\\frac{\\text{im}(z)}{\\text{re}(z)}\\right)","\\text{current_row}","\\text{easter}","\\text{if","\\text{im}(z)^2}","\\text{length}","\\text{length}(c_i)","\\text{length}^2.","\\text{pivot_row},","\\text{pivot}_{\\text{col}})","\\text{ratio}","\\text{ratio}?\"","\\text{velocity}","\\text{width}","\\text{width}.","\\text{year}~\\%~19,","\\text{year}~\\%~4,","\\text{year}~\\%~7,","\\tfrac{length}{2}","\\theta","\\theta(1).","\\theta(2^n),","\\theta(3),","\\theta(\\frac{3n}{2}","\\theta(\\log(n))","\\theta(n).","\\theta(n^2)","\\theta(n^3),","\\theta)","\\theta,","\\theta.","\\theta}","\\time","\\usepackage{gnuplottex}","\\vdot","\\xi","\\xi)","\\xi))dx","\\xi)d\\xi","\\xi)g(\\xi)d\\xi","\\xi}","]","])","]),","],","].","];","^","^\\infti","^^","^a.","^self.","_","_)","_),","_,","_.weight))","_________________________________________________________________________","__abs__(self)","__add__(self,","__author__","__construct(int","__init__(self)","__init__(self):","__init__(self,","__len__(self)","__muldc3","__muldc3,","__name__","__name__==\"__main__\":","__repr__","__rmatmul__(self,","__rmul__(self,","__str__","__str__(self)","__str__(self):","__tostring():","_children","_dt,","_dt;","_i","_po","_res,","_res;","_timesteps,","_timesteps;","_xmax,","_xmax;","_}","`((0","`(setf","`and`","`april","`b`","`children`","`dequeue`","`div`","`enqueue`","`first`","`front`","`iterative_cooley_tukey`","`march","`mod`","`not`","`number_of_partners`.","`on`","`person`","`pop`","`preference_list`","`push`","`second`","`size`","`top`","a%b","a%b,b","a'","a',","a'_i","a(\\text{curr_row},","a(\\text{pivot}_{\\text{row}},","a(t)\\delta","a(t+\\delta","a)","a)(ab","a)(negative?","a))","a)))","a)))))","a));","a))]))","a),","a).partial_cmp(&polar_angle(&start,","a).powf(v)","a):","a);","a)]","a)^2","a)^n","a*((1","a*((1+1/a)^v","a,","a.","a.ab","a.abs();","a.absolutevalu","a.add(b.mul(new","a.col","a.each_index","a.equals(b);","a.getx(),","a.gety());","a.len();","a.length","a.length;","a.map","a.prefer","a.rows)","a.rows];","a.shape[0]):","a.shape[1]","a.shape[1])):","a.shape[1]:","a.siz","a.weight","a.x","a.x)","a.x))","a.x)*(c.i","a.x);","a.y)","a.y));","a.y)*(c.x","a.y);","a:","a;","a=$(ab","a=1","a=30","a=30,","a==b","a=abs(a);","a=b","a>10","a>b:","a@(xa,","a[(a.row","a[(i","a[(i,","a[(k,","a[(row,","a[0],","a[0].length","a[0].length;","a[1])","a[1],","a[2*i+1])","a[2*i]","a[2*i])","a[2]","a[2],","a[3],","a[3][4]","a[col]","a[col];","a[end])","a[i","a[i,","a[i,col]","a[i,col]*a[row,j]","a[i,col]/a[row,col]","a[i,j]","a[i]","a[i])","a[i]))","a[i][col]","a[i][i];","a[i][j]","a[i][j];","a[indices[i]]","a[max_i,","a[max_index,","a[p]","a[p],","a[p][c]","a[pivot]","a[pivot];","a[pivot_i,","a[pivot_row,","a[r+1:]","a[r,","a[r:]","a[r]","a[r],","a[r][c]","a[r][j]","a[r][r]","a[row","a[row,","a[row,col]","a[row,i]","a[row,j]*fract","a[row][col];","a[row][i]","a[row][j];","a[rowa]","a[rowa];","a[rowb]","a[rowb];","a\\left(\\left(1+\\frac{1}{a}\\right)^v","a]","a])","a^*_i","a_0","a_0,","a_1","a_2","a_i","a_n","a_{n}","aa","aab","ab","aba","abbbbab","abbbbab.","abbcccdddd","abbcccdddd.","abbrevi","abc","abil","abilities)","about,","about.","about:","abov","above,","above.","above:","above;","above?","aboveground","abruptli","abs($a);","abs($b);","abs()","abs(a","abs(a)","abs(a);","abs(a:a)","abs(a:b)","abs(b)","abs(b);","abs(in1)","abs(in2)","abs(p","abs(p)","abs(pi_estim","abs(sin(imaginary_f(z(x,y))*pi))**thresh)","abs)","abs,","abs.","abs2.(opr.wfc)","absolut","absolutes.","abstract","abstractions.","abysmal!","abz","academ","acc","acc*dt","acc*dt*dt","acc*dt;","acc,","acc:","acc::float64,","acceler","accelerating,","acceleration!","acceleration,","accept","acceptable,","access","access_image(img::array{float64},","accord","accordingly.","accordingly;","account","account.","accru","accum","accumul","accur","accuraci","accurate:","achiev","acknowledg","acm","acm,","act","action","action,","action.","actions:","activ","actual","ad","ad:\"","ad:\")","ad:\");","ad:\",","ad:\\n\"","ad:\\n\");","ad:~%\"","adapt","add","add(nod","addchild($child);","addchild(tre","addit","addition,","additionally,","addlast:","addpattern","address","addresses.","addsd","adequ","adjust","admittedly,","advanc","advantag","advantage.","adventur","advic","ae","aes.","affect","affin","affine;","after,","after.","afterwards,","ag","again","again,","again.","again...","again:","age,","agnostic,","agnostic.\"","ago,","agree;","ahead","ahem","aim","al","al,","al.,","algorithm","algorithm!","algorithm)","algorithm).","algorithm,","algorithm.","algorithm:","algorithm;","algorithm?","algorithms,","algorithms.","algorithms:","alia","alias","aliases,","alic","alice'","alice,","align","all!","all((man.has_partn","all,","all.","all;","alloc","allow","allowed\"","allud","along","along!","alphabet","alphabet,","alphabets:","alreadi","already.","also,","also.","alter","altern","although","altogeth","altogether!","altogether,","alway","always)","always,","amara","amaz","ambigu","ambiguous.","ambiti","american","amin","amount","an","analag","analog","analogu","analogy.","analysis,","analyt","analytically.","analyz","ancient","angl","angle\"","angle\")","angle(endpoint,","angle(point","angle(self,","angle(x,y)","angle.","angular","anim","animation,","animation.","animation:","animations,","animations.","annal","anomaly:","anoth","another,","another.","ans(rows);","ans;","answer","answer,","answer_grid","answer_grid[1:3,","any.","anymore.","anyon","anyth","anything,","anything.","anyway","anyway,","anyway.","anyway?","anywher","aold,","api","api,","api.","appar","apparent.","apparently,","appeal.","appear","appears,","append","append()","append(*n,","append(code,","append(code[:len(code)","append(cur.children,","append(hullpoints,","append(queue,","appendix.","appli","applic","applications,","applications.","applies,","appliquées.6.standish,","apply.","approach","appropri","appropriate.","appropriately,","appropriately.","approx","approx(y,","approx(z,","approxim","approximate.\\n\");","approximate_count","approximatecount","approximatecount(nitems,","approximation\"","approximation).","approximation,","april","april.","april}&","arbitrari","arbitrarili","arbitrary.","arc","arcan","archiv","archive!","archive,","archive.","archive.org/","archive:","archivists/algorithm","are...\")","are:","are:\"","are:\")","are:\");","are:\\n\");","are;","area","area,","area.","areas.","aren't","argmax(abs.(a[row:end,col]))","args)","args]","argu","arguabl","argument","aris","arises!","arithmet","arithmetic)","arithmetic,","arithmetic.","around","around\"","arr","arr)","arr[#arr","arrang","array","array(n)","array(n).fill(null);","array(node))","array)","array,","array.","array.length","array.new(size){|i|","array;","array?","array[i]","array[i];","array[i]];","array[j]","array[j];","array[j]]","array[rand()","array[string]):","array_pop($stack)))","array_shift($stack)))","array_shift($thi","arraylist","arraylist();","arraylist<>();","arraylist<>(mates);","arrays.","arrays.stream(a).foreach(x","art","art.","articles,","arxiv,","arxiv.org","as,","as:","ascens","ascertain","ascii","ascii_lowercas","ascii_lowercase[:num_pairs]]","ascii_uppercase,","ascii_uppercase[:num_pairs]]","aside,","ask","ask,","asm","aspect","aspect=\"equal\"","aspect=\"equal\")","assert(count","assert(test_grid","assess","assign","associ","assum","assumpt","assumption:","astound","astrolog","astronom","asymmetr","asymmetric.","at(zeros(n,","at.","at:","atan(item.i","atan2","atan2(","atan2(p.i","atan2(point[1]","atan2(y,x)","atan2(y1","atom","atoms,","attack","attempt","attend","attent","attention.","attr_read","attr_writ","attract","attractor","attractor,","attractor.","attractor;","attractors,","attractors.","attractors:","attribut","audienc","audience'","augment","author","author.","author:","auto","auto&","automat","auxiliari","avail","available.","averag","average!","avg","avoid","avoided,","aw","away","awful,","ax","ax=axes,","axes.","axes.get_xticklines():","axes.get_yticklines():","axes.imshow(","axes.set_title(\"$f(x)=z^2$\")","axes.set_xlabel(\"$re(z)$\")","axes.set_ylabel(\"$im(z)$\")","axi","axis,","axis.","axis:","axis_num","axis_num^2","a{b};","a}{2}\\\\","b","b!","b'_i","b'_i=1","b)","b)(euclid","b))","b))(euclid","b)))","b))))","b)).unwrap());","b))]","b).","b):","b);","b)]","b){","b,","b,a","b.","b.ab","b.abs();","b.absolutevalu","b.getx(),","b.gety()","b.gety());","b.prefer","b.weight),","b.x","b.x);","b.y));","b.y,","b.y;","b.zero?","b:","b::int64)","b::point,","b::uint64)","b::vector{float64},","b;","b=$(ab","b=0","b=abs(b);","b@(xb,","b[0]","b[0],","b[0];","b[1]","b[1],","b[1]}","b[2]","b[2],","b[3],","b[i]","b]","b^*_i","b_0","b_0:","b_1","b_i","b_n","ba","bab","bacccdba.","bachelor","bachelor,","bachelors.dequeue.propose()","bachelors.enqueue(this)","bachelors.push(girl.fiance);","bachelors.shift();","bachelors[","bachelors[bachelors_s","bachelors_size]","back","back,","back.","back_substitution(&a);","back_substitution(a)","back_substitution(a):","back_substitution(a:","back_substitution(a::array{float64,2})","back_substitution(const","background","backquot","backsubs(const","backsubs(equations);","backsubstitut","backsubstitution(a","backsubstitution(a)","backsubstitution(double[][]","backtrack","backward","backwards,","bad","bad,","baffl","bag","baker","balanc","ball","bamboozl","banking.","bar","bar.","barn","barnsley","barnsley_hutchinson","barnsley_hutchinson,","barnsley_prob","barnsley_probabilities)","barycent","barycenter.","base","base(name)","base,","basement","bases,","bases.","bash","basi","basic","basically,","basics:","bat","bba","bc","bc)","bc.getx())","bc.gety()))","bc.magnitude()));","be","be,","be.","be:","be;","beauti","beautiful,","beautifulli","becam","becker","becom","becomes!","beda","bede,","befor","before!","before).","before,","before.","before:","before;","before?","began","begin","begin(freq),","begin(initial),","begin,","behave,","behavior","behavior.","behaviors:","behind","behind.","beholder,","being,","believ","bell","bellow","belong","below","below)!","below),","below):","below,","below.","below:","belt.","benchmark","benchmarks,","benchmarktools,","beneath","benefit","benoit,","best","best.","better","better!","better.","better:","between","between,","bewildering.","beyond","beyond:","bf","bfs(root);","bfs(tree)","bfs.","bfs:\"","bfs:\")","bfs:\");","bfs:'","bfs:\\n\");","bfs:~%\")","bfs_queue","bfs_queue(&root);","bfs_queue(n)","bfs_queue(n:","bfs_queue(n::node)","bfs_queue(nod","bfs_queue(node)","bfs_queue(node):","bfs_queue(root)","bfs_queue(root);","bfs_queue(struct","bfs_queue(tree)","bfs_queue:","bfs_queue_end_push","bfs_queue_end_push:","bfs_queue_loop","bfs_queue_loop:","bfs_queue_push_child","bfs_queue_push_child:","bfs_queue_return","bfs_queue_return:","bfsqueue()","bfsqueue(n","bfsqueue(node:","bi@","bias","bibbity_bobb","bibbity_bobbity:","bibliographi","big","big)","bigger","biggest","biggr","billion","bin","bin(x)","bin,","bin.","bin[1]","bin[2]","bin_id(x)","bin_width","bin_width)","bin_width/2,","binari","binary!🔤","binary🔤❗️","binary,","binary:","binary_root","binary_tre","bind","bins=bins,","bioinformatics.","biologi","birthday","bisect","bisect(tre","bit","bit,","bit.","bit.\"","bit...","bit:","bit?","bit_indic","bit_indices[i]","bit_indices[i][end","bit_reverse(x)","bit_reverse(x);","bit_reverse(x,","bit_reverse(x:","bit_reverse:","bit_reverse_entries:","bit_reverse_idxs(math.log2(n));","bit_reverse_return","bitlogic,","bitlogic.","bitlogic:","bitmask","bitreverse(a::array)","bitreverse(x)","bits)","bits),","bits).","bits,","bits.","bits.push_back(b);","bits;","bits?","bitshift","bitstr","bitstr_len,","bitstr_len]","bitstr_siz","bitstr_size,","bitstring(indices[i]))","bitstring)","bitstring);","bitstring,","bitstring.","bitstring::string)","bitstring;","bitstring?","bitstring_build","bitstring_builder*","bitstrings:","black","blank","blanketli","blend","blissfulli","block","blog","blowfish","blowfish:","blue","blue),","bluntly,","blur","blur\"","blurrier","bnum","bnum)","boast","bob","bob'","bobbity\"","bobbity\")","bobbity\");","bobbity\",","bobbity\";","bobbity)\")","bobbity)\";","boca","bodi","body.","boggl","boil","boltzmann","boltzmann,","book","book\");","book,","book.","books,","bool","bool)","bool,","boolean","border","boring,","born","bose","both","both!","both,","bottom","bottom,","bottom.","bottom.\"","bottom.\"\"\"","bottom;","bounc","bound","boundari","boundaries.","boundaries:","boundary.","bounds,","bounds[1,1]","bounds[1,1])","bounds[1,1])/dx),","bounds[2,1]","bounds[2,1])","bounds[2,1])/dx))","box","box,","box.","box::new(left),","box::new(right),","box—mul","boyfriend","bra","braket","branch","branch(left,","branch(left:","branch(node1,","branch(node_ptr","branch)","branch))","branch);","branch.","branch.freq","branch.left","branch.right","branch:","branches.","branch}","breadth","break","break;","breath","brevity,","brief","briefli","bright","bright,","brilliant!","bring","britain","britain?","broader","broadli","brogli","brought","brows","browser","btree","bucket","build","build_codebook(empty(),","build_codebook(leaf(char,","build_codebook(left,","build_codebook(node(left,","build_codebook(right,","build_codebook(tree)","build_huffman_tree(message)","build_huffman_tree(message):","builder","builder,","buildtre","buildtree(messag","buildtree(message)","built","built.","bulk","bunch","busi","butterfli","butterflies,","butterflies.","butterfly\"","butterfly(x)","butterfly(z[start_index:start_index","butterfly:","button:","by,","bypass","byte","b|","b}{2}\\\\","c","c#","c'","c'_0","c'_i","c'_{i","c)","c))","c)),","c))]","c),","c);","c++","c++,","c++14,","c,","c.","c.clone()","c.data[cur_loc.x","c.data[p.x","c.dup","c.gety()","c.max_i","c.max_x","c.max_x)","c.prefer","c/","c/*","c/+)","c/c++,","c/exp","c/stringifi","c1)","c1),","c:","c::point)","c::vector{float64},","c;","c==b","c?","c@(xc,","c[0]","c[0],","c[1],","c[2],","c[i","c[i]","c[j]","c]","c]))","c^*_i","c_0","c_1","c_i","c_i'","c_in","c_in,","c_n","c_prime","c_prime[0]","c_prime[1]","c_prime[i","c_prime[i]","c_{n","cabs,","caesar","caeser","cairo","calcul","calculate,","calculate_energy(&par,","calculate_energy(par,","calculate_energy(par:","calculate_energy(param","calculate_energy(struct","calculateenergi","calculation,","calculation.","calculation:","calculations.\"","calculator,","calculu","calendar","calendar,","calendar.","calendars.","calendrier,","call","calle","calloc","calloc((q","calloc(0,","calloc(1,","calloc(4,","calloc,","cambridg","camp\"","campbel","can!","can't","can.","can:","candid","candidate,","canni","canva","canvas[cur_loc]","canvas[current_loc]","canvas[current_location]","canvas[loc]","canvas[location]","canvas[neighbor]","canvas[neighbour]","canvas[p]","canvas[possible_neighbor]","canvas[x]","canvas_size[1]","canvas_size[2]","capabl","capac","capacity,","capacity;","capcaiti","capit","care","carefulli","carlo","carlo\"","carlo([int]$n)","carlo,","carlo.","carlo.core)","carray","carri","cartesian","cartesian_box_muller!(input_pts,","cartesian_box_muller(input_pts,","cartesian_kernel!(cpu(),","cartesian_kernel!(cudadevice(),","cartesian_kernel!(input_pts,","cartesianindex","cartesianindex(","cartesianindex(0,","cartesianindex(1,","cartesianindex(1,1)","cartesianindex(ceil(int,","cartesianindex{","cartesianindic","case","case!","case),","case,","case.","case:","case;","cases!","cases,","cases.","cast","catch","categori","categories:","categorized.","caus","caveat","caveats.","cb","cb,","cb[char]","cbar","cbar.set_ticklabels([\"$0.0$\",","cbar.set_ticks([0.0,","cbbbc!","cblabel","cbrang","cbtic","ccw","ccw(a,","ccw(a::point,","ccw(const","ccw(gift[j],","ccw(p1,","ccw(point","ccw(struct","cdq","ceasar","ceil(int,","ceil(int,(bounds[2,2]","celebr","cell","cell)","cell_index","cell_index(keys(n),","cell_index(keys(parent),","cell_index(values(n),","cell_index(values(parent),","center","center),","center)^2","center)^2)","center+1)**2","center+1)**2)/(2*sigma**2))","center,","center.","central","centuri","centuries,","centuries.","century.","certain","certainli","certainly,","certainti","certainty.","cexp","cexp(","cexp()","cexp,","cf","chain","challeng","chan'","chanc","chang","change,","change.","channel","chao","chaos_game(","chaos_game(10000,","chaos_game(10_000,","chaos_game(initial_loc","chaos_game(iters:","chaos_game(n,","chaos_game(n::int,","chaos_game(point(0,","chaos_game(struct","chaosgam","chaosgame($n,","chaosgame(10000,","chaosgame(int","chapman","chapter","chapter,","chapter.","chapter:","chapters,","chapters.","char","char)","char)*str]","char)c];","char)tre","char*","char**","char,","charact","character","character,","character.","characters,","characters:","charcount","charged,","charli","chars.reduce((counts,","chart","cheatsheet","check","check,","check.tex","check1","check1);","check2","check2);","check:","chemistry.","child","child'","child)","child))","child)))","child)))))","child,","child.","children","children'","children)","children))","children)):","children,","children.","children:","children::vector{node}","children;","children_count","children_count❗️","children_count❗️❗️","children_s","children_size,","children_size;","childrencount)","childrencount);","children|value|children_s","children❗️","child};","child❗️","chinmaya","chip","chk1","chk1);","chk2","chk2);","choic","choice(shape_points))","choice(shape_points))]","choice,","choice.","choice;","choices(hutchinson_op,","choices,","choices:","choices[currenttopchoiceindex++];","choos","choose(const","choose(inputpoints));","choose,","choose.","choosematch():","choosemate()","choosetreebranch(bit)","choosetreebranch(bit:","chore.","chose","chosen","chosen,","chosen:","choseth","christendom.","christian","christoph","chunk","chunks,","chunks.","church","church'","ciccotosto","cipher","cipher\"","cipher,","cipher:","circl","circle\"","circle(1.0);","circle(doubl","circle,","circle.","circle.c","circle:","circle?","circles?","circle}}{\\text{tot","circuit","circuits:","cl","claim","clang++","clarification.)","clarity),","clarity:","class","class.","classic","classifi","classvariablenames:","claud","clean","clean,","cleaner","cleaner,","cleanest","cleanli","cleanup:","clear","clear,","clear.","clear:","clearli","clearly,","clergi","click","climate,","clobber","clockwis","clockwise)","clockwise,","clockwise?","clockwise?\"\"\"","clojur","clone)]","close","close(outfile)","close?","closed,","closer","closest","clutter,","cm,","cmath","cmovnz","cmp","cmp(&self,","cmp_points(const","cmp_points);","cn","cn)","cn))","cnt","coast","coastlin","coconut","coconut.","code","code!","code)","code)))))","code);","code)]","code+'0')","code+'1')","code,","code.","code.append(0));","code.append(1));","code.deletecharat(code.length()","code.tostring());","code/","code:","code::string,","code='')","code]","codearr","codearr)","codebase.","codeblock","codebook","codebook'","codebook(it","codebook)","codebook);","codebook*","codebook,","codebook.","codebook.decode(&encoded);","codebook.encode(input);","codebook.entryset())","codebook.getorelse(c,","codebook.insert(value,","codebook.put(node.letter,","codebook.put(symbol,","codebook/tre","codebook:","codebook::codebook(it","codebook::decode(it","codebook::encode(it","codebook::node::~node()","codebook;","codebook[0][0]","codebook[c]).join(\"\"),","codebook[i]","codebook[n.key]=\"0\"","codebook])","codebook_free(struct","codebook_ptr","codebook_recurse!(branch.left,","codebook_recurse!(branch.right,","codebook_recurse!(branch::branch,","codebook_recurse!(leaf::leaf,","codebook_recurse!(n,","codebook_recurse(const","codebook_recurse(tre","codebook_recurse(tree,","codebook_s","codebook_size,","codebook_size]","codebookrecurse(c,","codebookrecurse(left,","codebookrecurse(nod","codebookrecurse(node.left,","codebookrecurse(node.right,","codebookrecurse(node:","codebookrecurse(right,","codebookrecurse(root,","codebookreverse()","coder","coder))","coder]","codes(begin(s),","codes(codes),","codes,","codes.decode(begin(string),","codes;","codes[256];","codes[i]);","codeword","codeword.","codewords.","coding.","coeffici","coefficients.","coefficients.\"\"\"","coin","col","col):","col);","col,","col]","col]))","col];","colinear","collabor","collaps","collect","collect(2020:2030)","collect:","collections.shuffle(preferredmates);","collinear","collinear.","colloqui","color","color(f_val,","color(x,y)","color.","colorbar","colored,","colored.","coloring,","coloring:","colors,","coloss","cols)","cols);","cols,","cols:","cols]","column","column)","column)))","column,","column.","columns,","columns.","combin","come","comfort","comisd","comma","command","command,","command.","command:","commands:","comment","comments.","common","common,","common.","commonli","commun","communicating.","communication,","community,","community.","commut","compar","comparable.","compareto(nod","comparison","compatriot","compel","compil","compiler,","complain","complet","complete,","complete.","completed.","completeness.","complex","complex(0,","complex(math.random(),","complex)","complex::new(1.0_f64,","complex::new(par.k[i],","complexity.","complic","complicated).","complicated.","complicated:","compon","component,","component.","components,","components.","compos","composit","comprehens","comprehension,","compress","compression!","compression,","compression.","comput","computation","computation,","computation.","computation:","computations,","compute_sobel(signal)","compute_sobel(signal):","computer,","computer.","computer?","computers.","computers?","computers?\"","computing.","computu","computus([int]$year,","computus(int","computus(y)","computus(y,","computus(year","computus(year,","computus(year:","computus(year;","computus,","computus.(a)","computus.(a;","conc","concat","concat(&result,","concat(char**","concat_char(char**","concat_char(result,","concaten","concatenation,","concatmap","concav","concept","concept,","conceptu","concern","concerns,","concession,","conclud","conclus","conclusion,","concret","condens","condit","condition\"","conditionals,","conditions,","conditions.","conditions:","condon","configur","configuration,","configuration:","confin","confus","confusing.","conglomer","conj(wfc_r)","conjug","conjugate.","connect","consecut","consequ","consequences:","consid","consider","consider:","consist","console.log(","console.log(\"[#]\\nqueu","console.log(\"[#]\\nrecurs","console.log(\"[#]\\nstack","console.log(\"[0.0","console.log(\"[1.0","console.log(\"[2.0","console.log(\"\\ngirls\");","console.log(\"\\npairings\");","console.log(\"cooley","console.log(\"guys\");","console.log(\"ha","console.log(\"it","console.log(\"th","console.log('[#]\\nmodulu","console.log('[#]\\nsubtract","console.log();","console.log(`${girl.name}:","console.log(`${guy.name}:","console.log(`${stormer.time}`);","console.log(`${stormer.vel}`);","console.log(`${time}`);","console.log(`${velocity.time}`);","console.log(`${velocity.vel}`);","console.log(`(${p.x},","console.log(`[#]\\ntim","console.log(`[#]\\nveloc","console.log(decoded);","console.log(encoded.string);","console.log(euclidmod(64","console.log(euclidsub(128","console.log(numberqueue.dequeue());","console.log(numberqueue.front());","console.log(numberqueue.size());","console.log(numberstack.pop());","console.log(numberstack.size());","console.log(numberstack.top());","console.log(tree.id);","console.println(","console.write(choice.name);","console.write(queue.peek().id","console.write(stack.peek().id","console.write(tree.id","console.writeline(\"[#]\\nmodulu","console.writeline(\"[#]\\nqueu","console.writeline(\"[#]\\nrecurs","console.writeline(\"[#]\\nstack","console.writeline(\"[#]\\nsubtract","console.writeline(\"galeshapleyalgorithm\");","console.writeline();","console.writeline(check);","console.writeline(check2);","console.writeline(man.nam","console.writeline(woman.nam","const","const&","const*","const;","constant","constant(a::array{float64})","constant(a::uint64,","constant,","constantli","constants!","constants,","constants.","constexpr","constitu","constrain","constrained,","constraint","constrict","constrictions.","construct","constructed.","construction,","constructor(name)","consult","consum","consume(","contact","contact.","contain","containers.map(k,v);","contains?","contend","content","context","context.","context?","contextlib","contin","continu","continue,","continue.","continue;","continues.","continuing,","continuing:","contour","contour.","contours.","contractive.","contractivity,","contradiction.","contrast","contribut","contribute,","contributors.md","contributors.md.","contributors.md:","control,","control.monad.st","convent","converg","convers","conversation,","convert","convert(int,ceil(log2(length(a))))","convert(int,ceil(log2(length(x))))","convex","convex,","convexhul","convexhull.foreach(p","convexhull;","convexhull[0]);","convinc","convolut","convoluted!","convolution!","convolution\"","convolution,","convolution.","convolution1d","convolution:","convolutions,","convolutions.","convolutions:","convolutions?","convolv","convolve_cyclic(signal,","convolve_cyclic(signal::array{t,","convolve_fft(signal1,","convolve_fft(signal1::array{t},","convolve_fft(x,","convolve_linear(signal,","convolve_linear(signal::array{t,","convolve_linear(x,","convolvecyclic(double[]","convolvelinear(double[]","convolvelinear(x,","cool","cool.","cooler","cooley","cooley_tukey","cooley_tukey(&x);","cooley_tukey(&x.iter().skip(1).step_by(2).cloned().collect::>());","cooley_tukey(begin(recursive),","cooley_tukey(doubl","cooley_tukey(it","cooley_tukey(x)","cooley_tukey(x):","cooley_tukey(x);","cooley_tukey(x.filter((_,","cooley_tukey(x:","cooley_tukey(x[1:2:n])","cooley_tukey(x[2:2:n])","cooley_tukey:","cooley_tukey_end","cooley_tukey_end:","cooley_tukey_loop","cooley_tukey_loop:","cooley_tukey_mov","cooley_tukey_mov_data","cooley_tukey_mov_data:","cooley_tukey_moved:","cooley_tukey_return","cooley_tukey_return:","cooley_tukey_split","cooley_tukey_split:","cooley_tukey_spliting:","coord","coordin","coordinate,","coordinates)","coordinates,","coordinates.","coordinates[0];","coordinates[1];","coordinates[2];","coords)","copi","copy(c)","copy(d)","copy(men)","copy(women)","copy)]","copy,","copyright.","core","corner","corner:","cornerston","correct","correct,","correct.","correct;","correctly.","correl","correlation,","correspond","cos(theta)","cos(x)","cosin","cosine,","cost","costli","costly.","cough)","couldn't","count","count($x));","count(&self)","count(0ull)","count)","count))))))","count,","count.","count:","count;","countdown(n","counted,","counted.","counter","counter!","counter(message)","counter,","counter.","counter_clockwise(&hull[hull.len()","counter_clockwise(a:","counter_clockwise(hull[","counter_clockwise(p,","counter_clockwise(p1","counter_clockwise(p1,","counterclockwise\"","counterclockwise(p1,","counting!","counting\"","counting,","counting:","counts,","counts.","counts:","counts;","counts[(unsign","counts[256]","counts[char]","counts[i];","counts_size,","counts_size]","counts_size],","count❗️","coupl","cours","course!).","course)","course,","cover","covered.","cpow(par.k[i],","cpow(par.x[i]","cpp","cprime","cprime[0]","cprime[i","cprime[i]","cpu","cpu,","cpu.","cr.","crack","craft.","crate","crazi","crazy,","creat","create.","create_btree()","create_btree();","create_circle(image_resolution,","create_codebook(huffman_tree)","create_codebook(n::node)","create_gaussian_kernel(kernel_size)","create_gaussian_kernel(kernel_size):","create_grid(n,","create_group(struct","create_rand_dist(4096^2,[0,1])","create_rand_dist(4096^2,[0,1],","create_rand_dist(n,","create_sobel_operators()","create_sobel_operators():","create_tre","create_tree()","create_tree();","create_tree(2,","create_tree(3,","create_tree(3,2)","create_tree(int","create_tree(levels,","create_tree(node(),","create_tree(node,","create_tree(num_row","create_tree(num_row:","create_tree(num_row::int64,","create_tree(num_rows,","create_tree(phrase)","create_tree(phrase::string)","create_tree:","create_tree_children","create_tree_children:","create_tree_leaf","create_tree_leaf:","create_tree_return","create_tree_return:","createallchildren(nod","createbitstring(str","createbranch","createbranch(nod","createcodebook(mayberoot:","createcodebook(tree)","createcodebook(tree);","created.","createdictionary(nod","createdictionary(node.leftchild,","createdictionary(node.rightchild,","createdictionary(root,","createleaf(char","createsawtooth(int","createtre","createtree()","createtree(2,","createtree(3,","createtree(numrow,","createtree(numrows:","createtree(originaltext)","createtree(phrase:","createtree(row","createtree(rows,","createtree(str)","createtree(str);","creation","creation.","creativ","cri","criterion","crop","cross","crosses.","crucial","crunching.","cryptograph","cryptographi","cryptography\"","cryptography,","cryptography.","cryptography:","crystal","cuarray)","cube","cube!","cube\"","cube,","cube:","cuda","cuda.@sync.","cuda.@tim","cudakernel","cumulprob","cur","cur.char","cur.children...)","cur.id","cur.id)","cur.left","cur.right","cur_loc","cur_loc,","cur_loc.y]","cur_point","curpoint","curpoint;","curr_point","curr_point)","curr_product","curr_product)","current","current)","current))","current.left","current.right","current.value);","current;","current_loc","current_loc,","current_location,","current_nod","current_node.children:","currently,","currentnod","currenttopchoic","currenttopchoiceindex","curv","curve.","custom","cut","cutoff","cutoff)","cutoff::int64)","cvtsi2sdq","cvttsd2si","cvx","cvx))","cvx)]","cycl","cycle)","cycle,","cyclic","cypher.","c|","c}{2}\\\\","d","d')","d'_0","d'_0.","d'_i","d'_i.","d'_n.","d'_{i","d)","d))","d),","d):","d+e","d+e+22\\text{","d+e.","d,","d,31))","d.clone()","d.count","d.dup","d.length","d:","d::vector{float64},","d=28","d=28,","d=29","d[0]","d[0]].join(\"\\t\")","d[1])","d[1]),","d[1]].join(\"\\t\")","d[2])","d[2]),","d[2]].join(\"\\t\")","d[3])","d[3]),","d[i","d[i+1]","d[i]","d[j","d[j]","d\\mathbf{r}","d\\mathbf{x}","d\\mathbf{x}.","d\\xi","d^*_i","d_0","d_1","d_glibcxx_debug","d_i","d_in","d_in:","d_n","d_{n","damage.","dangerous!","dart","dash","dashtyp","data","data'","data)))","data);","data,","data.","data.array","data.array.carray","data.complex","data.funct","data.list","data.map","data.ratio","data.to_vec(),","data:","data;","data[index]","data[target]","datafil","dataset","datasets.","datastructur","datastructures,","data{std::move(decoder),","date","date.","dates.","david","day","day!","day,","day.","days),","days,","days.","de","dead","deal","death","debat","debug","dec","decad","decay","decent","decid","decim","decis","decod","decode(&self,","decode(bitstring,","decode(const","decode(enc,","decode(encoded,","decode(encoded.string,","decode(encoded:","decode(huffman_tree,","decode(huffman_tree::node,","decode(it","decode(messag","decode,","decode:","decode_dfs(&self,","decode_don","decode_done:","decode_loop","decode_loop:","decode_loop_char","decode_loop_char:","decode_loop_char_branch","decode_loop_char_branch:","decode_recurse(const","decode_recurse(input","decode_recurse(input,","decode_singl","decode_single(it,","decoded()","decoded)","decoded);","decoded:","decoded_messag","decoded_message)","decoded_message.append(inverse_dict[key])","decoded_message:","decoder)","decoder))","decoder;","decoder]","decoding.","decreas","decrement","decrypt","decrypt,","decrypting.","deduc","deem","deep.\"","deep.\"\"\"","deeper","deepli","def","default","default:","defaultparamet","defin","defined.","definit","definition)","definition,","definition:","definitions,","definitions:","definitions;","degre","degrees,","del","delambre)","delete!(mentowomen,","delimitedfil","delimitedfiles,","delta","delv","demand.","demonstr","denomin","denominator)","denominator,","denot","densiti","densities.","density\"","density,","density.iter().sum::()","density:","density=true)","density[j],","density[j].real,","density[opr.size];","dep","depend","dependence,","depict","depth","depth,","depth_count","depthcount,","dequ","deque()","deque([node])","deque.new","dequeu","dequeue!(nodes)","dequeue!(q)","dequeue!(weights)[1]","dequeue(&mut","dequeue(&q);","dequeue()","dequeue():","dequeue();","dequeue(self)","dequeue(struct","dequeue:","dequeue_return","dequeue_return:","derefer","deriv","derivatives.","derivatives:","descend","describ","describe,","descript","descriptions,","descriptor","deserv","design","desir","desire,","desired.","desktop","destroy","destroy_tree(root);","destroy_tree(root_binary);","destruct","destructively\"","detail","detail:","details,","details.","detect","detection,","detector.","determin","determinist","dev","develop","developed.","development.","deviat","deviates,","deviation,","deviations.","devic","devis","devot","df","dfs(&self,","dfs.","dfs:\"","dfs:\")","dfs:\");","dfs:'","dfs:\\n\");","dfs:~%\")","dfs_recurs","dfs_recursive(&root);","dfs_recursive(...)","dfs_recursive(child)","dfs_recursive(child);","dfs_recursive(n)","dfs_recursive(n:","dfs_recursive(n::node)","dfs_recursive(nod","dfs_recursive(node(value,","dfs_recursive(node)","dfs_recursive(node):","dfs_recursive(root)","dfs_recursive(root);","dfs_recursive(struct","dfs_recursive(tree)","dfs_recursive:","dfs_recursive_bt_return","dfs_recursive_bt_return:","dfs_recursive_bt_size0","dfs_recursive_bt_size0:","dfs_recursive_bt_size1","dfs_recursive_bt_size1:","dfs_recursive_bt_size2","dfs_recursive_bt_size2:","dfs_recursive_children","dfs_recursive_children:","dfs_recursive_inorder_btre","dfs_recursive_inorder_btree(&root_binary);","dfs_recursive_inorder_btree(binary_tree)","dfs_recursive_inorder_btree(children[0])","dfs_recursive_inorder_btree(children[1])","dfs_recursive_inorder_btree(children{1})","dfs_recursive_inorder_btree(children{2})","dfs_recursive_inorder_btree(left);","dfs_recursive_inorder_btree(n)","dfs_recursive_inorder_btree(n.children[0]);","dfs_recursive_inorder_btree(n.children[1])","dfs_recursive_inorder_btree(n.children[1]);","dfs_recursive_inorder_btree(n.children[2])","dfs_recursive_inorder_btree(n:","dfs_recursive_inorder_btree(n::node)","dfs_recursive_inorder_btree(nod","dfs_recursive_inorder_btree(node(value,","dfs_recursive_inorder_btree(node)","dfs_recursive_inorder_btree(node):","dfs_recursive_inorder_btree(node.children[0])","dfs_recursive_inorder_btree(node.children[1])","dfs_recursive_inorder_btree(right);","dfs_recursive_inorder_btree(root_binary)","dfs_recursive_inorder_btree(root_binary);","dfs_recursive_inorder_btree(rootb)","dfs_recursive_inorder_btree(struct","dfs_recursive_inorder_btree:","dfs_recursive_po_children","dfs_recursive_po_children:","dfs_recursive_po_return","dfs_recursive_po_return:","dfs_recursive_postord","dfs_recursive_postorder(&root);","dfs_recursive_postorder(child)","dfs_recursive_postorder(child);","dfs_recursive_postorder(n)","dfs_recursive_postorder(n:","dfs_recursive_postorder(n::node)","dfs_recursive_postorder(nod","dfs_recursive_postorder(node(value,","dfs_recursive_postorder(node)","dfs_recursive_postorder(node):","dfs_recursive_postorder(root)","dfs_recursive_postorder(root);","dfs_recursive_postorder(struct","dfs_recursive_postorder(tree)","dfs_recursive_postorder:","dfs_recursive_return","dfs_recursive_return:","dfs_stack","dfs_stack(&root);","dfs_stack(...)","dfs_stack(n)","dfs_stack(n:","dfs_stack(n::node)","dfs_stack(nod","dfs_stack(node)","dfs_stack(node):","dfs_stack(root)","dfs_stack(root);","dfs_stack(struct","dfs_stack(tree)","dfs_stack:","dfs_stack_end_push","dfs_stack_end_push:","dfs_stack_loop","dfs_stack_loop:","dfs_stack_push_child","dfs_stack_push_child:","dfs_stack_return","dfs_stack_return:","dfsinord","dfsinorder(root_binary);","dfsinorder(tree)","dfsinorder(tree.children[0]);","dfsinorder(tree.children[1]);","dfsinorderbinarytree.","dfsinorderbinarytree:","dfsiterative(root);","dfsiterative(tree)","dfspostord","dfspostorder(root);","dfspostorder(tree)","dfspreorder(root);","dfspreorder(tree)","dfsqueue(tre","dfsrecurs","dfsrecursive()","dfsrecursive(c);","dfsrecursive(child)","dfsrecursive(n","dfsrecursive(n);","dfsrecursive(nod","dfsrecursive(node:","dfsrecursive(this);","dfsrecursive(tre","dfsrecursive.","dfsrecursiveinorderbinari","dfsrecursiveinorderbinary()","dfsrecursiveinorderbinary()!\");","dfsrecursiveinorderbinary(nod","dfsrecursiveinorderbinary(node.children.get(0));","dfsrecursiveinorderbinary(node.children.get(1));","dfsrecursiveinorderbinary(node:","dfsrecursiveinorderbinary(this);","dfsrecursiveinorderbinary(this.root);","dfsrecursiveinorderbinary(tre","dfsrecursiveinorderbinary(tree._children[0]);","dfsrecursiveinorderbinary(tree._children[1]);","dfsrecursiveinorderbtree(n","dfsrecursiveinorderbtree(n.children[0])","dfsrecursiveinorderbtree(n.children[1])","dfsrecursivepostorder()","dfsrecursivepostorder(c);","dfsrecursivepostorder(child)","dfsrecursivepostorder(n","dfsrecursivepostorder(n);","dfsrecursivepostorder(nod","dfsrecursivepostorder(node:","dfsrecursivepostorder(this);","dfsrecursivepostorder(tre","dfsrecursivepostorder)].","dfsrecursivepostorder.","dfsstack","dfsstack()","dfsstack(n","dfsstack(node:","dfsstack(tre","dfsstack.","dft","dft(&x);","dft(doubl","dft(iter","dft(x)","dft(x):","dft(x);","dft(x:","dft.","dft:","dft:\"","dft_end_i","dft_end_i:","dft_end_j","dft_end_j:","dft_loop_i","dft_loop_i:","dft_loop_j","dft_loop_j:","dftmat","diagon","diagonalization,","diagram","diagram,","diagram:","diagrams.","dial","dice","dice),","dice,","dice.","dict","dict((v,","dict([(v,","dict(codebook)","dict(map(m","dict(map(w","dict)","dict);","dict::dict{char,string})","dict;","dict[leaf.key]","dict[node.key]","dictat","dictionari","dictionary();","dictionary)","dictionary);","dictionary,","dictionary.","dictionary;","dictionary[character];","dict{char,string}()","dict{string,string}","dict{string,string}()","dict{string,vector{string}}","didn't","die","dietmar","diff","differ","differences:","different?","differenti","differently,","difficult","diffrint","diffus","diffv","diffv))))","dig","digit","digit.","digits:end]","dil","dil,","dilut","dimens","dimension","dimension)","dimension,","dimension.","dimension:","dimensional;","dimensionality,","dimensions!\")","dimensions,","dimensions.","direct","direction,","direction.","directions,","directions.","directli","directly,","directori","directory.","dirti","disappears.","disciplin","discontinu","discord","discov","discoveri","discrep","discret","discrete,","discuss","discuss.","discussion,","discussion.","disect","disguise.","display","display,","dissimilar","dist(0,","distanc","distance.","distil","distinct","distinct.","distinctli","distinguish","distract","distracting,","distribut","distribution(0.0,","distribution(rng);","distribution(s)","distribution)","distribution,","distribution.","distribution:","distribution?","distributions),","distributions,","distributions.","div","div(bnum,2)","div(n,","div(n,2)","div(par.timesteps,","dive","diverg","divergence,","divf","divid","divis","division),","divisor","divisor\"","divisor)","divisor.","divsd","divsor","dk","dk,","dk:","dk::float64","dk;","dmrg,","do","do!","do,","do.","do?","docker","document","document,","documentation,","documents,","does!","doesn't","domain","domain,","domain.","domain;","domains\"","domains:","don't","don't.","donald","done","done,","done.","door","doors,","dot","doubl","double)","double):","double,","double.random(in:","double[3];","double[]","double[][]","double[length];","double[outputsize];","double[rows];","double[size];","double]","doublearray","doublearray):","doublearray,","doublearrayof(0.0,","doublearrayof(1.0,","doublearrayof(4.0,","doublearrayof(7.0,","doubli","doubt","down","down\"","down,","down.","down.\"","downto","downwards.","dp","drama","dramat","drand()","drand();","drand()};","drastic","draw","drawback","drawn","drawn.","drop","dst","dst,","dst;","dst_len","dt","dt)","dt))","dt)))","dt),","dt):","dt,","dt:","dt::float64","dt::float64)","dt::float64,","dt;","dt^2","dt^3,","dtor","dtype=complex)","dtype=float)","duct","due","dumb","dump","dup","duplic","duplicate(build","duplicate(const","duplicate(get_code(codebook,","duplicates.","dure","during,","dwell","dword","dx","dx)","dx))","dx),","dx);","dx,","dx:","dx::float64","dx;","dx_1\\dot","dx_{10}.","dx}","dynam","dynamic_cast(cur))","dynamic_cast(current_node))","d}{2}\\\\","e","e(\\mathbf{x})","e(\\mathbf{x})/t\\right],","e(\\mathbf{x})}{t}","e(x_1,","e(x_1,...,x_{10})","e(x_1,\\dot","e)","e))","e)))","e),","e).to_","e);","e,","e.","e.g","e.g.:","e=","e=6","e=6,","e^(","e^(n*k*2*pi*(1/len)*(","e^v","e^{","e^{2","e^{255}","e^{2\\pi","each","each.","earli","earlier,","earth","earth'","earth,","earth.","earthfail","easi","easier","easiest","easili","east","east,","easter","easter\"","easter\"))","easter)","easter)))","easter,","easter.","easter:","easter?","easter_d","easterd","eastern","easy:","eavesdropp","eavesdropper.","eax","eax,","ecc","echelon","echelon)","echo","ecx","ecx,","edg","edge!).","edge)","edge.","edi","edi,","edit","educ","edx","edx,","effect","effect,","effect.","effici","efficient.","effort","eigenst","eigenvalu","einstein","either.","either:","elabor","electromagnetism,","electron","elegantli","elem","element","element'","element)","element);","element,","element.","element:","element;","elementari","elements,","elements.","elemindex","elems)","elems,","elias,","elif","elimin","elimination\")","elimination,","elimination.","elimination:","elimination:\")","elimination:\");","elimination:\\n\");","ellipsoid","ellipt","elm","else).","else,","else:","elseif","elsevier,","em,","emb","embed","emojicod","empir","empti","empty()","empty,","empty:","enc)","enc,","enclos","encod","encode(\"bibb","encode(\"bibbity_bobbity\")","encode(&self,","encode()","encode(codebook,","encode(codebook::dict{char,","encode(const","encode(it","encode(messag","encode(originaltext,","encode(phrase:","encode(str)","encode:","encode_calculate_length","encode_calculate_length:","encode_calculate_new_bit_offset","encode_calculate_new_bit_offset:","encode_don","encode_done:","encode_messag","encode_message:","encode_message_bit","encode_message_bits:","encode_message_bits_qword","encode_message_bits_qword:","encode_message_bits_try_overflow","encode_message_bits_try_overflow:","encoded)","encoded);","encoded.tree);","encoded:","encoded_messag","encoded_message)","encoded_message):","encoded_message:","encoded_str","encoded_string(codebook","encoded_string(std::str","encoder;","encoder_rec(&decoder,","encoder_rec(b","encoder_t","encoder_t&","encoder_t();","encoding.","encoding:","encodingresult","encodingresult(str","encompass","encount","encourag","encrypt","encryption:","end","end(code),","end(encoder))","end(encoder),","end(freq))","end(freq),","end(initial),","end(iterative));","end(recursive));","end(ret),","end(s)))","end(s)),","end(string));","end)","end).","end,","end.","end='","end='')","end_point","end_point;","endfunct","endif","endmethod","endpoint","endpoint)","endpoint)):","endpoint):","endpoint.equal(hullpoint)","endpoint.equal(hullpoints[0])","endpoint:","endpoint;","endpoints)","endpoints;","endpoints[1]","endpoints[1])","endpoints[1],","endpoints[1]]","endpoints[2]","endwhil","energi","energy)","energy,","energy.","energy_fin","energy_final*par.dx","energy_k","energy_k,","energy_k[i]","energy_r","energy_r).r","energy_r[i]","energy_r[i])","enforc","engag","engin","engineering,","engineering.","enjoy","enjoy.","enlighten","enough","enqueu","enqueue!(nodes,","enqueue!(q,","enqueue!(q,neighbor)","enqueue(&mut","enqueue(&q,","enqueue(const","enqueue(data:","enqueue(self,","enqueue(struct","enqueue(t","enqueue(value)","enqueue:","enqueue_append","enqueue_append:","enqueued,","enqueued:","ensur","enter","entir","entirely,","entirely:","entireti","entri","entry.","enum","enumerate(encoded_message):","enumerate(trees)","ep,","epslatex","epslatex.","eq","eq(&self,","eq)","eqns.size(),","eqns.size();","eqns[0].size();","eqns[i]);","equal","equal,","equals(object","equals(point","equat","equation!","equation,","equation.","equation:","equations,","equations.","equations:","equations;","equations?","equations{","equilater","equilibrium","equinox","equival","era","era!","err(why)","error","error🔤❗️","error(\"postord","error)))","error,","error.","error:","error_fmt:","errors!","escap","esi","esi,","especi","essence,","essenti","essentially,","establish","estaim","estim","estimate)))","estimate))))","estimate_fmt:","et","etc).","etc.","etc.),","etc.).","euclid","euclid%","euclid'","euclid($a,","euclid()","euclid)","euclid_mod","euclid_mod()","euclid_mod(0,","euclid_mod(128","euclid_mod(64","euclid_mod(a","euclid_mod(a,","euclid_mod(a:","euclid_mod(a::int64,","euclid_mod(b,","euclid_mod(in1,","euclid_mod(int","euclid_mod:","euclid_mod_fmt","euclid_mod_fmt:","euclid_rem(64","euclid_rem(mut","euclid_sub","euclid_sub()","euclid_sub(0,","euclid_sub(128","euclid_sub(64","euclid_sub(a","euclid_sub(a,","euclid_sub(a:","euclid_sub(a::int64,","euclid_sub(in1,","euclid_sub(int","euclid_sub(mut","euclid_sub(x","euclid_sub(x,","euclid_sub,","euclid_sub:","euclid_sub_fmt","euclid_sub_fmt:","euclidean","euclideanalgo","euclideanalgorithm","euclideanalgorithm();","euclideanalgorithm.c","euclideanalgorithm.euclidmod(64","euclideanalgorithm.euclidsub(128","euclidian","euclidmod","euclidmod(64*67,","euclidmod(a,","euclidmod(a,b)","euclidmod(a:","euclidmod(int","euclidmod:","euclidsub","euclidsub(128*12,","euclidsub(a,","euclidsub(a,b)","euclidsub(a:","euclidsub(int","euclidsub:","euler'","ev","evalst","evalu","evaluate,","even","even[k]","evenli","evens)","event","events,","events.","eventu","eventually,","everybodi","everyon","everyone'","everyone.","everyth","everything,","everywher","everywhere,","evid","evil","evil.","evol","evolution.","evolv","evolves,","exact","exact,","exactli","exactly,","exactly.","exampl","example,","example.","example:","examplequeue()","examplequeue();","examples!","examples,","examplestack()","examplestack();","except","exception(\"not","excit","exclud","exclus","exclusive\"","execut","exist","exist,","exist.","existed,","exists!","exists,","exists.","exit","exit_success;","exp","exp(","exp(x)","exp,","exp.(","expand","expans","expansion,","expansion.","expect","expect,","expect.","expect:","expectation.","expected,","expens","expensive.","experi","experiment","experiment,","experiment.","experiment?","experimentalist","experiments,","experiments.","experiments.core)","experiments:","explain","explain,","explain.","explain:","explan","explanation,","explanation.","explicit","explicitli","explicitly:","exploit","explor","exploration,","expon","exponent,","exponenti","exponential(value,","exponential(value::int64,","exponential.","exponentially.","exponentials,","exponentials.","export","expres","express","expressions.","extend","extens","extent","extent=(","extern","extra","extraordinari","ey","eye.","e}\"","e}\".fmt","e}';","e}`;","f","f'({self.x},","f'leaf({self.char},","f'node({str(self.left)},","f'{self.name}:","f(2)=1.","f(3)=2.","f(\\mathbf{x})","f(\\mathbf{x}).","f(\\mathbf{x})d\\mathbf{x}.","f(\\mathbf{x})d\\mathbf{x}},","f(\\mathbf{x})d\\mathbf{x}}.","f(\\xi)","f(a)","f(centers,","f(cpu(),","f(cudadevice(),","f(n)","f(n),","f(n).","f(n)}","f(n)}.","f(x')","f(x(t+\\delta","f(x)","f(x)).item())","f(x),","f(x).","f(x)},","f(x,","f(x_t),","f(x_t).","f(z)","f(z)!","f(z).","f(z):","f(z)=z^2.","f)","f*g=c","f,","f.","f.write(\"{0}\\t{1}\\n\".format(*point))","f.write(\"{0}\\t{1}\\n\".format(p.x,","f1)","f1+f2)","f2))","f64","f64)","f64))","f64)).exp()","f64)).exp();","f64).log2()","f64).sqrt()).collect()","f64).sqrt();","f64);","f64,","f64;","f:","f=f,","f[n]","f^{(n)}(x)","f_1","f_1(p)","f_1,","f_2","f_2(p)","f_2,","f_3","f_3(p)","f_3,","f_4","f_4(p)","f_4,","f_val","f_val_ab","fabs(a[pivot","fabs(eqns[pivot][i]))","fabs_const:","face","facet","fact","fact,","factor","factor,","factor[1:half])","factor[1:half],","factorial.)","factors)))","factors.","fail","failure_count","failure_count))","failures')","fair,","fairli","fall","fals","false)","false):","false):6}\".fmt","false);","false;","false})","familiar","famou","fan","fano","fano,","fantast","faq","far","far.","fashion","fashion,","fashion.","fast","fast!","fast,","fast.","fast?","faster","faster,","fastest","favor","favored.","favorit","feasibl","featur","feature!","features,","features;","februari","fed","feebl","feel","female,","fern","fern\"","fern,","fern.","fern:","festival.","few","few.","few:","fewer","fft","fft'","fft(&mut","fft(&x);","fft()","fft(doubl","fft(opr.wfc)","fft(wfc_k,","fft(wfc_r)","fft(x)","fft(x:","fft)","fft))))))","fft,","fft.","fft.core","fft.process(x.as_mut_slice(),","fft:\"","fft;","fft_output","fftplanner::new(false);","fftplanner::new(inverse);","ffts.","fftw","fftw)","fftw3","fftw_backward","fftw_backward,","fftw_complex","fftw_destroy_plan(p);","fftw_estimate);","fftw_execute(p);","fftw_forward),","fftw_forward,","fftw_plan","fftw_plan_dft_1d((int)n,","fftw_plan_dft_1d(static_cast(x.size()),","fi","fi)","fianc","fiance.recieveproposal(this);","fiance:","field","field,","fields:","fig,","fig.colorbar(","fig.savefig(\"domain.png\")","fight","figur","file","file),","file,","file.","file.flush()","file.gp","file::create(&path)","file_0000.dat,","file_0001.dat,","file_0002.dat,","filenam","files,","files;","fill","fill\"","fill,","fill.","fill?","fillstep","filter","filter$(in_circle$(?,","filter$(x","filter)","filter,","filter,\"","filter.","filter.length);","filter.shape[0]),","filter.shape[1]),","filter:","filter::array{t,","filter?","filter[i","filter_array):","filter_array,","filters\"","filters,","filters.","filters:","final","final_bitstr","final_canvas).all()","final_canvas,","final_str","finally,","find","find;","find_neighbors(","find_neighbors(c,","find_neighbors(canvas,","find_neighbors(grid,","find_neighbors(struct","find_neighbours(canvas,","findfirst(m","findstablemarriages(list","findstablemarriages(women,","findstablematches(men:","fine","fine.","finger","finger.","fingerprint","fingers?","fingertips,","finish.","finished;","finit","finite:","first","first)","first,","first.","first;","first[i]);","first[k","first[k];","first_point_it","firsti","firstly,","firxt","fit","fix","fl,","flags,","flajolet","flatmap","flavor.","fld(13","fld(k,","fld(year,","fledgl","flexibl","fli","flip","flip(children)","flip.","float","float)","float):","float,","float.","float64","float64(point.x","float64)","float:","floats,","flonum","flood","floor","floor(abs(f(z(x,y)))))","floor(x/bin_width)","flowchart","fluctuat","fluid","fluids,","flush","fmap","fmt.print(\"[\")","fmt.printf(\"%9.4f","fmt.printf(\"%d","fmt.printf(\"[%f]\\n\",","fmt.printf(\"i","fmt.printf(\"x=%f","fmt.println(\"[#]\\nmodulu","fmt.println(\"[#]\\nsubtract","fmt.println(\"[#]\\ntim","fmt.println(\"[#]\\nveloc","fmt.println(\"[0.0","fmt.println(\"[1.0","fmt.println(\"[2.0","fmt.println(\"\\nencoded:\",","fmt.println(\"]\")","fmt.println(\"codebook:\")","fmt.println(\"decoded:\",","fmt.println(\"gauss","fmt.println(\"gaussian","fmt.println(\"ha","fmt.println(\"origin","fmt.println(\"solut","fmt.println(\"th","fmt.println(\"thi","fmt.println()","fmt.println(check1)","fmt.println(check2)","fmt.println(string(r),","fmt.println(time)","fmt.println(vel)","fmt:","fmt_tree","fmt_tree:","fn","focu","focus","follow","follow;","following,","following:","followit","follows)","follows,","follows:","food","footbal","for(","for)),","for.","forc","foreach","foreach($year","forego","forest","forev","forg","forgotten","form","form\"","form,","form.","form:","formal","formalism.","formally):","formally,","format","format!(\"april","format!(\"march","format!(\"output{}.dat\",","format!(\"{:18}\",","format!(\"{:?}\",","format!(\"{}\\t{}\\n\",","format,","former,","formerli","formula","formula,","formula:","formulas,","formulations.","forth","fortran","fortran,","fortunately,","forward","forward,","forward.","forward_dict","forward_dict[char]","found","found,","foundat","four","four:","fourier","fprintf(\"not","fprintf(\"perc","fprintf(\"th","fprintf('%u","fprintf('\\n')","fprintf('\\nbf","fprintf('\\ndf","frac","fractal","fractals,","fraction","fraction,","fraction;","fractions).","framework,","frederick","free","free!","free(heap","free(q","free(q.data);","free(stk.data);","free(tree);","free,","free.","free_group(men,","free_group(struct","free_group(women,","free_queu","free_queue(q);","free_queue(struct","free_queue:","free_stack","free_stack(stk);","free_stack(struct","free_stack:","free_tre","free_tree:","free_tree_free_array","free_tree_free_array:","free_tree_free_kid","free_tree_free_kid:","free_tree_return","free_tree_return:","freefal","freeli","freq","freq,","freq.emplace_back(1,","freqmap","freqmap[char]","freqmap[char].freq++","freqmap[char];","frequenc","frequencies,","frequencies.most_common()","frequency)","frequency,","frequency.","frequency;","frequency]","frequency_array(message)","frequency_array(str)","frequencymap","frequencymap.entryset())","frequent","friday","friend","friendlier,","from(input:","from,","from.","fromintegr","front","front(&self)","front()","front():","front();","front(self)","front,","front_point","front_pointer.reset();","front_pointer:","front_pointer;","frontel","fst","full","full,","full_linear_output","fulli","fulllinearoutput","fun","fun.","func","func(a,","function","function'","function(a,","function(canvas)","function):","function,","function.","function:","function?","functions,","functions.","functions.6.lundmark,","functions:","functions;","functions?","fundament","funky,","furious","further","further,","fuss!","futur","future!","future,","future.","fuzzier","f}{\\partial","g","g'","g''","g'')","g')","g()","g():","g(\\xi),","g(r)","g(x)","g(x,y)","g,","g.","g=g):","g[n]","g_i","g_x","g_y^2}","g_{\\text{total}}","gale","galeshapley(men,","galeshapley(men::preferences,","galeshapleyalgorithm","galeshapleyalgorithm.c","galeshapleyalgorithm.rungaleshapleyalgorithm(women,","gambler!","game","game\"","game).","game,","games,","games.","gammison","gases,","gate","gate,","gate:","gates,","gathro","gathros,","gauss","gauss'","gauss,","gauss.","gauss_jordan(&mut","gauss_jordan(a:","gauss_jordan(doubl","gauss_jordan_elimination!(a)","gauss_jordan_elimination!(a::array{float64,2})","gauss_jordan_elimination(a)","gauss_jordan_elimination(a):","gausseast","gaussian","gaussian,","gaussian.","gaussian;","gaussian?","gaussian_elimination!(a)","gaussian_elimination!(a::array{float64,2})","gaussian_elimination(&mut","gaussian_elimination((doubl","gaussian_elimination(a)","gaussian_elimination(a):","gaussian_elimination(a:","gaussian_elimination(doubl","gaussian_valu","gaussianelimin","gaussianelimination(a","gaussianelimination(a)","gaussianelimination(a);","gaussianelimination(double[][]","gaussianelimination(std::vector","gaussians.","gaussjordan","gaussjordan(a","gaussjordan(a)","gaussjordan(a);","gaussjordan(double[][]","gaussjordan(std::vector","gave","gcd","gcd_minus(128","gcd_minus(a,","gcd_mod(64","gcd_mod(a,","gdwarf","gem","gender","gener","general,","general.","generate_codebook","generate_codebook(*huffman_tree);","generate_codebook(const","generate_codebook:","generate_codebook_branch","generate_codebook_branch:","generate_codebook_recurs","generate_codebook_recurse:","generate_codebook_recurse_don","generate_codebook_recurse_done:","generate_tre","generate_tree(2,","generate_tree(3,","generate_tree(const","generate_tree(input);","generate_tree(int","generate_tree:","generate_tree_branch","generate_tree_branches:","generate_tree_count_char","generate_tree_count_chars:","generate_tree_don","generate_tree_done:","generate_tree_leav","generate_tree_leaves:","generate_tree_leaves_count","generate_tree_leaves_counters:","generate_tree_leaves_setup","generate_tree_leaves_setup:","generate_tree_one_leaf","generate_tree_one_leaf:","generate_tree_ret","generate_tree_ret:","generatecodebook(root","generatecodebook(root)","generation:","generators.","genet","genius.\"","genpreferences(mannames::vector{string},","genpreferences(mnames,","genuin","geometr","geometri","geometry.","georg","get","get,","get;","get_code(codebook,","get_code(const","get_queu","get_queue(size_t","get_queue(sizeof(struct","get_queue:","get_stack","get_stack();","get_stack(size_t","get_stack(sizeof(struct","get_stack:","getchildren():","getclass().getname()","getfrequ","gethashcode()","getid():","getmatch():","getmate()","getname():","getnexttopchoice();","getpreferences():","getpreferredmates()","getter\"","getter.\"","getx()","gety()","giallouraki","gif","gift","gift\"","gift)","gift))","gift)))))","gift.","gift.add(new","gift.get(0);","gift.len()","gift.remove(start)","gift.size());","gift.stream()","gift.sublist(1,","gift:","gift[0]","gift[j]","giftwrap","giftwrap)","gimp,","girl","girl.prefer","girlfriend,","girls)","girls);","git","gitbook","github","github)","give","given","given_id","given_radiu","given_radius❗️","givennodes)","givennodes.tolist();","glanc","glance,","global","global_random_device;","global_rng(global_random_device());","global_rng);","glory!","gnuplot","gnuplot,","gnuplot.","go","go!","go,","go.","goal","goal,","gobbledygook","goe","going.","gone","good","good!","good,","googl","gotta","gotten","gpu","gpu,","gpus)","gradient","gradient,","gradient.","gradient:","graham","graham_scan!(points)","graham_scan!(points::vector{point})","graham_scan(gift):","graham_scan(mut","graham_scan(points);","graham_scan(std::vector&","graham_scan(struct","graham_scan(test_gift)","grahamscan","grahamscan(list","grahamscan(point","grahamscan(points)","grahamscan(points);","grain","grant","graph","graphic","graphics.","graviti","gray,","great","great!","great,","great.","greater","greatest","greatli","greec","greek","green","green,","gregorian","grew,","grey","greyscal","grid","grid,","grid.","grid;","grid[1:2,:]","grid[2,:]","grid[3,:]","grid[neighbor_x][neighbor_y]","grid[x][y]","grid_ext","grid_extents)","grid_extents,","grid_extents/2","gridlin","gridlines(f_val,","gridlines(x,y)","gridlines(x,y))","gridlines.","grid{","groceri","ground","group","group.","groups,","grover'","grow","grown","grows.","grumpili","gt","gtx","guarante","guess","guid","guide,","guide.","guidelin","guston","gustorn","guy","guy.engageto(girl);","guy.prefer","guy.preferences)","guys)","gx","gy","gy.^2)","g|\\psi(\\mathbf{r},t)|^2","h","h(p)","h(z)","h.len()","h.pop().(*node)","h.pop().(*node),","h_r","hack:","hacki","hai","hairs.","half","half)","half,","half.","half:","halfway","hall/crc","hamiltonian","hamiltonian.","hamiltonians.","hamzaoui,","hana","hand","hand,","hand.","handi","handl","hands,","hans,","happen","happen!","happens).","happens,","happens:","happili","hard","hardwar","hardware,","hardware...","hardware;","harm","harmon","harsh","has_cuda_gpu()","has_partner(self):","hasfiance()","hash","hashmap","hashmap)","hashmap,","hashmap::new();","hashmap<>(),","hashmap<>();","hashmap};","haskel","haskell,","hast","hausdorff","have","have,","have.","haven't","head","header","heap","heap'","heap)","heap*","heap,","heap.init(h)","heap.pop(h).(*node)","heap.push(h,","heap_data,","heap_data]","heap_free(&heap);","heap_free(struct","heap_len,","heap_len]","heap_len],","heap_pop","heap_pop(&heap);","heap_pop(struct","heap_push","heap_push(&heap,","heap_push(struct","heap_push:","heap_push_don","heap_push_sift_up:","heap_size,","hear","heard,","heart","heart\"","heart,","heart.","heartili","heat","heavili","height,","height.","heights,","heisenberg","held","help","helper","helper::make_decoder(first,","helper::make_encoder(*decoder);","helps.","henc","hence,","henrik,","here","here'","here,","here.","here:","here;","here?","hermitian","hero","heroic","hesit","hexagons?","hidden","hide","high","high!","high,","high.","higher","higher)","higher,","highest","highlight","highlighted,","himself","himself!","hire","histep","histogram","histogram[bin]","histogram[i,j])^2","histograms\"","histor","histori","history,","hit","hitch...","hobbi","hobbies:","hoist","hold","hold.","holiday","home.","honest","honest,","honestly,","honkit","hood","hop","hope","hopefulli","hopefully,","horizont","horribl","host","hot","hotli","hour","hous","housdorff","how?","however,","hs","hsl","hsv","hsv,","hsv2rgb(angle(real_f(z(x,y)),","html","https://discord.gg/pb976sy.","https://discord.gg/pr2e9s6","https://github.com/alanforr/complex","https://github.com/algorithm","https://www.algorithm","https://www.twitch.tv/leioslab","https://www.youtube.com/user/leioso","hue","huffman","huffman,","huffman.","huffman::encoded_string(to_be_encoded);","huffman_decode(codebook,","huffman_encode(codebook,","huffman_tre","huffman_tree,","huffman_tree:","huffmancod","huffmancoding();","huffmancoding.c","huffmancoding.decode(result);","huffmancoding.encode(\"bibb","huffmancoding.nod","huffmanencod","huffmantre","huffmantree(\"bibbity_bobbity\");","huffmantree(str","huffmantree,","huffmantree.createtree();","huffmantree.decode(encoded));","huffmantree.encode();","huffmantree::branch","huffmantree::from(input);","huffmantree::leaf","huge","hull","hull)","hull))","hull,","hull.","hull.add(0,","hull.add(pointonhull);","hull.append(point)","hull.append(point_on_hull)","hull.append(pt)","hull.get(i);","hull.get(m));","hull.length;","hull.set(i,","hull.set(m,","hull.size();","hull.slice(0,","hull.sort(comparator.comparingdouble(point","hull.sublist(0,","hull.unshift(pivot);","hull:","hull;","hull[","hull[0]","hull[1])","hull[1],","hull[i","hull[i],","hull[i]];","hull[m]]","hull_point","hull_points,","hull_points;","hull_points[0]));","hull_points[15];","hullpoint","hullpoint)","hullpoints[len(hullpoints)","human","hundr","hundred:","hungarian","hunter'","husband,","hut","hutchinson","hutchinson)","hutchinson_op","hutchinson_op,","hutchinson_op[0];","hyper","hypothet","h}{2","i'll","i'm","i)","i))","i))))","i)))))","i))))))","i))));","i);","i)]","i)];","i*dx","i*siz","i+(length(filter)/2)","i++;","i+1):","i,","i.","i.1).norm()","i.e.,","i32","i32,","i32queu","i32queue.dequeue().unwrap());","i32queue.enqueue(4);","i32queue.enqueue(5);","i32queue.enqueue(6);","i32queue.front().unwrap());","i32queue.size());","i32stack.pop().unwrap());","i32stack.push(4);","i32stack.push(5);","i32stack.push(6);","i32stack.size());","i32stack.top().unwrap());","i32stack:","i64","i64)","i64);","i64,","i;","i=0:18446744073709551615","i\\hat{h}_k]dt^2}{2}}\\right]\\psi(\\mathbf{r},t)","i\\hbar","i\\sin(\\theta))","i]","i];","iceberg","icompar","icon","id","id)","id);","id,","id:","id::int64","id;","idea","idea,","idea.","idea:","ideal","ideal,","ideal.","ideally,","ident","identif","identifi","idft","idft)","idiv","idx","idx)","ieee","ieee,","if","if($servois)","if(($d","if(22","if(a","if(isapprox(y,","if(isapprox(z,","if(mod1(i","if(n","if(points.empty())","if_tru","if_true:","iffalse:","ifft","ifft(np.multiply(fft(signal1),fft(signal2)))","ifft(opr.wfc)","iftrue:","ignor","ignored.","ilist","ill","im","im)","im*0.5*opr.v*par.dt)","im*0.5*par.k.^2*par.dt)","im;","im_tim","im_time,","im_time:","im_time::bool","im_time;","im_val","im_val::bool)","imag","imag(f(z))","image),","image,","image.","image:","image_resolution)","image_resolution))","images!","images,","images.","images/graph","images:","images?","imagin","imaginari","imaginary_f(z(x,y))),","imaginary_f(z)","imagine!","imaging,","immedi","impact","impl","implement","implement,","implement.","implementation,","implementations,","implementations.","implemented.","impli","implicit","implies:","implode(',',","import","importantly,","imposs","impossible,","impress","impressive!","improperly,","improv","improvise.","imput","imtim","imul","in!","in(number)","in,","in.","in2:","in:","in_array($preference,","in_circl","in_circle()","in_circle(doubl","in_circle(float","in_circle(p","in_circle(pos_x,","in_circle(x,","in_circle(x:","in_circle(x_pos::float64,","in_circle:","in_n,","inbetween","inbounds(canvas.shape,","inbounds(canvas_shape,","inbounds(canvas_size,","inbounds(cartesianindex","inbounds(size(canvas),","inbounds(struct","inbuilt","inc","incap","inches,","incircl","incircle($x,","incircle()","incircle(a.x,","incircle(doubl","incircle(r","incircle(x,","incircle(x:","incircle(xpos,","incircle_array","inclined).","inclined,","includ","include,","included\"","inclus","incomplete!","incomprehens","inconsistent.","incorpor","increas","increases,","increases.","incred","incredibly,","increment","increment(doubl","increment(int","increment(v,","increment(v:","indeed.","independ","index","index'","index(&self,","index)","index))))))","index).","index,","index.","index:","index;","index_mut(&mut","indexerror:","indexmut","indexmut};","indic","indices)","indices.","indices.\"","indices[i]","indici","individu","individually.","industri","industry,","ineffici","inefficient,","infin","infinit","infinitesim","inform","information,","information.","information:","ingenu","inher","inhibit","iniit","init","init(par,","init(par:","init(par::param,","init(value:","init_operators(struct","init_params(struct","initi","initial;","initial_canva","initial_canvas.copy()","initial_loc","initial_location,","initial_location.x,","initial_location.y,","initial_location[1],","initialize(@id","initialize(id,","initialized;","initially,","inlin","inner","inner,","innov","inord","inplac","input","input\"),","input)","input,","input.","input.chars().fold(hashmap::new(),","input.chars().map(|c|","input.chars().next();","input:","input;","input_i","input_pt","input_pts[1]","input_pts[1]^2","input_pts[2]","input_pts[2]^2","input_pts[i,","input_pts[tid,","input_pts[tid,1]","input_x","inputpoint","inputpoints)","inputpoints);","inputs.","insecur","insert","insid","instal","instanc","instanceof","instancevariablenames:","instead","instead,","instead.","instead?","institut","instruct","int","int(log2(n))","int)","int):","int)time(null));","int,","int32,","int64}()","int:","int]","int_queue.enqueue(4)","int_queue.enqueue(5)","int_queue.enqueue(9)","int_queue:","int_stack.push(4)","int_stack.push(5)","int_stack.push(9)","int_stack:","integ","integer,","integer.","integer.compare(this.id,","integer>>euclidmod:","integer>>euclidsub:","integers\"","integers.","integr","integral,","integrals:","integrate,","integration!","integration.","integration.\"","integration:","integration:'","integration:~%\")","integrators.","intend","intens","intense.","intent(in)","intent(inout)","interact","interact,","interactions.","intercal","intercept","interest","interest'","interest.choices.indexof(thi","interested!","interested,","interesting?","interestingly,","interfac","interface{}","interface{})","interior","interleav","intermedi","intern","interpret","interpret.","interpretation!","interpretation,","intersect","interv","intervals,","intial","into:","intqueu","intqueue.dequeue();","intqueue.enqueue(4);","intqueue.enqueue(5);","intqueue.enqueue(9);","intqueue.front();","intqueue;","intrins","intro","introduc","introduct","introductori","intstack","intstack.pop();","intstack.push(4);","intstack.push(5);","intstack.push(9);","intstack.top();","intstack;","intuit","intuitive,","intuitive.","intuitively,","invalidargumentexception('not","invent","invers","inverse)","inverse:","inverse_dict","inverse_dict:","inverse_dict['']","inverse_dict[key]","invert","investig","inviscid","involv","inward,","io","ioutputlin","ioutputline[]","iqueu","is!","is)","is).","is,","is.","is...","is:","is:\"","is:\")","is:\");","is:\\n\");","is:\\n%lf\\n\"","is:\\n%lf\\n[#]\\nveloc","is:`);","is:~%\")","is;","is_gaussian(input_pts;","is_leaf(const","isa(huffman_tree,","isa(input_pts,","isa(n,","isfree(candidate,","isfree(m,","isfree(person,","isinme(point","isiz","isize;","isleaf","isleftof(pointonhull,","isleftof(vector","islonely()","ismainmodule:","isn't","isnan(input_y))","isosampl","isosamples\"","issingle():","isstable(men::preferences,","issu","issue!","issue,","issue.","istack","it!","it'","it).","it,","it.","it:","it?","item","item,","item.","item.x","item.x)","item.y)","item:","items,","items.","items;","items?","iter","iterate.","iteration,","iteration.","iterations!","iterations\"","iterations,","iterative_cooley_tukey(&x);","iterative_cooley_tukey(begin(iterative),","iterative_cooley_tukey(doubl","iterative_cooley_tukey(it","iterative_cooley_tukey(x)","iterative_cooley_tukey(x):","iterative_cooley_tukey(x);","itertools::itertools;","itertools;","ith","itself","itself!","itself,","itself.","itz","iz","i{1};","j","j)","j)))))","j),","j)]","j)];","j*dx","j*stride","j+1):","j,","j;","j]","j]))","j]).","j]);","j];","ja","jame","james,","jan","januari","jar","jarvi","jarvis_cross(hull[i","jarvis_cross(point1::pos,","jarvis_cross(pos(0,0),","jarvis_march(const","jarvis_march(gift):","jarvis_march(gift:","jarvis_march(point","jarvis_march(points)","jarvis_march(points);","jarvis_march(points,","jarvis_march(points::vector{pos})","jarvis_march(test_gift)","jarvismarch","jarvismarch();","jarvismarch(arraylist","jarvismarch(gift);","jarvismarch(point","jarvismarch(points)","jarvismarch(points);","jarvismarch.c","jarvismarch.run(points);","java","java,","java.io.filewriter;","java.io.ioexception;","java.lang.math;","java.util.*;","java.util.arraylist;","java.util.arrays;","java.util.collections;","java.util.comparator;","java.util.linkedlist;","java.util.list;","java.util.queue;","java.util.random","java.util.random;","java.util.stack;","java.util.stream.collectors;","java.util.stream.doublestream;","javascript","javascript,","javascript/typescript","jbe","je","jean","jeffrey","jerk","jess","jewish","jge","jie","jimmi","jl","jle","jmp","jne","jnz","job","johann","john","john,","join","joke","jordan","jordan\")","jordan:\")","jordan:\");","joseph","journal","journey","journey.","joy","jr.","jsonserializ","jsonserialize():","jstor,","julia","julia'","julia,","julia;","julian","juliu","jz","k","k)","k))","k)]","k)].abs();","k)];","k,","k.","k.,","k.push(((i","k.push((i","k.push_back((static_cast(i)","k.reserve(res);","k:","k::vector{complex{float64}}","k::vector{float64}","k;","k[i]","ke,","ke.push(complex::new(","ke.reserve(size);","ke:","keep","kelley,","kept","kerckhoffs'","kernel","kernel!","kernel!(input_pts,","kernel,","kernel.","kernel:","kernel[i,j]","kernel_function(x,","kernel_s","kernel_size)","kernel_size))","kernel_size*0.5","kernelabstract","kernelabstractions.jl,","ket","key","key(key)","key)","key,","key.","key::char","key;","key=(p","key=(point","key=lambda","keys(men)","keys.","keyword","keywords,","kid","kill","kind","kinda","kinemat","kinet","kinetic","kineticop","kmax","knew","knob","know","know!","know,","know.","know:","knowledg","knowledge,","knowledge.","knowledge;","known","known:","konrad,","konstantin","kotlin","kotlin.math.absolutevalu","ks","ks)","kstep","kthxbye","l","l(c(w))","l)","l,","l.","l:a","l:b","l:c","l]","l_1","l_2","lab","label","label,","label=\"phas","label_0","label_0:","label_1","label_1:","label_2","label_2:","labels,","labels.","laboratories,","labview","lack","lagrangian","lambert","land","landscap","lang","lang:\"julia\"](code/julia/conv.jl)","lang=\"jl\"","langevin","languag","language'","language,","language.","languages,","languages.","laplacian,","larg","larger","largest","last","last)","last);","last,","last.","last;","last;)","lasty))))))","lasty]","later","later):","later,","later.","latest","latex","latex.","latter","law","lay","layer","lc","lea","lead","lead,","leader","leadit","leads'","leads)","leads,","leads;","leads_end","leads_end,","leaf","leaf(*t))","leaf(_,","leaf(c,","leaf(char,","leaf(char:","leaf(i,","leaf(int","leaf(symbol,","leaf(t,","leaf(weight,","leaf)","leaf.","leaf;","leap","learn","learning!","learning,","learning.","leastcommongend","leav","lecture.","lectures,","lefmost","left","left,","left.","left.count()","left.decode_dfs(&input[1..],","left.dfs(code.clone()","left.freq","left.weight","left:","left::union{leaf,","left;","left?","left_most_point(point","left_most_point(points)","left_most_point(struct","leftchild","leftchild,","leftchild.weight","leftchild;","leftmost","leftmost.x","leftmostpoint(point","leftmostpoint(points)","leftov","legend","legend,","legend.","lein","len","len()","len(a)","len(a[0])","len(children):","len(codebook)","len(d)","len(d_in)","len(encoded_message)","len(filter_array))","len(filter_array)),","len(gift)","len(message)","len(n)","len(n.children)","len(node.children)","len(old)","len(queue)","len(self)","len(self.__list)","len(stack)","len(trees)","len(x)","len(x))","len(y)","len)","len))))","len)]","lend","length","length(bachelors)","length(children)","length(filter)","length(filter)):i","length(points)","length(q)","length(s)","length(x)","length(x))","length(y)","length)","length)))","length,","length.","length;","length]","less","less(i,","lesson","lest","let","let'","letter","letter))","letter,","letter;","letters:","level","level.","levels:","leverag","lh","lhs(std::move(lhs)),","lhs,","lhs.frequenc","lhs.i","lhs;","librari","library.","licens","license.","license.md).","license.md;","licensing:","lie","life","life.","lift","liftarray","liftarray2","liikt","like","like,","like.","like:","likelihood","limit","limits.","line","line),","line,","line.","line:","linear","linear\"","linear(a::array{float64})","linear)","linear,","linearalgebra","linearli","linecolor","lines,","lines.","linger","link","linkedlist","linkedlist();","links:","lisp","list","list\"\"\"","list($b,","list()","list())","list(),","list();","list(a,","list(b,","list(c,","list(follows);","list(men).shuffle(random);","list(metropolis_iterate(x0,","list(set(gift))","list(women).shuffle(random);","list(x,","list(y,","list,","list.","list:","list;","list[man]","list[t]","list[woman]","listarray","listarray)","listarray,","listextens","listextensions.c","liter","literatur","literature,","littl","little,","live","livecod","liverpool","livestream:","load","loc","loc)","loc,","loc::cartesianindex,","loc[1]","loc[1]},","loc[1]}};","local","localdictionary)","localdictionary);","localdictionary.add(node.key[0],","locat","location!","location):","location,","location.","location.x","log","log(input_pts[1]))","log(input_pts[tid,1]))","log(r_0)","log2","log_2(n)","logarithm","logarithm\"","logarithm):","logarithm,","logarithm.","logarithmic(a::array{float64},","logarithmic(a[length(a)/2+1:end],","logic","logic.","logn","logscal","logscale,","lolatomroflsinnlos,","lolcod","lone","lonely!'","lonely.","lonely?","lonelyfollow","lonelyfollow.proposetonext();","lonelyfollows)","long","long)","long,","longer","longer.","look","loop","loop)","loop,","loop.","loop:","loops,","loops.","lose","lossless","lost","lot","lot.","love","loves.","loves:","low","low_index","lower","lower.","lowest","lowest.","lt","lua","luckily,","ludwig","lunar","ly","m","m\"","m'","m)","m))","m++;","m,","m.","m.!)","m.assoc","m.empti","m.fromlist","m.fromlistwith","m.getkey());","m.getpreferredmates());","m.getvalue()));","m.getvalue());","m.insert","m.propose(women)","m.receiveoptions(women);","m.tolist","m;","m?","m]","m]g[m]","m_pi","machin","machine,","machine.","machines,","machines.","made","made.","mag","magic","magic,","magic.","magic:","magnitud","magnitude!","magnitude()","magnitude,","magnitude.","magnitude:","magnitude_shading(f_val)","magnitude_shading(f_val):","magnitude_shading(x,y)","magnitude_shading(x,y),","mahdi","mahesh","mailman","main","main()","main():","main(args:","main(string[]","main:","mainli","major","mak","make","make([]float64,","make([]point,","make([]rune,","make(codebook)","make(map[rune]*node)","make_codebook(self)","make_decoder(it","make_encoder(nod","make_person_list(size_t","makeoper","makepair","makeparamet","makequeue(iterable)","makequeue(nodes);","male,","malloc","malloc(4","malloc(length","malloc(sizeof(doubl","malloc(sizeof(double)","malloc,","man","man(\"a\"),","man(\"b\"),","man(\"c\"),","man(\"d\"),","man(\"e\")","man(name:","man(str","man):","man*):","man.choic","man.choices)","man.has_partner:","man.prefer","man.propose_to_next()","man;","manag","mani","manipul","mannames))","mantissa","mantissa.","manual","manually.","map","map$(","map$(forward_dict[]))","map$(location.__add__))","map$(p","map$(pow$(?,","map$(recursive_fill$(canvas,","map$(t","map$(weight)","map,","map[c]","map[char,","map[rune]str","mapm_","maps,","march","march,","march.","march}&","margin","mariu","mark","markdown","market","markov","marri","marriag","marriages\"\"\"","married,","marsaglia","mask","mask:","mass","massiv","master","mat","mat,","mat.xi","mat.xx","mat.xz","mat.yi","mat.yx","mat.yz","mat.zi","mat.zx","mat.zz","mat1.shape[1]","mat2):","mat2.shape[0],","mat2.shape[1])","mat:","match","mate","mate)","mate,","mate.","mate.m","mate;","materi","material;","mates)","math","math,","math.","math.ab","math.abs(a)","math.abs(a);","math.abs(a[pivot][col]))","math.abs(b)","math.abs(b))","math.abs(b);","math.abs(piestim","math.abs(radius);","math.abs(row[c]);","math.acos(","math.atan2(a.i","math.atan2(float64(point.i","math.atan2(p.i","math.const","math.fft","math.floor(math.random()","math.floor(n","math.funct","math.max(0,","math.max(signal.length,","math.pi","math.pi)","math.pi);","math.pow(point.x,","math.pow(point.y,","math.pow(y,","math.rang","math.sqrt","math.sqrt(math.pow(x,","math/ceil","math/pi","mathemat","mathematical.","mathematician","mathematics,","mathematics.","mathjax.hub.queue([\"typeset\",mathjax.hub]);","mathématiqu","matlab","matlab,","matmul(struct","matmult","matplotlib.cm","matplotlib.color","matplotlib.colors.hsv_to_rgb(hsv)","matplotlib.pyplot","matric","matrices.","matrices:","matrix","matrix!","matrix)","matrix,","matrix.","matrix:\"","matrix:\")","matrix::new(","matrix;","matrix_mul(self,","matrixmultiplication(double[][]","matter","matter.","matters!","matthew","max","max(1,","max(len(signal),","max_i","max_index","max_row","max_valu","max_x,","max_y;","maximum","maximumbi","maximumby)","maxval","mayb","maybegetacharact","mayberoot.foreach(c","mayberoot.getorelse(leaf('?',","mayberoot:","mayl","mazzuca","mazzuca.","mcmc,","me,","me.","mean","mean,","mean.","mean?","mean_valu","mean_value)","meaning","meaningful.","means,","meant","meanwhile,","measur","measurement,","mechan","mechanics!","mechanics,","mechanics.","media,","mediev","member","members.","memcpi","memcpy(dst,","memcpy(points,","memcpy(tmp","memcpy(tmp,","memcpy(tmp_point","memcpy(wfc_k,","memcpy(wfc_r,","memcpy,","memori","memory,","memset","memset(y,","memset,","men","men)","men)):","men);","men,","men.foreach(m","men.select(&:lonely?)","men.to[queue]","men/women","men:","men:')","men[bachelor]","men[husband]","mention","mentioned,","mentowomen","mentowomen)]","mentowomen,","mentowomen::pairs,","mentowomen[bachelor]","merg","mervin","mess","messag","message)","message):","message,","message,:cod","message.","message:","message:',","messeng","messenger'","messenger).","messenger;","messi","met","meter","method","method!","method'","method),","method,","method.","method.\"","method:","methodolog","methods\"","methods,","methods.","meton","metric","metric.","metropoli","metropolis\"","metropolis_iterate()","metropolis_iterate(x0,","metropolis_step(x)","metropolis_step(x,","michael","mid","mid)","mid))","middl","middle)))","midpoint","migrat","millennia","millennia.","million","min(1,","min(gift)","min(gift,","min(location)","min(p)","min(true_values))","mind","mind,","mind:","mine.","minesweep","minim","minimum","minimum(tuple(loc))","minimumbi","minimumby)","minu","minut","mirror","mislead","mismatch","misrepresent","miss","missed,","missed.","mit","mix","mix,","mix:","mkay","mktabl","mname","mod","mod(15","mod(19","mod(2","mod(4","mod(a,","mod(a,b);","mod(a:","mod(int","mod(year,","mod1(x,","mod_check","mod_check:","mod_loop","mod_loop:","mode","model","models)","moder","modern","modif","modifi","modulo","modulo(a,b)","modulu","modulus.\"","molecules,","moment","moment,","momentum","momentum,","momentum.","monday","mont","monte_carlo(10000000);","monte_carlo(samples)","montecarlo","montecarlo();","montecarlo(1000);","montecarlo(100000)","montecarlo.c","montecarlo.run(10000000);","montecarlointegr","montecarlopi","montecarlopi(100_000);","month","month)","month,","month.","months),","months,","months:","moon","moon'","moon).","moon,","moon.","more","more,","more.","moreover,","morri","morris'","morsel","most,","mostdesir","mostli","mother","mother'","motion","motiv","mov","movap","move","move,","movement","movements.","moves.","movi","movq","movsd","movup","msg","msg)","msg_data,","msg_data]","msg_len,","msvc","mu","mu)","mu,","mu;","mu[1],","mu[2]]","much","much,","much.","muller","mulsd","mult","multidimension","multidimensional,","multimedia","multipl","multipli","multiplication,","multiplication.","multiplication:","multiplications.","multiply,","mut","mutabl","my::queu","my::stack","myself","mystifying,","n","n'","n(doubl","n(v,","n(v,a),","n(v:","n)","n))","n),","n).exp()));","n):","n);","n+1","n,","n.","n.children","n.children)","n.children_s","n.count()))","n.id)","n.id);","n.value),","n.value);","n/2","n:","n::int64)","n;","n=1","n=1.","n=100)","n=100,","n=100:","n=2","n=2,","n=3,","n=4","n=7","n=7,","n[i]","n[i],","n[i].freq","n[j]","n[j],","n[j].freq","n\\time","n];","n^{\\text{th}}","n_2}","n_item","n_items:","n_items_float","n_items_float)","n_sampl","n_trial","n_trials:","n_v","n_v.","n_v:","n_{v+1}","n_{v}}","na","naiv","name","name\"","name)","name):","name,","name:","name;","namedtupl","namedtuple(\"point\",","namedtuple('testresults',","namely,","namely:","names,","namespac","nan","nan,","nan]","nand","nanosecond","natur","naïv","ndrange=size(input_pts)[1])","ne","near","nearbi","nearest","nearli","neat","neat?","necessari","necessarili","necessary!","necessary,","necessary.","need","need,","need.","needed,","needed.","needed?","neg","negative,","negative.","negoti","neighbor","neighbor,","neighbor.","neighbor_i","neighbor_x","neighbors);","neighbors,","neighbors.","neighbors.append(possible_neighbor)","neighbors.push_back(possible_neighbor);","neighbors:","neighbors;","neighbors[4];","neighbour","nest","never","nevertheless,","new","new(","new()","new(10.0,","new(node)","new(nodeheap)","new(par:","new(rows:","new(vector{node}(),","new(x:","new(xmax:","new(zeros(res),","new.","new:","new_c","new_c[0]","new_c[i]","new_d","new_d[0]","new_d[i+1]","new_d[i]","new_freq","new_nod","new_node;","new_tre","new_tree)","new_val","new_val)","new_val):","new_val:","new_val;","new_valu","new_value)","new_value))","new_value):","new_value);","new_value;","new_weight","new_x","new_x[k","newchildren","newchildren.","newdata","newdata.","newer","newlin","newline,","newlonelyfollow","newlonelyfollows.add(follow);","newlonelyfollows;","newnod","newnode)","newnode.char","newnode.freq","newton'","newtonian","next","next!","next((i","next,","next.","next...","next:","next;","next_choice(self):","next_index;","next_nod","next_nodes;","next_po","next_pos;","nextpo","nice","nice,","nicol","night","nil","nil)","nil))","nim","nitems)","nmsd","no.","nobodi","nocontour","node","node!.","node'","node(0,","node(1,","node(10,","node(11,","node(12,","node(2,","node(3,","node(4,","node(5,","node(6,","node(7,","node(8,","node(9,","node(const","node(freq),","node(id::int64)","node(int","node(key.tostring(),","node(leaf(b,","node(left","node(leftchild.key","node(lh","node(node(leaf(o,","node(node(leaf(y,","node(num_row)","node(num_rows,","node(rowcount);","node(str","node(tree_left,","node(value:","node)","node))","node)))","node))))","node));","node):","node*));","node*)dequeue(&q);","node*)malloc(num_children","node*)stack_pop(&stk);","node,","node.","node.children!","node.children![0])","node.children![1])","node.children)","node.children.append(child)","node.children.each{","node.children.s","node.children:","node.children?.append(child)","node.children?.count","node.children[0]","node.children[1]","node.createbranch(leftchild,","node.createleaf(n.key,","node.data","node.left","node.new(levels,","node.right","node.right;","node1","node1,","node1.weight","node10","node11","node11,","node12","node12});","node1[2]","node2","node2,","node2.weight)","node2[1]","node2[2]","node3","node3,","node3});","node4","node4});","node5","node5,","node6","node6});","node7","node7,","node8","node8});","node9","node9});","node:","node>>bf","node>>children","node>>children:","node>>data","node>>data:","node>>dfsinorderbinarytre","node>>dfsrecurs","node>>dfsrecursivepostord","node>>dfsstack","node[])","node_ptr","node_queu","node_stack","node_stack(end)","node_stack{end};","nodeheap","nodeheap)","nodeprioritylist","nodeprioritylist()","nodeprioritylist(list","nodeprioritylist(nodes);","nodeprioritylist.","nodeprioritylist.add(parentnode);","nodeprioritylist.pop();","nodes)","nodes,","nodes.","nodes.count;","nodes:","node{std::move(vec),","nois","noise.","nokey","nominally,","non","noncommerci","none","none)","none:","nonlinear","nonzero","noon","noprefix","nor:","norm","norm2","normal","normalize!(histogram)","normalize(kernel)","normalize:","normalize=false):","normalize=true)","north","north,","northeast,","northwest","not,","not.","not.\"\"\"","not:","not_bt","not_bt:","notabl","notat","notation","notation\",","notation)","notation),","notation,","notation.","notches)","note","note,","note:","notebook","noth","notic","notifi","now","now)","now,","now.","nowaday","nowadays,","np","np.abs(f_val)","np.abs(np.sin(np.pi","np.abs(opr.wfc)","np.angle(f_val))","np.arange(","np.arange(xmin","np.arange(xmin,","np.argmax(abs(a[pivot_row:,","np.array([","np.array([*output_gen$[:10000]])","np.array([10.,","np.array([[2,","np.array([self.x,","np.array):","np.average((height","np.concatenate((np.arange(0,","np.conj(wfc_r)","np.dot([[","np.dot([[1.0],","np.empty(res,","np.exp(","np.fft.fft(opr.wfc)","np.fft.fft(wfc_r)","np.fft.ifft((par.k","np.fft.ifft(opr.wfc)","np.floor(f_val_abs))","np.fromfunction(kernel_function,","np.histogram(x_dat,","np.imag(f_val)))","np.linalg.norm(kernel)","np.linalg.norm(x)","np.linalg.norm(y)","np.linspace(","np.mean(true_valu","np.meshgrid(coords,","np.moveaxis((hue,","np.pi)","np.pi),","np.pi,","np.pi])","np.power(gy,","np.random.choice([x_proposed,","np.random.uniform(","np.random.uniform(xmin,","np.real(f_val)))","np.real(fft_output))","np.savetxt(\"fft.dat\",","np.savetxt(\"out.dat\",","np.sqrt(0.1*kernel_size)","np.sqrt(b))).sum()","np.sqrt(nmsd)","np.sqrt(np.power(gx,","np.zeros((5,","np.zeros((image_resolution,","np.zeros((kernel_size,","np.zeros(a.shape[0]).t","np.zeros(output_size)","npair","npm","nrmsd","null","null)","null);","null,","null;","nullptr)","num","num1","num2","num2,","num_child","num_child)","num_child))","num_child):","num_child);","num_child,","num_child:","num_child::int64)","num_children)","num_children;","num_childs)","num_childs.times{children.push","num_childs:","num_hull_point","num_initial_point","num_op)","num_pair","num_points)","num_row","num_row,","num_row};","num_step","num_steps))","num_steps):","num_steps.","number","number\"","number\":","number'","number):","number,","number.","number;","number\\teaster\"","number\\teaster\")","number\\teaster\");","number\\teaster\\n\")","number\\teaster\\n\");","number_of_partn","number_of_partners)","number_of_partners),","number_of_partners,","number`teaster\"","numberqueu","numberqueue.enqueue(4);","numberqueue.enqueue(5);","numberqueue.enqueue(9);","numbers!","numbers,","numbers.","numbers:","numbers?\"","numberstack","numberstack.push(4);","numberstack.push(5);","numberstack.push(9);","numchild","numchildren)","numchildren:","numcor","numcores)","numelem","numelems)","numer","numerically.","numoutputpoints,","numpi","numrow","numrows,","numthread","numthreads)","nvidia","ny,","n}","o","o(1)","o(1).","o(3)","o(\\log","o(b),","o(log(n))?","o(n)","o(n)!","o(n),","o(n).","o(n^2)","o(n^2).","o(n^3)","o(n^3),","o)","o,","o.","o.frequency));","o3","obj","obj)","object","object,","object.","object.entries(charcounts).map(([key,","objects)","objects.","obnoxi","observ","observation.","observed.","observed;","obsolet","obtain","obviou","obvious","obvious!","obvious.","obvious:","obviously,","ocaml","occur","occur.","occurr","occurred.","occurs.","odd","odd[k];","odds)","odds)))","of","of!","of\"","of:","off!","off,","off.","offend","offer","offici","offset","offset,","offset]","offsets,","ofs(\"sierpinski.dat\");","oic","ok","ok(good)","ok,","okay.","old","old[0","old[l","old_point","old_point.x,","old_point.y,","old_val","old_val)","old_val,","old_val:","old_valu","old_value)","old_value))","old_value):","old_value,","old_value:","oldb","oldb.","older","omega","on","on,","on.","on:","onc","once,","once.","one,","one.","one...","one:","one:p)]","one;","one?","ones.","ongo","onlin","online,","onpropose(partner)","onto","op","op&","op@(oper","opaque,","open","open(\"output\"","open(\"output.dat\",","open(\"sierpinski.dat\",","open(filename,","oper","operation,","operation.","operation:","operations,","operations.","operator!=(const","operator!=(vector","operator&","operator*(const","operator*(doubl","operator*(point","operator*(std::array","operator+(point","operator+(std::array","operator,","operator.","operator:","operator==(const","operator==(vector","operators(len(par.x))","operators(length(par.x))","operators(param","operators(res)","operators)","operators,","operators.","operators:","operators::new(&par,","operators;","opn","oppos","opposit","opr","opr)","opr);","opr.k","opr.ke[j];","opr.pe[j];","opr.r","opr.size,","opr.v","opr.v[i]","opr.v[j].re)","opr.v[j].real)","opr.wfc","opr.wfc,","opr.wfc.clone();","opr.wfc.iter().map(|x|","opr.wfc[j]","opr:","opr::operators)","ops))","opt","optim","optimal,","optimally.","option","option,","option>","option[man]","option[node]","option[node]):","op}","orbit\"","orbits\"","ord","order","order🔤❗️","order).\"","order,","order.\"","ordering,","ordinari","organ","origin","origin,","origin.","origin.x);","origin.y,","origin;","origin=\"lower\"","origin=\"lower\",","original:","originalstr","originaltext","originaltext)","os","oscil","oscillations.","oscillator,","other","other)","other):","other,","other.","other.count()","other.count().cmp(&self.count())","other.count().partial_cmp(&self.count())","other.i","other.id);","other.weight;","other.x,","other.y)","other:","other_point","other_points[i]","others,","others.","otherwis","otherwise,","otherwise.\"\"\"","ourselves.","out","out!","out(number)","out)","out).unwrap();","out);","out,","out.","out.pdf.","out.push_back(std::make_pair(l","out.tex","out.write(\"\\n\")","out.write(output_string)","out:","out;","out[i,","out_n)","out_size)","out_size,","outcom","outcome,","outcome.","outcome:","outcomes.","outdo","outer","outfil","outfile.write(line)","outfile:","outlin","outline,","outpoint","output","output,","output.","output:","output_gen","output_point","output_points)","output_points[i,:]","output_pt","output_pts,","output_pts[tid,1]","output_pts[tid,2]","output_s","output_size)","output_size):","output_str","outputpoint","outputpoints(numoutputpoints);","outputpoints)","outputpoints;","outputs","outputs.","outputsize)","outright","outsid","outsider,","outta","over","over\"","over,","overal","overall,","overcompl","overflow","overjoy","overkill.","overlap","overrid","overwhelm","own,","own.","ownership","p","p(\\mathbf{r},","p(\\mathbf{x})","p(\\mathbf{x}),","p(h)","p(n)","p(n),","p(n).","p(t)","p(x)","p(x)\"","p(x),","p(x).","p(x)dx","p(x)dx,","p(x)dx.","p)","p))))","p):","p);","p)]","p+k","p,","p.","p.first","p.first;","p.getx()","p.gety()","p.i","p.key","p.name).join()}`)","p.plan_fft(x.len());","p.x","p.x,","p.y)","p.y))","p.y)))","p.y));","p.y),","p.y+1),","p.y]","p.y}","p.y},","p0","p0@(x,","p1","p1))","p1)))","p1)))))","p1.0)","p1.1)","p1.x)","p1.y)","p1.y)*(p2.x","p1.y)*(p3.x","p1.y);","p1[0])","p1[1])","p1^2","p2","p2\"","p2)","p2,","p2:","p2^2","p3","p3)","p3):","p3:","p:","p;","p=[a,","p=np","p[0]))","p]","p_1","p_2,","p_2}}{\\vec{p_3","p_3","p_4,","p_4}}","pa","packag","package.\")","package:","pad","page","page,","pages.","pain","paint","pair","pair:","paired,","pairs(map)","pairs)","pairs,","pairs.","palett","panic!(\"couldn't","panic!(\"unexpect","paper","paper,","paper.","par","par,","par.dt","par.dt)","par.dx","par.dx;","par.im_tim","par.im_time:","par.k[i].powi(2)).exp(),","par.res);","par.res;","par.res];","parallel","parallel,","param","param()","param(5.0,","param(xmax::float64,","param)","param,","param:","paramet","parameter","parameters,","parameters.\"\"\"","parameters::new(5.0,","params(doubl","params:","parent","parent_cel","parent_cell{1};","parent_index","parent_index;","parentnod","parse(int,","part","part,","parti","partial","partial_cmp(&self,","partialeq","partialeq,","partialord","partialord};","particl","particle'","particle.","particles\">","particles,","particles.","particular","particular,","particular.","particularli","parties.","partner","partner(self):","partner(self,","partner.nil?","partner.partn","partners.","partners[choice].onpropose(self)","parts.","parts:","parts;","paschal","pass","pass,","pass_count","passes,","past","path","path.display();","path::new(&path_name);","path_nam","patholog","pattern","pattern.","patterns,","paul","paus","pay","pb","pdf","pdflatex","pe,","pe.push(complex::new((","pe.push(complex::new(0.0_f64,","pe.reserve(size);","pe:","peak","peculiar","peek(weights)[2]","peopl","people.","per","percent","percent_error","percenterror","percival,","perfect","perfectli","perform","performance,","performed,","period","periodic,","permut","person","person'","person(name));","person(str","person)","person):","person,","person.","person._partner)","person.c","person.candidates.append(self)","person.generate(4,","person.new(","person:","person{false,","perspective,","perspective;","peter","phase","phase.","phases,","phd","phd,","phd.","phenomen","phenomenon.","philipp","php","php_eol","php_eol);","php_eol;","phrase","phrase)","phrase.flatmap(c","phrase::string)","physic","physical,","physically.","physicist","physicist.","physics,","physics.","physics?","pi","pi\"","pi)","pi))","pi))]","pi).abs()","pi);","pi,","pi/10.0),","pi/xmax,","pi:","pi;","pi_estim","pi_estimate)/math.pi","pi_estimate);","pi_estimate=monte_carlo(n)","pick","pick_preferred(self):","picount","pictori","pictur","piec","piece.","pieces.","piestim","piestimation);","piet","pinch.","pink","pivot","pivot)","pivot)));","pivot));","pivot);","pivot,","pivot.","pivot_angle)","pivot_col","pivot_col]","pivot_col]))","pivot_i","pivot_i]","pivot_row","pivots.","pixar","pixel","pixel.","pk","place","place.","planar","planb)","planck'","plane","plane,","plane.","planes.","planner","planner.plan_fft(n);","plate.","platform","play","pleas","please.","pleasur","plenti","plethora","plot","plot,","plot.","plot:","plot;","plot_output.plt","plots,","plots.","plotted,","plotted:","plotter","plotter.","plotting,","plotting.","plotting:","plt","plt.subplots(1,","plu","pluck","plug","plugin","pm","pm3d","png","pngcairo","po","point","point\"\"\"","point&","point(","point(*p))","point(*t))","point(0,","point(0,14),","point(0.5,","point(1,","point(1.0,","point(15,","point(2,","point(2,8)","point(5,","point(5,7),","point(6,","point(7,","point(9,","point(9,9),","point(b.getx()","point(c.getx()","point(doubl","point(double.max_value,","point(double[]","point(p.x","point(p.x+1,","point(p.x,","point(random(),","point(random.uniform(0,","point(rng.nextdouble(),","point(self.x","point(x,","point(x1,","point(x=0,","point)","point))","point)))","point))))","point));","point),","point):","point*","point*)","point,","point.","point.i","point.matrix_mul(operation);","point.x","point.x,","point.y))","point.y).as_str();","point.z","point.z,","point1.x,","point1.y)","point2","point2.i","point2.x,","point2.y)","point2::pos,","point2d","point3","point3.i","point3::new(","point3::new(0.0,","point3::new(0.20,","point3::new(0.23,","point3::new(0.26,","point3::new(0.85,","point3::pos)","point3d","point:","point;","point[0]","point[]","point[])","point[]:","point[n];","point_array","point_array))","point_i","point_on_hul","point_x","point_y🤛","pointer","pointonhul","pointonhull,","points\"\"\"","points)","points)))","points*","points*)))))","points,","points.","points.add(new","points.aggregate((leftmost,","points.begin()","points.end(),","points.is_empty()","points.reduce((leftmost,","points.retain(|a|","points.size())","points.slice(1).sort((a,","points.sort_unstable_by(|a,","points:","points[0]","points[0],","points[0];","points[1:]","points[1:m]","points[1])","points[1].x))","points[1].y,","points[1]];","points[2..points.len()].iter()","points[2]","points[4]","points[]","points[a].i","points[i+1]","points[i]","points[i])","points[i],","points[i];","points[j]","points[j];","points[m]","points[m]);","points[m],","points[randrange(points.size())];","pointtyp","pointvector","pointvector&","point{x:","point❗️","poison:","polar","polar_angle(&start,","polar_angle(ref,","polar_angle(reference:","polar_angle(start,","polar_angle(struct","polar_angles_sort(point","polar_angles_sort(points,","polar_angles_sort(struct","polar_box_muller!(input_pts,","polar_box_muller(input_pts,","polar_muller_noreplacement!(input_pts,","polar_muller_noreplacement!)","polar_muller_replacement!(input_pts,","polarangle(a,","polarangle(b,","polarangle(point","polarangle(point,","polarangle(ref,","polthier,","polynomi","poor","poor,","pop","pop!(s)","pop(&mut","pop()","pop():","pop();","pop(self)","pop.","pope).","pope;","popular","pore","portal","portion","portraits,","pos(1,","pos(2,","pos(3,","pos(point2.x","pos(point3.x","pos)","pos*2","pos,","pos,acc,","pos:","pos;","pos_i","pos_in","pos_x,","pos_y,","pose","posist","posit","position),","position,","position.","position.'''","positions)","positions,","positions.","positive,","possibilities,","possibl","possible,","possible.","possible_neighbor","possible_neighbor)","possible_neighbor):","possible_neighbor,","possible_neighbors)","possible_neighbors:","possible_neighbors{","possible_neighbour","post","postord","postorder\\n')","posts,","potenti","potential","potential,","potential.","potential.\"\"\"","potentialnextpointonhul","potentialnextpointonhull,","potentialnextpointonhull.","potentialnextpointonhull;","pow($positionx,","pow($positiony,","power","powerful,","powershel","pr","practic","practice,","practice.","practice:","pre","precis","precise)","precise.","precisely.","precision)","precision.","predecessor","predefin","predict","predict?","pref","pref))","pref):bachelors)","prefer","prefer,","preference;","preference_list;","preferences.indexof(man)","preferences:","preferred\"\"\"","preferredm","preferredmates)","preferredmates.remove(0);","preferredmates;","prefers(man:","prefers(men,","prefers(other)","prefers(prefs,","prefers(women,","prefix","prefix,","preform","prefs)","prefs[person])","premis","present","preserv","press,","presum","pretend","pretti","prev","prev_po","prev_pos,","prevalent.","prevent","previou","prevpo","prevpos,","prevpos:","primari","primarili","prime","principl","principle,","print","print!(\"thi","print!(\"{}","print(","print(\"\",","print(\"[#]","print(\"[#]\\nmodulu","print(\"[#]\\nqueu","print(\"[#]\\nrecurs","print(\"[#]\\nstack","print(\"[#]\\nsubtract","print(\"[#]\\ntim","print(\"[#]\\nveloc","print(\"\\(stormer.time)\")","print(\"\\(stormer.vel)\")","print(\"\\(velverlet.time)\")","print(\"\\(velverlet.vel)\")","print(\"\\(verlettime)\")","print(\"back","print(\"energi","print(\"gauss","print(\"gaussian","print(\"ha","print(\"not","print(\"original\")","print(\"output","print(\"th","print(\"year\\tservoi","print(\"{:.10f}\".format(time))","print(\"{:.10f}\".format(vel))","print('.',","print('[#]\\nmodulu","print('[#]\\nsubtract","print('\\n')","print('codebook:","print('codebook:',","print('decod","print('encod","print('f',","print('huffman","print('invalid","print('message:","print('message:',","print('prefer","print('th","print()","print(a,","print(a[2],","print(all(abs([y[i]","print(b[1],","print(back_substitution(a),","print(current_node.value,","print(euclid_mod(64","print(euclid_sub(128","print(euclidmod(a:","print(euclidsub(a:","print(f\"test","print(f\"us","print(f\"{'num_steps':>10s}","print(f\"{num_steps:10d}","print(f\"{year}\\t{computus(year,","print(f'{man.name}","print(first(q).id,","print(int_queue.dequeue())","print(int_queue.front())","print(int_stack.pop())","print(int_stack.top())","print(len(int_queue))","print(len(int_stack))","print(man)","print(n.id,","print(node.data)","print(node.data,","print(node.value,","print(point)","print(soln)","print(table.unpack(solution))","print(temp.value,","print(testresults(pass_count,","print(top(s).id,","print(value,","print(woman)","print).","print,","print:","print_codebook","print_int","print_messag","print_newlin","print_newline;","printcodebook()","printevolut","printf","printf(\"%d","printf(\"%lf\\n\",","printf(\"[#]\\nmodulu","printf(\"[#]\\nqueu","printf(\"[#]\\nrecurs","printf(\"[#]\\nstack","printf(\"[#]\\nsubtract","printf(\"[#]\\ntim","printf(\"[#]\\nveloc","printf(\"\\n\");","printf(\"codebook:\\n\");","printf(\"gaussian","printf(\"points:\\n\");","printf(\"th","printf(\"thi","printf(\"year\\tservoi","printf('","printf('%","printf('%s\\'","printf('[#]'.php_eol.'modulu","printf('[#]'.php_eol.'subtract","printf('ha","printf('th","printf,","printf.printf","printi","println","println!(","println!(\"[#]\\nmodulu","println!(\"[#]\\nqueu","println!(\"[#]\\nrecurs","println!(\"[#]\\nstack","println!(\"[#]\\nsubtract","println!(\"[#]\\ntim","println!(\"[#]\\nveloc","println!(\"[{:>19}]\",","println!(\"[{:?}","println!(\"ha","println!(\"solution:","println!(\"th","println!(\"year\\tservoi","println!(\"{:#?}\",","println!(\"{:?}\",","println!(\"{}\",","println!();","println(","println(\"$(a[i])\\t$(servois_numbers[i])\\t\\t$(easter_dates[i])\")","println(\"$(time)\")","println(\"$(vel)\")","println(\"$verlettime\")","println(\"${stormerverlet.time}\")","println(\"${stormerverlet.vel}\")","println(\"${velocityverlet.time}\")","println(\"${velocityverlet.vel}\")","println(\"[#]\\nmodulu","println(\"[#]\\nqueu","println(\"[#]\\nrecurs","println(\"[#]\\nstack","println(\"[#]\\nsubtract","println(\"[#]\\ntim","println(\"[#]\\nveloc","println(\"[$i]\")","println(\"[%","println(\"[%.1f,","println(\"[0.0","println(\"[1.0","println(\"[2.0","println(\"a","println(\"b","println(\"cannot","println(\"codebook","println(\"decod","println(\"encod","println(\"energi","println(\"estim","println(\"ha","println(\"it","println(\"matrix","println(\"not","println(\"origin","println(\"output","println(\"perc","println(\"recurs","println(\"solution:\")","println(\"system:\")","println(\"th","println(\"year\\tservoi","println()","println(a)","println(a[1])","println(a[2])","println(a[3])","println(a[i])","println(b)","println(euclid_mod(64","println(euclid_sub(128","println(euclidmod(64","println(euclidsub(128","println(hull)","println(img[index])","println(isstable(men,","println(length(a))","println(mentowomen)","println(soln)","println(value)","println,","printm","printmatrix(a","printmatrix(a)","printmatrix(const","printmatrixrow(row","printmatrixrow(row)","printmatrixrow(x)","printv","prioriti","priorityqueu","priorityqueue()","priorityqueue.add(new","priorityqueue.dequeue();","priorityqueue.enqueue({","priorityqueue.remove();","priorityqueue<>(comparator.comparingint(o","priorityqueue[node]()(ordering.by(","priorityqueue{node,","priorityqueue}","privat","private,","private:","probabilites.","probabilities)","probabilities):","probabilities);","probabilities.iter().enumerate()","probabilities:","probability)","probability,","probability.","probabl","problem","problem!","problem,","problem.","problem:","problem;","problems.","proc","proce","procedur","procedure,","process","process,","process.","process.stdout.write(current.id","process.stdout.write(tree.id","process:","processing),","processing.","processor","processor,","produc","product","product)","product,","product.","produkt","profession","professor","profound","program","program,","program.","program.c","programm","programmer,","programmers,","programmers.","programming,","progress","progress,","progress.","prohibit","project","project!","project.","project.clj","projects.","prolif","promis","promot","proof","proper,","properli","properti","properties.","property.","proport","propos","proposal,","proposal_index","proposals(number_of_partners);","propose()","propose():","propose(partners)","propose_to_next(self):","proposetonext()","prospect","prospect!","protect","provabl","provid","ps","pseudo","pseudocod","pt","pt)","pt):","pt,","pt.x,","pt.y};","pt;","ptr","ptr,","ptr[r12]","pub","public","public.","public:","publication,","publication.","publish","pull","pure","purpl","purple,","purpos","purpose.","purposes,","purposes.","purposes;","pursu","push","push!(bit_indices,","push!(hull,","push!(neighbors,","push!(ret.children,","push!(s,","push!(s,neighbor)","push(&mut","push(const","push(data:","push(self,","push(t","push(x","push/pop","push:","put","put,","put:","putstrln","puzzl","pv","pxor","py)","pythagorean","python","python,","python3","q","q)","q))","q),","q)~\\%~30","q)~\\%~7.","q,","q.","q.back","q.capac","q.data","q.empty():","q.front","q.front();","q.get()","q.pop();","q.push(loc);","q.push(neighbor);","q.put(neighbor)","q.put(p)","q;","q_i","qsort(points,","quadrant","quadratur","qualifi","qualiti","quantifi","quantiti","quantity,","quantity:","quantum","quarter","qubit","qubits!","qubits,","qubits.","queri","question","question!","question,","question.","question:","questions:","queu","queue","queue\");","queue🔤❗️","queue()","queue();","queue(generic[t]):","queue)","queue))","queue)))","queue,","queue.","queue.add(c);","queue.add(this.root);","queue.append(child)","queue.append(location)","queue.append(neighbour)","queue.count","queue.dequeue();","queue.empty?","queue.enqueue(c);","queue.enqueue(this);","queue.extend(¤t.children);","queue.extend(node.children)","queue.len()","queue.poll();","queue.pop().expect(\"th","queue.pop().unwrap();","queue.pop();","queue.pop(0)","queue.pop_front()","queue.popleft()","queue.push","queue.push(&n);","queue.push(...current.children);","queue.push(huffmantree::branch","queue.push_back(n);","queue.remove(at:","queue.shift","queue.shift();","queue:","queue::new();","queue;","queue<>();","queue[0]","queue[1:]","queue[int]","queue[man]()","queue\\n')","queue_array,","queue_back,","queue_cap,","queue_empty(struct","queue_fill!(canvas,","queue_fill!(grid,","queue_fill$(?,","queue_fill(","queue_fill(canvas,","queue_fill(struct","queue_fill(test_grid,","queue_front,","queue_res","queue_resize(q);","queue_resize(struct","queue_resize:","queue_size,","queue_test_func","queue_test_func):","queued,","queues,","queues.","queues.\"","queuetest","queue{","queue{cartesianindex}()","queue{node}()","queue❗️","quick","quickli","quickly,","quickly.","quiet","quit","quot","qword","qword]","r","r\"(bibbiti","r(\\cos(\\theta)","r(x,y)","r(x,y)*exp(theta(x,y)*sqrt(","r)","r)))","r++","r,","r.","r1","r10,","r10b,","r11","r11,","r11]","r12","r12,","r12:","r12]","r12d","r12d,","r13","r13,","r13:","r13]","r13d","r13d,","r14","r14,","r14]","r14d","r14d,","r15","r15,","r15]","r15],","r15d,","r2","r8","r8,","r8d,","r9","r9,","r9b","r9d,","r::vector{complex{float64}}","r;","r=\\sqrt{","r?","r\\cos(\\theta)","r\\sin(\\theta)","r\\sin(\\theta).","r]","r])","r^2.","r^2}{(2r)^2}","r_0","r_0)","r_0.","racket","racket/bas","racket/local)","racket/math)","radial","radians\"","radic","radiu","radius🤛","radius)","radius))","radius)))","radius),","radius):","radius.","radius:","radius=1)","rais","ran","rand","rand()","rand()*2","rand()]","rand(128)","rand(2,","rand,","rand::*;","rand::prelude::*;","rand::random();","rand::random::()","rand::thread_rng();","rand;","rand_max:","rand_max;","randengine(std::random_device{}());","randengine;","random","random()","random())","random();","random()]","random)","random),","random,","random.","random.new(42)","random.uniform(0,","random?","random_element(struct","random_pref_list","random_pref_list()};","randomgen","randomize()","randomli","randomr","random❗️","random❗️❗️","randrange(std::size_t","randx","randx:","randy:","rang","range\");","range(0,","range(1,","range(1,101)]","range(2020,","range(64):","range(64)][j])","range(a.shape[0]","range(a.shape[0]):","range(image_resolution):","range(len(density)):","range(max(0,","range(min(a.shape[0],","range(n","range(n):","range(num_child)))","range(num_child):","range(num_steps):","range(output_size):","range(output_size[0]):","range(output_size[1]):","range(par.timesteps):","range(pivot_i","range(pivot_row","range(row):","range(strid","range,","range.","rank","raouf,","rapidly,","rare","ratio","ratios.","raton,","rax","rax,","rax:","rax:rdx","rax]","ray","rbp","rbp,","rbx","rbx,","rcx","rcx,","rdi","rdi,","rdx","rdx,","re","re^{i","reach","read","readabl","reader","reader!).","reader'","reader.","readers,","readi","readili","reading!","readme.md","readonli","ready,","real","real(16),","real(8)","real(8),","real(energy_k[i]","real(f(z))","real,","real.","real_f(z)","realist","reality.","realiz","realized.","realli","realloc","realloc(*dst,","realloc(heap","realloc(stk","really,","realpart","realpart)","reappear","rear_point","rear_pointer.reset();","rear_pointer:","rear_pointer;","reason","reason,","reason.","reasons,","reasons.","reasons:","rec","receiv","receiveoptions(list","receiveproposal(person","receiver,","receiver.","recent","recieveproposal(man","reciproc","reckon","recogn","recommend","reconstruct","recreat","recurs","recurse(node,","recurse(node.left,","recurse(node.right,","recurse(tree,","recursion!","recursion,","recursion.","recursive.","recursive\\n')","recursive_fill!(canvas,","recursive_fill!(grid,","recursive_fill$(?,","recursive_fill(","recursive_fill(canvas,","recursive_fill(grid,","recursive_fill(struct","recursive_fill(test_grid,","recursive_test_func","recursive_test_func):","recursively,","red","red,","red.","redefin","reduc","redund","ref","ref))","ref.","ref.x))","ref.y),","ref[0])","ref[1],","refer","reference,","reference.x)","reference.y).atan2(point.x","reflection,","regard","regardless","regardless,","region","region,","regist","register,","register.","registers,","registers:","regular","regularli","regularly,","reinhold,","reiniti","reinterpret_cast(x.data());","reinterpret_cast(y.data());","reject","rel","relat","relax!\"","released.","relev","reli","remain","remaind","remainingprefer","remark","rememb","reminder,","remov","removefirst.","render","renorm","renorm_factor","reorder","rep","repeat","repel","repercussions,","repl","replac","replaced,","replacement:","replacement?","repli","replic","replot","report","repositori","repository:","repres","represent","representations:","represents,","request","request,","request.","requir","require(\"complex.js\");","required.","requires.","res)","res));","res);","res,","res/2:","res:","res::int64","res::int64,","res;","res])","research","research,","research.","research;","resembl","reshap","resiz","resolut","resolution\"","resolution)","resolution,","resolv","resourc","respect","respectively.","respectively:","rest","rest.","restor","restrict","result","result!","result)","result))","result);","result,","result.dictionary)","result.join(\"\");","result.push(node.key);","result.push(value);","result:","result:\"","result:\")","result:\");","result:'","result:')","result:'),","result:'.php_eol.'%s',","result:\\n\"","result:\\n\",","result:\\n\";","result:\\n$(check1)\")","result:\\n$(check2)\")","result:\\n$result\"","result:\\n%d\\n\"","result:\\n%d\\n\",","result:\\n{}\",","result:`n$(mod","result:`n$(sub","result:~%\")","result;","result=$(euclid_mod","result=$(euclid_sub","result[i","result[i]","results!","results,","results.","ret","ret(number_of_partners);","ret);","ret,","ret.pop_back();","ret.push_back(p.second);","ret;","ret=$1","ret_cross","ret_cross*ret_cross","retain","retriev","return","return(at(rand(n,2))","return(rand(n,2)","return:","return;","reus","revers","reversal,","reverse(bit_indices[i])","reversecodebook","reversecodebook.put(m.getvalue(),","reversedo:","revert","review","revis","revised.","revolut","revolutionari","revolutionary,","revolv","rgb","rgb.","rh","rhs(std::move(rhs))","rhs)","rhs.frequency;","rhs.x,","rhs.y};","rhs:","rhs;","rhs[0].i","rhs[0].x","rhs[0].z","rhs[1].i","rhs[1].x","rhs[1].z","rhs[2].i","rhs[2].x","rhs[2].z","rich","rid","right","right!","right)","right))","right));","right),","right,","right.","right.count(),","right.decode_dfs(&input[1..],","right.dfs(code.clone()","right.freq","right.frequency,","right.weight,","right:","right::union{leaf,","right;","right?","right]","rightchild","rightchild)","rightchild);","rightchild.key,","rightchild.weight,","rightchild;","rigor","rigorous,","rijndael","rip","rly,","rly?","rm","rn)","rnd","rng","rng()","rng)","rng.gen(),","rng.gen()};","rng.gen::();","rng.gen_range(0.0_f64,","rng.nextdouble());","robert","robust","robust.","roll","roll\"","roll.","roman","rome.","ronald","room,","root","root\")","root)","root))","root,","root.left","root.right","root;","root_bin","root_binari","rootb","rootbinari","rootbinary)","rosenthal,","rot","rot13,","rot13:","rotat","rotate\"","rotation\"","rotation,","rotation.","rotation:","rotations,","rotations.","rough","roughli","round","rounded.","rounding)","row","row\"","row'","row)","row)))))","row++;","row,","row.","row:","row;","row?","row[c]","row[j]","rowa,","rowb)","rowcount","rowcount,","rows'","rows)","rows,","rows.","rows:","rows};","rsa","rsa:","rsi","rsi,","rsi]","rsp","rsp,","rstep","rubi","rule","rule,","run","run!","run(int","run(list","run,","run.","rune","rungaleshapleyalgorithm(list","runtim","runtime,","runtime.","runtime:","ruse),","rust","rustfft::fftplanner;","rustfft::num_complex::complex;","rustfft;","rustl","ryzen","s","s\"","s\"${(21","s\"april","s\"march","s)","s)))","s.","s.pop();","s.push(loc);","s.push(neighbor);","s.top();","s:check_1","s:check_2","s:euclid_mod(64","s:euclid_mod(a,","s:euclid_sub(128","s:euclid_sub(a,","s[0],","s[1]]","s[2:]:","s_i","s_x","s_x*a","s_y*a.","sacrif","saem","safe","said,","salt.","same","same)","same,","same.","sampl","sampled,","samples)","samples.\")","samples.\");","samples.🔤❗️","samples❗️","sampling)","sampling,","sampling.","sampling?","sanderson","saniti","sar","satisfi","satisfied.","satur","saturation,","save","save_encod","savor","saw","sawtooth","say","say,","saying,","says:","scala","scala.collection.mutable._","scala.collection.mutable.{map,","scalarmapp","scalarmappable(matplotlib.colors.normalize(0.0,","scale","scale,","scale.","scale:","scale;","scale?\"","scales,","scaling\"","scaling,","scan","scanl","scanl1","scanlin","scanr","scatter","scenario","schacher","scheme","scheme,","scheme.","schemes,","schemes.","schloss","schloss.","scholars,","schonhag","school","school,","school.","schrödinger","scienc","science,","science.","scientif","scientific,","scientist","scientist.","scipy.fft","scon","scope","scope.","score(@partner)","score(partner)","scrambl","scratch","scratch:","screen,","screen;","script","script,","script.gp","script.gp)","script:","scripts,","sea","search","search,","search.","search.\"","second","second)","second,","secondly,","secondnumb","seconds.","secret","secret.","secretli","section","section,","section.","section:","section;","sections!","sections,","sections.","sections;","sector","security.","see","see,","seed","seem","seemingli","seen","segment","segment.","segments,","segments.","select","select_array(","select_array(hutchinson_op,","select_array(hutchinson_op:","select_array(struct","self","self)","self,","self.","self.__list.append(element)","self.__list.pop()","self.__list.pop(0)","self.__list:","self.__list[","self.__list[0]","self._partn","self._partner._partn","self._partner:","self.candid","self.candidates.clear()","self.candidates:","self.children","self.col","self.count()","self.data","self.data.swap(a","self.data[row","self.decode_dfs(&input[start..],","self.dfs(string::from(\"\"),","self.dk","self.dt","self.dx","self.dx)","self.generate(size,","self.has_partn","self.has_partner()","self.i","self.im_tim","self.k","self.list.front()","self.list.last()","self.list.len()","self.list.pop()","self.list.pop_front()","self.list.push(item);","self.list.push_back(item);","self.lonely?","self.nam","self.next_choic","self.partial_cmp(other).unwrap()","self.partn","self.partner:","self.pref_index","self.prefer","self.preference)}'","self.preference:","self.preference[self.pref_index]","self.r","self.timestep","self.tree.decode(input)","self.v","self.valu","self.wfc","self.x","self.x)","self.x.partial_cmp(&other.x)","self.xmax","self.y)","self.y,","self.y.partial_cmp(&other.y)","self.z;","self::new(x,","send","sender","sender,","sens","sense!\"","sense,","sense.","sensitive;","sent","separ","seq","seq[float]","seq[float]):","sequenc","sequenti","seri","series,","seriou","serv","server","server:","servoi","servois\"","servois\",","servois'","servois)","servois)`t`t$(calcul","servois,","servois:","servois=false)","servois=false):","servois=true)","servois=true)}\\t\\t{computus(year)}\")","servois_numb","servoisnumb","servoisnumbers,","set","set\");","set,","set.","set;","setmatch(person","setmate(mostdesired);","setmate(person","setpreferences($preferences);","setpreferences(array","setter\"","setter.\"","settl","setup","sever","shade","shadows\"","shake","shall","shame.","shane,","shannon","shannon,","shape","shape,","shape.","shape?","shape?:","shape_point","shape_points)","shape_points):","shapepoint","shapepoints)","shapes)","shapes.","shapes:","shapes[rng.gen_range(0..shapes.len())];","shapley","share","sharealik","sharp","sharpli","shear","shearing)","shearing,","sheep","sheep,","sheep.","sheer","shell)","shi","shift","shl","shor'","short","short)","short,","shortcut:","shorter","should!","shouldn't","show","show:","showcas","shown","shownod","showpoint","shr","shudipto","shuffl","shuffle($preferences);","shuffle(girls);","shuffle(guys);","shuffle(iterable)","shuffle(man.preference)","shuffle(mannames)),","shuffle(size_t","shuffle(thi","shuffle(woman.preference)","shuffle(womannames)),","side","side,","side.","sierpinski","sierpinski.dat,","sift","sigma","sigma,","sign","signal","signal,","signal,\"","signal.","signal2):","signal2::array{t})","signal;","signal?","signal[k,","signals,","signals.","signifi","signific","significantli","significantly,","signing,","silly,","similar","similar)","similar).","similar,","similarity,","similarli","similarly,","simpl","simple,","simple.","simple:","simple_linear_output","simplelinearoutput","simpler","simpler,","simpler:","simplest","simpli","simplicity,","simplicity.","simplifi","simply:","simul","simulation,","simulation.","simulator,","simulators.","simultan","sin(theta)","sin(x)","sine","singl","singles.each","singles.empty?","singular","singular!\")","singular\");","singular,","singular.\")","singular.\");","singular.\\n\");","sinusoid","sit","site.","site:","situat","situation.","situation?","six","sixes,","size","size(&self)","size()","size():","size();","size(a,1)","size(a,2)","size(signal)","size(sx))","size(sy))","size)","size))","size).","size).to_a.shuffle(random:","size);","size,","size.","size:","size::int64)","size;","size[0]","size[1])","size];","size_t","size_t(0));","sizeof(codebook","sizeof(double));","sizeof(q","sizeof(stk","sizeof(struct","sizeof(tree)","sizeof(wfc_k));","sizeof(wfc_r));","sizeof(y));","skew","skill","skip","slice","slide","slight","slightli","slip","sliver","slope","slow","slow,","slower","slowest","slowest.","slowli","slowly,","small","small,","smaller","smallest","smallr","smalltask","smith,","smooth","smoothli","snapshot","snd","snd)","snippet","snippet,","snow","snprintf(out,","so!","so)","so),","so,","so.","so:","sobel","softwar","sol","sol;","sol[col]","sol[i]","sol[j]","sol[pivot_i]","solar","solid","soln","soln);","soln.join(\"\\t\")","soln:","soln[a.row","soln[i]","soln[j]","soln[j]*a[i,j]","solut","solution\");","solution,","solution.","solution.indices)","solution:","solution:\"","solution:\"\"\"","solution:\")","solution:%s',","solution:')","solution:\\n\");","solution;","solution?","solution[0]","solution[i","solution[i]","solution[j]","solution_grid","solution_grid);","solution_grid,","solution_grid[:3,]","solution_grid{","solutions.","solv","solvabl","solve,","solve;","solved.","solver","solver...","solvers.","some('0')","some('1')","some(approximate_count(n_items,","some(c)","some(current)","some(otherman)","some(this)","somehow","someon","someone,","someth","something).","something,","something...","sometim","sometimes,","somewhat","somewher","soon","soon!","soon,","sophist","sort","sort!(points,","sort(points[2:end],","sort)","sort.","sort.slice(points,","sort_by_bit_reverse(first,","sort_by_bit_reverse(it","sorted(gift,","sortedpt","sorting,","sorton","sorts.","soul","sourc","south,","southeast,","southwest,","space","space\"","space,","space.","space:","spacer","spaces,","spaces;","sparingly.","spatial","spawn","speaking,","special","specialty,","specif","specifi","specifically,","specifically:","specified,","specified.","specifiers,","spectral","sped","speed","speed,","spend","spent","spheric","spice","spin","split","split_op!(par,","split_op!(par::param,","split_op(&par,","split_op(par,","split_op(par:","split_op(param","split_op(struct","split_op.jl","splitop","splot","spot,","spread","spring","spring,","spring.","springer","springer,","spruce","spy?","sqrt","sqrt(","sqrt()","sqrt(0.1*kernel_size)","sqrt(0.75))","sqrt(0.75)),","sqrt(0.75)],","sqrt(n)","sqrt(n))","sqrt(renorm_factor)","sqrt(rms/n)","sqrt(x*x","sqrt.(gx.^2","squar","square\"","square).","square,","square.","square?","squares.","squares?","squares_array","srand((unsign","srand,","src)","src);","src,","src_len","ss","st","st)))","stabl","stable.","stable_marriage($men,","stable_marriage(array","stable_marriage(men,","stable_match(leadit","stablemarriag","stablemarriage(guys,","stablemarriage.findstablematches(a,","stablemarriage.man(\"adam\")","stablemarriage.man(\"bart\")","stablemarriage.man(\"colm\")","stablemarriage.woman(\"xena\")","stablemarriage.woman(\"yeva\")","stablemarriage.woman(\"zara\")","stablemarriageexampl","stablemarriageproblem","stablematch","stack","stack\");","stack🔤❗️","stack()","stack();","stack(generic[t]):","stack)","stack))","stack)))","stack))))","stack,","stack.","stack.\"","stack.\"\"\"","stack...)","stack.append(child)","stack.count","stack.empty?","stack.extend(¤t.children);","stack.extend(find_neighbours(canvas,","stack.extend(node.children)","stack.pop","stack.pop()","stack.pop();","stack.poplast()!","stack.push","stack.push(&n);","stack.push(...current.children);","stack.push(c);","stack.push(this);","stack.push(this.root);","stack:","stack::new();","stack;","stack<>();","stack[0]","stack[1:]","stack[int]","stack\\n')","stack_array,","stack_cap,","stack_empty(struct","stack_fill!(canvas,","stack_fill!(grid,","stack_fill$(?,","stack_fill(","stack_fill(canvas,","stack_fill(struct","stack_fill(test_grid,","stack_pop","stack_pop(&stk);","stack_pop(struct","stack_pop:","stack_pop_el","stack_pop_element:","stack_pop_return","stack_pop_return:","stack_push","stack_push(&stk,","stack_push(struct","stack_push:","stack_push_append","stack_push_append:","stack_size,","stack_test_func","stack_test_func):","stack_top,","stacks,","stacktest","stack{cartesianindex}()","stack{node}()","stack❗️","stage","stage,","stand","standalon","standard","standard,","standard.","standard:","star","start","start,","start.","start.angle(point)))","start:","start_index","start_loc","start_loc,","start_loc{1,","starting,","starting_loc","starting_location,","starts.","state","state,","state.","statement","statements,","statements:","states,","states.","static","static::dfsrecursive($child);","static::dfsrecursiveinorderbinary($tre","static::dfsrecursivepostorder($child);","static_cast(current_loc[0]);","static_cast(current_loc[1]);","static_cast(grid.size())};","static_cast(grid[0].size()),","static_cast(loc[0]);","static_cast(loc[1]);","static_cast(neighbor[0]);","static_cast(neighbor[1]);","static_cast(possible_neighbor[0]);","static_cast(possible_neighbor[1]);","statist","statistics,","statistics.","stay","stay.","std.math","std.math;","std.stdio","std.stdio;","std::abs(a);","std::abs(b);","std::array","std::array&","std::array;","std::back_inserter(ret));","std::back_inserter(ret),","std::begin;","std::cerr","std::cmp::min;","std::cmp::ordering;","std::cmp::{ord,","std::collections::vecdeque;","std::collections::{binaryheap,","std::complex(0.0,","std::complex;","std::copy(begin(code),","std::cout","std::default_random_engin","std::default_random_engine&","std::end;","std::exchange(b,","std::f64::consts::pi;","std::find_if(","std::find_if(begin(encoder),","std::find_if(begin(ret),","std::for_each(first,","std::fs::file;","std::fs::write(\"./out.dat\",","std::fs::write(\"./sierpinski.dat\",","std::generate(","std::generate_n(std::back_inserter(ret),","std::generate_n(std::back_inserter(vec),","std::invalid_argument(","std::invalid_argument(\"attempt","std::io::write;","std::iota(begin(ret),","std::iter::from_fn(||","std::make_pair(it,","std::make_pair(last,","std::make_shared(","std::make_shared>(element);","std::make_unique(l);","std::make_unique(std::move(lhs),","std::make_unique>(element);","std::min_element(points.begin(),","std::move(bits)));","std::move(encoder)});","std::move(new_node);","std::move(ret.back());","std::move(rhs));","std::move(top_point","std::move(top_pointer);","std::mt19937","std::ofstream","std::ops::{index,","std::optional,","std::ostream&","std::pair","std::path::path;","std::queue","std::queue{};","std::random_devic","std::shared_ptr","std::shared_ptr>","std::shuffle(begin(ret),","std::size_t","std::size_t;","std::sort(begin(freq),","std::sqrt(0.75)},","std::stack","std::stack{};","std::string","std::swap(eqns[pivot],","std::swap(points[i],","std::swap;","std::to_string((21","std::to_string(22","std::to_string(d","std::transform(","std::uint32_t(log2(static_cast(size))));","std::uniform_int_distribution(0,","std::uniform_real_distribution(0.0,","std::unique_ptr>","std::vector","std::vector&","std::vector(),","std::vector();","std::vector(a.size(),","std::vector(opr.size,","std::vector(points.begin(),","std::vector(s","std::vector;","std::vector>","std::vector>&","std::vector>();","std::vector>;","std::vector{};","std=c++17","stem","stem,","stem.","step","step,","step.","step:","step?","steps)","steps.","steps:","stereotyp","stick","sticky.","still","still,","stk","stk)","stk.capac","stk.data","stk.top","stk;","stolen?","stop","storag","storage.","store","stori","storm,","stormer","stormer_fmt","stormer_fmt:","stormer_verlet","stormer_verlet(&time,","stormer_verlet(5,","stormer_verlet(5.0,","stormer_verlet(doubl","stormer_verlet(mut","stormer_verlet(pos,","stormer_verlet(pos::float64,","stormer_verlet:","stormer_verlet_loop","stormer_verlet_loop:","stormer_verlet_return","stormer_verlet_return:","stormerverlet","stormerverlet(5,","stormerverlet(5.,","stormerverlet(5.0,","stormerverlet(_pos:","stormerverlet(pos,","stormerverlet(pos:","stormerverlet(pos_in,","story.","storytel","str","str((21","str(0)))","str(22","str(codebook))","str(d","str(self.__list)","str(tree))","str)","str:","str:gmatch(\".\")","str[257];","straddl","straight","straightforward","straightforward,","straightforward.","straightforward:","straightforwardli","strang","strassen","strategi","strategy,","strategy:","strategy?","strcat(*dst,","stream","streaming.","strengthen","strformat","strictli","stride","stride)","stride):","string","string\"","string(0)))","string(22","string(bit_indices[i][end","string(char)","string(code)","string(code,","string(codes.encode(begin(s),","string(cur.char)","string(current.key)","string(d","string(density[j])","string(huffman_tree.key)","string(i)","string(lpad(string(i","string(mod(21","string(par.x[j])","string(real(opr.v[j]))","string)","string):","string,","string.","string:","string::from(\"\");","string::new();","string;","string]","string]()","string]):","stringbuild","stringbuilder());","stringbuilder();","stringtoencode)","stringtoencode;","string},","strip","strive","strlen(*dst);","strlen(src);","strong","stronger","struct","structur","structure,","structure.","structure?","structures,","strung","student","students).","studi","studio","stuff,","stun","stupid!","style","style:","style=\"width:100%\"/>","style=\"width:80%\"/>","style=\"width:80%\">","sub","sub(","sub*","subclass:","subdivis","subdivision),","subject","subjective.","submission,","submissions;","submit","subroutin","subrow","subsd","subsect","subsections:","subsequ","subset","subsitution\")","substitut","substitute,","substitution\"","substitution,","substitution.","substitution:","subtract","subtraction\"","subtraction,","subtraction:","success","such","such,","such.","suddenli","suffic","suggest","suit","suitabl","suitor","suitor)","suitors.add(suitor);","suitors.contains(mostdesired))","sum","sum'","sum(density)","sum(energy_k","sum(histogram)","sum(squares_array)","sum)","sum.","sum.sqrt();","sum:","sum_matrix_dimensions(mat1,","sum_matrix_dimensions(signal,","summar","summary,","summat","summer","summer,","summer.","sun","sun,","sunday","sunni","super","super(name);","supercomput","superfluid","superimpos","supersed","support","support.","suppos","supposedli","suppress","suppress(indexerror):","sure","sure,","sure.","surface,","surpris","surprising.","surprisingli","surprisingly,","surround","survey","suspect","swap","swap(&heap","swap(first[b],","swap(i,","swap(struct","swap_rows(&mut","swap_rows(a,","swap_rows(doubl","swaprow","swaprow(a,","swaprow(double[][]","swift","switch","sx","sx))","sx,","sy","sy))","sy,","symmetr","symmetric,","symmetrical,","sync","synchron","synchronized,","synod","syntax,","system","system!","system\"","system\")","system\");","system'","system,","system,\"","system,\")","system,\");","system,%s',","system,\\n\");","system.","system.collections.arraylist","system.collections.generic;","system.collections;","system.console.writeline(\"jarvismarch\");","system.console.writeline(\"run","system.console.writeline($\"th","system.console.writeline($\"{entry.key}","system.console.writeline($\"{point.x},","system.console.writeline($\"{result.bitstring}","system.console.writeline(originalstring);","system.err.println(\"not","system.err.println(\"th","system.io;","system.linq;","system.out.format(\"[%.1f,","system.out.format(\"ha","system.out.format(\"th","system.out.print(node.id","system.out.print(queue.peek().id","system.out.print(stack.peek().id","system.out.printf(\"%","system.out.printf(\"perc","system.out.println(\"[\"","system.out.println(\"[#]\\nmodulu","system.out.println(\"[#]\\nqueu","system.out.println(\"[#]\\nrecurs","system.out.println(\"[#]\\nstack","system.out.println(\"[#]\\nsubtract","system.out.println(\"[#]\\ntim","system.out.println(\"[#]\\nveloc","system.out.println(\"\\ngauss","system.out.println(\"\\nsolutions:\");","system.out.println(\"cod","system.out.println(\"decod","system.out.println(\"encod","system.out.println(\"estim","system.out.println(\"gaussian","system.out.println(\"gift:\");","system.out.println(\"wrapping:\");","system.out.println();","system.out.println(arrays.tostring(backsubstitution(a)));","system.out.println(arrays.tostring(x)));","system.out.println(euclidmod(64","system.out.println(euclidsub(128","system.out.println(intqueue.dequeue());","system.out.println(intqueue.front());","system.out.println(intqueue.size());","system.out.println(intstack.pop());","system.out.println(intstack.size());","system.out.println(intstack.top());","system.out.println(m","system.out.println(m.getkey()","system.out.println(stormerverlet.time);","system.out.println(stormerverlet.vel);","system.out.println(velocityverlet.time);","system.out.println(velocityverlet.vel);","system.out.println(verlettime);","system.out.println(w","system.random","system:","system;","systems!","systems,","systems.","systems:","systems;","t","t\".","t&","t)","t))","t)),","t));","t))\\delta","t),","t):","t)\\delta","t)}{2\\delta","t+dt)","t,","t.","t0","t0)","t1","t1)","t2","t2)","t2,","t:","t;","t^2","t^2)","t^2),","t^2).","t^3","t^3).","t^3.","t^3}{3","t^4)","t^4),","tab","tabl","table\"","table,","table.remove(freq)","table.remove(freq),","table.sort(arr,","table:","tackl","tactic","tag.","tail","tak","take","taken","takes.","takewhil","talk","tape","target","target),","target;","task","task.","tasks:","tastes.","taught","taylor","tba","tdma,","teach","teacher","technic","techniqu","techniques,","techniques.","technolog","technology,","tediou","tell","temp","temp)","temp))","temp)))))","temp);","temp._children)","temp.children","temp.children!","temp.children)","temp.children.each{","temp:","temp;","temp[b]","temp[i]","temp[k","temp[k]","temp_","temp_children","temp_nod","temp_node,","temp_node.weight)","temp_po","temp_pos,","temp_pos;","temp_str","temp_string))","temp_vector","temperatur","temperature)","templat","template(par.x[j],","temporari","temporarili","temppo","temppos:","temppos;","tempt","temp❗️","tend","tent","term","term,","term.","termin","terminal,","terminator:\"","terminolog","terms)","terms))))","terms.","ternari","terribl","territory!","ters","test","test\"","test()","test():","test_approximate_count(n_trials:","test_gift","test_grid","test_grid(grid,","test_grid(initial_canvas,","test_metropolis_iter","test_metropolis_iterate(num_steps,","testing,","testresult","tests\"","tests,","testtre","tex","tex,","text","text!","text,","text.","text:","textbook","textbook.","tfollow","thank","that!","that'","that,","that.","that:","that?","them),","them,","them.","theme","theme,","theme:","themes,","themselv","themselves.","then,","then.","theon","theorem","theorem,","theori","theorist","theory,","theory.","there!","there'","there,","there.","thereafter.","therebi","therefor","therefore,","theta","theta(x,y)","thin)","thing","thing,","thing:","things!","things,","things.","things:","think","think!","thinking,","thinner","third","third,","this)","this,","this.","this.bitstr","this.children","this.createallchildren(this.root,","this.data","this.data.findindex(x","this.data.push(value);","this.data.shift();","this.dfsrecursive(this.root);","this.dfsrecursivepostorder(this.root);","this.dictionari","this.frequ","this.i","this.id","this.key","this.left","this.leftchild","this.lett","this.list","this.list.add(element);","this.list.get(0);","this.list.get(this.size()","this.list.length;","this.list.pop();","this.list.push(data);","this.list.remove(0);","this.list.remove(this.size()","this.list.shift();","this.list.size();","this.list[0];","this.list[this.list.length","this.mat","this.mate.m","this.nam","this.nod","this.nodes.binarysearch(newnode);","this.nodes.sort();","this.preferences.indexof(other)","this.radiu","this.right","this.rightchild","this.root","this.size();","this.stringtoencod","this.tim","this.tre","this.vel","this.weight","this.x","this.x)","this.y;","this.z","this:","this;","this?","this_fft","this_fft.process(new_x.as_mut_slice(),","thm","thoma","thomas(","thomas(&a,","thomas(a","thomas(a,","thomas(a:","thomas(a::vector{float64},","thomas(doubl","thomas_algorithm($a,","thomas_algorithm(a,","thomas_algorithm(x,","thomasalgorithm(a,","thomasalgorithm(double[]","those","though","though,","though.","thought","thought,","thought.","thought:","thousand","thread","thread_loc","thread_rng();","threads,","threads.","three","thresh","threshold","threshold)","threshold):","threshold.","threshold:","through","throughout","throw","thrown","thu","thumb","thumb,","thus,","tic","tick","tick.set_visible(false)","tics,","tid","tilmann","tilt","time","time!","time)","time)))","time);","time,","time.","time:","time;","time_sv);","time_v","time_v);","time_vv);","timeless","times,","times.","timestep","timestep!","timestep,","timestep.","timestep:","timesteps,","timesteps.","timesteps:","timesteps::int64","timesteps::int64,","timesteps;","timesv","timev","timeveloc","timevv","tip","titl","title,","title.","titles,","tittl","tlead","tmp","tmp(n);","tmp))","tmp.children)","tmp.x);","tmp.y);","tmp1[9],","tmp2[9];","tmp;","tmp[n];","tmp_point","tmp_points[0]","tmp_points[i]","tmp_points[i];","tmp_points[m]","tmp_points[m];","tmp_points[siz","tmp_points[size];","to.","to:","to_","to_be_encod","to_choic","today","today.","today?\"","togeth","together!","together,","together.","together.)","together:","told","told,","toler","tomorrow","too!","too,","took","tool","tool!","toolchain","tools,","top","top(&self)","top()","top().","top():","top();","top(self)","top)","top,","top.","top;","top_point","top_pointer:","top_pointer;","topair","topchoice,","topel","topic","topic,","topic:","topics.","tosortedlist","toss","toss,","tostring()","total","total.","touch","tour","toward","tpref","track","tradit","traditionally,","train","trait","traj","traj)","trajectori","transcrib","transcript","transform","transform!","transform\"","transform,","transform.","transform.\"","transform;","transform?","transform_matrix","transform_matrix*x","transformation,","transformation.","transformations,","transformations:","transforms!","transforms,","transforms.","transit","translat","translation,","translation.","transpos","transpose)","trap","trap,","trap.","travel","travers","traversal🔤️❗️","traversal,","traversal:","traverse(node.left,","traverse(node.right,","traverse(root,","traverse(treenod","treat","treat!","tree","tree!\"","tree!\")","tree!\");","tree!');","tree!';","tree\"","tree\")","tree'","tree')","tree($numofrows);","tree(2,","tree(3,","tree(int","tree)","tree))","tree)))))","tree));","tree))]","tree);","tree*","tree*));","tree**","tree,","tree.","tree.\"","tree.\"\"\"","tree.\"))))","tree.\\n\"","tree.\\n\");","tree._children)","tree.bfsqueue();","tree.c","tree.children.foreach(dfspostorder);","tree.children.foreach(dfspreorder);","tree.dequeue()","tree.dfsrecursive();","tree.dfsrecursiveinorderbinary();","tree.dfsrecursivepostorder();","tree.dfsstack();","tree.headopt","tree.java","tree.make_codebook();","tree:","tree:\"","tree:\")","tree:\");","tree:'","tree:',","tree:\\n\");","tree:~%\")","tree;","tree?","tree[1]","tree\\n')","tree_children,","tree_count,","tree_count]","tree_count],","tree_free(struct","tree_free(tre","tree_left","tree_left,","tree_left,weight_left","tree_left]","tree_left],","tree_num_children,","tree_right","tree_right)","tree_right,","tree_right,weight_right","tree_right]","tree_right],","tree_siz","tree_size,","tree_traversal.c","tree_value,","tree_value]","tree_value],","treenod","treenode(int","treenode(left.frequ","treenode(m.getkey(),","treenode(str","trees\");","trees.insert(index,","trees.pop()","trees.popleft()","trees:","trees[0]","treetravers","treetraversal::dfsqueue($node);","treetraversal::dfsrecursive($node);","treetraversal::dfsrecursiveinorderbinary($node);","treetraversal::dfsrecursivepostorder($node);","treetraversal::dfsstack($node);","tree}","trend","tri","trial","trials\"","triangl","triangle,","triangle.","triangle:","triangular","triangular,","triangular.","trick","trick!","trick.","tricki","tricky)","tricky.","tridiagon","trigger","trigonometr","trillion","trit","trivial","trivial!","trope","troubl","trouble.","true","true)","true):14}","true);","true,","true:","true;","true_valu","true_values)**2","truli","truncat","trust","truth","truth!","try:","ts","ts)","tself","tself)","tuesday","tug","tukey","tukey,","tune","tupl","tuple!(\"x\",","tuple(*(mat","tuple(create_tree(num_row","tuples,","turbul","turn","turn.","turn_counter_clockwise(p1:","twice","twice,","twice.concat(twice.map(x","twiddl","twist","twitch","twitch.","two","two.","two:","two_pass_huffman(\"b\")","two_pass_huffman(\"bbbbbbbb\")","two_pass_huffman(\"bibb","two_pass_huffman(phrase::string)","two_pi","two_pi:","type","types,","types.","typescript","typesetting,","typevar(\"t\")","typevar,","typic","t}","t}.","u","u32);","u64)","u64,","u_1","u_1/\\sqrt{r_0}","u_2","u_2),","u_2.","u_2/\\sqrt{r_0}.","u_2^2}.","ui","uklidmod","uklidsup","ultim","ultimately,","unaccept","unawar","unbound","uncertain","uncertainti","unchang","unclear,","unclear.","uncom","uncommon","under","undergo","underlying_","underlying_;","underneath","underneath.","underpinnings,","understand","understand,","understand.","understandable.","understood!","undocu","undoubtedli","unfair","unfeas","unfeasible.","unfortun","unfortunately,","uniform","uniform,","uniform.","uniform01))","uniform?","uniformli","union","union{leaf,","uniqu","unit","unititialized,","unitless","units,","units.","unity,","univers","universe.","unknowns,","unless","unlik","unlikely,","unlin","unlucky).","unmatch():","unnecessari","unnecessary.","unpack","unphysical,","unport","unreachable()","unreachable();","unrel","unsatisfying!","unscrambl","unset","unsettl","unsign","unsurprisingly,","until","untrain","unusu","unword","unwrap","up","up\"","up,","up,\"","up.","updat","updated.","updating!","upon","upper","upto","upward","url","us","us,","usa,","usabl","use)","use:","used,","used.","used;","used}}","useful","useful)","useful.","useless.","user","using,","using.","using:","usiz","usize)","usize))","usize)]","usize)];","usize,","usual","utility.h","utility_h","utter","v","v\"","v'","v',","v(\\mathbf{r})","v(\\mathbf{r},t)","v(n)","v(t)","v(t),","v(t)\\delta","v(t+\\delta","v(t+\\frac{1}{2}\\delta","v)","v))","v,","v.","v.iter().zip(y.iter()).all(|i|","v.push(complex::new(","v.reserve(size);","v.x","v.y;","v0","v0)","v1","v2","v3","v:","v::vector{complex{float64}}","v;","v=1.","v=255.","v=\\frac{\\delta","v[i]","v[i].re).exp()));","v[i].re).exp(),","v]","v_0t","v_offset).powi(2),","v_offset:","vagu","vague,","vague.","val","valid","valu","value\"","value(v)","value)","value),","value).","value,","value.","value.weight);","value:","value;","values).","values,","values.","values:","values?","value|children_s","vanish.","var","var_a","var_b","vari","variabl","variable,","variable.","variables,","variant","variat","varies.","varieti","variou","vcat(x_odd","vec","vec![","vec![0.0,","vec![0.01,","vec![0.0;","vec![1.0,","vec![4.0,","vec![7.0,","vec![],","vec![complex::new(0.0_f64,","vec![n];","vec![start,","vec)","vec)]","vec,","vec1","vec1.x*vec2.i","vec1.y*vec2.x","vec2","vec3","vec3&","vec3{initial_location[0],","vec3{};","vec::from(x);","vec::new(),","vec::new();","vec::with_capacity(64);","vec::with_capacity(par.res);","vec::with_capacity(res);","vec;","vec>","vec>,","vecdequ","vecdeque::new(),","vecdeque::new();","vector","vector'","vector(","vector(0,","vector(15,","vector(2,","vector(5,","vector(6,","vector(7,","vector(9,","vector(int","vector,","vector.","vector.'''","vector_complex","vector_r","vectors,","vectors.","vector{float64}(","vector{float64}(vcat(0:512/2","vector{float64}(vcat(0:res/2","vector{pos}()","vel","vel)","vel))))","vel);","vel*dt","vel:","vel:vel)","vel;","vel_sv)","vel_sv);","vel_vv)","vel_vv);","veloc","velocity!","velocity,","velocity_fmt","velocity_fmt:","velocity_verlet","velocity_verlet(&time,","velocity_verlet(5,","velocity_verlet(5.0,","velocity_verlet(doubl","velocity_verlet(mut","velocity_verlet(pos,","velocity_verlet(pos::float64,","velocity_verlet:","velocity_verlet_loop","velocity_verlet_loop:","velocity_verlet_return","velocity_verlet_return:","velocityverlet","velocityverlet(5,","velocityverlet(5.,","velocityverlet(5.0,","velocityverlet(_pos:","velocityverlet(pos,","velocityverlet(pos:","velocityverlet(pos_in,","velsv","velsv)","velverlet","velvv","velvv)","veri","verifi","verlet","verlet(&time,","verlet(5,","verlet(5.,","verlet(5.0,","verlet(_pos:","verlet(doubl","verlet(mut","verlet(pos,","verlet(pos:","verlet(pos::float64,","verlet(pos_in,","verlet:","verlet_fmt","verlet_fmt:","verlet_integr","verlet_loop","verlet_loop:","verlet_return","verlet_return:","verlettim","verletvalu","verletvalues(doubl","verletvalues(time,","verletvalues(v","versa.","version","versions.","vertic","vetting.","via","vice","vicinity,","video","video,","view","villain","viml","viren","virtual","visibl","visible.","visit","visit.","visual","visualization,","visualizations,","voffset)","voffset).^2","voffset,","voffset:","voffset::float64,","void","vortex","vortic","vs","vx","vx)","vx)))","vx)]","vx:\"","v}","w","w)","w))","w,","w.","w.fiance.getorelse(stablemarriage.man(\"nobody\")).name))","w.getmate()));","w.getpreferredmates());","w.name","w.receiveoptions(men);","w0","w:","w;","w_i","wai,","wait","wait(cartesian_box_muller!(input_pts,","wait(polar_box_muller!(input_pts,","walk","walk\"","walk,","walk.","walker","walker'","walker,","wall","wander","wanderin","wanna","want","want!","want,","want.","wants,","war","warm","warm.","warn","warp","warp.","was:","wash","wasn't","wast","watch","wave","wave\"","wave\",","wave,","wave.","wave;","waveform,","wavefunct","wavefunction,","wavefunction.","wavefunctions,","wavefunctions.","wavelength.","wavevector","wavevectors,","wavey","wavey,","way","way!","way,","way.","way:","way;","ways,","ways.","wcast","wconvers","wdoubl","we'll","we'r","we'v","website:","wednesday","week","week,","weekli","weight","weight(leaf(char,","weight(left)","weight(new_tree))","weight(node(left,","weight(right)","weight(tree())","weight)","weight,","weight:","weight::int64","weight;","weight?","weight])","weight_left","weight_right","weights[temp_string]","weinstein","weird","weird.","well","well\"\"\"","well),","well,","well.","well...","west","west,","west.","western","wextra","wfc","wfc'","wfc)","wfc.push(complex::new(","wfc.reserve(size);","wfc0","wfc0)","wfc:","wfc::vector{complex{float64}}","wfc_c","wfc_c(opr.size);","wfc_c.*opr.v","wfc_c[i]","wfc_c[i].scale(0.5_f64);","wfc_c[opr.size];","wfc_k","wfc_k(opr.wfc);","wfc_k)","wfc_k,","wfc_k[i]","wfc_k[opr.size];","wfc_offset).powi(2))","wfc_offset:","wfc_r","wfc_r(opr.wfc);","wfc_r[i].conj();","wfc_r[i];","wfc_r[opr.size];","wfcconj","wfcoffset)","wfcoffset).^2/2)","wfcoffset,","wfcoffset:","wfcoffset::float64)","wformat=2","what'","what,","whatev","wheel","whenev","where'","where,","wherea","wherev","whether","whichev","while(*next_point_it","while(b","while(length(nodes)","while(length(q)","while(length(s)","while(length(weights)","while,","while:","whilefalse:","whiletrue:","white","white,","whitespac","whole","whose","why)","why),","why,","wide","wide.","wider","wider.","widescreen","width","wife","wife)","wifi","wiki","wikipedia)","wild","wild:","will","win","wind","winding.","wise","wish","wish!","with.","with:","with_new_bit(bits,","with_new_bit(std::move(bits),","with_new_bit(std::vector","within","within.","without","wname","wnames)","wnon","wnull","wobbl","wold","woman","woman(\"f\"),","woman(\"g\"),","woman(\"h\"),","woman(\"i\"),","woman(\"j\"),","woman(name:","woman(str","woman.choic","woman.choices)","woman.fi","woman.pick_preferred()","woman.prefer","woman;","woman?.partner.name);","womannames))","womannames::vector{string})","women","women)","women):","women,","women.","women.size()","women/men.","women:","women:')","women::preferences)","women::preferences,","womentoman::pairs)","womentoman[candidate])","womentomen","womentomen)","womentomen[candidate]","womentomen[candidate])","won't","wonder","word","word.","words,","work","work!","work,","work.","work:","worked.","works,","works.","world","world\"","world,","world.","world;","worlds,","worri","worry!","worse!","worse,","worse.","worst","worst,","worth","worthwhil","would'v","wouldn't","woverload","wpedant","wrap","wrap.","write","write(*,","write(*,'(a)')","write(*,*)","write(outfile,","write,","write:","writedlm(\"sierpinski.dat\",","writefil","writeln!(file,","writeln(\"[#]\\nmodulu","writeln(\"[#]\\nsubtract","writeln(\"estim","writeln(\"perc","writeln;","writing,","written","written.","wrong","wrong;","wshadow","wsign","wunus","x","x'","x(t","x(t)","x(t),","x(t)}{\\delta","x(t+","x(t+\\delta","x(t\\pm","x)","x))","x);","x*x","x*x+y*i","x,","x,i","x,y;","x.","x.(*node);","x.1).re);","x.append(random())","x.len();","x.len()];","x.length","x.length);","x.length;","x.map((_,","x.norm().powi(2)).collect();","x.prefer","x.push(complex::new(real,","x.push(xmax","x.reduce((a,","x.reserve(res);","x.to_vec();","x.weight","x/ytic","x0","x0)","x0):","x1","x2","x64","x:","x::float64","x::vector{float64}","x;","x=0.","x[0]","x[0]))","x[0]);","x[1]","x[1]))","x[1]);","x[2]","x[2]))","x[2]);","x[64],","x[b]","x[c]","x[half+i]*factor[i]","x[i","x[i+1])","x[i]","x[i];","x[indexes[i]]);","x[j]","x[k","x[k]","x[n]","x[n];","x[r]","x\\sigma","x],","x^2","x^2+y^2","x^2}","x^2},","x^2}.","x^2}}{\\displaystyle\\int_{","x_0","x_0'''","x_0.","x_2,","x_dat","x_dat)","x_even","x_i","x_i,","x_i.","x_k","x_n","x_new","x_odd","x_pos^2","x_posit","x_propos","x_t","x_{10})}{t}\\right]\\","x_{i+1}","x_{t+1}","xa)","xadisten","xam4lor","xlabel","xmax","xmax)","xmax),","xmax);","xmax+xmax/res:2*xmax/res:xmax),","xmax,","xmax:","xmax::float64","xmax;","xmin,","xmm0","xmm0,","xmm1","xmm1,","xmm2","xmm2,","xmm3","xmm3,","xmm4","xmm4,","xmm5","xmm5,","xmm6","xmm6,","xmm7","xmm7,","xmmword","xold","xor","xorp","xpo","xrang","xrange[","xs","xs)","xs)**2)).sum(axis=0)","xtic","xvalue,","xvalue;","xx","xx,","xy","xy,","xy_array","xy_array.^2;","xz,","x|","x}","x}{\\delta","y","y\")","y(x.size(),","y)","y)))","y):","y)=","y*i","y*y)","y,","y.","y.as_mut_slice());","y.into_iter().map(|i|","y.iter()","y.length","y.prefer","y1)","y:","y::float64","y;","y=%f\\n\",","y=0):","y=x","y=x.","y[0]","y[64],","y[half+i]","y[i","y[i]","y[k]","y[n];","y[size];","y\\sigma","y^2","y_1,","y_2,","y_i,","y_n,","y_pos::float64)","y_pos^2","y_posit","ya","ya)","yb)","yc)","year","year!","year\"","year'","year,","year.","year:","years)","years,","years.","years.for_each(|year|","yes.","yet.","yield","ylabel","york","york,","you!","you'd","you'r","you,","younger,","yourself","youtub","youtube,","ypo","ypos)","yr","yrang","yrange[","ys","ytic","yvalue)","yvalue;","yx","yx,","yy","yy)","yy,","yz,","z","z(x,y)","z)","z).foreach(","z**2","z,","z.","z.prefer","z:","z;","z=1.","z[0]","z[64];","z[i","z[i]","z[start_index+k","z\\in\\mathbb{r}","z^2","z^2,","z^2.","z_1","z_1,","z_2","z_2).","z_2,","z_i","z_imag","z_n),","z_real","z_real,","zero","zero!","zero):","zero.","zero:","zero:p),","zero?","zeros(5,5)","zeros(ceil(int,(bounds[1,2]","zeros(kernel_size,","zeros(n,","zeros(n,2)","zeros(res))","zeros(res),","zeros(rows)","zeros.","zip","zip(point,","zip4","zipwith","zipwith3","zoom","zx,","zy,","zz;","{","{\"\"","{\",","{%","{'nrmsd':10s}\")","{0,","{0.0,","{0.5,","{1,","{1.0,","{15,","{2,","{2.0,","{22","{3,","{4.0,","{5,","{5.0,","{6,","{7,","{7.0,","{9,","{:.3f}\".format(percent_error))","{:.3f}\".format(pi_estimate))","{:.3}%\",","{:?}","{:?}\",","{:?}][x]","{:messag","{bool","{c[1]","{computus(year,","{d","{d[1]","{drand(),","{entry.value}\");","{k","{k,","{lhs.x","{loc[0]","{loc[0],","{man.partner.name}')","{math.abs(piestim","{next_nodes{:},","{node1,","{node10,","{node1[1],","{node2,","{node5,","{node6,","{node_stack{:}","{nrmsd:5.1%}\")","{null,","{number}","{n};","{p.x","{p.x,","{piestimate}\");","{point.y}\");","{q},","{result.bitstring.length}\");","{samples:_}","{self.n})'","{self.y})'","{str(self.right)})'","{t","{wfc","{x0:5.2f}\")","{{","{{0.0,","{{3.0,","{{}});","{}","{}\",","{});","{}:","{};","|","|>","|\\psi(\\mathbf{r},t)|^2","|\\sin(\\pi\\times\\text{re}(f(z)))^t|\\times|\\sin(\\pi\\times\\text{im}(f(z)))^t|,","|acc,","|child|","|i|","|j|","|mut","|m|","|round|","|y|","|z|","||","}","})","}));","}).collect()","});","},","}.","};","~=","~a\"","~isempty(child)","~isempty(children{1})","~isempty(node_queue)","~isempty(node_stack)","~queue()","~stack()","~}~%\"","ševčíková,","–","—","↩️","↪️","≠","⏫","⏹","▶️","◀️","◀️🙌","☝️","✖️","❎","❗️","❗️🤛❗️","❗️❗️","➕","➖","➗","➡️","⬅️","⬆️","⭐️","️🔁","️🔼🐇⬆️","️↪️","️⏫🐇⬆️"],"pipeline":["stopWordFilter","stemmer"]},"store":{"./":{"url":"./","title":"Algorithm Archive","keywords":"","body":"The Arcane Algorithm Archive\nThe Arcane Algorithm Archive is a collaborative effort to create a guide for all important algorithms in all languages.\nThis goal is obviously too ambitious for a book of any size, but it is a great project to learn from and work on and will hopefully become an incredible resource for programmers in the future.\nTo change the language, please use the UI at the top of the site:\n\n \n\n\nHere are some essential links:\n\nBook / website: https://www.algorithm-archive.org/\nGitHub repository: https://github.com/algorithm-archivists/algorithm-archive\nYouTube channel (LeiosOS): https://www.youtube.com/user/LeiosOS\nTwitch livestream: https://www.twitch.tv/leioslabs\nDiscord server: https://discord.gg/Pr2E9S6\n\nNote that this project is essentially a book about algorithms collaboratively written by an online community.\nFortunately, there are a lot of algorithms out there, which means that there is a lot of content material available.\nUnfortunately, this means that we will probably never cover every algorithm ever created and instead need to focus on what the community sees as useful and necessary.\nThat said, we'll still cover a few algorithms for fun that have very little, if any practical purpose.\nIf you would like to contribute, feel free to go to any chapter with code associated with it and implement that algorithm in your favorite language, and then submit the code via pull request.\nYou can find help and instructions regarding the contribution process in our How to Contribute wiki entry.\nHopefully, this project will grow and allow individuals to learn about and try their hand at implementing different algorithms for fun and (potentially) useful projects.\nIf nothing else, it will be an enjoyable adventure for our community.\nThanks for reading and let me know if there's anything wrong or if you want to see something implemented in the future!\n\nLicense\nThe code examples for this project are licensed under the MIT license (found in LICENSE.md).\nAll text content is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License with attribution specified at the end of every chapter.\nAll graphics are licensed under the license stated at the end of every chapter.\nIf no attribution is specified, please attribute James Schloss.\n\n"},"contents/introduction/introduction.html":{"url":"contents/introduction/introduction.html","title":"Introduction","keywords":"","body":"Introduction\nPeople learn differently, there's no doubt about that. I for one, have never been able to follow a lecture. No matter how interesting the subject might be, the teacher or professor either moves too slowly or too quickly, and in both cases I lose the motivation to study and learn outside of class. Looking back at all my past lectures, this is a bit of a shame. I genuinely love learning! In fact, nowadays there's nothing I enjoy more than poring through the ArXiv, looking for the latest and greatest algorithms in physics and computer science. Sure, I cannot understand them all, but sometimes it's nice to be completely overwhelmed and chip away at problems one piece at a time. In the end, modern research is a conglomeration of fun little (or big) puzzles to solve; however, I find that many papers are too harsh for most people to tackle without a significant background in computer science or physics. For this reason, they are ignored by the public. We live in an era where nearly the entire sum of human knowledge is available at our fingertips, and yet people are blissfully unaware of the unique ideas and challenges that are pushing our understanding forward.\nI guess that is the point of this work. Throughout the past few years, I have been collecting small morsels of knowledge that are hard to express in any meaningful way through blog posts, YouTube, or twitch streaming. YouTube, for example, is a great place to introduce the general idea of an algorithm; however, I personally find it a poor choice to show a worked example. Twitch is great to show everything, but spending 5 hours programming up an algorithm for the first time is generally not everyone's idea of fun. Blog posts work well for this type of material; however, they lack a comprehensive nature that I tend to enjoy. So what's left? Well, I suppose that would be a book, which is an incredibly exciting prospect!\nSee, when I was younger, maybe around Jr. High School age, I really wanted to become an author. I spent as much free time as I could manage writing fantastical stories about heroes and villains creating their own worlds and redefining reality. It was (and still is) an enjoyable hobby of mine. In many ways, my love of storytelling is echoed in my love of science and mathematics. In my mind, every discovery is its own story -- an adventure just waiting to be understood! It seems incredible to me that I now have the chance to combine my two favorite hobbies: writing and learning.\nNow, to be clear, I am not a master computer scientist. In fact, my degree is in physics and at the time of writing, I am in a PhD program studying quantum systems; however, I really, really love learning algorithms. About a year or two ago, I started a Twitch stream focused on computational physics. Almost every day, I would get up at 5:00AM and livecode something I had never coded before. It was incredibly fun and through working with the community, we learned a lot. In addition, I found my programming abilities improving significantly, and I learned to see the power in a community of hobby programmers.\nThis text is a natural extension of that idea -- a community effort to learn as much as possible about as many algorithms as we can. Because of this, I feel like I should be as honest as possible about the nature of this book. As mentioned, I am not classically trained in computer science, so for the most part, I will be learning right along with you, the reader. My hope is to advance my own understanding of computer science while also providing a comprehensive guide for those wishing to improve their own understanding as well.\nFor this reason, I hesitate to call this a work a \"textbook\" and would prefer to think of it as a lab notebook of sorts. It will be an archive filled with cool ideas in computer science and physics that I hope will be interesting in their own right. My hope is that this book perfectly straddles the line between comprehensiveness and pleasure and will be an enjoyable read for anyone at any stage on their hobby programming journey.\nKeeping with the community theme, this book is freely available on GitHub and GitHub pages. Please feel free to read / browse the content available there. If you have any questions / comments / concerns, please let me know. This book is a community project and will only work if there is a community that works on it!\nAs a final note before beginning the bulk text, I would like for this book to be \"language agnostic.\" This basically means that I would like to use pseudocode in the main text, but provide source code in any language you could want in the appendix. Though this may seem a little counter-intuitive, I think it offers the greatest flexibility for myself as the author and for the community to develop their own code in any way they please. In fact, if you feel inclined, please feel free to implement your own version of any algorithm mentioned in this text. If you submit it and it passes all my ahem rigorous tests, then I can throw it at the end of each chapter with attribution to you!\nSo I guess that's all for now. Because this book is freely available online, I may be heavily modifying the content as we delve deeper into the archive of arcane algorithms.\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/how_to_contribute/how_to_contribute.html":{"url":"contents/how_to_contribute/how_to_contribute.html","title":"How To Contribute","keywords":"","body":"How to Contribute to the Algorithm Archive\nThe Algorithm Archive is an effort to learn about and teach algorithms as a community.\nAs such, it requires a certain level of trust between community members.\nFor specific details on how to contribute, please consult the How to Contribute guide.\nIf you are having trouble with git and version control, please also check out this video series with more details.\nIn addition, we also have an FAQ and a code style guide, which is currently being written for all languages submitted to the Algorithm Archive so far.\nCurrently, we are not accepting chapter submissions; however, we will allow for this in the near future.\nFor now, here are the basics for submitting code to the Algorithm Archive:\n\nStyle: We are developing a code style guide for all the languages in the Algorithm Archive. For the most part, follow standard style guidelines associated with your language of choice. Your code should be readable and understandable to anyone -- especially those who are new to the language. In addition, remember that your code will be displayed in this book, so try to keep to around 80 columns, try to remove any visual clutter, and keep variable names clean and understandable.\nLicensing: All the code from this project will be under the MIT license found in LICENSE.md; however, the text will be under a Creative Commons Attribution-NonCommercial 4.0 International License.\nCONTRIBUTORS.md: After contributing code, please echo your name to the end of CONTRIBUTORS.md with echo \"- name\" >> CONTRIBUTORS.md.\nBuilding the Algorithm Archive: Before every submission, you should build the Algorithm Archive on your own machine. To do this, install Node and use npm install and then npm run serve in the main directory (where README.md is). This will provide a local URL to go to to view the archive in your browser of choice. Use this server to make sure your version of the Algorithm Archive works cleanly for the chapter you are updating!\n\nTo submit code, go to the code/ directory of whatever chapter you want and add another directory for your language of choice.\nYou can also help out by reviewing code, if you have the ability to review a language (and want to be asked to do so), please add yourself to the Code Reviewers list\nWe use two GitBook plugins to allow users to flip between languages on different algorithms.\nOne is the theme-api, and the other is the include-codeblock api.\nWe need the following statements in the markdown file for these to work together:\n{% method %}\n{% sample lang=\"jl\" %}\n[import:1-17, lang:\"julia\"](code/julia/conv.jl)\n{% endmethod %}\n\nFor this example, we are starting the theme-api method and importing lines 1-17 from a sample Julia snippet from the code directory.\nNote that to standardize the language capitalization schemes, we ask that each language's sample lang is the file extension for their code, cpp for C++, hs for Haskell, etc.\nThis keeps the title in the theme-api consistent across different languages.\nAlso note that depending on the algorithm, there might be in-text code snippets that also need to be written.\nI'll update this page as the project grows.\nIf you would like to be a part of the ongoing discussion, please feel free to join our discord server: https://discord.gg/pb976sY.\nThanks for all the support and considering contributing to the Algorithm Archive!\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/code_reviews/code_reviewers.html":{"url":"contents/code_reviews/code_reviewers.html","title":"Code Reviewers","keywords":"","body":"Code Reviewers\nIf you are comfortable reviewing a language, please add yourself to the table below:\n\n\n\nLanguage\nReviewers\n\n\n\n\nasm-x64\n\n\n\nbash\n\n\n\nc\n@amaras\n\n\nc#\n\n\n\nclojure\n\n\n\ncoconut\n@amaras\n\n\nc++\n@ShadowMitia\n\n\ncrystal\n\n\n\nD\n\n\n\ndart\n\n\n\nelm\n\n\n\nemojicode\n\n\n\nfactor\n\n\n\nfortran\n@leios\n\n\ngnuplot\n@leios\n\n\ngo\n\n\n\nhaskell\n\n\n\njava\n\n\n\njavascript\n@ntindle,@ShadowMitia\n\n\njulia\n@leios\n\n\nkotlin\n\n\n\nlabview\n\n\n\nlolcode\n\n\n\nlisp\n\n\n\nlua\n\n\n\nmatlab\n\n\n\nnim\n\n\n\nocaml\n@ShadowMitia\n\n\nphp\n\n\n\npiet\n\n\n\npowershell\n\n\n\npython\n@ntindle,@ShadowMitia,@amaras,@PeanutbutterWarrior\n\n\nr\n\n\n\nracket\n\n\n\nruby\n\n\n\nrust\n@ShadowMitia,@PeanutbutterWarrior\n\n\nscala\n\n\n\nscheme\n\n\n\nscratch\n@leios\n\n\nsmalltask\n\n\n\nswift\n\n\n\ntypescript\n@ntindle\n\n\nv\n\n\n\nviml\n\n\n\nwhitespace\n\n\n\n\nIf you are comfortable reviewing a toolchain change, please add yourself to the list below:\n\n\n\nFeature\nReviewers\n\n\n\n\nDev Container\n@ntindle, @ShadowMitia\n\n\nDocker\n@ntindle, @ShadowMitia\n\n\nGithub Actions\n@ntindle\n\n\nHonkit\n\n\n\nScons\n@amaras,@PeanutbutterWarrior\n\n\nChapters\n@leios\n\n\n\n"},"contents/data_structures/data_structures.html":{"url":"contents/data_structures/data_structures.html","title":"Data Structures","keywords":"","body":"Data Structures\nThis is a book about algorithms.\nThe fundamental building blocks of algorithms are data structures, and thus as more algorithms are added to the Archive, more data structures will be added to this section.\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/stacks_and_queues/stacks_and_queues.html":{"url":"contents/stacks_and_queues/stacks_and_queues.html","title":"Stacks and Queues","keywords":"","body":"Stacks and Queues\nStacks and Queues are two sides of the same coin in computer science. They are both simple data structures that hold multiple elements, but allow you to use a single element at a time. The biggest difference between the two structures is the order in which you can access the elements in the data structure.\nIn stacks, data follows Last In, First Out (LIFO), which basically means that whichever element you put in last will be the first element you take out. It acts exactly like a stack in real life. If you put a book on a stack of other books, the first book you will look at when sifting through the stack will be the book you just put on the stack.\nIn Queues, data follows First In, First Out (FIFO), which means that whichever element you put in first will be the first element you take out. Imagine a queue of people. It would be unfair if the first person in line for groceries were not the first person to receive attention once the attendant finally shows up.\nFor the most part, though, queues and stacks are treated the same way. There must be a way to:\n\nlook at the first element (top())\nto remove the first element (pop())\nto push elements onto the data structure (push())\n\nThe notation for this depends on the language you are using. Queues, for example, will often use dequeue() instead of pop() and front() instead of top(). You will see the language-specific details in the source code under the algorithms in this book, so for now it's simply important to know what stacks and queues are and how to access elements held within them.\nExample Code\nHere is a simple implementation of a stack:\ninterface IStack {\n /**\n * `pop` removes last element from the stack and returns the same\n */\n pop(): T;\n /**\n * `push` adds element to last of the stack and returns the size\n */\n push(data: T): number;\n /**\n * `size` return size or length of the stack\n */\n size(): number;\n /**\n * `top` returns last element of the stack\n */\n top(): T;\n}\n\nclass Stack implements IStack {\n private readonly list: Array = [];\n\n public push(data: T) {\n return this.list.push(data);\n }\n\n public pop() {\n return this.list.pop();\n }\n\n public size() {\n return this.list.length;\n }\n\n public top() {\n return this.list[this.list.length - 1];\n }\n}\n\nfunction exampleStack() {\n const numberStack = new Stack();\n\n numberStack.push(4);\n numberStack.push(5);\n numberStack.push(9);\n\n console.log(numberStack.pop());\n console.log(numberStack.size());\n console.log(numberStack.top());\n}\n\nexampleStack();\n\nimport java.util.List;\nimport java.util.ArrayList;\n\n\npublic class StackTest {\n\n public static void main(String[] args) {\n IStack intStack = new Stack<>();\n\n intStack.push(4);\n intStack.push(5);\n intStack.push(9);\n\n System.out.println(intStack.pop());\n System.out.println(intStack.size());\n System.out.println(intStack.top());\n }\n\n}\n\n\ninterface IStack {\n /*\n * 'pop' removed the last element from the stack and returns it\n */\n T pop();\n\n /*\n * 'push' adds an element to at the end of the stack and returns the new size\n */\n int push(T element);\n\n /*\n * 'size' returns the length of the stack\n */\n int size();\n\n /*\n * 'top' returns the first element of the stack\n */\n T top();\n}\n\n\nclass Stack implements IStack {\n\n private List list;\n\n public Stack() {\n this.list = new ArrayList<>();\n }\n\n public T pop() {\n return this.list.remove(this.size() - 1);\n }\n\n public int push(T element) {\n this.list.add(element);\n return this.size();\n }\n\n public int size() {\n return this.list.size();\n }\n\n public T top() {\n return this.list.get(this.size() - 1);\n }\n\n}\n\n#include\n#include\n#include\n\nnamespace my {\n /**\n * implementation using linked list\n * [value][next] -> [value][next] -> ... -> [value][next]\n * (top Node) (intermediat Nodes)\n * left most Node represents top element of stack\n */\n template\n struct Node {\n /**\n * next: will store right Node address\n */\n T value;\n std::unique_ptr> next;\n Node(const T& V) : value(V) { }\n };\n\n template\n class stack {\n private:\n /**\n * top_pointer: points to left most node\n * count: keeps track of current number of elements present in stack\n */\n std::unique_ptr> top_pointer;\n size_t count;\n public:\n stack() : count(0ULL) { }\n\n void push(const T& element) {\n auto new_node = std::make_unique>(element);\n new_node->next = std::move(top_pointer);\n top_pointer = std::move(new_node);\n count = count + 1;\n }\n\n void pop() {\n if (count > 0) {\n top_pointer = std::move(top_pointer->next);\n count = count - 1;\n }\n }\n\n T& top() {\n assert(count > 0 and \"calling top() on an empty stack\");\n return top_pointer->value;\n }\n // returning mutable reference can very be usefull if someone wants to modify top element\n\n T const& top() const {\n assert(count > 0 and \"calling top() on an empty stack\");\n return top_pointer->value;\n }\n\n size_t size() const { return count; }\n\n bool empty() const { return count == 0; }\n\n ~stack() {\n while (top_pointer.get() != nullptr) {\n top_pointer = std::move(top_pointer->next);\n }\n }\n };\n}\n\nint main() {\n my::stack intStack;\n\n intStack.push(4);\n intStack.push(5);\n intStack.push(9);\n\n int topElement = intStack.top();\n intStack.pop();\n std::cout \nstruct Stack {\n list: Vec\n}\n\nimpl Stack {\n fn new() -> Self {\n Stack {\n list: Vec::new(),\n }\n }\n\n // Note that this returns a reference to the value\n // This is in contrast to pop which gives ownership of the value\n fn top(&self) -> Option {\n self.list.last()\n }\n\n fn pop(&mut self) -> Option {\n self.list.pop()\n }\n\n fn push(&mut self, item: T) {\n self.list.push(item);\n }\n\n fn size(&self) -> usize {\n self.list.len()\n }\n}\n\nfn main() {\n let mut i32stack: Stack = Stack::new();\n\n i32stack.push(4);\n i32stack.push(5);\n i32stack.push(6);\n\n println!(\"{:?}\", i32stack.pop().unwrap()); // 6\n println!(\"{:?}\", i32stack.size()); // 2\n println!(\"{:?}\", i32stack.top().unwrap()); // 5\n}\n\n#!/usr/bin/env python3\n\n__author__ = \"Michael Ciccotosto-Camp\"\n\nfrom typing import TypeVar, Generic\n\n\nT = TypeVar(\"T\")\n\n\nclass Stack(Generic[T]):\n def __init__(self) -> None:\n self.__list: list[T] = []\n\n def pop(self) -> T:\n return self.__list.pop()\n\n def push(self, element: T) -> int:\n self.__list.append(element)\n return len(self)\n\n def top(self) -> T:\n return self.__list[-1]\n\n def __len__(self) -> int:\n return len(self.__list)\n\n def __str__(self) -> str:\n return str(self.__list)\n\n\ndef main() -> None:\n int_stack: Stack[int] = Stack()\n\n int_stack.push(4)\n int_stack.push(5)\n int_stack.push(9)\n\n print(int_stack.pop())\n print(len(int_stack))\n print(int_stack.top())\n\n\nif __name__ == \"__main__\":\n main()\n\n\n\nHere is a simple implementation of a queue:\ninterface IQueue {\n /**\n * `dequeue` removes first element from the queue and returns the same\n */\n dequeue(): T;\n /**\n * `enqueue` adds element to last of the queue and returns the size\n */\n enqueue(data: T): number;\n /**\n * `size` return size or length of the queue\n */\n size(): number;\n /**\n * `front` returns first element of the queue\n */\n front(): T;\n}\n\nclass Queue implements IQueue {\n private readonly list: Array = [];\n\n public enqueue(data: T) {\n return this.list.push(data);\n }\n\n public dequeue() {\n return this.list.shift();\n }\n\n public size() {\n return this.list.length;\n }\n\n public front() {\n return this.list[0];\n }\n}\n\nfunction exampleQueue() {\n const numberQueue = new Queue();\n\n numberQueue.enqueue(4);\n numberQueue.enqueue(5);\n numberQueue.enqueue(9);\n\n console.log(numberQueue.dequeue());\n console.log(numberQueue.size());\n console.log(numberQueue.front());\n}\n\nexampleQueue();\n\nimport java.util.List;\nimport java.util.ArrayList;\n\npublic class QueueTest {\n\n public static void main(String[] args) {\n IQueue intQueue = new Queue<>();\n\n intQueue.enqueue(4);\n intQueue.enqueue(5);\n intQueue.enqueue(9);\n\n System.out.println(intQueue.dequeue());\n System.out.println(intQueue.size());\n System.out.println(intQueue.front());\n }\n\n}\n\n\ninterface IQueue {\n\n /*\n * 'dequeue' removes the first element from the queue and returns it\n */\n T dequeue();\n\n /*\n * 'enqueue' adds an element at the end of the queue and returns the new size\n */\n int enqueue(T element);\n\n\n /*\n * 'size' returns the size of the queue\n */\n int size();\n\n /*\n * 'front' returns the first element of the queue without removing it\n */\n T front();\n}\n\n\nclass Queue implements IQueue {\n\n private List list;\n\n public Queue() {\n this.list = new ArrayList<>();\n }\n\n public T dequeue() {\n return this.list.remove(0);\n }\n\n public int enqueue(T element) {\n this.list.add(element);\n return this.size();\n }\n\n public int size() {\n return this.list.size();\n }\n\n public T front() {\n return this.list.get(0);\n }\n\n}\n\n#include\n#include\n#include\n\nnamespace my {\n /**\n * implementation using linked list\n * [value][next] -> [value][next] -> ... -> [value][next]\n * (front Node) (intermediat Nodes) (rear Node)\n */\n template\n struct Node {\n /**\n * next: will store right Node address\n */\n T value;\n std::shared_ptr> next;\n Node(const T& V) : value(V) { }\n };\n\n template\n class queue {\n private:\n /**\n * front_pointer: points to left most node\n * count: keeps track of current number of elements present in queue\n * rear_pointer: points to most recent Node added into the queue, which is right most Node\n */\n std::shared_ptr> front_pointer;\n std::shared_ptr> rear_pointer;\n size_t count;\n public:\n queue() : count(0ULL) { }\n\n void enqueue(const T& element) {\n auto new_node = std::make_shared>(element);\n if (count > 0) {\n rear_pointer->next = new_node;\n rear_pointer = new_node;\n } else {\n rear_pointer = front_pointer = new_node;\n }\n count = count + 1;\n }\n\n void dequeue() {\n if (count > 1) {\n front_pointer = front_pointer->next;\n count = count - 1;\n } else if (count == 1) {\n front_pointer.reset();\n rear_pointer.reset();\n count = count - 1;\n }\n }\n\n T& front() {\n assert(count > 0 && \"calling front on an empty queue\");\n return front_pointer->value;\n }\n\n T const& front() const {\n assert(count > 0 && \"calling front on an empty queue\");\n return front_pointer->value;\n }\n\n size_t size() const { return count; }\n\n bool empty() const { return count == 0; }\n\n ~queue() {\n while (front_pointer.get() != nullptr) {\n front_pointer = front_pointer->next;\n }\n }\n };\n}\n\nint main() {\n my::queue intQueue;\n intQueue.enqueue(4);\n intQueue.enqueue(5);\n intQueue.enqueue(9);\n\n int frontElement = intQueue.front();\n intQueue.dequeue();\n std::cout \nuse std::collections::VecDeque;\n\nstruct Queue {\n list: VecDeque\n}\n\nimpl Queue {\n fn new() -> Self {\n Queue{\n list: VecDeque::new(),\n }\n }\n\n // Note that this returns a reference to the value\n // This is in contrast to dequeue which gives ownership of the value\n fn front(&self) -> Option {\n self.list.front()\n }\n\n fn dequeue(&mut self) -> Option {\n self.list.pop_front()\n }\n\n fn enqueue(&mut self, item: T) {\n self.list.push_back(item);\n }\n\n fn size(&self) -> usize {\n self.list.len()\n }\n}\n\nfn main() {\n let mut i32queue = Queue::new();\n\n i32queue.enqueue(4);\n i32queue.enqueue(5);\n i32queue.enqueue(6);\n\n println!(\"{:?}\", i32queue.dequeue().unwrap()); // 4\n println!(\"{:?}\", i32queue.size()); // 2\n println!(\"{:?}\", i32queue.front().unwrap()); // 5\n}\n\n#!/usr/bin/env python3\n\n__author__ = \"Michael Ciccotosto-Camp\"\n\nfrom typing import TypeVar, Generic\n\n\nT = TypeVar(\"T\")\n\n\nclass Queue(Generic[T]):\n def __init__(self) -> None:\n self.__list: list[T] = list()\n\n def dequeue(self) -> T:\n return self.__list.pop(0)\n\n def enqueue(self, element: T) -> int:\n self.__list.append(element)\n return len(self)\n\n def front(self) -> T:\n return self.__list[0]\n\n def __len__(self) -> int:\n return len(self.__list)\n\n def __str__(self) -> str:\n return str(self.__list)\n\n\ndef main() -> None:\n int_queue: Queue[int] = Queue()\n\n int_queue.enqueue(4)\n int_queue.enqueue(5)\n int_queue.enqueue(9)\n\n print(int_queue.dequeue())\n print(len(int_queue))\n print(int_queue.front())\n\n\nif __name__ == \"__main__\":\n main()\n\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/mathematical_background/mathematical_background.html":{"url":"contents/mathematical_background/mathematical_background.html","title":"Mathematical Background","keywords":"","body":"Mathematical Background\nNo matter who you ask, programming requires at least a little math.\nThat said, for most programmers, it doesn't require too much.\nFor the most part, depending on your specialty, you will probably not see too much calculus or differential equations.\nHonestly, you could probably get away with what you learned in high school.\nHowever, this is a book about algorithms, and algorithms sometimes require a deeper understanding of mathematics.\nThis section attempts to provide the mathematical foundations that you will need to understand certain algorithms.\nAs we add new algorithms and need new mathematical tools, we will add them to this section.\nA notable exception to this rule will be in the case of classes of algorithms that require domain-specific knowledge, like quantum simulations or bioinformatics.\nIn those cases, we will place the mathematical methods in more relevant sections.\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/tree_traversal/tree_traversal.html":{"url":"contents/tree_traversal/tree_traversal.html","title":"Tree Traversal","keywords":"","body":"Tree Traversal\nTrees are naturally recursive data structures, and because of this, we cannot access their elements like we might access the elements of a vector or array. Instead, we need to use more interesting methods to work through each element. This is often called Tree Traversal, and there are many different ways to do this. For now, we will restrict the discussion to two common and related methods of tree traversal: Depth-First and Breadth-First Search. Note that trees vary greatly in shape and size depending on how they are used; however, they are composed primarily of nodes that house other, children nodes, like so:\nstruct Node\n children::Vector{Node}\n ID::Int64\n Node(ID::Int64) = new(Vector{Node}(), ID)\nend\n\nstruct node {\n std::vector children;\n size_t value;\n};\n\npublic class Tree\n{\n public int Id { get; private set; }\n private List _children = new List();\n\nstruct node {\n struct node *children;\n size_t children_size;\n int id;\n};\n\nprivate class Node implements Comparable {\n public ArrayList children;\n public int id;\n\n public Node(int id) {\n this.children = new ArrayList();\n this.id = id;\n }\n\n @Override\n public int compareTo(Node other) {\n // Need to implement Comparable and override this\n // method because of the method BFSQueue() which uses Queues\n // and must know how to check if two nodes are the same or not\n return Integer.compare(this.id, other.id);\n }\n}\n\nfunction createTree(rows, children) {\n if (rows === 0) {\n return { id: rows, children: [] };\n }\n\n return {\n id: rows,\n children: [...Array(children).keys()].map(() => createTree(rows - 1, children))\n };\n}\n\nAs a note, a node struct is not necessary in javascript, so this is an example of how a tree might be constructed.\nclass Node:\n def __init__(self):\n self.data = None\n self.children = []\n\n\n \nstruct Node {\n children: Vec,\n value: u64,\n}\n\ndata Tree a = Node\n { node :: a,\n forest :: [Tree a]\n }\n\nclass Node {\n var value: Int\n var children: [Node]?\n\n init(value: Int, children: [Node]) {\n self.value = value\n self.children = children\n }\n}\n\nclass Tree implements JsonSerializable\n{\n private $id;\n private $children = [];\n\n public function __construct(int $id, array $children = [])\n {\n $this->id = $id;\n $this->children = $children;\n }\n\n public function getId(): int\n {\n return $this->id;\n }\n\n public function getChildren(): array\n {\n return $this->children;\n }\n\n public function addChild(Tree $child): void\n {\n $this->children[] = $child;\n }\n\n public function jsonSerialize(): array\n {\n return [\n 'id' => $this->id,\n 'children' => $this->children,\n ];\n }\n}\n\nclass Node \n property id, children \n def initialize(@id : Int32, @children : Array(Node))\n end \nend\n\nObject subclass: #Node\n instanceVariableNames: 'children data'\n classVariableNames: ''\n package: ''\n\nNode>>children\n \"Children getter.\"\n ^ children\n\nNode>>children: newChildren\n \"Children setter.\"\n children := newChildren.\n\nNode>>data\n \"Data getter\"\n ^ data\n\nNode>>data: newData\n \"Data setter\"\n data := newData.\n\ntype node struct {\n id int\n children []*node\n}\n\n.equ tree_children, 0\n.equ tree_num_children, 8\n.equ tree_value, 12\n.equ tree_size, 16\n\n🦃 ⏹ 🍇\n 🔘 ⏫\n\n(defstruct node data children)\n\nnode = @(k,v) containers.Map(k,v);\n\ndata Node(value: int, children: Node[])\n\n\n\nBecause of this, the most straightforward way to traverse the tree might be recursive. This naturally leads us to the Depth-First Search (DFS) method:\nfunction DFS_recursive(n::Node)\n # Here we are doing something...\n print(n.ID, \" \")\n\n for child in n.children\n DFS_recursive(child)\n end\nend\n\n// Simple recursive scheme for DFS\nvoid dfs_recursive(node const& n) {\n // Here we are doing something...\n std::cout \npublic void DFSRecursive()\n{\n DFSRecursive(this);\n\n void DFSRecursive(Tree tree)\n {\n Console.Write(tree.Id + \" \");\n\n foreach (var c in tree._children)\n DFSRecursive(c);\n }\n}\n\nvoid dfs_recursive(struct node n) {\n printf(\"%d \", n.id);\n\n if (n.children) {\n for (size_t i = 0; i \nprivate void dfsRecursive(Node node) {\n System.out.print(node.id + \" \");\n\n for (Node n : node.children) {\n dfsRecursive(n);\n }\n}\n\nfunction dfsPreorder(tree) {\n if (!tree) {\n return;\n }\n\n process.stdout.write(tree.id + \" \");\n tree.children.forEach(dfsPreorder);\n}\n\ndef dfs_recursive(node):\n if node.data != None:\n print(node.data, end=' ')\n\n for child in node.children:\n dfs_recursive(child)\n\n\n \nfn dfs_recursive(n: &Node) {\n print!(\"{} \", n.value);\n\n for child in &n.children {\n dfs_recursive(child);\n }\n}\n\ndfs :: Tree a -> [a]\ndfs (Node x ts) = x : concatMap dfs ts\n\nfunc dfsRecursive(node: Node) {\n print(node.value, terminator:\" \")\n\n for child in node.children! {\n dfsRecursive(node: child)\n }\n}\n\npublic static function DFSRecursive(Tree $tree): void\n{\n echo $tree->getId() . ' ';\n foreach ($tree->getChildren() as $child) {\n static::DFSRecursive($child);\n }\n}\n\ndef dfs_recursive(node) \n print \"#{node.id} \"\n node.children.each{ |child| dfs_recursive child } \nend\n\nNode>>dfsRecursive\n \"Recursive depth first search.\"\n Transcript show: data; cr.\n children collect: [ :child | child dfsRecursive ]\n\nNode>>dfsRecursivePostOrder\n\nfunc dfsRecursive(n *node) {\n fmt.Printf(\"%d \", n.id)\n for _, child := range n.children {\n dfsRecursive(child)\n }\n}\n\n# rdi - children ptr\n# rsi - value|children_size\ndfs_recursive:\n push r12\n push r13\n mov r12, rdi\n mov r13, rsi\n mov rdi, OFFSET fmt_tree # Handle the current node\n shr rsi, 32 # The tree value is in the upper 32 bits\n xor rax, rax\n call printf\n mov r13d, r13d # Zero out the top 32 bits\n add r13, r12 # Pointer pointing after the last element of the children array\ndfs_recursive_children:\n cmp r12, r13 # If we reached the end, return\n je dfs_recursive_return\n mov rdi, QWORD PTR [r12]\n mov rsi, QWORD PTR [r12 + 8]\n call dfs_recursive\n add r12, tree_size\n jmp dfs_recursive_children\ndfs_recursive_return:\n pop r13\n pop r12\n ret\n\n 🌌🐕 depth_count children_count❗️\n🍉\n\n❗️ 🆔 ➡️ 🔢 🍇\n ↩️ id\n🍉\n\n❗️ 🧒 ➡️ 🍨🐚🌲🍆 🍇\n\n(defun dfs-recursive (node)\n \"A depth first approach for printing out all values in a tree.\"\n (when (node-data node)\n (format t \"~a \" (node-data node)))\n (loop for child in (node-children node) do\n (dfs-recursive child)))\n\nfunction DFS_recursive(n)\n\n cell_index = @(a, b) a{b};\n ID = cell_index(keys(n), 1);\n\n fprintf('%u ', ID);\n\n children = cell_index(values(n), 1);\n for i = children\n child = i{1};\n if ~isempty(child)\n DFS_recursive(child);\n end\n end\nend\n\ndef dfs_recursive(Node(value, children)):\n \"\"\"A depth first approach for printing out all values in a tree.\"\"\"\n print(value, end=' ')\n for child in children:\n dfs_recursive(child)\n\n\n\nAt least to me, this makes a lot of sense. We fight recursion with recursion! First, we first output the node we are on and then we call DFS_recursive(...) on each of its children nodes. This method of tree traversal does what its name implies: it goes to the depths of the tree first before going through the rest of the branches. In this case, the ordering looks like:\n\n \n\n\nNote that the in the code above, we are missing a crucial step: checking to see if the node we are using actually exists! Because we are using a vector to store all the nodes, we will be careful not to run into a case where we call DFS_recursive(...) on a node that has yet to be initialized; however, depending on the language we are using, we might need to be careful of this to avoid recursion errors!\nNow, in this case the first element searched through is still the root of the tree. This type of tree traversal is known as pre-order DFS. We perform an action (output the ID) before searching through the children. If we shift the function around and place the data output at the end of the function, we can modify the order in which we search through the tree to be post-order and look something like this:\nfunction DFS_recursive_postorder(n::Node)\n\n for child in n.children\n DFS_recursive_postorder(child)\n end\n\n # Here we are doing something...\n print(n.ID, \" \")\nend\n\nvoid dfs_recursive_postorder(node const& n) {\n for (auto const& child : n.children) {\n dfs_recursive_postorder(child);\n }\n std::cout \npublic void DFSRecursivePostorder()\n{\n DFSRecursivePostorder(this);\n\n void DFSRecursivePostorder(Tree tree)\n {\n foreach (var c in tree._children)\n DFSRecursivePostorder(c);\n\n Console.Write(tree.Id + \" \");\n }\n}\n\nvoid dfs_recursive_postorder(struct node n) {\n for (size_t i = 0; i \nprivate void dfsRecursivePostOrder(Node node) {\n for (Node n : node.children) {\n dfsRecursivePostOrder(n);\n }\n\n // Here we are doing something ...\n System.out.print(node.id + \" \");\n}\n\nfunction dfsPostorder(tree) {\n if (!tree) {\n return;\n }\n\n tree.children.forEach(dfsPostorder);\n process.stdout.write(tree.id + \" \");\n}\n\ndef dfs_recursive_postorder(node):\n for child in node.children:\n dfs_recursive_postorder(child)\n\n if node.data != None:\n print(node.data, end=' ')\n\n\n \nfn dfs_recursive_postorder(n: &Node) {\n for child in &n.children {\n dfs_recursive_postorder(child);\n }\n\n print!(\"{} \", n.value);\n}\n\ndfsPostOrder :: Tree a -> [a]\ndfsPostOrder (Node x ts) = concatMap dfsPostOrder ts ++ [x]\n\nfunc dfsRecursivePostOrder(node: Node) {\n for child in node.children! {\n dfsRecursivePostOrder(node: child)\n }\n\n print(node.value, terminator:\" \")\n}\n\npublic static function DFSRecursivePostorder(Tree $tree): void\n{\n foreach ($tree->getChildren() as $child) {\n static::DFSRecursivePostorder($child);\n }\n echo $tree->getId() . ' ';\n}\n\ndef dfs_recursive_postorder(node) \n node.children.each{ |child| dfs_recursive_postorder child }\n print \"#{node.id} \"\nend\n\n children collect: [ :child | (child dfsRecursivePostOrder)].\n Transcript show: data; cr.\n\nNode>>dfsInOrderBinaryTree\n \"Recursive depth first search on a binary tree in order.\"\n children size > 2 ifTrue: [\n\nfunc dfsRecursivePostorder(n *node) {\n for _, child := range n.children {\n dfsRecursivePostorder(child)\n }\n fmt.Printf(\"%d \", n.id)\n}\n\n# rdi - children ptr\n# rsi - value|children_size\ndfs_recursive_postorder:\n push r12\n push r13\n push r14\n mov r12, rdi\n mov r13, rsi\n mov r14, rsi\n mov r13d, r13d # Zero out the top 32 bits\n add r13, r12 # Pointer pointing after the last element of the children array\ndfs_recursive_po_children:\n cmp r12, r13 # If we reached the end, return\n je dfs_recursive_po_return\n mov rdi, QWORD PTR [r12]\n mov rsi, QWORD PTR [r12 + 8]\n call dfs_recursive_postorder\n add r12, tree_size\n jmp dfs_recursive_po_children\ndfs_recursive_po_return:\n mov rdi, OFFSET fmt_tree # Handle the current node\n mov rsi, r14\n shr rsi, 32 # The tree value is in the upper 32 bits\n xor rax, rax\n call printf\n pop r14\n pop r13\n pop r12\n ret\n\n🍉\n\n📗 Depth-First Search Recursive pre-order 📗\n❗️ 🌀 🍇\n 😀 🔡 id 10❗️❗️\n\n 🔂 child children 🍇\n 🌀 child❗️\n\n(defun dfs-recursive-postorder (node)\n \"A depth first approach for printing out all values in a tree starting from the bottom.\"\n (loop for child in (node-children node) do\n (dfs-recursive-postorder child))\n (when (node-data node)\n (format t \"~a \" (node-data node))))\n\nfunction DFS_recursive_postorder(n)\n\n cell_index = @(a, b) a{b};\n\n children = cell_index(values(n), 1);\n for i = children\n child = i{1};\n if ~isempty(child)\n DFS_recursive_postorder(child);\n end\n end\n\n ID = cell_index(keys(n), 1);\n fprintf('%u ', ID);\n\nend\n\ndef dfs_recursive_postorder(Node(value, children)):\n \"\"\"A depth first approach for printing out all values in a tree starting from the bottom.\"\"\"\n for child in children:\n dfs_recursive_postorder(child)\n print(value, end=' ')\n\n\n\n \n\n\nIn this case, the first node visited is at the bottom of the tree and moves up the tree branch by branch. In addition to these two types, binary trees have an in-order traversal scheme that looks something like this:\n# This assumes only 2 children, but accounts for other possibilities\nfunction DFS_recursive_inorder_btree(n::Node)\n\n if (length(n.children) == 2)\n DFS_recursive_inorder_btree(n.children[1])\n print(n.ID, \" \")\n DFS_recursive_inorder_btree(n.children[2])\n elseif (length(n.children) == 1)\n DFS_recursive_inorder_btree(n.children[1])\n print(n.ID, \" \")\n elseif (length(n.children) == 0)\n print(n.ID, \" \")\n else\n println(\"Not a binary tree!\")\n end\nend\n\nvoid dfs_recursive_inorder_btree(node const& n) {\n switch (n.children.size()) {\n case 2:\n dfs_recursive_inorder_btree(n.children[0]);\n std::cout \npublic void DFSRecursiveInorderBinary()\n{\n DFSRecursiveInorderBinary(this);\n\n void DFSRecursiveInorderBinary(Tree tree)\n {\n switch (tree._children.Count)\n {\n case 2:\n DFSRecursiveInorderBinary(tree._children[0]);\n Console.Write(tree.Id + \" \");\n DFSRecursiveInorderBinary(tree._children[1]);\n break;\n case 1:\n DFSRecursiveInorderBinary(tree._children[0]);\n Console.Write(tree.Id + \" \");\n break;\n case 0:\n Console.Write(tree.Id + \" \");\n break;\n default:\n throw new Exception(\"Not binary tree!\");\n }\n }\n}\n\nvoid dfs_recursive_inorder_btree(struct node n) {\n switch (n.children_size) {\n case 2:\n dfs_recursive_inorder_btree(n.children[0]);\n printf(\"%d \", n.id);\n dfs_recursive_inorder_btree(n.children[1]);\n break;\n case 1:\n dfs_recursive_inorder_btree(n.children[0]);\n printf(\"%d \", n.id);\n break;\n case 0:\n printf(\"%d \", n.id);\n break;\n default:\n printf(\"This is not a binary tree.\\n\");\n break;\n }\n}\n\nprivate void dfsRecursiveInOrderBinary(Node node) {\n switch (node.children.size()) {\n case 2:\n dfsRecursiveInOrderBinary(node.children.get(0));\n System.out.print(node.id + \" \");\n dfsRecursiveInOrderBinary(node.children.get(1));\n break;\n case 1:\n dfsRecursiveInOrderBinary(node.children.get(0));\n System.out.print(node.id + \" \");\n break;\n case 0:\n System.out.print(node.id + \" \");\n break;\n default:\n System.err.println(\"Not a binary tree at dfsRecursiveInOrderBinary()!\");\n }\n}\n\nfunction dfsInorder(tree) {\n if (!tree) {\n return;\n }\n\n switch (tree.children.length) {\n case 2:\n dfsInorder(tree.children[0]);\n console.log(tree.id);\n dfsInorder(tree.children[1]);\n break;\n case 1:\n dfsInorder(tree.children[0]);\n console.log(tree.id);\n break;\n case 0:\n console.log(tree.id);\n break;\n default:\n throw new Error(\"Postorder traversal is only valid for binary trees\");\n }\n}\n\ndef dfs_recursive_inorder_btree(node):\n if len(node.children) == 2:\n dfs_recursive_inorder_btree(node.children[0])\n print(node.data, end=' ')\n dfs_recursive_inorder_btree(node.children[1])\n elif len(node.children) == 1:\n dfs_recursive_inorder_btree(node.children[0])\n print(node.data, end=' ')\n elif len(node.children) == 0:\n print(node.data, end=' ')\n else:\n print(\"Not a binary tree!\")\n\n\n \nfn dfs_recursive_inorder_btree(n: &Node) {\n match &n.children[..] {\n [left, right] => {\n dfs_recursive_inorder_btree(left);\n print!(\"{} \", n.value);\n dfs_recursive_inorder_btree(right);\n }\n [left] => {\n dfs_recursive_inorder_btree(left);\n print!(\"{} \", n.value);\n }\n [] => print!(\"{} \", n.value),\n _ => print!(\"This is not a binary tree. \"),\n }\n}\n\ndfsInOrder :: Tree a -> [a] -- For binary trees only\ndfsInOrder (Node x []) = [x]\ndfsInOrder (Node x [l]) = dfsInOrder l ++ [x] -- Single branch assumed to be left\ndfsInOrder (Node x [l, r]) = dfsInOrder l ++ [x] ++ dfsInOrder r\ndfsInOrder _ = error \"Not a binary tree\"\n\nfunc dfsRecursiveInOrderBinary(node: Node) {\n if node.children?.count == 2 {\n dfsRecursiveInOrderBinary(node: node.children![0])\n print(node.value, terminator:\" \")\n dfsRecursiveInOrderBinary(node: node.children![1])\n } else if node.children?.count == 1 {\n dfsRecursiveInOrderBinary(node: node.children![0])\n print(node.value, terminator:\" \")\n } else if node.children?.count == 0 {\n print(node.value, terminator:\" \")\n } else {\n print(\"Not a binary tree!\")\n }\n}\n\npublic static function DFSRecursiveInorderBinary(Tree $tree): void\n{\n switch (count($tree->getChildren())) {\n case 2:\n static::DFSRecursiveInorderBinary($tree->getChildren()[0]);\n echo $tree->getId() . ' ';\n static::DFSRecursiveInorderBinary($tree->getChildren()[1]);\n break;\n case 1:\n static::DFSRecursiveInorderBinary($tree->getChildren()[0]);\n echo $tree->getId() . ' ';\n break;\n case 0:\n echo $tree->getId() . ' ';\n break;\n default:\n throw new InvalidArgumentException('Not a binary tree!');\n break;\n }\n}\n\ndef dfs_recursive_inorder_btree(node) \n case node.children.size\n when 2\n dfs_recursive_inorder_btree node.children[0]\n print \"#{node.id} \"\n dfs_recursive_inorder_btree node.children[1] \n when 1 \n dfs_recursive_inorder_btree node.children[0]\n print \"#{node.id} \"\n when 0 \n print \"#{node.id} \"\n else \n print \"Not a binary tree!\"\n end \nend\n\n ^self.\n ].\n children size = 2 ifTrue: [\n (children at: 1) dfsInOrderBinaryTree: value.\n ].\n Transcript show: data; cr.\n children size >= 1 ifTrue: [\n (children at: 0) dfsInOrderBinaryTree: value.\n ].\n ^self.\n\nNode>>dfsStack\n \"Depth-first search with a stack.\"\n | stack top |\n\nfunc dfsRecursiveInorderBtree(n *node) {\n switch len(n.children) {\n case 2:\n dfsRecursiveInorderBtree(n.children[0])\n fmt.Printf(\"%d \", n.id)\n dfsRecursiveInorderBtree(n.children[1])\n case 1:\n dfsRecursiveInorderBtree(n.children[0])\n fmt.Printf(\"%d \", n.id)\n case 0:\n fmt.Printf(\"%d \", n.id)\n default:\n fmt.Println(\"This is not a binary tree\")\n }\n}\n\n# rdi - children ptr\n# rsi - value|children_size\ndfs_recursive_inorder_btree:\n push r12\n push r13\n mov r12, rdi\n mov r13, rsi\n mov rax, rsi\n mov eax, eax\n cmp rax, 0 # Check what type of tree it is.\n je dfs_recursive_bt_size0\n cmp rax, 16\n je dfs_recursive_bt_size1\n cmp rax, 32\n je dfs_recursive_bt_size2\n mov rdi, OFFSET not_bt # If the tree is not binary then print a warning\n xor rax, rax\n call printf\n jmp dfs_recursive_bt_return\ndfs_recursive_bt_size0:\n mov rdi, OFFSET fmt_tree # If the node is a leaf then print its id\n shr rsi, 32\n xor rax, rax\n call printf\n jmp dfs_recursive_bt_return\ndfs_recursive_bt_size1:\n mov rdi, QWORD PTR [r12] # If the node has 1 child then call the function and print the id\n mov rsi, QWORD PTR [r12 + 8]\n call dfs_recursive_inorder_btree\n mov rdi, OFFSET fmt_tree\n mov rsi, r13\n shr rsi, 32\n xor rax, rax\n call printf\n jmp dfs_recursive_bt_return\ndfs_recursive_bt_size2:\n mov rdi, QWORD PTR [r12] # Same as above just print id inbetween the calls\n mov rsi, QWORD PTR [r12 + 8]\n call dfs_recursive_inorder_btree\n mov rdi, OFFSET fmt_tree\n mov rsi, r13\n shr rsi, 32\n xor rax, rax\n call printf\n mov rdi, QWORD PTR [r12 + 16]\n mov rsi, QWORD PTR [r12 + 24]\n call dfs_recursive_inorder_btree\ndfs_recursive_bt_return:\n pop r13\n pop r12\n ret\n\n🍉\n\n📗 Depth-First Search Recursive post-order 📗\n❗️ 🍥 🍇\n 🔂 child children 🍇\n 🍥 child❗️\n 🍉\n\n 😀 🔡 id 10❗️❗️\n🍉\n\n📗\n Depth-First Search Recursive Inorder Binary\n This assumes only 2 children.\n📗\n❗️ 🍭 ➡️ 🍬⏹ 🍇\n ↪️ 🐔 children❗️ ▶️ 2 🍇\n ↩️ 🆕⏹⏫❗️\n\n(defun dfs-recursive-inorder-btree (node)\n \"A depth first search approach for printing all values in a binary tree.\"\n (case (length (node-children node))\n (2\n (dfs-recursive-inorder-btree (first (node-children node)))\n (format t \"~a \" (node-data node))\n (dfs-recursive-inorder-btree (second (node-children node))))\n (1\n (dfs-recursive-inorder-btree (first (node-children node)))\n (format t \"~a \" (node-data node)))\n (0\n (format t \"~a \" (node-data node)))\n (t\n (print \"Invalid binary tree.\"))))\n\nfunction DFS_recursive_inorder_btree(n)\n\n cell_index = @(a, b) a{b};\n ID = cell_index(keys(n), 1);\n children = cell_index(values(n), 1);\n\n if length(children) == 2\n DFS_recursive_inorder_btree(children{1})\n fprintf('%u ', ID)\n DFS_recursive_inorder_btree(children{2})\n elseif length(children) == 1\n if ~isempty(children{1})\n DFS_recursive_inorder_btree(children{1})\n end\n fprintf('%u ', ID)\n else\n fprintf(\"Not a binary tree!\")\n end\nend\n\ndef dfs_recursive_inorder_btree(Node(value, children)):\n \"\"\"A depth first search approach for printing all values in a binary tree.\"\"\"\n case len(children):\n match 2:\n dfs_recursive_inorder_btree(children[0])\n print(value, end=' ')\n dfs_recursive_inorder_btree(children[1])\n match 1:\n dfs_recursive_inorder_btree(children[0])\n print(value, end=' ')\n match 0:\n print(value, end=' ')\n else:\n print('Invalid binary tree')\n\n\n\n\n \n\n\nThe order here seems to be some mix of the other 2 methods and works through the binary tree from left to right.\nNow, at this point, it might seem that the only way to search through a recursive data structure is with recursion, but this is not necessarily the case! Rather surprisingly, we can perform a DFS non-recursively by using a stack, which are data structures that hold multiple elements, but only allow you to interact with the very last element you put in. The idea here is simple:\n\nPut the root node in the stack\nTake it out and put in its children\nPop the top of the stack and put its children in\nRepeat 3 until the stack is empty\n\nIn code, it looks like this:\nfunction DFS_stack(n::Node)\n s = Stack{Node}()\n push!(s, n)\n\n while(length(s) > 0)\n print(top(s).ID, \" \")\n temp = pop!(s)\n for child in temp.children\n push!(s, child)\n end\n end\nend\n\nvoid dfs_stack(node const& n) {\n // this stack holds pointers into n's `children` vector,\n // or its children's `children` vector.\n std::stack stack;\n stack.push(&n);\n\n while (stack.size() > 0) {\n auto const& temp = *stack.top();\n stack.pop();\n std::cout \npublic void DFSStack()\n{\n var stack = new Stack();\n stack.Push(this);\n\n while (stack.Count != 0)\n {\n Console.Write(stack.Peek().Id + \" \");\n var temp = stack.Pop();\n\n foreach (var c in temp._children)\n stack.Push(c);\n }\n}\n\nvoid dfs_stack(struct node n) {\n struct stack stk = get_stack(sizeof(struct node*));\n stack_push(&stk, &n);\n struct node *tmp;\n\n while (!stack_empty(&stk)) {\n tmp = (struct node*)stack_pop(&stk);\n if (!tmp) {\n break;\n }\n\n printf(\"%d \", tmp->id);\n for (size_t i = 0; i children_size; ++i) {\n stack_push(&stk, &tmp->children[i]);\n }\n }\n\n free_stack(stk);\n}\n\npublic void dfsStack() {\n Stack stack = new Stack();\n stack.push(this.root);\n\n Node tmp;\n\n while (stack.size() != 0) {\n System.out.print(stack.peek().id + \" \");\n tmp = stack.pop();\n\n for (Node c : tmp.children) {\n stack.push(c);\n }\n }\n}\n\nfunction dfsIterative(tree) {\n const stack = [tree];\n while (stack.length > 0) {\n const current = stack.pop();\n process.stdout.write(current.id + \" \");\n stack.push(...current.children);\n }\n}\n\ndef dfs_stack(node):\n stack = [node]\n while stack:\n node = stack.pop()\n stack.extend(node.children)\n print(node.data, end=' ')\n\n\n \nfn dfs_stack(n: &Node) {\n let mut stack = vec![n];\n\n while let Some(current) = stack.pop() {\n print!(\"{} \", current.value);\n stack.extend(¤t.children);\n }\n}\n\ndfsStack :: Tree a -> [a]\ndfsStack t = go [t]\n where\n go [] = []\n go ((Node x ts) : stack) = x : go (ts ++ stack)\n\nfunc dfsStack(node: Node) {\n var stack = [node]\n var temp: Node\n\n while stack.count > 0 {\n temp = stack.popLast()!\n print(temp.value, terminator:\" \")\n\n for child in temp.children! {\n stack.append(child)\n }\n }\n}\n\npublic static function DFSStack(Tree $tree): void\n{\n $stack = [$tree];\n $temp = null;\n\n while (null !== ($temp = array_pop($stack))) {\n echo $temp->getId() . ' ';\n foreach ($temp->getChildren() as $child) {\n $stack[] = $child;\n }\n }\n}\n\ndef dfs_stack(node) \n stack = [node] \n\n until stack.empty? \n temp = stack.pop \n print \"#{temp.id} \"\n temp.children.each{ |child| stack.push child } \n end \nend\n\nNode>>dfsStack\n \"Depth-first search with a stack.\"\n | stack top |\n stack := Stack new.\n stack push: self.\n [stack size > 0] whileTrue: [\n top := stack pop.\n Transcript show: (top data); cr.\n top children reverseDo: [ :child |\n stack push: child.\n ].\n ].\n\nfunc dfsStack(n *node) {\n stack := []*node{n}\n\n for len(stack) > 0 {\n cur := stack[0]\n stack = stack[1:]\n fmt.Printf(\"%d \", cur.id)\n stack = append(cur.children, stack...)\n }\n}\n\n# rdi - children ptr\n# rsi - value|children_size\ndfs_stack:\n push r12\n push r13\n push r14\n sub rsp, 16 # Create stack\n mov r12, rsp\n push rsi # Save node to use as pointer\n push rdi\n mov rdi, r12\n call get_stack # Init stack\n mov rdi, r12\n mov rsi, rsp\n call stack_push # Push node\n mov rdi, r12 # Pop stack\n call stack_pop\ndfs_stack_loop:\n test rax, rax # Test if stack is empty\n jz dfs_stack_return\n mov r13, rax\n mov rdi, OFFSET fmt_tree # Print id\n mov esi, DWORD PTR [r13 + 12]\n xor rax, rax\n call printf\n mov eax, DWORD PTR [r13 + 8] # Get start and end of array\n mov r13, QWORD PTR [r13]\n lea r14, [r13 + rax]\ndfs_stack_push_child:\n cmp r13, r14 # Check if the pointers are the same\n je dfs_stack_end_push\n mov rdi, r12 # Push node into the stack\n mov rsi, r13\n call stack_push\n add r13, tree_size\n jmp dfs_stack_push_child\ndfs_stack_end_push:\n mov rdi, r12 # Pop stack\n call stack_pop\n jmp dfs_stack_loop\ndfs_stack_return:\n mov rdi, r12 # Free stack\n call free_stack\n add rsp, 32\n pop r14\n pop r13\n pop r12\n ret\n\n\n ↪️ 🐔 children❗️ ▶️ 0 🍇\n 🍭🐽 children 0❗️❗️\n 😀 🔡 id 10❗️❗️\n 🍭🐽 children 1❗️❗️\n 🍉\n 🙅 🍇\n 😀 🔡 id 10❗️❗️\n 🍉\n ↩️ 🤷‍♀️\n🍉\n\n📗 Depth-First Search Stack 📗\n❗️ 🥞 🍇\n 🍨 🐕 🍆 ➡️ stack\n\n(defun dfs-stack (node)\n \"A depth first approach for printing out all values in a tree using a stack.\"\n (loop\n with stack = (list node)\n with temp = nil\n while (> (length stack) 0) do\n (format t \"~a \" (node-data (first stack)))\n (setf temp (pop stack))\n (loop for child in (node-children temp) do\n (push child stack))))\n\nfunction DFS_stack(n)\n\n cell_index = @(a, b) a{b};\n node_stack = {n};\n\n while ~isempty(node_stack)\n\n parent = node_stack{end};\n node_stack(end) = [];\n\n ID = cell_index(keys(parent), 1);\n fprintf('%u ', ID);\n\n children = cell_index(values(parent), 1);\n\n for i = flip(children)\n child = i{1};\n if ~isempty(child)\n node_stack = {node_stack{:} child};\n end\n end\n end\nend\n\ndef dfs_stack(node is Node):\n \"\"\"A depth first approach for printing out all values in a tree using a stack.\"\"\"\n stack = [node]\n while stack:\n current_node = stack.pop()\n print(current_node.value, end=' ')\n for child in current_node.children:\n stack.append(child)\n\n\n\nAll this said, there are a few details about DFS that might not be ideal, depending on the situation. For example, if we use DFS on an incredibly long tree, we will spend a lot of time going further and further down a single branch without searching the rest of the data structure. In addition, it is not the natural way humans would order a tree if asked to number all the nodes from top to bottom. I would argue a more natural traversal order would look something like this:\n\n \n\n\nAnd this is exactly what Breadth-First Search (BFS) does! On top of that, it can be implemented in the same way as the DFS_stack(...) function above, simply by swapping the stack for a queue, which is similar to a stack, except that it only allows you to interact with the very first element instead of the last. In code, this looks something like:\nfunction BFS_queue(n::Node)\n q = Queue{Node}()\n enqueue!(q, n)\n\n while(length(q) > 0)\n print(first(q).ID, \" \")\n temp = dequeue!(q)\n for child in temp.children\n enqueue!(q, child)\n end\n end\nend\n\nvoid bfs_queue(node const& n) {\n std::queue queue;\n queue.push(&n);\n\n while (queue.size() > 0) {\n auto const& temp = *queue.front();\n queue.pop();\n\n std::cout \npublic void BFSQueue()\n{\n var queue = new Queue();\n queue.Enqueue(this);\n\n while (queue.Count != 0)\n {\n Console.Write(queue.Peek().Id + \" \");\n var temp = queue.Dequeue();\n\n foreach (var c in temp._children)\n queue.Enqueue(c);\n }\n}\n\nvoid bfs_queue(struct node n) {\n struct queue q = get_queue(sizeof(struct node*));\n enqueue(&q, &n);\n struct node *tmp;\n\n while (!queue_empty(&q)) {\n tmp = (struct node*)dequeue(&q);\n if (!tmp) {\n break;\n }\n\n printf(\"%d \", tmp->id);\n for (size_t i = 0; i children_size; ++i) {\n enqueue(&q, &tmp->children[i]);\n }\n }\n\n free_queue(q);\n}\n\npublic void bfsQueue() {\n Queue queue = new LinkedList();\n queue.add(this.root);\n\n while (queue.size() != 0) {\n System.out.print(queue.peek().id + \" \");\n Node temp = queue.poll(); // return null if the queue is empty\n\n if (temp != null) {\n for (Node c : temp.children) {\n queue.add(c);\n }\n }\n }\n}\n\nfunction bfs(tree) {\n const queue = [tree];\n while (queue.length > 0) {\n const current = queue.shift();\n process.stdout.write(current.id + \" \");\n queue.push(...current.children);\n }\n}\n\ndef bfs_queue(node):\n queue = [node]\n while queue:\n node = queue.pop(0)\n queue.extend(node.children)\n print(node.data)\n\n\n \nfn bfs_queue(n: &Node) {\n let mut queue = VecDeque::new();\n queue.push_back(n);\n\n while let Some(current) = queue.pop_front() {\n print!(\"{} \", current.value);\n queue.extend(¤t.children);\n }\n}\n\nbfs :: Tree a -> [a]\nbfs (Node x ts) = x : go ts\n where\n go [] = []\n go ts = map node ts ++ go (concatMap forest ts)\n\nfunc bfsQueue(node: Node) {\n var queue = [node]\n var temp: Node\n\n while queue.count > 0 {\n temp = queue.remove(at: 0)\n print(temp.value, terminator:\" \")\n\n for child in temp.children! {\n queue.append(child)\n }\n }\n}\n\npublic static function DFSQueue(Tree $tree): void\n{\n $stack = [$tree];\n $temp = null;\n\n while (null !== ($temp = array_shift($stack))) {\n echo $temp->getId() . ' ';\n foreach ($temp->getChildren() as $child) {\n $stack[] = $child;\n }\n }\n}\n\ndef bfs_queue(node) \n queue = Deque.new [node]\n\n until queue.empty? \n temp = queue.shift\n print \"#{temp.id} \"\n temp.children.each{ |child| queue.push child }\n end \nend\n\nNode>>bfs\n \"A breadth-first tree search using queues.\"\n | queue current |\n queue := LinkedList with: self.\n [ queue size > 0 ] whileTrue: [\n current := queue first.\n queue removeFirst.\n Transcript show: (current data); cr.\n current children collect: [ :child |\n queue addLast: child\n ].\n ].\n\nfunc bfsQueue(n *node) {\n queue := []*node{n}\n\n for len(queue) > 0 {\n cur := queue[0]\n queue = queue[1:]\n fmt.Printf(\"%d \", cur.id)\n queue = append(queue, cur.children...)\n }\n}\n\n# rdi - children ptr\n# rsi - value|children_size\nbfs_queue:\n push r12\n push r13\n push r14\n sub rsp, 20 # Create queue\n mov r12, rsp\n push rsi # Save node to use as pointer\n push rdi\n mov rdi, r12\n call get_queue # Init queue\n mov rdi, r12\n mov rsi, rsp\n call enqueue # enqueue node\n mov eax, DWORD PTR [r12 + 8]\n mov edi, DWORD PTR [r12 + 12]\nbfs_queue_loop:\n cmp eax, edi\n je bfs_queue_return\n mov rdi, r12 # dequeue\n call dequeue\n test rax, rax # Test if queue is empty\n jz bfs_queue_return\n mov r13, rax\n mov rdi, OFFSET fmt_tree # Print id\n mov esi, DWORD PTR [r13 + 12]\n xor rax, rax\n call printf\n mov eax, DWORD PTR [r13 + 8] # Get start and end of array\n mov r13, QWORD PTR [r13]\n lea r14, [r13 + rax]\nbfs_queue_push_child:\n cmp r13, r14 # Check if the pointers are the same\n je bfs_queue_end_push\n mov rdi, r12 # enqueue node\n mov rsi, r13\n call enqueue\n add r13, tree_size\n jmp bfs_queue_push_child\nbfs_queue_end_push:\n mov eax, DWORD PTR [r12 + 8]\n mov edi, DWORD PTR [r12 + 12]\n jmp bfs_queue_loop\nbfs_queue_return:\n mov rdi, r12 # Free queue\n call free_queue\n add rsp, 36\n pop r14\n pop r13\n pop r12\n ret\n\n 🐽 stack 🐔 stack❗️ ➖ 1❗️ ➡️ temp\n 🐨 stack 🐔 stack❗️ ➖ 1❗️\n\n 😀 🔡 🆔 temp❗️ 10❗️❗️\n\n 🧒 temp❗️ ➡️ temp_children\n 🔂 child temp_children 🍇\n 🐻 stack child❗️\n 🍉\n 🍉\n🍉\n\n📗 Breadth-First Search Queue 📗\n❗️ 🏢 🍇\n 🍨 🐕 🍆 ➡️ queue\n\n(defun bfs-queue (node)\n \"A breadth first search approach for printing out all values in a tree.\"\n (loop\n with queue = (list node)\n with temp = nil\n while (> (length queue) 0) do\n (format t \"~a \" (node-data (first queue)))\n (setf temp (pop queue))\n ;; If the queue is empty, the queue should be filled with the children nodes.\n (if (eql queue nil)\n (setf queue (node-children temp))\n (nconc queue (node-children temp)))))\n\nfunction BFS_queue(n)\n\n cell_index = @(a, b) a{b};\n node_queue = {n};\n\n while ~isempty(node_queue)\n next_nodes = {};\n for parent_cell = node_queue\n parent = parent_cell{1};\n ID = cell_index(keys(parent), 1);\n fprintf('%u ', ID);\n children = cell_index(values(parent), 1);\n for i = children\n child = i{1};\n if ~isempty(child)\n next_nodes = {next_nodes{:}, child};\n end\n end\n end\n node_queue = next_nodes;\n end\nend\n\ndef bfs_queue(node is Node):\n \"\"\"A breadth first search approach for printing out all values in a tree.\"\"\"\n queue = deque([node])\n while queue:\n current_node = queue.popleft()\n print(current_node.value, end=' ')\n for child in current_node.children:\n queue.append(child)\n\n\n\nVideo Explanation\nHere is a video describing tree traversal:\n\n\n\n\nExample Code\nusing DataStructures, Printf\n\nstruct Node\n children::Vector{Node}\n ID::Int64\n Node(ID::Int64) = new(Vector{Node}(), ID)\nend\n\nfunction DFS_recursive(n::Node)\n # Here we are doing something...\n print(n.ID, \" \")\n\n for child in n.children\n DFS_recursive(child)\n end\nend\n\nfunction DFS_recursive_postorder(n::Node)\n\n for child in n.children\n DFS_recursive_postorder(child)\n end\n\n # Here we are doing something...\n print(n.ID, \" \")\nend\n\n# This assumes only 2 children, but accounts for other possibilities\nfunction DFS_recursive_inorder_btree(n::Node)\n\n if (length(n.children) == 2)\n DFS_recursive_inorder_btree(n.children[1])\n print(n.ID, \" \")\n DFS_recursive_inorder_btree(n.children[2])\n elseif (length(n.children) == 1)\n DFS_recursive_inorder_btree(n.children[1])\n print(n.ID, \" \")\n elseif (length(n.children) == 0)\n print(n.ID, \" \")\n else\n println(\"Not a binary tree!\")\n end\nend\n\nfunction DFS_stack(n::Node)\n s = Stack{Node}()\n push!(s, n)\n\n while(length(s) > 0)\n print(top(s).ID, \" \")\n temp = pop!(s)\n for child in temp.children\n push!(s, child)\n end\n end\nend\n\nfunction BFS_queue(n::Node)\n q = Queue{Node}()\n enqueue!(q, n)\n\n while(length(q) > 0)\n print(first(q).ID, \" \")\n temp = dequeue!(q)\n for child in temp.children\n enqueue!(q, child)\n end\n end\nend\n\n# function to create a simple, balanced tree\nfunction create_tree(num_row::Int64, num_child::Int64)\n ret = Node(num_row)\n if (num_row == 0)\n return ret\n end\n\n for i = 1:num_child\n child = create_tree(num_row - 1, num_child)\n push!(ret.children, child)\n end\n\n return ret\nend\n\nfunction main()\n root = create_tree(2, 3)\n\n println(\"[#]\\nRecursive DFS:\")\n DFS_recursive(root);\n println()\n\n println(\"[#]\\nRecursive Postorder DFS:\")\n DFS_recursive_postorder(root);\n println()\n\n println(\"[#]\\nStack-based DFS:\")\n DFS_stack(root);\n println()\n\n println(\"[#]\\nQueue-based BFS:\")\n BFS_queue(root);\n println()\n\n root_binary = create_tree(3,2)\n println(\"[#]\\nRecursive Inorder DFS for Binary Tree:\")\n DFS_recursive_inorder_btree(root_binary)\n println()\nend\n\nmain()\n\n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing std::size_t;\n\nstruct node {\n std::vector children;\n size_t value;\n};\n\n// Simple recursive scheme for DFS\nvoid dfs_recursive(node const& n) {\n // Here we are doing something...\n std::cout stack;\n stack.push(&n);\n\n while (stack.size() > 0) {\n auto const& temp = *stack.top();\n stack.pop();\n std::cout queue;\n queue.push(&n);\n\n while (queue.size() > 0) {\n auto const& temp = *queue.front();\n queue.pop();\n\n std::cout (), 0};\n }\n\n std::vector vec;\n std::generate_n(std::back_inserter(vec), num_child, [&] {\n return create_tree(num_row - 1, num_child);\n });\n\n return node{std::move(vec), num_row};\n}\n\nint main() {\n // Creating Tree in main\n auto root = create_tree(2, 3);\n auto binary_root = create_tree(3, 2);\n std::cout \nTree.cs\nusing System;\nusing System.Collections.Generic;\n\nnamespace TreeTraversal\n{\n public class Tree\n {\n public int Id { get; private set; }\n private List _children = new List();\n\n public Tree(int depthCount, int childrenCount)\n {\n Id = 1;\n\n if (depthCount > 0)\n {\n for (int i = 0; i ();\n stack.Push(this);\n\n while (stack.Count != 0)\n {\n Console.Write(stack.Peek().Id + \" \");\n var temp = stack.Pop();\n\n foreach (var c in temp._children)\n stack.Push(c);\n }\n }\n\n public void BFSQueue()\n {\n var queue = new Queue();\n queue.Enqueue(this);\n\n while (queue.Count != 0)\n {\n Console.Write(queue.Peek().Id + \" \");\n var temp = queue.Dequeue();\n\n foreach (var c in temp._children)\n queue.Enqueue(c);\n }\n }\n }\n}\n\nProgram.cs\nusing System;\n\nnamespace TreeTraversal\n{\n class Program\n {\n static void Main(string[] args)\n {\n var tree = new Tree(2, 3);\n Console.WriteLine(\"[#]\\nRecursive DFS:\");\n tree.DFSRecursive();\n Console.WriteLine();\n\n Console.WriteLine(\"[#]\\nRecursive Postorder DFS:\");\n tree.DFSRecursivePostorder();\n Console.WriteLine();\n\n Console.WriteLine(\"[#]\\nStack-based DFS:\");\n tree.DFSStack();\n Console.WriteLine();\n\n Console.WriteLine(\"[#]\\nQueue-based BFS:\");\n tree.BFSQueue();\n Console.WriteLine();\n\n tree = new Tree(3, 2);\n Console.WriteLine(\"[#]\\nRecursive Inorder DFS for Binary Tree:\");\n tree.DFSRecursiveInorderBinary();\n Console.WriteLine();\n }\n }\n}\n\nutility.h\n#ifndef UTILITY_H\n#define UTILITY_H\n\n#include \n#include \n#include \n#include \n\nstruct stack {\n void **data;\n size_t top, capacity, size;\n};\n\nstruct queue {\n void **data;\n size_t front, back, capacity;\n};\n\nstruct stack get_stack(size_t size) {\n struct stack stk;\n\n stk.data = malloc(4 * size);\n stk.capacity = 4;\n stk.top = 0;\n\n return stk;\n}\n\nbool stack_empty(struct stack *stk) {\n return stk->top == 0;\n}\n\nvoid stack_push(struct stack *stk, void *element) {\n if (stk->top == stk->capacity) {\n stk->capacity *= 2;\n stk->data = realloc(stk->data, stk->capacity * sizeof(stk->data[0]));\n }\n\n stk->data[stk->top++] = element;\n}\n\nvoid *stack_pop(struct stack *stk) {\n if (stack_empty(stk)) {\n return NULL;\n }\n\n return stk->data[--stk->top];\n}\n\nvoid free_stack(struct stack stk) {\n free(stk.data);\n}\n\nstruct queue get_queue(size_t size) {\n struct queue q;\n\n q.data = calloc(4, size);\n q.front = 0;\n q.back = 0;\n q.capacity = 4;\n\n return q;\n}\n\nbool queue_empty(struct queue *q) {\n return q->front == q->back;\n}\n\nvoid queue_resize(struct queue *q) {\n size_t size = sizeof(q->data[0]);\n void **tmp = calloc((q->capacity * 2), size);\n memcpy(tmp, q->data + q->front, (q->capacity - q->front) * size);\n memcpy(tmp + q->capacity - q->front, q->data, (q->front - 1) * size);\n\n free(q->data);\n\n q->data = tmp;\n q->back = q->capacity - 1;\n q->front = 0;\n q->capacity *= 2;\n}\n\nvoid enqueue(struct queue *q, void *element) {\n if (q->front == (q->back + 1) % q->capacity) {\n queue_resize(q);\n }\n\n q->data[q->back] = element;\n q->back = (q->back + 1) % q->capacity;\n}\n\nvoid *dequeue(struct queue *q) {\n if (queue_empty(q)) {\n return NULL;\n }\n\n void *ret = q->data[q->front];\n q->front = (q->front + 1) % q->capacity;\n\n return ret;\n}\n\nvoid free_queue(struct queue q) {\n free(q.data);\n}\n\n#endif //UTILITY_H\n\ntree_traversal.c\n#include \"utility.h\"\n\n#include \n#include \n#include \n\nstruct node {\n struct node *children;\n size_t children_size;\n int id;\n};\n\nstruct node create_tree(int rows, size_t num_children) {\n struct node n = {NULL, 0, rows};\n\n if (rows > 0) {\n n.children = (struct node*)malloc(num_children * sizeof(struct node));\n n.children_size = num_children;\n for (size_t i = 0; i 0) {\n for (size_t i = 0; i id);\n for (size_t i = 0; i children_size; ++i) {\n stack_push(&stk, &tmp->children[i]);\n }\n }\n\n free_stack(stk);\n}\n\nvoid bfs_queue(struct node n) {\n struct queue q = get_queue(sizeof(struct node*));\n enqueue(&q, &n);\n struct node *tmp;\n\n while (!queue_empty(&q)) {\n tmp = (struct node*)dequeue(&q);\n if (!tmp) {\n break;\n }\n\n printf(\"%d \", tmp->id);\n for (size_t i = 0; i children_size; ++i) {\n enqueue(&q, &tmp->children[i]);\n }\n }\n\n free_queue(q);\n}\n\nint main() {\n struct node root = create_tree(2, 3);\n\n printf(\"[#]\\nRecursive DFS:\\n\");\n dfs_recursive(root);\n printf(\"\\n\");\n\n printf(\"[#]\\nRecursive Postorder DFS:\\n\");\n dfs_recursive_postorder(root);\n printf(\"\\n\");\n\n printf(\"[#]\\nStack-based DFS:\\n\");\n dfs_stack(root);\n printf(\"\\n\");\n\n printf(\"[#]\\nQueue-based BFS:\\n\");\n bfs_queue(root);\n printf(\"\\n\");\n\n destroy_tree(root);\n struct node root_binary = create_tree(3, 2);\n\n printf(\"[#]\\nRecursive Inorder DFS for Binary Tree:\\n\");\n dfs_recursive_inorder_btree(root_binary);\n printf(\"\\n\");\n\n destroy_tree(root_binary);\n return 0;\n}\n\nTree.java\nimport java.util.ArrayList;\nimport java.util.LinkedList;\nimport java.util.Queue;\nimport java.util.Stack;\n\npublic class Tree {\n public Node root;\n\n public Tree(int rowCount, int childrenCount) {\n // this.root is the root node of the Tree\n this.root = new Node(rowCount);\n this.createAllChildren(this.root, rowCount-1, childrenCount);\n }\n\n\n public void dfsRecursive() {\n this.dfsRecursive(this.root);\n }\n\n private void dfsRecursive(Node node) {\n System.out.print(node.id + \" \");\n\n for (Node n : node.children) {\n dfsRecursive(n);\n }\n }\n\n\n public void dfsRecursivePostOrder() {\n this.dfsRecursivePostOrder(this.root);\n }\n\n private void dfsRecursivePostOrder(Node node) {\n for (Node n : node.children) {\n dfsRecursivePostOrder(n);\n }\n\n // Here we are doing something ...\n System.out.print(node.id + \" \");\n }\n\n\n public void dfsRecursiveInOrderBinary() {\n dfsRecursiveInOrderBinary(this.root);\n }\n\n private void dfsRecursiveInOrderBinary(Node node) {\n switch (node.children.size()) {\n case 2:\n dfsRecursiveInOrderBinary(node.children.get(0));\n System.out.print(node.id + \" \");\n dfsRecursiveInOrderBinary(node.children.get(1));\n break;\n case 1:\n dfsRecursiveInOrderBinary(node.children.get(0));\n System.out.print(node.id + \" \");\n break;\n case 0:\n System.out.print(node.id + \" \");\n break;\n default:\n System.err.println(\"Not a binary tree at dfsRecursiveInOrderBinary()!\");\n }\n }\n\n\n public void dfsStack() {\n Stack stack = new Stack();\n stack.push(this.root);\n\n Node tmp;\n\n while (stack.size() != 0) {\n System.out.print(stack.peek().id + \" \");\n tmp = stack.pop();\n\n for (Node c : tmp.children) {\n stack.push(c);\n }\n }\n }\n\n public void bfsQueue() {\n Queue queue = new LinkedList();\n queue.add(this.root);\n\n while (queue.size() != 0) {\n System.out.print(queue.peek().id + \" \");\n Node temp = queue.poll(); // return null if the queue is empty\n\n if (temp != null) {\n for (Node c : temp.children) {\n queue.add(c);\n }\n }\n }\n }\n\n\n private void createAllChildren(Node node, int rowCount, int childrenCount) {\n if (rowCount {\n public ArrayList children;\n public int id;\n\n public Node(int id) {\n this.children = new ArrayList();\n this.id = id;\n }\n\n @Override\n public int compareTo(Node other) {\n // Need to implement Comparable and override this\n // method because of the method BFSQueue() which uses Queues\n // and must know how to check if two nodes are the same or not\n return Integer.compare(this.id, other.id);\n }\n }\n\n public static void main(String[] args) {\n Tree tree = new Tree(2, 3);\n\n System.out.println(\"[#]\\nRecursive DFS:\");\n tree.dfsRecursive();\n System.out.println();\n\n System.out.println(\"[#]\\nRecursive Postorder DFS:\");\n tree.dfsRecursivePostOrder();\n System.out.println();\n\n\n System.out.println(\"[#]\\nStack-based DFS:\");\n tree.dfsStack();\n System.out.println();\n\n\n System.out.println(\"[#]\\nQueue-based BFS:\");\n tree.bfsQueue();\n System.out.println();\n\n\n // Uncommenting the following 2 lines will result in an exception thrown because at least one Node of the Tree has more than 2 children and therefor a DFSRecursiveInorderBinary doesn't work.\n //System.out.println(\"Using in-order binary recursive DFS : (fail)\");\n //tree.dfsRecursiveInOrderBinary();\n\n tree = new Tree(3, 2);\n System.out.println(\"[#]\\nRecursive Inorder DFS for Binary Tree:\");\n tree.dfsRecursiveInOrderBinary();\n System.out.println();\n }\n}\n\nfunction createTree(rows, children) {\n if (rows === 0) {\n return { id: rows, children: [] };\n }\n\n return {\n id: rows,\n children: [...Array(children).keys()].map(() => createTree(rows - 1, children))\n };\n}\n\nfunction dfsPreorder(tree) {\n if (!tree) {\n return;\n }\n\n process.stdout.write(tree.id + \" \");\n tree.children.forEach(dfsPreorder);\n}\n\nfunction dfsPostorder(tree) {\n if (!tree) {\n return;\n }\n\n tree.children.forEach(dfsPostorder);\n process.stdout.write(tree.id + \" \");\n}\n\nfunction dfsInorder(tree) {\n if (!tree) {\n return;\n }\n\n switch (tree.children.length) {\n case 2:\n dfsInorder(tree.children[0]);\n console.log(tree.id);\n dfsInorder(tree.children[1]);\n break;\n case 1:\n dfsInorder(tree.children[0]);\n console.log(tree.id);\n break;\n case 0:\n console.log(tree.id);\n break;\n default:\n throw new Error(\"Postorder traversal is only valid for binary trees\");\n }\n}\n\nfunction dfsIterative(tree) {\n const stack = [tree];\n while (stack.length > 0) {\n const current = stack.pop();\n process.stdout.write(current.id + \" \");\n stack.push(...current.children);\n }\n}\n\nfunction bfs(tree) {\n const queue = [tree];\n while (queue.length > 0) {\n const current = queue.shift();\n process.stdout.write(current.id + \" \");\n queue.push(...current.children);\n }\n}\n\nconst root = createTree(2, 3);\nconsole.log(\"[#]\\nRecursive DFS:\");\ndfsPreorder(root);\nconsole.log();\nconsole.log(\"[#]\\nRecursive Postorder DFS:\");\ndfsPostorder(root);\nconsole.log();\nconsole.log(\"[#]\\nStack-based DFS:\");\ndfsIterative(root);\nconsole.log();\nconsole.log(\"[#]\\nQueue-based BFS:\");\nbfs(root);\nconsole.log();\nconst root_binary = createTree(3, 2);\nconsole.log(\"[#]\\nRecursive Inorder DFS for Binary Tree:\");\ndfsInorder(root_binary);\nconsole.log();\n\nclass Node:\n def __init__(self):\n self.data = None\n self.children = []\n\ndef create_tree(node, num_row, num_child):\n node.data = num_row\n\n if num_row > 0:\n for i in range(num_child):\n child = create_tree(Node(), num_row-1, num_child)\n node.children.append(child)\n\n return node\n\n\ndef dfs_recursive(node):\n if node.data != None:\n print(node.data, end=' ')\n\n for child in node.children:\n dfs_recursive(child)\n\n\ndef dfs_recursive_postorder(node):\n for child in node.children:\n dfs_recursive_postorder(child)\n\n if node.data != None:\n print(node.data, end=' ')\n\n\n# This assumes only 2 children, but accounts for other possibilities\ndef dfs_recursive_inorder_btree(node):\n if len(node.children) == 2:\n dfs_recursive_inorder_btree(node.children[0])\n print(node.data, end=' ')\n dfs_recursive_inorder_btree(node.children[1])\n elif len(node.children) == 1:\n dfs_recursive_inorder_btree(node.children[0])\n print(node.data, end=' ')\n elif len(node.children) == 0:\n print(node.data, end=' ')\n else:\n print(\"Not a binary tree!\")\n\n\ndef dfs_stack(node):\n stack = [node]\n while stack:\n node = stack.pop()\n stack.extend(node.children)\n print(node.data, end=' ')\n\ndef bfs_queue(node):\n queue = [node]\n while queue:\n node = queue.pop(0)\n queue.extend(node.children)\n print(node.data)\n\n\ndef main():\n tree = create_tree(Node(), 2, 3)\n\n print(\"[#]\\nRecursive DFS:\")\n dfs_recursive(tree)\n print()\n\n print(\"[#]\\nRecursive Postorder DFS:\")\n dfs_recursive_postorder(tree)\n print()\n\n print(\"[#]\\nStack-based DFS:\")\n dfs_stack(tree)\n print()\n\n print(\"[#]\\nQueue-based BFS:\")\n bfs_queue(tree)\n print()\n\n binary_tree = create_tree(Node(), 3, 2)\n\n print(\"[#]\\nRecursive Inorder DFS for Binary Tree:\")\n dfs_recursive_inorder_btree(binary_tree)\n print()\n\nif __name__ == '__main__':\n main()\n\nThe code snippets were taken from this Scratch project\n\n \nuse std::collections::VecDeque;\n\n#[derive(Debug)]\nstruct Node {\n children: Vec,\n value: u64,\n}\n\nfn dfs_recursive(n: &Node) {\n print!(\"{} \", n.value);\n\n for child in &n.children {\n dfs_recursive(child);\n }\n}\n\nfn dfs_recursive_postorder(n: &Node) {\n for child in &n.children {\n dfs_recursive_postorder(child);\n }\n\n print!(\"{} \", n.value);\n}\n\nfn dfs_recursive_inorder_btree(n: &Node) {\n match &n.children[..] {\n [left, right] => {\n dfs_recursive_inorder_btree(left);\n print!(\"{} \", n.value);\n dfs_recursive_inorder_btree(right);\n }\n [left] => {\n dfs_recursive_inorder_btree(left);\n print!(\"{} \", n.value);\n }\n [] => print!(\"{} \", n.value),\n _ => print!(\"This is not a binary tree. \"),\n }\n}\n\nfn dfs_stack(n: &Node) {\n let mut stack = vec![n];\n\n while let Some(current) = stack.pop() {\n print!(\"{} \", current.value);\n stack.extend(¤t.children);\n }\n}\n\nfn bfs_queue(n: &Node) {\n let mut queue = VecDeque::new();\n queue.push_back(n);\n\n while let Some(current) = queue.pop_front() {\n print!(\"{} \", current.value);\n queue.extend(¤t.children);\n }\n}\n\nfn create_tree(num_row: u64, num_child: u64) -> Node {\n if num_row == 0 {\n return Node {\n children: vec![],\n value: 0,\n };\n }\n\n let children = (0..num_child)\n .map(|_| create_tree(num_row - 1, num_child))\n .collect();\n\n Node {\n children,\n value: num_row,\n }\n}\n\nfn main() {\n let root = create_tree(2, 3);\n\n println!(\"[#]\\nRecursive DFS:\");\n dfs_recursive(&root);\n println!();\n\n println!(\"[#]\\nRecursive Postorder DFS:\");\n dfs_recursive_postorder(&root);\n println!();\n\n println!(\"[#]\\nStack-based DFS:\");\n dfs_stack(&root);\n println!();\n\n println!(\"[#]\\nQueue-based BFS:\");\n bfs_queue(&root);\n println!();\n\n println!(\"[#]\\nRecursive Inorder DFS for Binary Tree:\");\n let root_binary = create_tree(3, 2);\n dfs_recursive_inorder_btree(&root_binary);\n println!();\n}\n\ndata Tree a = Node\n { node :: a,\n forest :: [Tree a]\n }\n deriving (Show)\n\ndfs :: Tree a -> [a]\ndfs (Node x ts) = x : concatMap dfs ts\n\ndfsPostOrder :: Tree a -> [a]\ndfsPostOrder (Node x ts) = concatMap dfsPostOrder ts ++ [x]\n\ndfsInOrder :: Tree a -> [a] -- For binary trees only\ndfsInOrder (Node x []) = [x]\ndfsInOrder (Node x [l]) = dfsInOrder l ++ [x] -- Single branch assumed to be left\ndfsInOrder (Node x [l, r]) = dfsInOrder l ++ [x] ++ dfsInOrder r\ndfsInOrder _ = error \"Not a binary tree\"\n\ndfsStack :: Tree a -> [a]\ndfsStack t = go [t]\n where\n go [] = []\n go ((Node x ts) : stack) = x : go (ts ++ stack)\n\nbfs :: Tree a -> [a]\nbfs (Node x ts) = x : go ts\n where\n go [] = []\n go ts = map node ts ++ go (concatMap forest ts)\n\ncreateTree :: Int -> Int -> Tree Int\ncreateTree 0 _ = Node 0 []\ncreateTree numRow numChild = Node numRow children\n where\n children = map (createTree (numRow - 1)) $ replicate numChild numChild\n\nmain = do\n let testTree = createTree 2 3\n showNodes = unwords . map show\n putStrLn \"[#]\\nRecursive DFS:\"\n putStrLn $ showNodes $ dfs testTree\n putStrLn \"[#]\\nRecursive Postorder DFS:\"\n putStrLn $ showNodes $ dfsPostOrder testTree\n putStrLn \"[#]\\nStack-based DFS:\"\n putStrLn $ showNodes $ dfsStack testTree\n putStrLn \"[#]\\nQueue-based BFS:\"\n putStrLn $ showNodes $ bfs testTree\n putStrLn \"[#]\\nRecursive Inorder DFS for Binary Tree:\"\n putStrLn $ showNodes $ dfsInOrder $ createTree 3 2\n\nclass Node {\n var value: Int\n var children: [Node]?\n\n init(value: Int, children: [Node]) {\n self.value = value\n self.children = children\n }\n}\n\nfunc createTree(numRows: Int, numChildren: Int) -> Node {\n let node = Node(value: numRows, children: [])\n\n if numRows > 0 {\n for _ in 1...numChildren {\n let child = createTree(numRows: numRows-1, numChildren: numChildren)\n node.children?.append(child)\n }\n }\n\n return node\n}\n\nfunc dfsRecursive(node: Node) {\n print(node.value, terminator:\" \")\n\n for child in node.children! {\n dfsRecursive(node: child)\n }\n}\n\nfunc dfsRecursivePostOrder(node: Node) {\n for child in node.children! {\n dfsRecursivePostOrder(node: child)\n }\n\n print(node.value, terminator:\" \")\n}\n\nfunc dfsRecursiveInOrderBinary(node: Node) {\n if node.children?.count == 2 {\n dfsRecursiveInOrderBinary(node: node.children![0])\n print(node.value, terminator:\" \")\n dfsRecursiveInOrderBinary(node: node.children![1])\n } else if node.children?.count == 1 {\n dfsRecursiveInOrderBinary(node: node.children![0])\n print(node.value, terminator:\" \")\n } else if node.children?.count == 0 {\n print(node.value, terminator:\" \")\n } else {\n print(\"Not a binary tree!\")\n }\n}\n\nfunc dfsStack(node: Node) {\n var stack = [node]\n var temp: Node\n\n while stack.count > 0 {\n temp = stack.popLast()!\n print(temp.value, terminator:\" \")\n\n for child in temp.children! {\n stack.append(child)\n }\n }\n}\n\nfunc bfsQueue(node: Node) {\n var queue = [node]\n var temp: Node\n\n while queue.count > 0 {\n temp = queue.remove(at: 0)\n print(temp.value, terminator:\" \")\n\n for child in temp.children! {\n queue.append(child)\n }\n }\n}\n\nfunc main() {\n let root = createTree(numRows: 2, numChildren: 3)\n\n print(\"[#]\\nRecursive DFS:\")\n dfsRecursive(node: root)\n print()\n\n print(\"[#]\\nRecursive Postorder DFS:\")\n dfsRecursivePostOrder(node: root)\n print()\n\n print(\"[#]\\nStack-based DFS:\")\n dfsStack(node: root)\n print()\n\n print(\"[#]\\nQueue-based BFS:\")\n bfsQueue(node: root)\n print()\n\n let rootBinary = createTree(numRows: 3, numChildren: 2)\n\n print(\"[#]\\nRecursive Inorder DFS for Binary Tree:\")\n dfsRecursiveInOrderBinary(node: rootBinary)\n print()\n}\n\nmain()\n\nid = $id;\n $this->children = $children;\n }\n\n public function getId(): int\n {\n return $this->id;\n }\n\n public function getChildren(): array\n {\n return $this->children;\n }\n\n public function addChild(Tree $child): void\n {\n $this->children[] = $child;\n }\n\n public function jsonSerialize(): array\n {\n return [\n 'id' => $this->id,\n 'children' => $this->children,\n ];\n }\n}\n\nclass TreeTraversal\n{\n public static function DFSRecursive(Tree $tree): void\n {\n echo $tree->getId() . ' ';\n foreach ($tree->getChildren() as $child) {\n static::DFSRecursive($child);\n }\n }\n\n public static function DFSRecursivePostorder(Tree $tree): void\n {\n foreach ($tree->getChildren() as $child) {\n static::DFSRecursivePostorder($child);\n }\n echo $tree->getId() . ' ';\n }\n\n public static function DFSRecursiveInorderBinary(Tree $tree): void\n {\n switch (count($tree->getChildren())) {\n case 2:\n static::DFSRecursiveInorderBinary($tree->getChildren()[0]);\n echo $tree->getId() . ' ';\n static::DFSRecursiveInorderBinary($tree->getChildren()[1]);\n break;\n case 1:\n static::DFSRecursiveInorderBinary($tree->getChildren()[0]);\n echo $tree->getId() . ' ';\n break;\n case 0:\n echo $tree->getId() . ' ';\n break;\n default:\n throw new InvalidArgumentException('Not a binary tree!');\n break;\n }\n }\n\n public static function DFSStack(Tree $tree): void\n {\n $stack = [$tree];\n $temp = null;\n\n while (null !== ($temp = array_pop($stack))) {\n echo $temp->getId() . ' ';\n foreach ($temp->getChildren() as $child) {\n $stack[] = $child;\n }\n }\n }\n\n public static function DFSQueue(Tree $tree): void\n {\n $stack = [$tree];\n $temp = null;\n\n while (null !== ($temp = array_shift($stack))) {\n echo $temp->getId() . ' ';\n foreach ($temp->getChildren() as $child) {\n $stack[] = $child;\n }\n }\n }\n}\n\nfunction generate_tree(int $numOfRows, int $numOfChildren): Tree\n{\n $node = new Tree($numOfRows);\n\n if ($numOfRows > 0) {\n for ($i = 0; $i addChild($child);\n }\n }\n\n return $node;\n}\n\n$node = generate_tree(2, 3);\n\necho '[#]' . PHP_EOL . 'Recursive DFS:' . PHP_EOL;\nTreeTraversal::DFSRecursive($node);\necho PHP_EOL;\n\necho '[#]' . PHP_EOL . 'Recursive Postorder DFS:' . PHP_EOL;\nTreeTraversal::DFSRecursivePostorder($node);\necho PHP_EOL;\n\necho '[#]' . PHP_EOL . 'Stack-based DFS:' . PHP_EOL;\nTreeTraversal::DFSStack($node);\necho PHP_EOL;\n\necho '[#]' . PHP_EOL . 'Queue-based BFS:' . PHP_EOL;\nTreeTraversal::DFSQueue($node);\necho PHP_EOL;\n\n// If you want to try to run binary order on a non-binary tree,\n// comment out the generation of the new tree below.\n// If you do that, an exception will be thrown\n$node = generate_tree(3, 2);\necho '[#]' . PHP_EOL . 'Recursive Inorder DFS for Binary Tree:' . PHP_EOL;\nTreeTraversal::DFSRecursiveInorderBinary($node);\necho PHP_EOL;\n\nclass Node \n property id, children \n def initialize(@id : Int32, @children : Array(Node))\n end \nend \n\ndef dfs_recursive(node) \n print \"#{node.id} \"\n node.children.each{ |child| dfs_recursive child } \nend\n\ndef dfs_recursive_postorder(node) \n node.children.each{ |child| dfs_recursive_postorder child }\n print \"#{node.id} \"\nend \n\ndef dfs_recursive_inorder_btree(node) \n case node.children.size\n when 2\n dfs_recursive_inorder_btree node.children[0]\n print \"#{node.id} \"\n dfs_recursive_inorder_btree node.children[1] \n when 1 \n dfs_recursive_inorder_btree node.children[0]\n print \"#{node.id} \"\n when 0 \n print \"#{node.id} \"\n else \n print \"Not a binary tree!\"\n end \nend \n\ndef dfs_stack(node) \n stack = [node] \n\n until stack.empty? \n temp = stack.pop \n print \"#{temp.id} \"\n temp.children.each{ |child| stack.push child } \n end \nend \n\ndef bfs_queue(node) \n queue = Deque.new [node]\n\n until queue.empty? \n temp = queue.shift\n print \"#{temp.id} \"\n temp.children.each{ |child| queue.push child }\n end \nend \n\ndef create_tree(levels, num_childs) \n\n children = [] of Node \n unless levels == 0 \n num_childs.times{children.push create_tree levels-1, num_childs } \n end \n\n Node.new(levels, children) \nend\n\ndef main \n root = create_tree levels: 2, num_childs: 3\n\n puts \"[#]\\nRecursive DFS:\"\n dfs_recursive root\n puts \n\n puts \"[#]\\nRecursive Postorder DFS:\" \n dfs_recursive_postorder root \n puts \n\n puts \"[#]\\nStack-based DFS:\"\n dfs_stack root \n puts \n\n puts \"[#]\\nQueue-based BFS:\"\n bfs_queue root \n puts \n\n root_bin = create_tree levels: 3, num_childs: 2\n\n puts \"[#]\\nRecursive Inorder DFS for Binary Tree:\"\n dfs_recursive_inorder_btree root_bin\n puts\nend \n\nmain\n\nObject subclass: #Node\n instanceVariableNames: 'children data'\n classVariableNames: ''\n package: ''\n\nNode>>children\n \"Children getter.\"\n ^ children\n\nNode>>children: newChildren\n \"Children setter.\"\n children := newChildren.\n\nNode>>data\n \"Data getter\"\n ^ data\n\nNode>>data: newData\n \"Data setter\"\n data := newData.\n\nNode>>dfsRecursive\n \"Recursive depth first search.\"\n Transcript show: data; cr.\n children collect: [ :child | child dfsRecursive ]\n\nNode>>dfsRecursivePostOrder\n \"Recursive depth first search (post-order).\"\n children collect: [ :child | (child dfsRecursivePostOrder)].\n Transcript show: data; cr.\n\nNode>>dfsInOrderBinaryTree\n \"Recursive depth first search on a binary tree in order.\"\n children size > 2 ifTrue: [\n Transcript show: 'This is not a binary tree!'; cr.\n ^self.\n ].\n children size = 2 ifTrue: [\n (children at: 1) dfsInOrderBinaryTree: value.\n ].\n Transcript show: data; cr.\n children size >= 1 ifTrue: [\n (children at: 0) dfsInOrderBinaryTree: value.\n ].\n ^self.\n\nNode>>dfsStack\n \"Depth-first search with a stack.\"\n | stack top |\n stack := Stack new.\n stack push: self.\n [stack size > 0] whileTrue: [\n top := stack pop.\n Transcript show: (top data); cr.\n top children reverseDo: [ :child |\n stack push: child.\n ].\n ].\n\nNode>>bfs\n \"A breadth-first tree search using queues.\"\n | queue current |\n queue := LinkedList with: self.\n [ queue size > 0 ] whileTrue: [\n current := queue first.\n queue removeFirst.\n Transcript show: (current data); cr.\n current children collect: [ :child |\n queue addLast: child\n ].\n ].\n\n| test |\ntest := Node new: 1 children: { Node new: 2.\n Node new: 3 children: { Node new: 4.\n Node new: 5. } }.\ntest dfsRecursive.\ntest dfsRecursivePostorder.\ntest dfsInOrderBinaryTree.\ntest dfsStack.\ntest bfs.\n\npackage main\n\nimport \"fmt\"\n\ntype node struct {\n id int\n children []*node\n}\n\nfunc dfsRecursive(n *node) {\n fmt.Printf(\"%d \", n.id)\n for _, child := range n.children {\n dfsRecursive(child)\n }\n}\n\nfunc dfsRecursivePostorder(n *node) {\n for _, child := range n.children {\n dfsRecursivePostorder(child)\n }\n fmt.Printf(\"%d \", n.id)\n}\n\nfunc dfsRecursiveInorderBtree(n *node) {\n switch len(n.children) {\n case 2:\n dfsRecursiveInorderBtree(n.children[0])\n fmt.Printf(\"%d \", n.id)\n dfsRecursiveInorderBtree(n.children[1])\n case 1:\n dfsRecursiveInorderBtree(n.children[0])\n fmt.Printf(\"%d \", n.id)\n case 0:\n fmt.Printf(\"%d \", n.id)\n default:\n fmt.Println(\"This is not a binary tree\")\n }\n}\n\nfunc dfsStack(n *node) {\n stack := []*node{n}\n\n for len(stack) > 0 {\n cur := stack[0]\n stack = stack[1:]\n fmt.Printf(\"%d \", cur.id)\n stack = append(cur.children, stack...)\n }\n}\n\nfunc bfsQueue(n *node) {\n queue := []*node{n}\n\n for len(queue) > 0 {\n cur := queue[0]\n queue = queue[1:]\n fmt.Printf(\"%d \", cur.id)\n queue = append(queue, cur.children...)\n }\n}\n\nfunc createTree(numRow, numChild int) *node {\n if numRow == 0 {\n return &node{id: 0}\n }\n\n cur := new(node)\n cur.id = numRow\n\n for x := 0; x \n.intel_syntax noprefix\n\n# System V calling convention cheatsheet\n# Params: rdi, rsi, rdx, rcx, r8, r9, xmm0-7\n# Return: rax (int 64 bits), rax:rdx (int 128 bits), xmm0 (float)\n# Callee cleanup: rbx, rbp, r12-15\n# Scratch: rax, rdi, rsi, rdx, rcx, r8, r9, r10, r11\n\n.section .rodata\n not_bt: .string \"This is not a binary tree.\\n\"\n fmt_tree: .string \"%d \\n\"\n\n .equ stack_size, 16\n .equ stack_array, 0\n .equ stack_top, 8\n .equ stack_cap, 12\n\n .equ queue_size, 20\n .equ queue_array, 0\n .equ queue_front, 8\n .equ queue_back, 12\n .equ queue_cap, 16\n\n .equ tree_children, 0\n .equ tree_num_children, 8\n .equ tree_value, 12\n .equ tree_size, 16\n.section .text\n .global main\n .extern printf, malloc, free, memcpy\n\n# rdi - stack ptr\nget_stack:\n push r12\n mov r12, rdi\n mov rdi, 32 # Creating a 32 byte array\n call malloc\n mov QWORD PTR [r12], rax # Saving the data into the stack\n mov DWORD PTR [r12 + 8], 0\n mov DWORD PTR [r12 + 12], 32\n pop r12\n ret\n\n# rdi - stack ptr\n# rsi - element ptr\nstack_push:\n push r12\n push r13\n push r14\n mov r12, rdi # Saving the variables\n mov r13, rsi\n mov r14d, DWORD PTR [r12 + 8]\n mov esi, DWORD PTR [r12 + 12]\n cmp rsi, r14 # Check if top is equal to capacity\n jne stack_push_append\n shl rsi, 1 # Calculate new capacity in bytes\n mov DWORD PTR [r12 + 12], esi # Saving new capcaity\n mov rdi, [r12]\n call realloc # Making the array bigger\n mov QWORD PTR [r12], rax\nstack_push_append:\n add r14, 8\n mov rax, QWORD PTR [r12]\n lea rax, [rax + r14]\n mov QWORD PTR [rax], r13 # Saving element and new top\n mov DWORD PTR [r12 + 8], r14d\n pop r14\n pop r13\n pop r12\n ret\n\n# rdi - stack ptr\n# RET rax - element ptr\nstack_pop:\n push r12\n mov r12d, DWORD PTR [rdi + 8] # Get top\n test r12, r12 # Check if top is zero\n jne stack_pop_element\n xor rax, rax # Return 0\n jmp stack_pop_return\nstack_pop_element:\n mov rax, [rdi]\n lea rax, [rax + r12] # Get the element\n mov rax, QWORD PTR [rax]\n sub r12, 8 # Subtract 1 from top and save it\n mov DWORD PTR [rdi + 8], r12d\nstack_pop_return:\n pop r12\n ret\n\n# rdi - stack ptr\nfree_stack:\n mov rdi, QWORD PTR [rdi]\n call free # Free stack array\n ret\n\n# rdi - queue ptr\nget_queue:\n push r12\n mov r12, rdi\n mov rdi, 32 # Create a 32 byte array\n call malloc\n mov QWORD PTR [r12], rax # Saving data to the queue pointer\n mov QWORD PTR [r12 + 8], 0\n mov DWORD PTR [r12 + 16], 32\n pop r12\n ret\n\n# rdi - queue ptr\nqueue_resize:\n push r12\n push r13\n push r14\n mov r12, rdi\n mov edi, DWORD PTR [r12 + 16] # Get new capacity and create new array\n shl rdi, 1\n call malloc\n mov r13, rax\n mov r14, QWORD PTR[r12]\n mov rdi, r13 # Copy data from front to capacity\n mov eax, DWORD PTR [r12 + 8]\n lea rsi, [r14 + rax]\n mov edx, DWORD PTR [r12 + 16]\n sub edx, DWORD PTR [r12 + 8]\n call memcpy\n mov eax, DWORD PTR [r12 + 16] # Copy data from start of array to front\n sub eax, DWORD PTR [r12 + 8]\n lea rdi, [r13 + rax]\n mov rsi, r14\n mov edx, DWORD PTR [r12 + 8]\n call memcpy\n mov rdi, r14 # New array has front at 0 and back at the old capacity\n call free # So free the old array then save the new queue\n mov QWORD PTR [r12], r13\n mov eax, DWORD PTR [r12 + 16]\n sub rax, 8\n mov DWORD PTR [r12 + 12], eax\n mov DWORD PTR [r12 + 8], 0\n mov eax, DWORD PTR [r12 + 16]\n shl rax, 1\n mov DWORD PTR [r12 + 16], eax\n pop r14\n pop r13\n pop r12\n ret\n\n# rdi - queue ptr\n# rsi - element\nenqueue:\n push r12\n push r13\n push r14\n push r15\n mov r12, rdi # Saving parameters\n mov r13, rsi\n mov r14d, DWORD PTR [rdi + 8]\n mov eax, DWORD PTR [rdi + 12]# Calculating new back\n add eax, 8\n mov edi, DWORD PTR [r12 + 16]\n cdq\n idiv edi\n cmp rdx, r14 # Check if front and new back are equal\n jne enqueue_append\n mov rdi, r12 # If so resize the queue\n call queue_resize\nenqueue_append:\n mov r14, QWORD PTR [r12] # Saving the element\n mov r15d, DWORD PTR [r12 + 12]\n lea r14, [r14 + r15]\n mov QWORD PTR [r14], r13\n mov r14d, DWORD PTR [r12 + 16]# Calculating new back and then saving it\n add r15, 8\n mov rax, r15\n cdq\n idiv r14d\n mov DWORD PTR [r12 + 12], edx\n pop r15\n pop r14\n pop r13\n pop r12\n ret\n\n# rdi - queue ptr\n# RET rax - element\ndequeue:\n push r12\n push r13\n mov r12d, DWORD PTR [rdi + 8] # Check if queue is empty\n mov r13d, DWORD PTR [rdi + 12]\n xor rax, rax\n cmp r12, r13\n je dequeue_return # if empty return null\n mov r12, QWORD PTR [rdi] # else return element pointer\n mov r13d, DWORD PTR [rdi + 8]\n lea r13, [r12 + r13]\n mov eax, DWORD PTR [rdi + 8]\n add eax, 8\n mov r12d, DWORD PTR [rdi + 16] # Calculate new front\n cdq\n idiv r12d\n mov DWORD PTR [rdi + 8], edx # Save new front\n mov rax, QWORD PTR [r13]\ndequeue_return:\n pop r13\n pop r12\n ret\n\n# rdi - queue ptr\nfree_queue:\n mov rdi, QWORD PTR [rdi] # Free queue array\n call free\n ret\n\n# rdi - levels\n# rsi - children_size\n# RET rax:rdx - the tree - children|value|children_size\ncreate_tree:\n push rbx\n push r12\n push r13\n push r14\n push r15\n mov r12, rdi\n mov r13, rsi\n test rdi, rdi\n jz create_tree_leaf\n mov r14, rsi # We'll allocate sizeof(tree) * children_size bytes of memory\n shl r14, 4 # save the size calculation to a callee-saved register so we can reuse it after the malloc\n mov rdi, r14\n call malloc\n mov r15, rax # Save the children address twice, once for the return value, once for the loop variable\n mov rbx, rax\n lea r14, [rax + r14] # Calculate the address of the element after last of the children array\ncreate_tree_children:\n cmp rbx, r14\n je create_tree_return\n lea rdi, [r12 - 1] # levels - 1\n mov rsi, r13\n call create_tree\n mov QWORD PTR [rbx], rax # Save the created tree to memory\n mov QWORD PTR [rbx + 8], rdx # The offset of children_size, writing out explicitly would've made the line way too long\n add rbx, tree_size\n jmp create_tree_children\ncreate_tree_leaf:\n mov r15, 0\n xor r13, r13 # Leaves won't have any children\ncreate_tree_return:\n mov rax, r15 # The children pointer will be in r15\n mov rdx, r12\n shl rdx, 32 # The tree's value will be the current \"levels\"\n shl r13, 4\n or rdx, r13 # Generate the return value by moving the value to the upper 32 bits\n pop r15\n pop r14\n pop r13\n pop r12\n pop rbx\n ret\n\n# rdi - children ptr\n# rsi - children size\nfree_tree:\n push r12\n push r13\n push r14\n push r15\n test rdi, rdi # Make sure the pointer is non-zero\n jz free_tree_return\n mov r12, rdi # Saving array\n lea r13, [r12 + rsi] # Get start and end of the array\n mov r14, r12\nfree_tree_free_kid:\n cmp r14, r13 # Loop thought the array and free all children\n je free_tree_free_array\n mov rdi, QWORD PTR [r14]\n mov esi, DWORD PTR [r14 + 8]\n call free_tree\n add r14, tree_size\n jmp free_tree_free_kid\nfree_tree_free_array:\n mov rdi, r12 # Free the array\n call free\nfree_tree_return:\n pop r15\n pop r14\n pop r13\n pop r12\n ret\n\n# rdi - children ptr\n# rsi - value|children_size\ndfs_recursive:\n push r12\n push r13\n mov r12, rdi\n mov r13, rsi\n mov rdi, OFFSET fmt_tree # Handle the current node\n shr rsi, 32 # The tree value is in the upper 32 bits\n xor rax, rax\n call printf\n mov r13d, r13d # Zero out the top 32 bits\n add r13, r12 # Pointer pointing after the last element of the children array\ndfs_recursive_children:\n cmp r12, r13 # If we reached the end, return\n je dfs_recursive_return\n mov rdi, QWORD PTR [r12]\n mov rsi, QWORD PTR [r12 + 8]\n call dfs_recursive\n add r12, tree_size\n jmp dfs_recursive_children\ndfs_recursive_return:\n pop r13\n pop r12\n ret\n\n# rdi - children ptr\n# rsi - value|children_size\ndfs_recursive_postorder:\n push r12\n push r13\n push r14\n mov r12, rdi\n mov r13, rsi\n mov r14, rsi\n mov r13d, r13d # Zero out the top 32 bits\n add r13, r12 # Pointer pointing after the last element of the children array\ndfs_recursive_po_children:\n cmp r12, r13 # If we reached the end, return\n je dfs_recursive_po_return\n mov rdi, QWORD PTR [r12]\n mov rsi, QWORD PTR [r12 + 8]\n call dfs_recursive_postorder\n add r12, tree_size\n jmp dfs_recursive_po_children\ndfs_recursive_po_return:\n mov rdi, OFFSET fmt_tree # Handle the current node\n mov rsi, r14\n shr rsi, 32 # The tree value is in the upper 32 bits\n xor rax, rax\n call printf\n pop r14\n pop r13\n pop r12\n ret\n\n# rdi - children ptr\n# rsi - value|children_size\ndfs_recursive_inorder_btree:\n push r12\n push r13\n mov r12, rdi\n mov r13, rsi\n mov rax, rsi\n mov eax, eax\n cmp rax, 0 # Check what type of tree it is.\n je dfs_recursive_bt_size0\n cmp rax, 16\n je dfs_recursive_bt_size1\n cmp rax, 32\n je dfs_recursive_bt_size2\n mov rdi, OFFSET not_bt # If the tree is not binary then print a warning\n xor rax, rax\n call printf\n jmp dfs_recursive_bt_return\ndfs_recursive_bt_size0:\n mov rdi, OFFSET fmt_tree # If the node is a leaf then print its id\n shr rsi, 32\n xor rax, rax\n call printf\n jmp dfs_recursive_bt_return\ndfs_recursive_bt_size1:\n mov rdi, QWORD PTR [r12] # If the node has 1 child then call the function and print the id\n mov rsi, QWORD PTR [r12 + 8]\n call dfs_recursive_inorder_btree\n mov rdi, OFFSET fmt_tree\n mov rsi, r13\n shr rsi, 32\n xor rax, rax\n call printf\n jmp dfs_recursive_bt_return\ndfs_recursive_bt_size2:\n mov rdi, QWORD PTR [r12] # Same as above just print id inbetween the calls\n mov rsi, QWORD PTR [r12 + 8]\n call dfs_recursive_inorder_btree\n mov rdi, OFFSET fmt_tree\n mov rsi, r13\n shr rsi, 32\n xor rax, rax\n call printf\n mov rdi, QWORD PTR [r12 + 16]\n mov rsi, QWORD PTR [r12 + 24]\n call dfs_recursive_inorder_btree\ndfs_recursive_bt_return:\n pop r13\n pop r12\n ret\n\n# rdi - children ptr\n# rsi - value|children_size\ndfs_stack:\n push r12\n push r13\n push r14\n sub rsp, 16 # Create stack\n mov r12, rsp\n push rsi # Save node to use as pointer\n push rdi\n mov rdi, r12\n call get_stack # Init stack\n mov rdi, r12\n mov rsi, rsp\n call stack_push # Push node\n mov rdi, r12 # Pop stack\n call stack_pop\ndfs_stack_loop:\n test rax, rax # Test if stack is empty\n jz dfs_stack_return\n mov r13, rax\n mov rdi, OFFSET fmt_tree # Print id\n mov esi, DWORD PTR [r13 + 12]\n xor rax, rax\n call printf\n mov eax, DWORD PTR [r13 + 8] # Get start and end of array\n mov r13, QWORD PTR [r13]\n lea r14, [r13 + rax]\ndfs_stack_push_child:\n cmp r13, r14 # Check if the pointers are the same\n je dfs_stack_end_push\n mov rdi, r12 # Push node into the stack\n mov rsi, r13\n call stack_push\n add r13, tree_size\n jmp dfs_stack_push_child\ndfs_stack_end_push:\n mov rdi, r12 # Pop stack\n call stack_pop\n jmp dfs_stack_loop\ndfs_stack_return:\n mov rdi, r12 # Free stack\n call free_stack\n add rsp, 32\n pop r14\n pop r13\n pop r12\n ret\n\n# rdi - children ptr\n# rsi - value|children_size\nbfs_queue:\n push r12\n push r13\n push r14\n sub rsp, 20 # Create queue\n mov r12, rsp\n push rsi # Save node to use as pointer\n push rdi\n mov rdi, r12\n call get_queue # Init queue\n mov rdi, r12\n mov rsi, rsp\n call enqueue # enqueue node\n mov eax, DWORD PTR [r12 + 8]\n mov edi, DWORD PTR [r12 + 12]\nbfs_queue_loop:\n cmp eax, edi\n je bfs_queue_return\n mov rdi, r12 # dequeue\n call dequeue\n test rax, rax # Test if queue is empty\n jz bfs_queue_return\n mov r13, rax\n mov rdi, OFFSET fmt_tree # Print id\n mov esi, DWORD PTR [r13 + 12]\n xor rax, rax\n call printf\n mov eax, DWORD PTR [r13 + 8] # Get start and end of array\n mov r13, QWORD PTR [r13]\n lea r14, [r13 + rax]\nbfs_queue_push_child:\n cmp r13, r14 # Check if the pointers are the same\n je bfs_queue_end_push\n mov rdi, r12 # enqueue node\n mov rsi, r13\n call enqueue\n add r13, tree_size\n jmp bfs_queue_push_child\nbfs_queue_end_push:\n mov eax, DWORD PTR [r12 + 8]\n mov edi, DWORD PTR [r12 + 12]\n jmp bfs_queue_loop\nbfs_queue_return:\n mov rdi, r12 # Free queue\n call free_queue\n add rsp, 36\n pop r14\n pop r13\n pop r12\n ret\n\nmain:\n push r12\n push r13\n mov rdi, 3\n mov rsi, 3\n call create_tree\n mov r12, rax\n mov r13, rdx\n mov rdi, rax\n mov rsi, rdx\n call bfs_queue\n mov rdi, r12\n mov rsi, r13\n mov esi, esi\n call free_tree\n pop r13\n pop r12\n ret\n\n🦃 ⏹ 🍇\n 🔘 ⏫\n\n ❗️ 🔡 ➡️ 🔡 🍇\n ↪️ 🐕 🙌 🆕⏹⏫❗️ 🍇\n ↩️ 🔤The given tree is not binary!🔤\n 🍉\n ↩️ 🔤🔤\n 🍉\n🍉\n\n🐇 🌲 🍇\n 🖍🆕 id 🔢\n 🖍🆕 children 🍨🐚🌲🍆\n\n 🆕 depth_count 🔢 children_count 🔢 🍇\n 1 ➡️ 🖍id\n 🍨🍆 ➡️ 🖍children\n\n 🌌🐕 depth_count children_count❗️\n 🍉\n\n 🔐 🆕 ⭐️ given_id 🔢 depth_count 🔢 children_count 🔢 🍇\n given_id ➡️ 🖍id\n 🍨🍆 ➡️ 🖍children\n\n 🌌🐕 depth_count children_count❗️\n 🍉\n\n ❗️ 🆔 ➡️ 🔢 🍇\n ↩️ id\n 🍉\n\n ❗️ 🧒 ➡️ 🍨🐚🌲🍆 🍇\n ↩️ children\n 🍉\n\n 📗 Depth-First Search Recursive pre-order 📗\n ❗️ 🌀 🍇\n 😀 🔡 id 10❗️❗️\n\n 🔂 child children 🍇\n 🌀 child❗️\n 🍉\n 🍉\n\n 📗 Depth-First Search Recursive post-order 📗\n ❗️ 🍥 🍇\n 🔂 child children 🍇\n 🍥 child❗️\n 🍉\n\n 😀 🔡 id 10❗️❗️\n 🍉\n\n 📗\n Depth-First Search Recursive Inorder Binary\n This assumes only 2 children.\n 📗\n ❗️ 🍭 ➡️ 🍬⏹ 🍇\n ↪️ 🐔 children❗️ ▶️ 2 🍇\n ↩️ 🆕⏹⏫❗️\n 🍉\n\n ↪️ 🐔 children❗️ ▶️ 0 🍇\n 🍭🐽 children 0❗️❗️\n 😀 🔡 id 10❗️❗️\n 🍭🐽 children 1❗️❗️\n 🍉\n 🙅 🍇\n 😀 🔡 id 10❗️❗️\n 🍉\n ↩️ 🤷‍♀️\n 🍉\n\n 📗 Depth-First Search Stack 📗\n ❗️ 🥞 🍇\n 🍨 🐕 🍆 ➡️ stack\n\n 🔁 ❎ 🐔 stack❗️ 🙌 0❗️ 🍇\n 🐽 stack 🐔 stack❗️ ➖ 1❗️ ➡️ temp\n 🐨 stack 🐔 stack❗️ ➖ 1❗️\n\n 😀 🔡 🆔 temp❗️ 10❗️❗️\n\n 🧒 temp❗️ ➡️ temp_children\n 🔂 child temp_children 🍇\n 🐻 stack child❗️\n 🍉\n 🍉\n 🍉\n\n 📗 Breadth-First Search Queue 📗\n ❗️ 🏢 🍇\n 🍨 🐕 🍆 ➡️ queue\n\n 🔁 ❎ 🐔 queue❗️ 🙌 0❗️ 🍇\n 🐽 queue 0❗️ ➡️ temp\n 🐨 queue 0❗️\n\n 😀 🔡 🆔 temp❗️ 10❗️❗️\n\n 🧒 temp❗️ ➡️ temp_children\n 🔂 child temp_children 🍇\n 🐻 queue child❗️\n 🍉\n 🍉\n 🍉\n\n 🔐 ❗️ 🌌 depth_count 🔢 children_count 🔢 🍇\n ↪️ ❎ depth_count ◀️🙌 1❗️ 🍇\n 🔂 i 🆕⏩⏩ 0 children_count❗️ 🍇\n 🐻 children 🆕🌲⭐️ 🤜id ✖️ 10 ➕ i ➕ 1🤛 🤜depth_count ➖ 1🤛 children_count❗️❗️\n 🍉\n 🍉\n 🍉\n🍉\n\n🏁 🍇\n 🆕🌲🆕 3 3❗️ ➡️ tree\n 😀 🔤Tree Traversal🔤️❗️\n 😀 🔤🌀 - Depth-First Search Recursive pre-order🔤❗️\n 🌀tree❗️\n 😀 🔤🍥 - Depth-First Search Recursive post-order🔤❗️\n 🍥tree❗️\n 😀 🔤🥞 - Depth-First Search Stack🔤❗️\n 🥞tree❗️\n 😀 🔤🏢 - Breadth-First Search Queue🔤❗️\n 🏢tree❗️\n\n 😀 🔤🍭 - Depth-First Search Recursive Inorder Binary - Error🔤❗️\n 💭 Calling the Depth-First Search Recursive Inorder Binary method here does\n 💭 result in an error, since \"tree\" is not a binary tree.\n ️↪️ 🍭tree❗️ ➡️ return 🍇\n 😀 🔡return❗❗️️\n 🍉\n\n 🆕🌲🆕 3 2❗️ ➡️ binary_tree\n 😀 🔤🍭 - Depth-First Search Recursive Inorder Binary🔤❗️\n ️↪️ 🍭binary_tree❗️ ➡️ return 🍇\n 😀 🔡return❗❗️️\n 🍉\n🍉\n\n;;;; Tree traversal in Common Lisp\n\n(defstruct node data children)\n\n(defun dfs-recursive (node)\n \"A depth first approach for printing out all values in a tree.\"\n (when (node-data node)\n (format t \"~a \" (node-data node)))\n (loop for child in (node-children node) do\n (dfs-recursive child)))\n\n(defun dfs-recursive-postorder (node)\n \"A depth first approach for printing out all values in a tree starting from the bottom.\"\n (loop for child in (node-children node) do\n (dfs-recursive-postorder child))\n (when (node-data node)\n (format t \"~a \" (node-data node))))\n\n(defun dfs-recursive-inorder-btree (node)\n \"A depth first search approach for printing all values in a binary tree.\"\n (case (length (node-children node))\n (2\n (dfs-recursive-inorder-btree (first (node-children node)))\n (format t \"~a \" (node-data node))\n (dfs-recursive-inorder-btree (second (node-children node))))\n (1\n (dfs-recursive-inorder-btree (first (node-children node)))\n (format t \"~a \" (node-data node)))\n (0\n (format t \"~a \" (node-data node)))\n (t\n (print \"Invalid binary tree.\"))))\n\n(defun dfs-stack (node)\n \"A depth first approach for printing out all values in a tree using a stack.\"\n (loop\n with stack = (list node)\n with temp = nil\n while (> (length stack) 0) do\n (format t \"~a \" (node-data (first stack)))\n (setf temp (pop stack))\n (loop for child in (node-children temp) do\n (push child stack))))\n\n(defun bfs-queue (node)\n \"A breadth first search approach for printing out all values in a tree.\"\n (loop\n with queue = (list node)\n with temp = nil\n while (> (length queue) 0) do\n (format t \"~a \" (node-data (first queue)))\n (setf temp (pop queue))\n ;; If the queue is empty, the queue should be filled with the children nodes.\n (if (eql queue nil)\n (setf queue (node-children temp))\n (nconc queue (node-children temp)))))\n\n(defun make-tree (num-rows num-child)\n \"Creates a simple tree, where every node has 'num-child' children and is 'num-rows' deep.\"\n ;; A tree with 0 rows can't be created.\n (if (eql num-rows 0)\n (make-node\n :data 0\n :children nil)\n (make-node\n :data num-rows\n :children (loop repeat num-child collect (make-tree (1- num-rows) num-child)))))\n\n;; A tree for testing\n(defvar tree (make-tree 2 3))\n\n;; A binary tree for testing\n(defvar binary-tree (make-tree 3 2))\n\n;; Should print: 3 2 1 1 1 2 1 1 1 2 1 1 1\n(format t \"[#]~%Recursive DFS:~%\")\n(dfs-recursive tree)\n(format t \"~%\")\n\n;; Should print: 1 1 1 2 1 1 1 2 1 1 1 2 3\n(format t \"[#]~%Recursive Postorder DFS:~%\")\n(dfs-recursive-postorder tree)\n(format t \"~%\")\n\n;; Should print: 3 2 1 1 1 2 1 1 1 2 1 1 1\n(format t \"[#]~%Stack-based DFS:~%\")\n(dfs-stack tree)\n(format t \"~%\")\n\n;; Should print: 3 2 2 2 1 1 1 1 1 1 1 1 1\n(format t \"[#]~%Queue-based BFS:~%\")\n(bfs-queue tree)\n(format t \"~%\")\n\n;; Should print: 1 2 1 3 1 2 1\n(format t \"[#]~%Recursive Inorder DFS for Binary Tree:~%\")\n(dfs-recursive-inorder-btree binary-tree)\n(format t \"~%\")\n\nmain()\n\n%% Functions\n\nfunction root = create_tree()\n node = @(k,v) containers.Map(k,v);\n\n node2 = node(2, {{}}); node3 = node(3, {{}}); node4 = node(4, {{}});\n node6 = node(6, {{}}); node7 = node(7, {{}}); node8 = node(8, {{}});\n node10 = node(10, {{}}); node11 = node(11, {{}}); node12 = node(12, {{}});\n\n node1 = node(1, {node2, node3, node4});\n node5 = node(5, {node6, node7, node8});\n node9 = node(9, {node10, node11, node12});\n\n root = node(0, {node1, node5, node9});\nend\n\nfunction root = create_btree()\n node = @(k,v) containers.Map(k,v);\n\n node2 = node(2, {{}}); node3 = node(3, {{}});\n node5 = node(5, {{}}); node6 = node(6, {{}});\n\n node1 = node(1, {node2, node3});\n node4 = node(4, {node5, node6});\n\n root = node(0, {node1, node4});\nend\n\nfunction DFS_recursive(n)\n\n cell_index = @(a, b) a{b};\n ID = cell_index(keys(n), 1);\n\n fprintf('%u ', ID);\n\n children = cell_index(values(n), 1);\n for i = children\n child = i{1};\n if ~isempty(child)\n DFS_recursive(child);\n end\n end\nend\n\nfunction DFS_recursive_postorder(n)\n\n cell_index = @(a, b) a{b};\n\n children = cell_index(values(n), 1);\n for i = children\n child = i{1};\n if ~isempty(child)\n DFS_recursive_postorder(child);\n end\n end\n\n ID = cell_index(keys(n), 1);\n fprintf('%u ', ID);\n\nend\n\nfunction DFS_recursive_inorder_btree(n)\n\n cell_index = @(a, b) a{b};\n ID = cell_index(keys(n), 1);\n children = cell_index(values(n), 1);\n\n if length(children) == 2\n DFS_recursive_inorder_btree(children{1})\n fprintf('%u ', ID)\n DFS_recursive_inorder_btree(children{2})\n elseif length(children) == 1\n if ~isempty(children{1})\n DFS_recursive_inorder_btree(children{1})\n end\n fprintf('%u ', ID)\n else\n fprintf(\"Not a binary tree!\")\n end\nend\n\nfunction DFS_stack(n)\n\n cell_index = @(a, b) a{b};\n node_stack = {n};\n\n while ~isempty(node_stack)\n\n parent = node_stack{end};\n node_stack(end) = [];\n\n ID = cell_index(keys(parent), 1);\n fprintf('%u ', ID);\n\n children = cell_index(values(parent), 1);\n\n for i = flip(children)\n child = i{1};\n if ~isempty(child)\n node_stack = {node_stack{:} child};\n end\n end\n end\nend\n\nfunction BFS_queue(n)\n\n cell_index = @(a, b) a{b};\n node_queue = {n};\n\n while ~isempty(node_queue)\n next_nodes = {};\n for parent_cell = node_queue\n parent = parent_cell{1};\n ID = cell_index(keys(parent), 1);\n fprintf('%u ', ID);\n children = cell_index(values(parent), 1);\n for i = children\n child = i{1};\n if ~isempty(child)\n next_nodes = {next_nodes{:}, child};\n end\n end\n end\n node_queue = next_nodes;\n end\nend\n\nfunction main()\n root = create_tree();\n rootb = create_btree();\n\n fprintf('\\nDFS Recursive\\n')\n DFS_recursive(root)\n\n fprintf('\\nDFS Recursive Postorder\\n')\n DFS_recursive_postorder(root)\n\n fprintf('\\nDFS Recursive Inorder Binary Tree\\n')\n DFS_recursive_inorder_btree(rootb)\n\n fprintf('\\nDFS Stack\\n')\n DFS_stack(root)\n\n fprintf('\\nBFS Queue\\n')\n BFS_queue(root) \n fprintf('\\n')\nend\n\nfrom collections import deque\n\ndata Node(value: int, children: Node[])\n\ndef dfs_recursive(Node(value, children)):\n \"\"\"A depth first approach for printing out all values in a tree.\"\"\"\n print(value, end=' ')\n for child in children:\n dfs_recursive(child)\n\ndef dfs_recursive_postorder(Node(value, children)):\n \"\"\"A depth first approach for printing out all values in a tree starting from the bottom.\"\"\"\n for child in children:\n dfs_recursive_postorder(child)\n print(value, end=' ')\n\ndef dfs_recursive_inorder_btree(Node(value, children)):\n \"\"\"A depth first search approach for printing all values in a binary tree.\"\"\"\n case len(children):\n match 2:\n dfs_recursive_inorder_btree(children[0])\n print(value, end=' ')\n dfs_recursive_inorder_btree(children[1])\n match 1:\n dfs_recursive_inorder_btree(children[0])\n print(value, end=' ')\n match 0:\n print(value, end=' ')\n else:\n print('Invalid binary tree')\n\ndef dfs_stack(node is Node):\n \"\"\"A depth first approach for printing out all values in a tree using a stack.\"\"\"\n stack = [node]\n while stack:\n current_node = stack.pop()\n print(current_node.value, end=' ')\n for child in current_node.children:\n stack.append(child)\n\ndef bfs_queue(node is Node):\n \"\"\"A breadth first search approach for printing out all values in a tree.\"\"\"\n queue = deque([node])\n while queue:\n current_node = queue.popleft()\n print(current_node.value, end=' ')\n for child in current_node.children:\n queue.append(child)\n\ndef create_tree(num_rows, num_child):\n \"\"\"Creates a simple tree, where every node has\n 'num_child' children and is 'num_rows' deep.\"\"\"\n if num_rows == 0:\n return Node(0, ())\n else:\n return Node(num_rows, tuple(create_tree(num_rows-1, num_child)\n for _ in range(num_child)))\n\n\nif __name__ =='__main__':\n # A ternary tree for testing\n tree = create_tree(2, 3)\n\n print(\"[#]\\nRecursive DFS:\")\n dfs_recursive(tree)\n print()\n\n print(\"[#]\\nRecursive Postorder DFS:\")\n dfs_recursive_postorder(tree)\n print()\n\n print(\"[#]\\nStack-based DFS:\")\n dfs_stack(tree)\n print()\n\n print(\"[#]\\nQueue-based BFS:\")\n bfs_queue(tree)\n print()\n\n # And a binary tree for testing\n binary_tree = create_tree(3, 2)\n\n print(\"[#]\\nRecursive Inorder DFS for Binary Tree:\")\n dfs_recursive_inorder_btree(binary_tree)\n print()\n\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"DFSpreorder\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"DFSpostorder\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"DFSinorder\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"BFSsimple\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/euclidean_algorithm/euclidean_algorithm.html":{"url":"contents/euclidean_algorithm/euclidean_algorithm.html","title":"Euclidean Algorithm","keywords":"","body":"Euclidean Algorithm\nComputer science is (almost by definition) a science about computers -- a device first conceptualized in the 1800's. Computers have become so revolutionary, that it is difficult to think of our lives today without them. That said, algorithms are much older and have existed in the world for millennia. Incredibly, a few of the algorithms created before the Common Era (AD) are still in use today. One such algorithm was first described in Euclid's Elements (~ 300 BC) and has come to be known as the Euclidean Algorithm.\nThe algorithm is a simple way to find the greatest common divisor (GCD) of two numbers, which is useful for a number of different applications (like reducing fractions). The first method (envisioned by Euclid) uses simple subtraction:\nfunction s:euclid_sub(a, b)\n let l:a = abs(a:a)\n let l:b = abs(a:b)\n\n while l:a != l:b\n if l:a > l:b\n let l:a -= l:b\n else\n let l:b -= l:a\n endif\n endwhile\n\n return l:a\nendfunction\n\nint euclid_sub(int a, int b) {\n a = abs(a);\n b = abs(b);\n\n while (a != b) {\n if (a > b) {\n a -= b;\n } else {\n b -= a;\n }\n }\n\n return a;\n}\n\npublic int EuclidSub(int a, int b)\n{\n // Math.Abs for negative number support\n a = Math.Abs(a);\n b = Math.Abs(b);\n\n while (a != b)\n {\n if (a > b)\n a = a - b;\n else\n b = b - a;\n }\n\n return a;\n}\n\n(defn euclid-sub [a b]\n (loop [i (Math/abs a) j (Math/abs b)]\n (if (= i j)\n i\n (if (> i j)\n (recur (- i j) j)\n (recur i (- j i))))))\n\nint euclid_sub(int a, int b) {\n a = std::abs(a);\n b = std::abs(b);\n\n while (a != b) {\n if (a > b) {\n a -= b;\n } else {\n b -= a;\n }\n }\n\n return a;\n}\n\npublic static int euclidSub(int a, int b) {\n a = Math.abs(a);\n b = Math.abs(b);\n\n while (a != b) {\n if (a > b) {\n a -= b;\n } else {\n b -= a;\n }\n }\n\n return a;\n}\n\nfun euclidSub(a: Int, b: Int): Int {\n var a = a.absoluteValue\n var b = b.absoluteValue\n\n while (a != b) {\n if (a > b) a -= b\n else b -= a\n }\n\n return a\n}\n\nfunction euclidSub(a, b) {\n a = Math.abs(a);\n b = Math.abs(b);\n\n while (a !== b) {\n if (a > b) {\n a -= b;\n } else {\n b -= a;\n }\n }\n\n return a;\n}\n\n(defun euclid-sub (a b)\n \"Finds the greatest common divsor for any two integers\"\n (defun euclid-sub* (a b)\n \"Finds the greatest common divisor for any two positive integers\"\n (if (eql a b)\n a\n (if (> a b)\n (euclid-sub* (- a b) b)\n (euclid-sub* a (- b a)))))\n (euclid-sub* (abs a) (abs b)))\n\ndef euclid_sub(a, b):\n\n a = abs(a)\n b = abs(b)\n\n if a == 0:\n return b\n elif b == 0:\n return a\n\n while a != b:\n if a > b:\n a -= b\n else:\n b -= a\n\n return a\n\neuclidSub :: Integer -> Integer -> Integer\neuclidSub a b = inner (abs a) (abs b)\n where\n inner x y\n -- if a = b, then the gcd is a\n | x == y = x\n -- if a \nfn euclid_sub(mut a: i64, mut b: i64) -> i64 {\n a = a.abs();\n b = b.abs();\n while a != b {\n if a \nlet euclid_sub a b =\n let rec inner a b =\n if a = b then\n a\n else if a \nfunc euclidSub(a, b int) int {\n a = abs(a)\n b = abs(b)\n\n for a != b {\n if a > b {\n a -= b\n } else {\n b -= a\n }\n }\n\n return a\n}\n\nfunc euclidSub(a: Int, b: Int) -> Int {\n var a = abs(a)\n var b = abs(b)\n\n while (a != b) {\n if (a > b) {\n a -= b\n } else {\n b -= a\n }\n }\n\n return a\n}\n\nfunction gcd = euclidSub(a,b)\n\n a = abs(a);\n b = abs(b);\n\n while a ~= b\n if a > b\n a = a - b;\n else\n b = b - a;\n end\n end\n\n gcd = a;\nend\n\nlocal function euclid_sub(a, b)\n a = math.abs(a)\n b = math.abs(b)\n\n while a ~= b do\n if a > b then\n a = a-b\n else\n b = b-a\n end\n end\n\n return a\nend\n\nfunction euclid_sub(a::Int64, b::Int64)\n a = abs(a)\n b = abs(b)\n\n while (a != b)\n if (a > b)\n a -= b\n else\n b -= a\n end\n end\n\n return a\nend\n\nfunc euclid_sub(in1, in2: int): int =\n var\n a = abs(in1)\n b = abs(in2)\n\n while a != b:\n if a > b:\n a -= b\n else:\n b -= a\n\n result = a\n\n\neuclid_sub:\n mov rax, rdi # Get abs of a\n sar rax, 31\n xor rdi, rax\n sub rdi, rax\n mov rax, rsi # Get abs of b\n sar rax, 31\n xor rsi, rax\n sub rsi, rax\n jmp check\nloop:\n cmp rdi, rsi # Find which is bigger\n jle if_true\n sub rdi, rsi # If a is bigger then a -= b\n jmp check\nif_true:\n sub rsi, rdi # Else b -= a\ncheck:\n cmp rsi, rdi # Check if a and b are not equal\n jne loop\n mov rax, rdi # Return results\n\nINTEGER FUNCTION euclid_sub(a, b)\n IMPLICIT NONE\n INTEGER, INTENT(INOUT) :: a, b\n\n a = ABS(a)\n b = ABS(b)\n\n DO WHILE (a /= b)\n\n IF (a > b) THEN\n a = a - b\n ELSE\n b = b - a\n END IF\n END DO\n\n euclid_sub = a\n\nEND FUNCTION euclid_sub\n\nfunction euclid_sub(int $a, int $b): int\n{\n $a = abs($a);\n $b = abs($b);\n\n while ($a !== $b) {\n if ($a > $b) {\n $a = $a - $b;\n } else {\n $b = $b - $a;\n }\n }\n\n return $a;\n}\n\n: euclid- ( a b -- gcd )\n [ abs ] bi@\n [ 2dup = ]\n [\n ! make sure the lower number is deeper\n 2dup >= [ swap ] when\n over -\n ! leaves us with stack { }\n ]\n until\n ! we have the GCD twice now, drop one\n drop\n;\n\nEuclidian algorithm subtraction method.\nEnter two positive integers. \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nThe \nend.\n\ndef euclid_sub(a: Int, b: Int): Int =\n (Math.abs(a), Math.abs(b)) match {\n case (0, _) | (_, 0) => 0\n case (x, y) if x euclid_sub(x, y - x)\n case (x, y) if x > y => euclid_sub(x - y, y)\n case _ => a\n\n(define (euclid_sub a b)\n (local ((define (euclid_sub* x y)\n (if (= x y)\n x\n (if (> x y)\n (euclid_sub* (- x y) y)\n (euclid_sub* x (- y x))\n )\n )\n )) (euclid_sub* (abs a) (abs b))\n )\n )\n\ndef gcd_minus(a, b)\n a = a.abs\n b = b.abs\n until a == b\n if a > b\n a -= b\n else\n b -= a\n end\n end\n a\nend\n\nInteger>>euclidSub: secondNumber\n \"Euclidean algorithm with subtraction\"\n | a b |\n a := self abs.\n b := secondNumber abs.\n [ a == b ] whileFalse: [ \n a > b ifTrue: [ \n a := a - b.\n ] ifFalse: [ \n b := b - a.\n ].\n ].\n ^a.\n\n🐇 ❗️ 🔼 a 🔢 b 🔢 ➡️ 🔢 🍇\n 💭 Use 🏧 (returns the absolute value) to support negative numbers.\n 🏧a ❗️ ➡️ 🖍🆕var_a\n 🏧b ❗️ ➡️ 🖍🆕var_b\n\n ️🔁 ❎ var_a 🙌 var_b ❗️ 🍇\n ↪️ var_a ▶️ var_b 🍇\n var_a ⬅️ ➖ var_b\n 🍉\n 🙅 🍇\n var_b ⬅️ ➖ var_a\n 🍉\n 🍉\n\n ↩️ var_a\n🍉\n\nHOW IZ I UKLIDSUP YR NUM1 AN YR NUM2\n NUM1 R I IZ ABZ YR NUM1 MKAY\n NUM2 R I IZ ABZ YR NUM2 MKAY\n\n IM IN YR LOOP \n BOTH SAEM NUM1 AN NUM2, O RLY?\n YA RLY, FOUND YR NUM1\n OIC \n\n DIFFRINT NUM1 AN SMALLR OF NUM1 AN NUM2, O RLY?\n YA RLY, NUM1 R DIFF OF NUM1 AN NUM2\n NO WAI, NUM2 R DIFF OF NUM2 AN NUM1\n OIC\n IM OUTTA YR LOOP\n\nIF U SAY SO\n\neuclid_sub() {\n local a\n local b\n a=$(abs \"$1\")\n b=$(abs \"$2\")\n\n while (( a != b )); do\n if (( a > b )); then\n ((a -= b))\n else\n ((b -= a))\n fi\n done\n printf \"%s\" \"$a\"\n}\n\n// Euclidean algorithm with subtraction\nint euclid_sub(int a, int b) {\n a = abs(a);\n b = abs(b);\n\n while (a != b) {\n if (a > b) {\n a -= b;\n } else {\n b -= a;\n }\n }\n\n return a;\n}\n\n\n \n\n(define (euclid-sub a b)\n (cond \n [(or (negative? a)(negative? b))(euclid-sub (abs a)(abs b))] \n [(eq? a b) a]\n [(> a b)(euclid-sub(- a b) b)]\n [else\n (euclid-sub a (- b a))]))\n\n\n \n\nleave one line empty:\nfunction Sub-Euclid($a, $b) {\n $a = [Math]::Abs($a)\n $b = [Math]::Abs($b)\n\n while ($a -ne $b) {\n if ($a -gt $b) {\n $a = $a - $b\n } else {\n $b = $b - $a\n }\n }\n\n return $a\n}\n\ndef euclid_sub(a is int, 0) = a\naddpattern def euclid_sub(0, b is int) = b\n\naddpattern def euclid_sub(a is int, b is int):\n if a \n\n\nHere, we simply line the two numbers up every step and subtract the lower value from the higher one every timestep. Once the two values are equal, we call that value the greatest common divisor. A graph of a and b as they change every step would look something like this:\n\n \n\n\nModern implementations, though, often use the modulus operator (%) like so\nfunction s:euclid_mod(a, b)\n let l:a = abs(a:a)\n let l:b = abs(a:b)\n\n while l:b != 0\n let l:c = l:b\n let l:b = l:a % l:b\n let l:a = l:c\n endwhile\n\n return l:a\nendfunction\n\nint euclid_mod(int a, int b) {\n a = abs(a);\n b = abs(b);\n\n while (b != 0) {\n int temp = b;\n b = a % b;\n a = temp;\n }\n\n return a;\n}\n\npublic int EuclidMod(int a, int b)\n{\n // Math.Abs for negative number support\n a = Math.Abs(a);\n b = Math.Abs(b);\n\n while (b != 0)\n {\n var temp = b;\n b = a % b;\n a = temp;\n }\n\n return a;\n}\n\n(defn euclid-mod [a b]\n (loop [i (Math/abs a) j (Math/abs b)]\n (if (zero? j)\n i\n (recur j (% i j)))))\n\n// Euclidean algorithm using modulus\nint euclid_mod(int a, int b) {\n a = std::abs(a);\n b = std::abs(b);\n\n while (b != 0) {\n a = std::exchange(b, a % b);\n }\n\n return a;\n}\n\npublic static int euclidMod(int a, int b) {\n while (b != 0) {\n int tmp = b;\n b = a % b;\n a = tmp;\n }\n\n return a;\n}\n\nfun euclidMod(a: Int, b: Int): Int {\n var a = a.absoluteValue\n var b = b.absoluteValue\n\n while (b != 0) {\n val tmp = b\n b = a % b\n a = tmp\n }\n\n return a\n}\n\nfunction euclidMod(a, b) {\n a = Math.abs(a);\n b = Math.abs(b);\n\n let temp;\n while (b !== 0) {\n temp = b;\n b = a % b;\n a = temp;\n }\n\n return a;\n}\n\n(defun euclid-mod (a b)\n \"Finds the greatest common divisor for any two integers\"\n (if (zerop b)\n (abs a)\n (euclid-mod b (mod a b))))\n\ndef euclid_mod(a, b):\n\n a = abs(a)\n b = abs(b)\n\n while b > 0:\n a, b = b, a % b\n\n return a\n\neuclidMod :: Integer -> Integer -> Integer\neuclidMod a b = inner (abs a) (abs b)\n where\n -- if a divides b, then gcd is a\n inner x 0 = x\n -- otherwise, recursively call inner with b and (a mod b) as new inputs\n inner x y = inner y (x `mod` y)\n\nfn euclid_rem(mut a: i64, mut b: i64) -> i64 {\n a = a.abs();\n b = b.abs();\n while b != 0 {\n let tmp = b;\n b = a % b;\n a = tmp;\n }\n\n a\n}\n\nlet euclid_mod a b =\n let rec inner a = function\n | 0 -> a\n | b -> inner b (a mod b)\n in (inner (abs a) (abs b))\n\nfunc euclidMod(a, b int) int {\n a = abs(a)\n b = abs(b)\n\n for b != 0 {\n a, b = b, a%b\n }\n\n return a\n}\n\nfunc euclidMod(a: Int, b: Int) -> Int {\n var a = abs(a);\n var b = abs(b);\n\n while (b != 0) {\n let temp = b\n b = a % b\n a = temp\n }\n\n return a\n}\n\nfunction gcd = euclidMod(a,b)\n\n a=abs(a);\n b=abs(b);\n\n while b > 0\n temp = b;\n b = mod(a,b);\n a = temp;\n end\n\n gcd = a;\nend\n\nlocal function euclid_mod(a, b)\n a = math.abs(a)\n b = math.abs(b)\n\n while b ~= 0 do\n a, b = b, a%b\n end\n\n return a\nend\n\nfunction euclid_mod(a::Int64, b::Int64)\n a = abs(a)\n b = abs(b)\n\n while(b != 0)\n b,a = a%b,b\n end\n\n return a\nend\n\nfunc euclid_mod(in1, in2: int): int =\n var\n a = abs(in1)\n b = abs(in2)\n\n while b != 0:\n let temp: int = b\n b = a mod b\n a = temp;\n\n result = a\n\n\n# rdi - a\n# rsi - b\n# RET rax - gcd of a and b\neuclid_mod:\n mov rax, rdi # Get abs of a\n sar rax, 31\n xor rdi, rax\n sub rdi, rax\n mov rax, rsi # Get abs of b\n sar rax, 31\n xor rsi, rax\n sub rsi, rax\n jmp mod_check\nmod_loop:\n xor rdx, rdx # Take the mod of a and b\n mov rax, rdi\n div rsi\n mov rdi, rsi # Set b to the mod of a and b\n mov rsi, rdx # Set a to b\nmod_check:\n cmp rsi, 0 # Check if b is non-zero\n jne mod_loop\n mov rax, rdi # Return the result\n\nINTEGER FUNCTION euclid_mod(a, b)\n IMPLICIT NONE\n INTEGER, INTENT(INOUT) :: a, b\n INTEGER :: temp\n\n DO WHILE (b > 0)\n temp = b\n b = MODULO(a,b)\n a = temp\n END DO\n\n euclid_mod = a\n\nEND FUNCTION euclid_mod\n\nfunction euclid_mod(int $a, int $b): int\n{\n $a = abs($a);\n $b = abs($b);\n\n while ($b !== 0) {\n list($b, $a) = [$a % $b, $b];\n }\n\n return $a;\n}\n\n: euclid% ( a b -- gcd )\n [ abs ] bi@ ! take both absolute values\n [ dup zero? ] ! check if `b` (on top) is 0\n [\n ! a b -> a b b -> b a b -> b a%b\n dup -rot mod\n ]\n until\n ! the zero is on top, so get rid of it\n drop\n;\n\nEuclidian algorithm modulo method.\nEnter two positive integers. \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nThe\nend.\n\n\ndef euclid_mod(a: Int, b: Int): Int =\n (Math.abs(a), Math.abs(b)) match {\n case (_, 0) => a\n case (a, b) => euclid_mod(b, a % b)\n\n(define (euclid_mod a b)\n (local ((define (euclid_mod* a b)\n (if (= 0 b)\n (abs a)\n (euclid_mod* b (modulo a b))\n )\n )) (euclid_mod* a b)\n )\n )\n\ndef gcd_mod(a, b)\n a = a.abs\n b = b.abs\n a, b = b, a%b until b.zero?\n a\nend\n\nInteger>>euclidMod: secondNumber\n \"Euclidean algorithm with modulus.\"\n | a b oldB |\n a := self abs.\n b := secondNumber abs.\n [ b == 0 ] whileFalse: [ \n oldB := b.\n b := a % b.\n a := oldB.\n ].\n ^a.\n\n🐇 ❗️ ⏫ a 🔢 b 🔢 ➡️ 🔢 🍇\n 💭 Use 🏧 (returns the absolute value) to support negative numbers.\n 🏧a ❗️ ➡️ 🖍🆕var_a\n 🏧b ❗️ ➡️ 🖍🆕var_b\n\n ️🔁 ❎ var_b 🙌 0 ❗️ 🍇\n var_b ➡️ temp\n var_a 🚮 var_b ➡️ 🖍var_b\n temp ➡️ 🖍var_a\n 🍉\n\n ↩️ var_a\n🍉\n\nHOW IZ I UKLIDMOD YR NUM1 AN YR NUM2\n NUM1 R I IZ ABZ YR NUM1 MKAY\n NUM2 R I IZ ABZ YR NUM2 MKAY\n\n IM IN YR LOOP \n BOTH SAEM NUM2 AN 0, O RLY?\n YA RLY, FOUND YR NUM1\n OIC\n\n I HAS A TMP ITZ NUM2\n NUM2 R MOD OF NUM1 AN NUM2\n NUM1 R TMP\n IM OUTTA YR LOOP\n\nIF U SAY SO\n\neuclid_mod() {\n local a\n local b\n a=$(abs \"$1\")\n b=$(abs \"$2\")\n\n while (( b != 0 )); do\n ((tmp = b))\n ((b = a % b))\n ((a = tmp))\n done\n printf \"%s\" \"$a\"\n}\n\n// Euclidean algorithm using modulus\nint euclid_mod(int a, int b) {\n int tmp;\n a = abs(a);\n b = abs(b);\n\n while (b != 0) {\n tmp = a % b;\n a = b;\n b = tmp;\n }\n\n return a;\n}\n\n\n \n\n(define (euclid-mod a b)\n (if (zero? b)\n a\n (euclid-mod b (modulo a b))))\n\n\n \n\nleave one line empty:\nfunction Mod-Euclid($a, $b) {\n $a = [Math]::Abs($a)\n $b = [Math]::Abs($b)\n\n while ($b -ne 0) {\n $tmp = $b\n $b = $a % $b\n $a = $tmp\n }\n\n return $a\n}\n\ndef euclid_mod(a is int, 0) = a\naddpattern def euclid_mod(0, b is int) = b\n\naddpattern def euclid_mod(a is int, b is int) = euclid_mod(b, a % b)\n\n\n\nHere, we set b to be the remainder of a%b and a to be whatever b was last timestep. Because of how the modulus operator works, this will provide the same information as the subtraction-based implementation, but when we show a and b as they change with time, we can see that it might take many fewer steps:\n\n \n\n\nThe Euclidean Algorithm is truly fundamental to many other algorithms throughout the history of computer science and will definitely be used again later. At least to me, it's amazing how such an ancient algorithm can still have modern use and appeal. That said, there are still other algorithms out there that can find the greatest common divisor of two numbers that are arguably better in certain cases than the Euclidean algorithm, but the fact that we are discussing Euclid two millennia after his death shows how timeless and universal mathematics truly is. I think that's pretty cool.\nVideo Explanation\nHere's a video on the Euclidean algorithm:\n\n\n\n\nExample Code\nfunction s:euclid_mod(a, b)\n let l:a = abs(a:a)\n let l:b = abs(a:b)\n\n while l:b != 0\n let l:c = l:b\n let l:b = l:a % l:b\n let l:a = l:c\n endwhile\n\n return l:a\nendfunction\n\nfunction s:euclid_sub(a, b)\n let l:a = abs(a:a)\n let l:b = abs(a:b)\n\n while l:a != l:b\n if l:a > l:b\n let l:a -= l:b\n else\n let l:b -= l:a\n endif\n endwhile\n\n return l:a\nendfunction\n\nlet s:check_1 = s:euclid_mod(64 * 67, 64 * 71)\nlet s:check_2 = s:euclid_sub(128 * 12, 128 * 77)\n\necho 'Modulus-based euclidean algorithm result:' s:check_1\necho 'subtraction-based euclidean algorithm result:' s:check_2\n\n#include \n#include \n\nint euclid_mod(int a, int b) {\n a = abs(a);\n b = abs(b);\n\n while (b != 0) {\n int temp = b;\n b = a % b;\n a = temp;\n }\n\n return a;\n}\n\nint euclid_sub(int a, int b) {\n a = abs(a);\n b = abs(b);\n\n while (a != b) {\n if (a > b) {\n a -= b;\n } else {\n b -= a;\n }\n }\n\n return a;\n}\n\nint main() {\n int check1 = euclid_mod(64 * 67, 64 * 81);\n int check2 = euclid_sub(128 * 12, 128 * 77);\n\n printf(\"[#]\\nModulus-based euclidean algorithm result:\\n%d\\n\", check1);\n printf(\"[#]\\nSubtraction-based euclidean algorithm result:\\n%d\\n\", check2);\n\n return 0;\n}\n\nEuclideanAlgorithm.cs\n// submitted by Julian Schacher (jspp)\nusing System;\n\nnamespace EuclideanAlgorithm\n{\n public class EuclideanAlgorithm\n {\n public int EuclidSub(int a, int b)\n {\n // Math.Abs for negative number support\n a = Math.Abs(a);\n b = Math.Abs(b);\n\n while (a != b)\n {\n if (a > b)\n a = a - b;\n else\n b = b - a;\n }\n\n return a;\n }\n\n public int EuclidMod(int a, int b)\n {\n // Math.Abs for negative number support\n a = Math.Abs(a);\n b = Math.Abs(b);\n\n while (b != 0)\n {\n var temp = b;\n b = a % b;\n a = temp;\n }\n\n return a;\n }\n }\n}\n\nProgram.cs\n// submitted by Julian Schacher (jspp)\nusing System;\n\nnamespace EuclideanAlgorithm\n{\n class Program\n {\n static void Main(string[] args)\n {\n var euclideanAlgorithm = new EuclideanAlgorithm();\n int check = euclideanAlgorithm.EuclidMod(64 * 67, 64 * 81);\n int check2 = euclideanAlgorithm.EuclidSub(128 * 12, 128 * 77);\n\n Console.WriteLine(\"[#]\\nModulus-based euclidean algorithm result:\");\n Console.WriteLine(check);\n Console.WriteLine(\"[#]\\nSubtraction-based euclidean algorithm result:\");\n Console.WriteLine(check2);\n }\n }\n}\n\n;; earthfail\n(defn euclid-sub [a b]\n (loop [i (Math/abs a) j (Math/abs b)]\n (if (= i j)\n i\n (if (> i j)\n (recur (- i j) j)\n (recur i (- j i))))))\n(defn euclid-mod [a b]\n (loop [i (Math/abs a) j (Math/abs b)]\n (if (zero? j)\n i\n (recur j (% i j)))))\n\n(print\n (euclid-sub (* 64 67)\n (* 64 81))\n (euclid-mod (* 128 12)\n (* 128 77)))\n\n#include \n#include \n#include \n\n// Euclidean algorithm using modulus\nint euclid_mod(int a, int b) {\n a = std::abs(a);\n b = std::abs(b);\n\n while (b != 0) {\n a = std::exchange(b, a % b);\n }\n\n return a;\n}\n\n// Euclidean algorithm with subtraction\nint euclid_sub(int a, int b) {\n a = std::abs(a);\n b = std::abs(b);\n\n while (a != b) {\n if (a > b) {\n a -= b;\n } else {\n b -= a;\n }\n }\n\n return a;\n}\n\nint main() {\n auto check1 = euclid_mod(64 * 67, 64 * 81);\n auto check2 = euclid_sub(128 * 12, 128 * 77);\n\n std::cout \n// submitted by lolatomroflsinnlos, modified by xam4lor\npublic class EuclideanAlgo {\n public static int euclidSub(int a, int b) {\n a = Math.abs(a);\n b = Math.abs(b);\n\n while (a != b) {\n if (a > b) {\n a -= b;\n } else {\n b -= a;\n }\n }\n\n return a;\n }\n\n public static int euclidMod(int a, int b) {\n while (b != 0) {\n int tmp = b;\n b = a % b;\n a = tmp;\n }\n\n return a;\n }\n\n public static void main(String[] args) {\n System.out.println(\"[#]\\nModulus-based euclidean algorithm result:\");\n System.out.println(euclidMod(64 * 67, 64 * 81));\n System.out.println(\"[#]\\nSubtraction-based euclidean algorithm result:\");\n System.out.println(euclidSub(128 * 12, 128 * 77));\n }\n}\n\nimport kotlin.math.absoluteValue\n\nfun euclidSub(a: Int, b: Int): Int {\n var a = a.absoluteValue\n var b = b.absoluteValue\n\n while (a != b) {\n if (a > b) a -= b\n else b -= a\n }\n\n return a\n}\n\nfun euclidMod(a: Int, b: Int): Int {\n var a = a.absoluteValue\n var b = b.absoluteValue\n\n while (b != 0) {\n val tmp = b\n b = a % b\n a = tmp\n }\n\n return a\n}\n\nfun main(args: Array) {\n println(\"[#]\\nModulus-based euclidean algorithm result:\")\n println(euclidMod(64 * 67, 64 * 81))\n println(\"[#]\\nSubtraction-based euclidean algorithm result:\")\n println(euclidSub(128 * 12, 128 * 77))\n}\n\nfunction euclidMod(a, b) {\n a = Math.abs(a);\n b = Math.abs(b);\n\n let temp;\n while (b !== 0) {\n temp = b;\n b = a % b;\n a = temp;\n }\n\n return a;\n}\n\nfunction euclidSub(a, b) {\n a = Math.abs(a);\n b = Math.abs(b);\n\n while (a !== b) {\n if (a > b) {\n a -= b;\n } else {\n b -= a;\n }\n }\n\n return a;\n}\n\nconsole.log('[#]\\nModulus-based euclidean algorithm result:')\nconsole.log(euclidMod(64 * 67, 64 * 81));\nconsole.log('[#]\\nSubtraction-based euclidean algorithm result:')\nconsole.log(euclidSub(128 * 12, 128 * 77));\n\n;;;; Euclidean algorithm implementation in Common Lisp\n\n(defun euclid-sub (a b)\n \"Finds the greatest common divsor for any two integers\"\n (defun euclid-sub* (a b)\n \"Finds the greatest common divisor for any two positive integers\"\n (if (eql a b)\n a\n (if (> a b)\n (euclid-sub* (- a b) b)\n (euclid-sub* a (- b a)))))\n (euclid-sub* (abs a) (abs b)))\n\n(defun euclid-mod (a b)\n \"Finds the greatest common divisor for any two integers\"\n (if (zerop b)\n (abs a)\n (euclid-mod b (mod a b))))\n\n(format T \"[#]~%Modulus-based euclidean algorithm result:~%\")\n(format T \"~d~%\" (euclid-sub (* 64 67) (* 64 81)))\n(format T \"[#]~%Subtraction-based euclidean algorithm result:~%\")\n(format T \"~d~%\" (euclid-mod (* 128 12) (* 128 77)))\n\n;; Quick test\n(assert\n (eql (euclid-sub (* 64 67) (* 64 81))\n (gcd (* 64 67) (* 64 81))))\n\n(assert\n (eql (euclid-mod (* 64 67) (* 64 81))\n (gcd (* 64 67) (* 64 81))))\n\ndef euclid_mod(a, b):\n\n a = abs(a)\n b = abs(b)\n\n while b > 0:\n a, b = b, a % b\n\n return a\n\ndef euclid_sub(a, b):\n\n a = abs(a)\n b = abs(b)\n\n if a == 0:\n return b\n elif b == 0:\n return a\n\n while a != b:\n if a > b:\n a -= b\n else:\n b -= a\n\n return a\n\nif __name__==\"__main__\":\n print('[#]\\nModulus-based euclidean algorithm result:'),\n print(euclid_mod(64 * 67, 64 * 81))\n print('[#]\\nSubtraction-based euclidean algorithm result:')\n print(euclid_sub(128 * 12, 128 * 77))\n\n-- Method 1: Euclid's original subtraction algorithm\n\neuclidSub :: Integer -> Integer -> Integer\neuclidSub a b = inner (abs a) (abs b)\n where\n inner x y\n -- if a = b, then the gcd is a\n | x == y = x\n -- if a Integer -> Integer\neuclidMod a b = inner (abs a) (abs b)\n where\n -- if a divides b, then gcd is a\n inner x 0 = x\n -- otherwise, recursively call inner with b and (a mod b) as new inputs\n inner x y = inner y (x `mod` y)\n\n-- _________________________________________________________________________\n\n-- Examples\n\nmain :: IO ()\nmain = do\n let chk1 = euclidMod (64 * 67) (64 * 81)\n chk2 = euclidSub (128 * 12) (128 * 77)\n putStrLn \"[#]\\nModulus-based euclidean algorithm result:\"\n print chk1\n putStrLn \"[#]\\nSubtraction-based euclidean algorithm result:\"\n print chk2\n\n// contributed by Nicole Mazzuca (ubsan)\n\nfn euclid_sub(mut a: i64, mut b: i64) -> i64 {\n a = a.abs();\n b = b.abs();\n while a != b {\n if a i64 {\n a = a.abs();\n b = b.abs();\n while b != 0 {\n let tmp = b;\n b = a % b;\n a = tmp;\n }\n\n a\n}\n\nfn main() {\n let chk1 = euclid_rem(64 * 67, 64 * 81);\n let chk2 = euclid_sub(128 * 12, 128 * 77);\n println!(\"[#]\\nModulus-based euclidean algorithm result:\\n{}\", chk1);\n println!(\"[#]\\nSubtraction-based euclidean algorithm result:\\n{}\", chk2);\n}\n\n(* contributed by Nicole Mazzuca (ubsan) *)\n\nlet euclid_mod a b =\n let rec inner a = function\n | 0 -> a\n | b -> inner b (a mod b)\n in (inner (abs a) (abs b))\n\nlet euclid_sub a b =\n let rec inner a b =\n if a = b then\n a\n else if a print_int |> print_newline;\n Printf.printf \"[#]\\nSubtraction-based euclidean algorithm result:\\n\";\n chk2 |> print_int |> print_newline\n\n// Submitted by Chinmaya Mahesh (chin123)\n\npackage main\n\nimport \"fmt\"\n\nfunc abs(a int) int {\n if a b {\n a -= b\n } else {\n b -= a\n }\n }\n\n return a\n}\n\nfunc main() {\n check1 := euclidMod(64*67, 64*81)\n check2 := euclidSub(128*12, 128*77)\n\n fmt.Println(\"[#]\\nModulus-based euclidean algorithm result:\")\n fmt.Println(check1)\n fmt.Println(\"[#]\\nSubtraction-based euclidean algorithm result:\")\n fmt.Println(check2)\n}\n\nfunc euclidSub(a: Int, b: Int) -> Int {\n var a = abs(a)\n var b = abs(b)\n\n while (a != b) {\n if (a > b) {\n a -= b\n } else {\n b -= a\n }\n }\n\n return a\n}\n\nfunc euclidMod(a: Int, b: Int) -> Int {\n var a = abs(a);\n var b = abs(b);\n\n while (b != 0) {\n let temp = b\n b = a % b\n a = temp\n }\n\n return a\n}\n\nfunc main() {\n print(\"[#]\\nModulus-based euclidean algorithm result:\")\n print(euclidMod(a: 64 * 67, b: 64 * 81))\n print(\"[#]\\nSubtraction-based euclidean algorithm result:\")\n print(euclidSub(a: 128 * 12, b: 128 * 77))\n}\n\nmain()\n\n// Submitted by Max Weinstein\n\nfunction gcd = euclidSub(a,b)\n\n a = abs(a);\n b = abs(b);\n\n while a ~= b\n if a > b\n a = a - b;\n else\n b = b - a;\n end\n end\n\n gcd = a;\nend\n\nfunction gcd = euclidMod(a,b)\n\n a=abs(a);\n b=abs(b);\n\n while b > 0\n temp = b;\n b = mod(a,b);\n a = temp;\n end\n\n gcd = a;\nend\n\nfunction euclid()\n ['[#] Modulus-based euclidean algorithm result: ',num2str(euclidMod(64 * 67, 64 * 81))]\n\n ['[#] Subtraction-based euclidean algorithm result: ',num2str(euclidSub(128 * 12, 128 * 77))]\nend\n\nlocal function euclid_sub(a, b)\n a = math.abs(a)\n b = math.abs(b)\n\n while a ~= b do\n if a > b then\n a = a-b\n else\n b = b-a\n end\n end\n\n return a\nend\n\nlocal function euclid_mod(a, b)\n a = math.abs(a)\n b = math.abs(b)\n\n while b ~= 0 do\n a, b = b, a%b\n end\n\n return a\nend\n\nlocal function main()\n print(\"[#]\\nModulus-based euclidean algorithm result:\")\n print(euclid_mod(64 * 67, 64 * 81))\n print(\"[#]\\nSubtraction-based euclidean algorithm result:\")\n print(euclid_sub(128 * 12, 128 * 77))\nend\n\nmain()\n\nfunction euclid_mod(a::Int64, b::Int64)\n a = abs(a)\n b = abs(b)\n\n while(b != 0)\n b,a = a%b,b\n end\n\n return a\nend\n\nfunction euclid_sub(a::Int64, b::Int64)\n a = abs(a)\n b = abs(b)\n\n while (a != b)\n if (a > b)\n a -= b\n else\n b -= a\n end\n end\n\n return a\nend\n\nfunction main()\n check1 = euclid_mod(64 * 67, 64 * 81);\n check2 = euclid_sub(128 * 12, 128 * 77);\n\n println(\"[#]\\nModulus-based euclidean algorithm result:\\n$(check1)\")\n println(\"[#]\\nSubtraction-based euclidean algorithm result:\\n$(check2)\")\n\nend\n\nmain()\n\nfunc euclid_mod(in1, in2: int): int =\n var\n a = abs(in1)\n b = abs(in2)\n\n while b != 0:\n let temp: int = b\n b = a mod b\n a = temp;\n\n result = a\n\nfunc euclid_sub(in1, in2: int): int =\n var\n a = abs(in1)\n b = abs(in2)\n\n while a != b:\n if a > b:\n a -= b\n else:\n b -= a\n\n result = a\n\nwhen isMainModule:\n echo \"[#]\\nModulus-based euclidean algorithm result:\"\n echo euclid_sub(64 * 67, 64 * 81)\n echo \"[#]\\nSubtraction-based euclidean algorithm result:\"\n echo euclid_mod(128 * 12, 128 * 77)\n\n.intel_syntax noprefix\n\n.section .rodata\n euclid_mod_fmt: .string \"[#]\\nModulus-based euclidean algorithm result:\\n%d\\n\"\n euclid_sub_fmt: .string \"[#]\\nSubtraction-based euclidean algorithm result:\\n%d\\n\"\n\n.section .text\n .global main\n .extern printf\n\n# rdi - a\n# rsi - b\n# RET rax - gcd of a and b\neuclid_mod:\n mov rax, rdi # Get abs of a\n sar rax, 31\n xor rdi, rax\n sub rdi, rax\n mov rax, rsi # Get abs of b\n sar rax, 31\n xor rsi, rax\n sub rsi, rax\n jmp mod_check\nmod_loop:\n xor rdx, rdx # Take the mod of a and b\n mov rax, rdi\n div rsi\n mov rdi, rsi # Set b to the mod of a and b\n mov rsi, rdx # Set a to b\nmod_check:\n cmp rsi, 0 # Check if b is non-zero\n jne mod_loop\n mov rax, rdi # Return the result\n ret\n\neuclid_sub:\n mov rax, rdi # Get abs of a\n sar rax, 31\n xor rdi, rax\n sub rdi, rax\n mov rax, rsi # Get abs of b\n sar rax, 31\n xor rsi, rax\n sub rsi, rax\n jmp check\nloop:\n cmp rdi, rsi # Find which is bigger\n jle if_true\n sub rdi, rsi # If a is bigger then a -= b\n jmp check\nif_true:\n sub rsi, rdi # Else b -= a\ncheck:\n cmp rsi, rdi # Check if a and b are not equal\n jne loop\n mov rax, rdi # Return results\n ret\n\nmain:\n mov rdi, 4288 # Call euclid_mod\n mov rsi, 5184\n call euclid_mod\n mov rdi, OFFSET euclid_mod_fmt # Print output\n mov rsi, rax\n xor rax, rax\n call printf\n mov rdi, 1536 # Call euclid_sub\n mov rsi, 9856\n call euclid_sub\n mov rdi, OFFSET euclid_sub_fmt # Print output\n mov rsi, rax\n xor rax, rax\n call printf\n xor rax, rax # Return 0\n ret\n\nINTEGER FUNCTION euclid_sub(a, b)\n IMPLICIT NONE\n INTEGER, INTENT(INOUT) :: a, b\n\n a = ABS(a)\n b = ABS(b)\n\n DO WHILE (a /= b)\n\n IF (a > b) THEN\n a = a - b\n ELSE\n b = b - a\n END IF\n END DO\n\n euclid_sub = a\n\nEND FUNCTION euclid_sub \n\nINTEGER FUNCTION euclid_mod(a, b)\n IMPLICIT NONE\n INTEGER, INTENT(INOUT) :: a, b\n INTEGER :: temp\n\n DO WHILE (b > 0)\n temp = b\n b = MODULO(a,b)\n a = temp\n END DO\n\n euclid_mod = a\n\nEND FUNCTION euclid_mod\n\nPROGRAM euclidean\n\n IMPLICIT NONE\n INTEGER :: a, b, euclid_sub, euclid_mod\n\n a = 64 * 67\n b = 64 * 81\n\n WRITE(*,'(a)') '[#]'\n WRITE(*,'(a)') 'Modulus-based euclidean algorithm result:'\n WRITE(*, '(g0)') euclid_mod(a, b)\n\n a = 128 * 12\n b = 128 * 77\n\n WRITE(*,'(a)') '[#]'\n WRITE(*,'(a)') 'Subtraction-based euclidean algorithm result:'\n WRITE(*, '(g0)') euclid_sub(a, b)\n\nEND PROGRAM euclidean\n\n $b) {\n $a = $a - $b;\n } else {\n $b = $b - $a;\n }\n }\n\n return $a;\n}\n\nfunction euclid_mod(int $a, int $b): int\n{\n $a = abs($a);\n $b = abs($b);\n\n while ($b !== 0) {\n list($b, $a) = [$a % $b, $b];\n }\n\n return $a;\n}\n\nprintf('[#]'.PHP_EOL.'Modulus-based euclidean algorithm result:'.PHP_EOL.'%s', euclid_mod(64 * 67, 64 * 81));\necho PHP_EOL;\nprintf('[#]'.PHP_EOL.'Subtraction-based euclidean algorithm result:'.PHP_EOL.'%s', euclid_sub(128 * 12, 128 * 77));\necho PHP_EOL;\n\n: euclid- ( a b -- gcd )\n [ abs ] bi@\n [ 2dup = ]\n [\n ! make sure the lower number is deeper\n 2dup >= [ swap ] when\n over -\n ! leaves us with stack { }\n ]\n until\n ! we have the GCD twice now, drop one\n drop\n;\n\n: euclid% ( a b -- gcd )\n [ abs ] bi@ ! take both absolute values\n [ dup zero? ] ! check if `b` (on top) is 0\n [\n ! a b -> a b b -> b a b -> b a%b\n dup -rot mod\n ]\n until\n ! the zero is on top, so get rid of it\n drop\n;\n\n42 56 euclid% . ! 14\n48 180 euclid% . ! 12\n\n42 56 euclid- . ! 14\n48 180 euclid- . ! 12\n\nHere is a readable version of the algorithms with comments. First, subtraction method:\nReading the input: a, b\n[SPACE][SPACE][SPACE][LF] push 0\n[SPACE][SPACE][SPACE][TAB][LF] push 1\n[TAB][LF][TAB][TAB] readi\n[TAB][LF][TAB][TAB] readi\n\nLoop: a, b => a, b-a\n[LF][SPACE][SPACE][LF] label_0:\n[SPACE][SPACE][SPACE][LF] push 0\n[TAB][TAB][TAB] retrieve\n[SPACE][SPACE][SPACE][TAB][LF] push 1\n[TAB][TAB][TAB] retrieve\n[TAB][SPACE][SPACE][TAB] sub\n[SPACE][LF][SPACE] dup\n[LF][TAB][SPACE][TAB][LF] jmp zero label_1\n[SPACE][LF][SPACE] dup\n[LF][TAB][TAB][TAB][SPACE][LF] jmp neg label_2\n[SPACE][SPACE][SPACE][LF] push 0\n[SPACE][LF][TAB] swap\n[TAB][TAB][SPACE] store\n[LF][SPACE][LF][LF] jmp label_0\n\nExit when a=b\n[LF][SPACE][SPACE][TAB][LF] label_1:\n[SPACE][SPACE][SPACE][LF] push 0\n[TAB][TAB][TAB] retrieve\n[TAB][LF][SPACE][TAB] printi\n[LF][LF][LF] end\n\nIf a>b: a, b => a-b, b\n[LF][SPACE][SPACE][TAB][SPACE][LF] label_2:\n[SPACE][SPACE][SPACE][LF] push 0\n[SPACE][LF][TAB] swap\n[TAB][SPACE][SPACE][TAB] sub\n[SPACE][SPACE][SPACE][TAB][LF] push 1\n[SPACE][LF][TAB] swap\n[TAB][TAB][SPACE] store\n[LF][SPACE][LF][LF] jmp label_0\n\nand modulo method:\nReading the input: a, b\n[SPACE][SPACE][SPACE][LF] push 0\n[SPACE][SPACE][SPACE][TAB][LF] push 1\n[TAB][LF][TAB][TAB] readi\n[TAB][LF][TAB][TAB] readi\n\nLoop: a, b => b, a%b\n[LF][SPACE][SPACE][LF] label_0:\n[SPACE][SPACE][SPACE][LF] push 0\n[TAB][TAB][TAB] retrieve\n[SPACE][LF][SPACE] dup\n[LF][TAB][SPACE][TAB][LF] jmp zero label_1\n[SPACE][SPACE][SPACE][TAB][LF] push 1\n[TAB][TAB][TAB] retrieve\n[SPACE][LF][TAB] swap\n[TAB][SPACE][TAB][TAB] mod\n[SPACE][SPACE][SPACE][LF] push 0\n[TAB][TAB][TAB] retrieve\n[SPACE][SPACE][SPACE][TAB][LF] push 1\n[SPACE][LF][TAB] swap\n[TAB][TAB][SPACE] store\n[SPACE][SPACE][SPACE][LF] push 0\n[SPACE][LF][TAB] swap\n[TAB][TAB][SPACE] store\n[LF][SPACE][LF][LF] jmp label_0\n\nExit when b=0\n[LF][SPACE][SPACE][TAB][LF] label_1:\n[SPACE][SPACE][SPACE][TAB][LF] push 1\n[TAB][TAB][TAB] retrieve\n[TAB][LF][SPACE][TAB] printi\n[LF][LF][LF][LF] end\n\nobject Euclid {\n\n def euclid_sub(a: Int, b: Int): Int =\n (Math.abs(a), Math.abs(b)) match {\n case (0, _) | (_, 0) => 0\n case (x, y) if x euclid_sub(x, y - x)\n case (x, y) if x > y => euclid_sub(x - y, y)\n case _ => a\n }\n\n def euclid_mod(a: Int, b: Int): Int =\n (Math.abs(a), Math.abs(b)) match {\n case (_, 0) => a\n case (a, b) => euclid_mod(b, a % b)\n }\n\n def main(args: Array[String]): Unit = {\n println(\"[#]\\nModulus-based euclidean algorithm result:\")\n println(euclid_mod(64 * 67, 64 * 81))\n println(\"[#]\\nSubtraction-based euclidean algorithm result:\")\n println(euclid_sub(128 * 12, 128 * 77))\n }\n\n}\n\n#lang racket\n\n(define (euclid_sub a b)\n (local ((define (euclid_sub* x y)\n (if (= x y)\n x\n (if (> x y)\n (euclid_sub* (- x y) y)\n (euclid_sub* x (- y x))\n )\n )\n )) (euclid_sub* (abs a) (abs b))\n )\n )\n\n(define (euclid_mod a b)\n (local ((define (euclid_mod* a b)\n (if (= 0 b)\n (abs a)\n (euclid_mod* b (modulo a b))\n )\n )) (euclid_mod* a b)\n )\n )\n\n(displayln \"[#]\\nModulus-based euclidean algorithm result:\")\n(displayln (euclid_sub (* 64 67) (* 64 81)))\n(displayln \"[#]\\nSubtraction-based euclidean algorithm result:\")\n(displayln (euclid_mod (* 128 12) (* 128 77)))\n\ndef gcd_mod(a, b)\n a = a.abs\n b = b.abs\n a, b = b, a%b until b.zero?\n a\nend\n\ndef gcd_minus(a, b)\n a = a.abs\n b = b.abs\n until a == b\n if a > b\n a -= b\n else\n b -= a\n end\n end\n a\nend\n\nprint \"[#]\\nModulus-based euclidean algorithm result:\\n\"\np gcd_mod(64 * 67, 64 * 81)\nprint \"[#]\\nSubtraction-based euclidean algorithm result:\\n\"\np gcd_minus(128 * 12, 128 * 77)\n\nInteger>>euclidSub: secondNumber\n \"Euclidean algorithm with subtraction\"\n | a b |\n a := self abs.\n b := secondNumber abs.\n [ a == b ] whileFalse: [ \n a > b ifTrue: [ \n a := a - b.\n ] ifFalse: [ \n b := b - a.\n ].\n ].\n ^a.\n\nInteger>>euclidMod: secondNumber\n \"Euclidean algorithm with modulus.\"\n | a b oldB |\n a := self abs.\n b := secondNumber abs.\n [ b == 0 ] whileFalse: [ \n oldB := b.\n b := a % b.\n a := oldB.\n ].\n ^a.\n\nTranscript show: ((64 * 67) euclidSub: (64 * 81)).\nTranscript cr.\nTranscript show: ((128 * 12) euclidMod: (128 * 77)).\n\n🐇 ⬆️ 🍇\n 🐇 ❗️ 🔼 a 🔢 b 🔢 ➡️ 🔢 🍇\n 💭 Use 🏧 (returns the absolute value) to support negative numbers.\n 🏧a ❗️ ➡️ 🖍🆕var_a\n 🏧b ❗️ ➡️ 🖍🆕var_b\n\n ️🔁 ❎ var_a 🙌 var_b ❗️ 🍇\n ↪️ var_a ▶️ var_b 🍇\n var_a ⬅️ ➖ var_b\n 🍉\n 🙅 🍇\n var_b ⬅️ ➖ var_a\n 🍉\n 🍉\n\n ↩️ var_a\n 🍉\n\n 🐇 ❗️ ⏫ a 🔢 b 🔢 ➡️ 🔢 🍇\n 💭 Use 🏧 (returns the absolute value) to support negative numbers.\n 🏧a ❗️ ➡️ 🖍🆕var_a\n 🏧b ❗️ ➡️ 🖍🆕var_b\n\n ️🔁 ❎ var_b 🙌 0 ❗️ 🍇\n var_b ➡️ temp\n var_a 🚮 var_b ➡️ 🖍var_b\n temp ➡️ 🖍var_a\n 🍉\n\n ↩️ var_a\n 🍉\n🍉\n\n🏁 🍇\n 😀 🔡 ️🔼🐇⬆️ 🤜64 ✖️ 67🤛 🤜64 ✖️ 81🤛 ❗️ 10 ❗️❗️\n 😀 🔡 ️⏫🐇⬆️ 🤜128 ✖️ 12🤛 🤜128 ✖️ 77🤛 ❗️ 10 ❗️❗️\n🍉\n\nHAI 1.2\n HOW IZ I ABZ YR NUM\n DIFFRINT NUM AN BIGGR OF NUM AN 0, O RLY?\n YA RLY, FOUND YR DIFF OF 0 AN NUM\n NO WAI, FOUND YR NUM\n OIC\n IF U SAY SO\n\n HOW IZ I UKLIDMOD YR NUM1 AN YR NUM2\n NUM1 R I IZ ABZ YR NUM1 MKAY\n NUM2 R I IZ ABZ YR NUM2 MKAY\n\n IM IN YR LOOP \n BOTH SAEM NUM2 AN 0, O RLY?\n YA RLY, FOUND YR NUM1\n OIC\n\n I HAS A TMP ITZ NUM2\n NUM2 R MOD OF NUM1 AN NUM2\n NUM1 R TMP\n IM OUTTA YR LOOP\n\n IF U SAY SO\n\n HOW IZ I UKLIDSUP YR NUM1 AN YR NUM2\n NUM1 R I IZ ABZ YR NUM1 MKAY\n NUM2 R I IZ ABZ YR NUM2 MKAY\n\n IM IN YR LOOP \n BOTH SAEM NUM1 AN NUM2, O RLY?\n YA RLY, FOUND YR NUM1\n OIC \n\n DIFFRINT NUM1 AN SMALLR OF NUM1 AN NUM2, O RLY?\n YA RLY, NUM1 R DIFF OF NUM1 AN NUM2\n NO WAI, NUM2 R DIFF OF NUM2 AN NUM1\n OIC\n IM OUTTA YR LOOP\n\n IF U SAY SO\n\n I HAS A CHECK1 ITZ I IZ UKLIDMOD YR PRODUKT OF 64 AN 67 AN YR PRODUKT OF 64 AN 81 MKAY\n I HAS A CHECK2 ITZ I IZ UKLIDSUP YR PRODUKT OF 128 AN 12 AN YR PRODUKT OF 128 AN 77 MKAY\n\n VISIBLE CHECK1\n VISIBLE CHECK2\nKTHXBYE\n\n#!/usr/bin/env bash\nabs() {\n local ret=$1\n if (( ret b )); then\n ((a -= b))\n else\n ((b -= a))\n fi\n done\n printf \"%s\" \"$a\"\n}\n\nresult=$(euclid_mod $((64 * 67)) $((64 * 81)))\necho -e \"[#]\\nModulus-based euclidean algorithm result:\\n$result\"\nresult=$(euclid_sub $((128 * 12)) $((128 * 77)))\necho -e \"[#]\\nSubtraction-based euclidean algorithm result:\\n$result\"\n\nimport std.stdio;\nimport std.math;\n\n// Euclidean algorithm using modulus\nint euclid_mod(int a, int b) {\n int tmp;\n a = abs(a);\n b = abs(b);\n\n while (b != 0) {\n tmp = a % b;\n a = b;\n b = tmp;\n }\n\n return a;\n}\n\n// Euclidean algorithm with subtraction\nint euclid_sub(int a, int b) {\n a = abs(a);\n b = abs(b);\n\n while (a != b) {\n if (a > b) {\n a -= b;\n } else {\n b -= a;\n }\n }\n\n return a;\n}\n\nvoid main()\n{\n auto check1 = euclid_mod(64 * 67, 64 * 81);\n auto check2 = euclid_sub(128 * 12, 128 * 77);\n\n writeln(\"[#]\\nModulus-based euclidean algorithm result:\\n\", check1);\n writeln(\"[#]\\nSubtraction-based euclidean algorithm result:\\n\", check2);\n}\n\nA text version of the program is provided for both versions.\nSubtraction\n\n \n\nCOMMAND STATE OF STACK\nin(number) A // Take A as an input\nduplicate AA // Start to take the absolute value of A\npush 1 1AA\nduplicate 11AA\nsubtract 0AA\ngreater 0/1A // 1 if A > 0, 0 if A 0, 1 if A 0, 0 if B 0, 1 if B B; 1 if true; 0 if false\n pointer BA // If A > B, DP goes one clockwise, otherwise, DP stays the same. \n\n // If A > B (DP has changed 1 clockwise)\n duplicate BBA\n push 3 3BBA\n push 1 13BBA\n roll BAB\n subtract AB // A = A - B\n push 2 2AB\n push 1 12AB\n roll BA\n // Go back to start of loop\n\n // If B > A (DP stayed the same)\n push 2 2BA\n push 1 12BA\n roll AB\n duplicate AAB\n push 3 3AAB\n push 1 13AAB\n roll ABA\n subtract BA // B = B - A\n // Go back to start of loop\n\n// Go down if a = b (end of while loop)\npop A\nout(number) - // Print out A when done.\nModulo\n\n \n\nCOMMAND STATE OF STACK\nin(number) A\nin(number) BA\n\n// Start of loop\nduplicate BBA\nnot 0/1 BA\nnot 1/0 BA\npointer BA\n\n // Go down if b ≠ 0\n duplicate TBA\n push 3 3TBA \n push 1 13TBA\n roll BAT\n mod BA // b = a mod b; a = t\n // Go back to the start of the loop\n\n// Go right if b = 0\npop A\nout(number) - // Print out A when done.\n(define (euclid-sub a b)\n (cond \n [(or (negative? a)(negative? b))(euclid-sub (abs a)(abs b))] \n [(eq? a b) a]\n [(> a b)(euclid-sub(- a b) b)]\n [else\n (euclid-sub a (- b a))]))\n\n(define (euclid-mod a b)\n (if (zero? b)\n a\n (euclid-mod b (modulo a b))))\n\n(display \"[#]\\nModulus-based euclidean algorithm result:\") (newline)\n(display (euclid-mod (* 64 67) (* 64 81))) (newline)\n\n(display \"[#]\\nSubtraction-based euclidean algorithm result:\") (newline)\n(display (euclid-sub (* 128 12) (* 128 77))) (newline)\n\nThe code snippets were taken from this Scratch project\n\n \n\nleave one line empty:\nfunction Sub-Euclid($a, $b) {\n $a = [Math]::Abs($a)\n $b = [Math]::Abs($b)\n\n while ($a -ne $b) {\n if ($a -gt $b) {\n $a = $a - $b\n } else {\n $b = $b - $a\n }\n }\n\n return $a\n}\n\nfunction Mod-Euclid($a, $b) {\n $a = [Math]::Abs($a)\n $b = [Math]::Abs($b)\n\n while ($b -ne 0) {\n $tmp = $b\n $b = $a % $b\n $a = $tmp\n }\n\n return $a\n}\n\nWrite-Host \"[#]`nSubtraction-based euclidean algorithm result:`n$(Mod-Euclid $(64 * 67) $(64 * 81))\"\nWrite-Host \"[#]`nModulus-based euclidean algorithm result:`n$(Sub-Euclid $(128 * 12) $(128 * 77))\"\n\ndef euclid_sub(a is int, 0) = a\naddpattern def euclid_sub(0, b is int) = b\n\naddpattern def euclid_sub(a is int, b is int):\n if a \n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"Euclidsub\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Euclidmod\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/matrix_methods/matrix_methods.html":{"url":"contents/matrix_methods/matrix_methods.html","title":"Matrix Methods","keywords":"","body":"Matrix Methods\nMathematics is the foundation for many areas of science and engineering, and it is not uncommon for these applications to require the manipulation of large matrices. Though these applications are not mathematics, they use mathematics in everything they do and the methods to manipulate matrices are certainly mathematical. For this reason, I feel we should tour many methods used to manipulate matrices into any usable form. For the most part, we can divide the mathematical matrix methods into the following categories:\n\nDiagonalization / Finding the Eigenvalues\nCreating upper and lower diagonal matrices\nSolving systems of Equations\n\nThere are certainly more methods out there, so don't be offended if I have failed to list one of your favorite types of algorithms. We'll be filling more in as we go along!\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/computational_geometry/computational_geometry.html":{"url":"contents/computational_geometry/computational_geometry.html","title":"Computational Geometry","keywords":"","body":"Computational Geometry\nWhen it comes to the different sectors of computational mathematics, there are none that bring me more joy than computational geometry.\nIn some sense, it is the foundation for almost every area of automatically generated two and three dimensional graphics.\nIf you have time to spend poring through some interesting research, I would definitely recommend going to the arXiv.org section for computational geometry.\nWe will add more to this section as the Archive evolves, so let me know of any algorithms that you would like to cover in the future!\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/gift_wrapping/gift_wrapping.html":{"url":"contents/gift_wrapping/gift_wrapping.html","title":"Gift Wrapping","keywords":"","body":"Gift Wrapping\nIf given a \"gift\", here defined as a random distribution of points in two or three dimensions, gift-wrapping algorithms allow programmers to find its convex hull -- the smallest convex shape that holds all interior points.\nThis is one of the many cases where the leap from two to three dimensions leads to an incredibly more complicated code.\nThat said, there is a rich history of algorithms to solve this problem.\nTo be fair, only the Jarvis March is classified as the gift wrapping algorithm; however, it's a neat name to give algorithms that solve for the convex hull of a distribution of points.\nStrictly speaking, though, the term is not entirely accurate for all convex hull methods.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/decision_problems/decision_problems.html":{"url":"contents/decision_problems/decision_problems.html","title":"Decision Problems","keywords":"","body":"Decision Problems\nI'll be honest here: I am not sure what section to put these problems in, so for now, they are in Computational Mathematics, but that may change in the near future.\nI'm also not sure whether we can classify these problems as decision problems at all; however, everything in this section is related to making informed decisions when assigning inputs to appropriate outputs.\nFor example, the Hungarian algorithm reads in a bunch of inputs (candidates for certain jobs or positions) and assigns each input to an output task while minimizing the cost associated with all inputs performing their designated task.\nOverall, these problems come up all over the place and are certainly worth studying in their own right!\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/physics_solvers/physics_solvers.html":{"url":"contents/physics_solvers/physics_solvers.html","title":"Physics Solvers","keywords":"","body":"Physics Solvers\nThere are certain algorithms that have been uniquely created to solve particular physical systems.\nFor example, the kinematic equation can be solved with Verlet integration and also with more general differential equation solvers.\nIn this section, we will place all algorithms and methods that are specific to physics and cannot be used in any other area.\nIt's worth noting that many algorithms used throughout the Archive can also be used to solve physics equations and physics lends itself more readily to computational methods than many other areas of scientific research, such as biology or chemistry.\nIn the future, we may also place several unique physical systems along with different methods to solve these systems.\nFor example, there are many different ways to solve the Schrödinger equation, heat equation, kinematic equation and several other systems that are unique to physics and there are benefits and drawbacks for solving certain physical systems in certain ways.\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/huffman_encoding/huffman_encoding.html":{"url":"contents/huffman_encoding/huffman_encoding.html","title":"Huffman Encoding","keywords":"","body":"Huffman Encoding\nIf there were ever a data compression method to take the world by storm, it would be Huffman encoding.\nIn fact, this was the method that got me into computational methods to begin with.\nI distinctly remember sitting in my data compression class and talking about the great information theorist Claude Shannon and Robert Fano, when suddenly my professor introduced a new kid to the mix: David Huffman.\nHe managed to rip the heart out of the methods described by leaders of the field and create a data compression method that was easier to understand and implement, while also providing more robust results, and apparently this was all done for a school project!\nIt was in that moment, I knew I would never amount to anything.\nI have since accepted that fact and moved on.\nHuffman encoding follows from the problem described in the Data Compression section.\nWe have a string that we want to encode into bits.\nHuffman encoding ensures that our encoded bitstring is as small as possible without losing any information.\nBecause it is both lossless and guarantees the smallest possible bit length, it outright replaces both Shannon and Shannon-Fano encoding in most cases, which is a little weird because the method was devised while Huffman was taking a course from Fano, himself!\nThe idea is somewhat straightforward in principle, but a little difficult to code in practice.\nBy creating a binary tree of the input alphabet, every branch can be provided a unique bit representation simply by assigning a binary value to each child and reading to a character in a leaf node if starting from the root node.\nSo now the question is: how do we create a binary tree?\nWell, here we build it from the bottom up like so:\n\nOrder all characters according to the frequency they appear in the input bitstring, with the most frequent character at the top of the list. Be sure to keep track of the frequencies, too!\nAdd the smallest two values together to create a new node with a new frequency.\nKeep doing step 2 until the tree is complete.\nRead the tree backwards from the root node and concatenate the final bitstring codeword. Keep all codewords and put them into your final set of codewords (sometimes called a codebook)\nEncode your phrase with the codebook.\n\nAnd that's it.\nHere's an image of what this might look like for the phrase bibbity_bobbity:\n\n \n\n\nThis will create a codebook that looks like this:\n\n\n\nCharacter\nBit Representation\n\n\n\n\nb\n0\n\n\ni\n100\n\n\nt\n101\n\n\ny\n110\n\n\no\n1110\n\n\n_\n1111\n\n\n\nand bibbity_bobbity becomes 01000010010111011110111000100101110.\nAs mentioned this uses the minimum number of bits possible for encoding.\nThe fact that this algorithm is both conceptually simple and provably useful is rather extraordinary to me and is why Huffman encoding will always hold a special place in my heart.\nVideo Explanation\nHere is a quick video explanation for Huffman encoding:\n\n\n\n\nExample Code\nIn code, this can be a little tricky. It requires a method to continually sort the nodes as you add more and more nodes to the system.\nThe most straightforward way to do this in some languages is with a priority queue, but depending on the language, this might be more or less appropriate.\nIn addition, to read the tree backwards, some sort of Depth First Search needs to be implemented.\nWhether you use a stack or straight-up recursion also depends on the language, but the recursive method is a little easier to understand in most cases.\nusing Test\n\n# This is for the PriorityQueue\nusing DataStructures\n\nstruct Leaf\n weight::Int64\n key::Char\nend\n\nstruct Branch\n right::Union{Leaf, Branch}\n left::Union{Leaf, Branch}\n weight::Int64\nend\n\nconst Node = Union{Leaf, Branch}\n\nfunction codebook_recurse!(leaf::Leaf, code::String,\n dict::Dict{Char,String})\n dict[leaf.key] = code\nend\n\nfunction codebook_recurse!(branch::Branch, code::String,\n dict::Dict{Char,String})\n codebook_recurse!(branch.left, string(code, \"1\"), dict)\n codebook_recurse!(branch.right, string(code, \"0\"), dict)\nend\n\n# This will depth-first search through the tree\n# to create bitstrings for each character.\n# Note: Any depth-first search method will work\n# This outputs encoding Dict to be used for encoding\nfunction create_codebook(n::Node)\n codebook = Dict{Char,String}()\n if isa(n, Leaf)\n codebook[n.key]=\"0\"\n else\n codebook_recurse!(n, \"\", codebook)\n end\n return codebook\nend\n\n# This outputs huffman tree to generate dictionary for encoding\nfunction create_tree(phrase::String)\n\n # creating weights\n weights = PriorityQueue()\n for i in phrase\n temp_string = string(i)\n if (haskey(weights, temp_string))\n weights[temp_string] += 1\n else\n weights[temp_string] = 1\n end\n end\n\n # Creating all nodes to iterate through\n nodes = PriorityQueue{Node, Int64}()\n while(length(weights) > 0)\n weight = peek(weights)[2]\n key = dequeue!(weights)[1]\n temp_node = Leaf(weight, key)\n enqueue!(nodes, temp_node, weight)\n end\n\n while(length(nodes) > 1)\n node1 = dequeue!(nodes)\n node2 = dequeue!(nodes)\n temp_node = Branch(node1, node2, node1.weight + node2.weight)\n enqueue!(nodes, temp_node, temp_node.weight)\n end\n\n huffman_tree = dequeue!(nodes)\n return huffman_tree\n\nend\n\nfunction encode(codebook::Dict{Char, String}, phrase::String)\n final_bitstring = \"\"\n for i in phrase\n final_bitstring = final_bitstring * codebook[i]\n end\n\n return final_bitstring\nend\n\nfunction decode(huffman_tree::Node, bitstring::String)\n current = huffman_tree\n final_string = \"\"\n for i in bitstring\n if isa(huffman_tree, Branch)\n if (i == '1')\n current = current.left\n else\n current = current.right\n end\n\n if (!isa(current, Branch))\n final_string *= string(current.key)\n current = huffman_tree\n end\n else\n final_string *= string(huffman_tree.key)\n end\n end\n\n return final_string\nend\n\nfunction two_pass_huffman(phrase::String)\n huffman_tree = create_tree(phrase)\n codebook = create_codebook(huffman_tree)\n bitstring = encode(codebook, phrase)\n final_string = decode(huffman_tree, bitstring)\n return final_string\nend\n\n@testset \"b-string tests\" begin\n @test two_pass_huffman(\"b\") == \"b\"\n @test two_pass_huffman(\"bbbbbbbb\") == \"bbbbbbbb\"\n @test two_pass_huffman(\"bibbity bobbity\") == \"bibbity bobbity\"\nend\n\nextern crate itertools;\n\nuse std::cmp::{Ord, Ordering, PartialOrd};\nuse std::collections::{BinaryHeap, HashMap};\n\nuse itertools::Itertools;\n\n#[derive(Debug)]\nenum HuffmanTree {\n Branch {\n count: i32,\n left: Box,\n right: Box,\n },\n Leaf {\n count: i32,\n value: char,\n },\n}\n\nimpl PartialEq for HuffmanTree {\n fn eq(&self, other: &Self) -> bool {\n self.count() == other.count()\n }\n}\n\nimpl Eq for HuffmanTree {}\n\nimpl PartialOrd for HuffmanTree {\n fn partial_cmp(&self, other: &Self) -> Option {\n other.count().partial_cmp(&self.count())\n }\n}\n\nimpl Ord for HuffmanTree {\n fn cmp(&self, other: &Self) -> Ordering {\n other.count().cmp(&self.count())\n }\n}\n\n#[derive(Debug)]\nstruct Codebook {\n codebook: HashMap,\n tree: HuffmanTree,\n}\n\nimpl HuffmanTree {\n pub fn from(input: &str) -> Self {\n let counts = input.chars().fold(HashMap::new(), |mut map, c| {\n *map.entry(c).or_insert(0) += 1;\n map\n });\n let mut queue = counts\n .iter()\n .map(|(&value, &count)| HuffmanTree::Leaf { value, count })\n .collect::>();\n\n while queue.len() > 1 {\n let left = queue.pop().unwrap();\n let right = queue.pop().unwrap();\n queue.push(HuffmanTree::Branch {\n count: left.count() + right.count(),\n left: Box::new(left),\n right: Box::new(right),\n })\n }\n\n queue.pop().expect(\"The Huffman tree has to have a root\")\n }\n\n pub fn count(&self) -> i32 {\n match *self {\n HuffmanTree::Branch { count, .. } => count,\n HuffmanTree::Leaf { count, .. } => count,\n }\n }\n\n pub fn make_codebook(self) -> Codebook {\n let mut codebook = HashMap::new();\n self.dfs(String::from(\"\"), &mut codebook);\n Codebook {\n codebook,\n tree: self,\n }\n }\n\n pub fn decode(&self, input: &str) -> String {\n let mut result = String::from(\"\");\n let mut start = 0;\n while !input[start..].is_empty() {\n start += self.decode_dfs(&input[start..], &mut result);\n }\n result\n }\n\n fn decode_dfs(&self, input: &str, result: &mut String) -> usize {\n let current = input.chars().next();\n match *self {\n HuffmanTree::Branch { ref left, .. } if current == Some('0') => {\n 1 + left.decode_dfs(&input[1..], result)\n }\n HuffmanTree::Branch { ref right, .. } if current == Some('1') => {\n 1 + right.decode_dfs(&input[1..], result)\n }\n HuffmanTree::Leaf { value, .. } => {\n result.push(value);\n 0\n }\n _ => panic!(\"Unexpected end of input\"),\n }\n }\n\n fn dfs(&self, code: String, codebook: &mut HashMap) {\n match *self {\n HuffmanTree::Branch {\n ref left,\n ref right,\n ..\n } => {\n left.dfs(code.clone() + \"0\", codebook);\n right.dfs(code.clone() + \"1\", codebook);\n }\n HuffmanTree::Leaf { value, .. } => {\n codebook.insert(value, code);\n }\n }\n }\n}\n\nimpl Codebook {\n fn encode(&self, input: &str) -> String {\n input.chars().map(|c| &self.codebook[&c]).join(\"\")\n }\n\n fn decode(&self, input: &str) -> String {\n self.tree.decode(input)\n }\n}\n\nfn main() {\n let input = \"bibbity bobbity\";\n\n let tree = HuffmanTree::from(input);\n let codebook = tree.make_codebook();\n let encoded = codebook.encode(input);\n let decoded = codebook.decode(&encoded);\n\n // Uncomment this line if you want to see the codebook/tree\n // println!(\"{:#?}\", codebook);\n println!(\"{}\", encoded);\n println!(\"{}\", decoded);\n}\n\n// Made by Guston and edited by Gathros\n#include \n#include \n#include \n#include \n\nstruct tree {\n struct tree* left;\n struct tree* right;\n\n int count;\n char value;\n};\n\nstruct bitstring_builder {\n char str[257];\n int next_index;\n};\n\nstruct codebook {\n char* codes[256];\n};\n\nstruct heap {\n struct tree** data;\n size_t length;\n size_t capacity;\n};\n\nbool is_leaf(const struct tree* t) {\n return !t->left && !t->right;\n}\n\nvoid swap(struct tree** lhs, struct tree** rhs) {\n struct tree* tmp = *lhs;\n *lhs = *rhs;\n *rhs = tmp;\n}\n\n/* The two concat functions are horribly inefficient */\nvoid concat(char** dst, const char* src) {\n size_t dst_len = strlen(*dst);\n size_t src_len = strlen(src);\n *dst = realloc(*dst, src_len + dst_len + 1);\n strcat(*dst, src);\n}\n\nvoid concat_char(char** dst, char c) {\n size_t len = strlen(*dst);\n *dst = realloc(*dst, len + 2);\n (*dst)[len] = c;\n (*dst)[len + 1] = '\\0';\n}\n\nchar* duplicate(const char* src) {\n size_t length = strlen(src);\n char* dst = malloc(length + 1);\n memcpy(dst, src, length + 1);\n return dst;\n}\n\nvoid heap_push(struct heap* heap, struct tree* value) {\n if (heap->capacity == heap->length) {\n heap->capacity = heap->capacity == 0 ? 4 : heap->capacity * 2;\n heap->data = realloc(heap->data, heap->capacity * sizeof(struct tree*));\n }\n heap->data[heap->length++] = value;\n\n size_t index = heap->length - 1;\n while (index) {\n size_t parent_index = (index - 1) / 2;\n if (heap->data[parent_index]->count data[index]->count) {\n break;\n }\n\n swap(&heap->data[parent_index], &heap->data[index]);\n index = parent_index;\n }\n}\n\nstruct tree* heap_pop(struct heap* heap) {\n if (!heap->length) {\n return NULL;\n }\n\n struct tree* result = heap->data[0];\n swap(&heap->data[0], &heap->data[--heap->length]);\n\n size_t index = 0;\n for (;;) {\n size_t target = index;\n size_t left = 2 * index + 1;\n size_t right = left + 1;\n\n if (left length &&\n heap->data[left]->count data[target]->count) {\n target = left;\n }\n\n if (right length &&\n heap->data[right]->count data[target]->count) {\n target = right;\n }\n\n if (target == index) {\n break;\n }\n\n swap(&heap->data[index], &heap->data[target]);\n index = target;\n }\n\n return result;\n}\n\nvoid heap_free(struct heap* heap) {\n free(heap->data);\n}\n\nstruct tree* generate_tree(const char* str) {\n int counts[256] = { 0 };\n\n for (; *str != '\\0'; ++str) {\n counts[(unsigned char)*str] += 1;\n }\n\n struct heap heap = { 0 };\n for (size_t i = 0; i value = (char)i;\n tree->count = counts[i];\n heap_push(&heap, tree);\n }\n }\n\n if (heap.length == 1) {\n struct tree* leaf = heap_pop(&heap);\n struct tree* root = calloc(0, sizeof(struct tree));\n root->left = leaf;\n root->count = leaf->count;\n heap_free(&heap);\n return root;\n }\n\n while (heap.length > 1) {\n struct tree* left = heap_pop(&heap);\n struct tree* right = heap_pop(&heap);\n struct tree* branch = calloc(1, sizeof(struct tree));\n branch->count = left->count + right->count;\n branch->left = left;\n branch->right = right;\n heap_push(&heap, branch);\n }\n\n struct tree* root = heap_pop(&heap);\n heap_free(&heap);\n return root;\n}\n\nvoid tree_free(struct tree* tree) {\n if (!tree) return;\n tree_free(tree->left);\n tree_free(tree->right);\n free(tree);\n}\n\nvoid codebook_recurse(const struct tree* tree,\n struct bitstring_builder* builder,\n struct codebook* codebook) {\n if (!tree) {\n return;\n }\n\n if (is_leaf(tree)) {\n builder->str[builder->next_index] = '\\0';\n codebook->codes[(unsigned char)tree->value] = duplicate(builder->str);\n return;\n }\n\n builder->str[builder->next_index++] = '0';\n codebook_recurse(tree->left, builder, codebook);\n builder->next_index -= 1;\n\n builder->str[builder->next_index++] = '1';\n codebook_recurse(tree->right, builder, codebook);\n builder->next_index -= 1;\n}\n\nstruct codebook generate_codebook(const struct tree* tree) {\n struct codebook codebook = { .codes = { 0 } };\n struct bitstring_builder builder = { .str = { 0 }, .next_index = 0 };\n codebook_recurse(tree, &builder, &codebook);\n return codebook;\n}\n\nvoid codebook_free(struct codebook* codebook) {\n int size = sizeof(codebook->codes) / sizeof(codebook->codes[0]);\n for (int i = 0; i codes[i]);\n }\n}\n\nconst char* get_code(const struct codebook* codebook, char c) {\n return codebook->codes[(unsigned char)c];\n}\n\nchar* encode(const char* input, struct tree** huffman_tree,\n struct codebook* codebook) {\n *huffman_tree = generate_tree(input);\n *codebook = generate_codebook(*huffman_tree);\n\n char* result = duplicate(get_code(codebook, *input));\n\n input += 1;\n\n for (; *input; ++input) {\n concat(&result, get_code(codebook, *input));\n }\n\n return result;\n}\n\nconst char* decode_recurse(const char* input, const struct tree* tree,\n char** result) {\n if (!tree) {\n return input;\n }\n\n if (is_leaf(tree)) {\n concat_char(result, tree->value);\n return input;\n }\n\n if (*input == '0') {\n return decode_recurse(input + 1, tree->left, result);\n } else {\n return decode_recurse(input + 1, tree->right, result);\n }\n}\n\nchar* decode(const char* input, const struct tree* tree) {\n char* result = calloc(1, 1);\n do {\n input = decode_recurse(input, tree, &result);\n } while (*input);\n return result;\n}\n\nint main() {\n struct tree* tree;\n struct codebook codebook;\n\n char* encoded = encode(\"bibbity bobbity\", &tree, &codebook);\n char* decoded = decode(encoded, tree);\n\n printf(\"Codebook:\\n\");\n for (int i = 0; i \nimport qualified Data.Map as M\nimport Data.List (insert, sort)\n\ndata Tree a = Leaf Int a\n | Node Int (Tree a) (Tree a)\n deriving (Show, Eq)\n\nfreq :: Tree a -> Int\nfreq (Leaf i _) = i\nfreq (Node i _ _) = i\n\ninstance (Eq a) => Ord (Tree a) where\n compare t1 t2 = compare (freq t1) (freq t2)\n\ngetFrequencies :: Ord a => [a] -> [(Int, a)]\ngetFrequencies = toSortedList . M.fromListWith (+) . flip zip (repeat 1)\n where toSortedList = sort . map swap . M.toList\n swap (a, i) = (i, a)\n\nbuildTree :: (Ord a) => [a] -> Maybe (Tree a)\nbuildTree = build . map (uncurry Leaf) . getFrequencies\n where build [] = Nothing\n build [t] = Just t\n build (t1:t2:ts) = build $ insert (Node (freq t1 + freq t2) t1 t2) ts\n\ndata Bit = Zero | One\n\ninstance Show Bit where\n show Zero = \"0\"\n show One = \"1\"\n\nencode :: (Ord a) => [a] -> (Maybe (Tree a), [Bit])\nencode s = (tree, msg)\n where\n tree = buildTree s\n msg = concatMap (table M.!) s\n table = case tree of\n Nothing -> M.empty\n Just t -> M.fromList $ mkTable (t, [])\n mkTable (Leaf _ a, p) = [(a, reverse p)]\n mkTable (Node _ t1 t2, p) = concatMap mkTable [(t1, Zero:p), (t2, One:p)]\n\ndecode :: (Ord a) => Maybe (Tree a) -> [Bit] -> [a]\ndecode Nothing _ = []\ndecode (Just t) m = path t m\n where path (Leaf _ a) m = a : path t m\n path (Node _ t1 _) (Zero: m) = path t1 m\n path (Node _ _ t2) (One: m) = path t2 m\n path _ _ = []\n\nmain = do\n let msg = \"bibbity bobbity\"\n (tree, encoded) = encode msg\n decoded = decode tree encoded\n putStrLn $ \"Endoding \\\"\" ++ msg ++ \"\\\": \" ++ concatMap show encoded\n putStrLn $ \"Length: \" ++ (show $ length encoded)\n putStrLn $ \"Decoding: \" ++ decoded\n\nHuffmanCoding.cs\n// submitted by Julian Schacher (jspp), thanks to gustorn for the help\nusing System;\nusing System.Collections.Generic;\nusing System.Linq;\n\nnamespace HuffmanCoding\n{\n public class EncodingResult\n {\n public string BitString { get; set; }\n public Dictionary Dictionary { get; set; }\n public HuffmanCoding.Node Tree { get; set; }\n\n public EncodingResult(string bitString, Dictionary dictionary, HuffmanCoding.Node tree)\n {\n this.BitString = bitString;\n this.Dictionary = dictionary;\n this.Tree = tree;\n }\n }\n\n public class HuffmanCoding\n {\n // The Node class used for the Huffman Tree.\n public class Node : IComparable\n {\n public Node LeftChild { get; set; }\n public Node RightChild { get; set; }\n public string BitString { get; set; } = \"\";\n public int Weight { get; set; }\n public string Key { get; set; }\n\n public bool IsLeaf => LeftChild == null && RightChild == null;\n\n // Creates a leaf. So just a node is created with the given values.\n public static Node CreateLeaf(char key, int weight) => new Node(key.ToString(), weight, null, null);\n // Creates a branch. Here a node is created by adding the keys and weights of both childs together.\n public static Node CreateBranch(Node leftChild, Node rightChild) => new Node(leftChild.Key + rightChild.Key, leftChild.Weight + rightChild.Weight, leftChild, rightChild);\n private Node(string key, int weight, Node leftChild, Node rightChild)\n {\n this.Key = key;\n this.Weight = weight;\n this.LeftChild = leftChild;\n this.RightChild = rightChild;\n }\n\n public int CompareTo(Node other) => this.Weight - other.Weight;\n }\n\n // Node with biggest value at the top.\n class NodePriorityList\n {\n public int Count => nodes.Count;\n\n private List nodes = new List();\n\n public NodePriorityList() { }\n public NodePriorityList(List givenNodes)\n {\n this.nodes = givenNodes.ToList();\n this.nodes.Sort();\n }\n\n public void Add(Node newNode)\n {\n var index = this.nodes.BinarySearch(newNode);\n if (index c)\n .Select(n => Node.CreateLeaf(n.Key, n.Count()))\n .ToList();\n\n // Convert list of nodes to a NodePriorityList.\n var nodePriorityList = new NodePriorityList(nodes);\n\n // Create Tree.\n while (nodePriorityList.Count > 1)\n {\n // Pop the two nodes with the smallest weights from the nodePriorityList and create a parentNode with the CreateBranch method. (This method adds the keys and weights of the childs together.)\n var leftChild = nodePriorityList.Pop();\n var rightChild = nodePriorityList.Pop();\n var parentNode = Node.CreateBranch(leftChild, rightChild);\n\n nodePriorityList.Add(parentNode);\n }\n\n return nodePriorityList.Pop();\n }\n\n private Dictionary CreateDictionary(Node root)\n {\n // We're using a string instead of a actual bits here, since it makes the code somewhat more readable and this is an educational example.\n var dictionary = new Dictionary();\n CreateDictionary(root, \"\", dictionary);\n return dictionary;\n\n void CreateDictionary(Node node, string bitString, Dictionary localDictionary)\n {\n if (node.IsLeaf)\n localDictionary.Add(node.Key[0], bitString);\n else\n {\n if (node.LeftChild != null)\n CreateDictionary(node.LeftChild, bitString + '0', localDictionary);\n if (node.RightChild != null)\n CreateDictionary(node.RightChild, bitString + '1', localDictionary);\n }\n }\n }\n\n\n private string CreateBitString(string input, Dictionary dictionary)\n {\n // We're using a string right here. While no compression is achieved with a string, it's the easiest way to display what the compressed result looks like. Also this is just an educational example.\n var bitString = \"\";\n foreach (var character in input)\n bitString += dictionary[character];\n\n return bitString;\n }\n }\n}\n\nProgram.cs\n// submitted by Julian Schacher (jspp), thanks to gustorn for the help\nusing System.Collections;\nusing System.Collections.Generic;\n\nnamespace HuffmanCoding\n{\n class Program\n {\n static void Main(string[] args)\n {\n var huffmanCoding = new HuffmanCoding();\n\n var result = huffmanCoding.Encode(\"bibbity bobbity\");\n // The bitStrings are just strings and provide no compression. Look in HuffmanCoding.cs for explanation.\n // Print dictionary.\n foreach (var entry in result.Dictionary)\n System.Console.WriteLine($\"{entry.Key} {entry.Value}\");\n // Print BitString.\n System.Console.WriteLine($\"{result.BitString} count: {result.BitString.Length}\");\n\n var originalString = huffmanCoding.Decode(result);\n System.Console.WriteLine(originalString);\n }\n }\n}\n\nlocal function frequency_array(str)\n -- Collect all frequency values into a dict\n local map = {}\n for c in str:gmatch(\".\") do -- Iterate over each character in str\n map[c] = (map[c] or 0) + 1 -- Increment map[c] (default 0) by 1\n end\n\n -- We have a dict of frequencies but we want it in a sorted list\n -- Dump each key value pair into an array\n local arr = {}\n for k, v in pairs(map) do\n arr[#arr + 1] = {k, v}\n end\n table.sort(arr, function(a, b) return a[2] > b[2] end) -- Sort by frequency descending\n return arr\nend\n\nlocal function build_huffman_tree(message)\n\n if #message == 0 then return end\n\n local freq = frequency_array(message)\n\n while #freq > 1 do -- Repeat until we have only 1 node\n\n -- Take two of the least frequent nodes\n local node1, node2 = table.remove(freq), table.remove(freq)\n\n -- Group node values in first index, and sum of node frequencies in second\n local node3 = { {node1[1], node2[1] }, node1[2] + node2[2] }\n\n local i = 1\n while i \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\n#include \n\nusing std::begin;\nusing std::end;\n\nnamespace huffman {\n\n[[noreturn]] inline void unreachable() {\n std::cerr ;\n using bitstring = std::vector;\n\n // this is a flatmap between char and a bitstring\n // there should only ever be one character with a given\n // value at any time.\n using encoder_t = std::vector>;\n\n struct leaf final : node {\n char key;\n\n leaf(int freq, char key) : node(freq), key(key) {}\n };\n\n struct branch final : node {\n node_ptr lhs;\n node_ptr rhs;\n\n branch(node_ptr lhs, node_ptr rhs)\n : node(lhs->frequency + rhs->frequency), lhs(std::move(lhs)),\n rhs(std::move(rhs)) {}\n };\n\n // this allows us to share [codebook]s among encoded strings\n struct data {\n node_ptr decoder;\n encoder_t encoder;\n };\n std::shared_ptr underlying_;\n\npublic:\n template \n codebook(Iter const first, Iter const last);\n\n template \n std::vector encode(Iter first, Iter last) const;\n\n template \n std::string decode(Iter first, Iter last) const;\n};\n\nstruct encoded_string {\n codebook codes;\n std::vector string;\n\n explicit encoded_string(std::string const& s)\n : codes(begin(s), end(s)), string(codes.encode(begin(s), end(s))) {}\n\n encoded_string(codebook codes, std::string const& s)\n : codes(codes), string(codes.encode(begin(s), end(s))) {}\n\n std::string decoded() const {\n return codes.decode(begin(string), end(string));\n }\n};\n\n// --- implementation ---\ninline codebook::node::~node() {}\n\ninline std::vector with_new_bit(std::vector bits, bool b) {\n bits.push_back(b);\n return bits;\n}\n\ntemplate \ncodebook::codebook(Iter const first, Iter const last) {\n struct helper {\n static node_ptr make_decoder(Iter const first, Iter const last) {\n // in this part of the function, we build up a frequency list\n // sorted by frequency, descending\n auto freq = std::vector();\n\n std::for_each(first, last, [&freq](char c) {\n auto const it = std::find_if(\n begin(freq), end(freq), [c](auto const& p) { return p.key == c; });\n if (it != end(freq)) {\n // it's already in the list\n it->frequency += 1;\n } else {\n // it's not already in the list\n freq.emplace_back(1, c);\n }\n });\n\n if (freq.empty()) {\n throw std::invalid_argument(\"attempted to codebook an empty range\");\n }\n\n std::sort(begin(freq), end(freq), [](auto const& lhs, auto const& rhs) {\n return lhs.frequency > rhs.frequency;\n });\n\n auto ret = std::vector>();\n std::transform(\n begin(freq), end(freq), std::back_inserter(ret), [](auto const l) {\n return std::make_unique(l);\n });\n\n while (ret.size() > 1) {\n auto rhs = std::move(ret.back());\n ret.pop_back();\n auto lhs = std::move(ret.back());\n ret.pop_back();\n\n auto new_node =\n std::make_unique(std::move(lhs), std::move(rhs));\n auto const new_freq = new_node->frequency;\n\n // look for the first element with a smaller frequency\n auto const it =\n std::find_if(begin(ret), end(ret), [new_freq](auto const& n) {\n return n->frequency bits, encoder_t& out) {\n if (auto l = dynamic_cast(cur)) {\n out.push_back(std::make_pair(l->key, std::move(bits)));\n } else if (auto b = dynamic_cast(cur)) {\n encoder_rec(b->lhs.get(), with_new_bit(bits, 0), out);\n encoder_rec(b->rhs.get(), with_new_bit(std::move(bits), 1), out);\n } else {\n unreachable();\n }\n }\n\n static encoder_t make_encoder(node const& decoder) {\n auto ret = encoder_t();\n\n encoder_rec(&decoder, std::vector(), ret);\n\n return ret;\n }\n };\n\n auto decoder = helper::make_decoder(first, last);\n auto encoder = helper::make_encoder(*decoder);\n underlying_ = std::make_shared(\n data{std::move(decoder), std::move(encoder)});\n}\n\ntemplate \nstd::vector codebook::encode(Iter const first, Iter const last) const {\n std::vector ret;\n\n auto& encoder = underlying_->encoder;\n std::for_each(first, last, [&ret, &encoder](char c) {\n auto const it =\n std::find_if(begin(encoder), end(encoder), [c](auto const& p) {\n return p.first == c;\n });\n if (it != end(encoder)) {\n auto const& code = it->second;\n std::copy(begin(code), end(code), std::back_inserter(ret));\n } else {\n throw std::invalid_argument(\n \"The range has a character which was not in the huffman set\");\n }\n });\n\n return ret;\n}\n\ntemplate \nstd::string codebook::decode(Iter const first, Iter const last) const {\n std::string ret;\n\n node const* const top = underlying_->decoder.get();\n\n // returns a pair:\n // the second member is the decoded character\n // the first member is the place we've gotten to in the range\n // i.e., if [0] is an 'a', and we have\n // [it, last) = { 0, 1, 1, 0 }\n // we return (it', 'a') such that\n // [it', last) = { 1, 1, 0 }\n auto decode_single =\n [top](Iter it, Iter const last) -> std::pair {\n node const* current_node = top;\n\n for (; it != last; ++it) {\n if (auto l = dynamic_cast(current_node)) {\n return std::make_pair(it, l->key);\n } else if (auto b = dynamic_cast(current_node)) {\n if (*it) {\n current_node = b->rhs.get();\n } else {\n current_node = b->lhs.get();\n }\n } else {\n unreachable();\n }\n }\n\n if (auto l = dynamic_cast(current_node)) {\n return std::make_pair(last, l->key);\n } else {\n throw std::invalid_argument(\n \"The range was not encoded with this huffman set\");\n }\n };\n\n for (auto it = first; it != last;) {\n auto p = decode_single(it, last);\n it = p.first;\n ret.push_back(p.second);\n }\n\n return ret;\n}\n\n} // namespace huffman\n\nint main() {\n std::string to_be_encoded = R\"(bibbity bobbity)\";\n\n auto encoded = huffman::encoded_string(to_be_encoded);\n\n std::cout \n;; earthfail\n(ns experiments.core)\n\n;; get a vector with chars and frequencies\n\n(defn tree-string [st]\n \"take a string st and return the huffmantree with the frequency of\n each character included\"\n ;; vector of [character frequency] pair\n ;; for every char in string, added it to hash-map\n ;; with value one if it doesn't exist or increment its value\n (def cf-vec (vec\n (reduce (fn [m c]\n (assoc m c (inc (get m c 0))))\n {}\n st)))\n ;; make a sorted list with nodes with bigger frequencies first\n ;; take the last two which will help in dividing the tree\n ;; the first and last elements before and after\n ;; the smallest two in the tree shouldn't change\n (loop [tree (sort-by last > cf-vec)]\n (if ( tree)\n mid (take-last 2 sorted-tree)\n set-mid (set mid)\n func (complement (partial contains? set-mid))\n firsty (take-while func tree)\n [middle lasty] (split-at 2\n (drop-while func tree))]\n (recur\n (concat\n firsty\n ;; make a list with the two element in one list and\n ;; the sum of their frequencies e.g\n ;; '(((node1 f1) (node2 f2)) f1+f2)\n (list (list middle (reduce #(+ %1 (last %2)) 0 middle)))\n lasty))))))\n\n(defn remove-freq [tree]\n \"remove the frequencies in the huffmantree tree\"\n (cond\n (char? tree) tree ; check if this is a branch\n ;; if the tree is a node and frequency then ignore frequency\n (integer? (second tree)) (remove-freq (first tree)) ;remove the frequency\n ;; if the tree consists of two nodes then apply to both and combine\n :else (list (remove-freq (first tree))\n (remove-freq (second tree)))))\n\n(defn hash-tree [tree]\n \"make a hashmap with code for each letter as key and the letter as\n value\"\n (cond\n (char? tree) {\"\" tree}\n :else\n (let [left-map (hash-tree (first tree))\n right-map (hash-tree (second tree))\n func #(apply hash-map ; apply hash-map because\n ; interleave return a seq\n (interleave\n (map (partial str %2) (keys %1)) ;add 0 or 1\n ;to the start\n ;of the keys\n (vals %1)))]\n ;; add \"0\" to the keys of left nodes and \"1\" to the right nodes\n (merge (func left-map \"0\") (func right-map \"1\")))))\n\n\n(defn coder [s hash-coder]\n \"take a string s and return a coded string\"\n (apply str (map hash-coder s)))\n\n(defn decoder [s hash-decoder]\n \"takes a string s and a hash-map hash-decoder and decode s\"\n ;; code keyword in hashmap is for storing codes untill they are\n ;; complete and can be decoded with the decoder\n (get (reduce (fn [m code] ; reduce return {:message\n ; message,:code _}\n (let [new-code (str (m :code) code)]\n (if-let [letter (get hash-decoder new-code)]\n ;; if there is a letter then add it to :message\n ;; and revert :code to empty\n (assoc (update m :message #(str % letter))\n :code \"\")\n ;; if there is not a letter then just add the\n ;; code letter to the :code\n (update m :code #(str % code)))))\n {:message \"\",:code \"\"}\n s)\n :message)) ;extract :message value\n;; ----------------EXAMPLE----------------\n(def st \"(bibbity bobbity)\")\n\n(def hash-decoder (->>\n st\n tree-string\n remove-freq\n hash-tree))\n(def hash-coder (clojure.set/map-invert hash-decoder))\n(println \"coding...\")\n(def code (coder st hash-coder))\n(clojure.pprint/pprint code)\n\n(println \"\\ndecoding...\")\n(clojure.pprint/pprint (decoder code hash-decoder))\n\n# Huffman Encoding\n# Python 2.7+\n# Submitted by Matthew Giallourakis\n\nfrom collections import Counter\n\n# constructs the tree\ndef build_huffman_tree(message):\n\n # get sorted list of character and frequency pairs\n frequencies = Counter(message)\n trees = frequencies.most_common()\n\n # while there is more than one tree\n while len(trees) > 1:\n\n # pop off the two trees of least weight from the trees list\n tree_left,weight_left = trees.pop()\n tree_right,weight_right = trees.pop()\n\n # combine the nodes and add back to the nodes list\n new_tree = [tree_left, tree_right]\n new_weight = weight_left + weight_right\n\n # find the first tree that has a weight smaller than new_weight and returns its index in the list\n # If no such tree can be found, use len(trees) instead to append\n index = next((i for i, tree in enumerate(trees) if tree[1] code dictionary\n forward_dict = dict(codebook)\n\n # replace each character with its code\n for char in message:\n encoded_message += forward_dict[char]\n\n return encoded_message\n\n# decodes a message\ndef huffman_decode(codebook, encoded_message):\n\n decoded_message = ''\n key = ''\n\n # build a code -> char dictionary\n inverse_dict = dict([(v, k) for k, v in codebook])\n\n # for each bit in the encoding\n # if the bit is in the dictionary, replace the bit with the paired character\n # else look at the bit and the following bits together until a match occurs\n # move to the next bit not yet looked at\n for index, bit in enumerate(encoded_message):\n key += bit\n if key in inverse_dict:\n decoded_message += inverse_dict[key]\n key = ''\n\n return decoded_message\n\ndef main():\n\n # test example\n message = 'bibbity_bobbity'\n tree = build_huffman_tree(message)\n codebook = build_codebook(tree)\n encoded_message = huffman_encode(codebook, message)\n decoded_message = huffman_decode(codebook, encoded_message)\n\n print('message: ' + message)\n print('huffman tree: ' + str(tree))\n print('codebook: ' + str(codebook))\n print('encoded message: ' + encoded_message)\n print('decoded message: ' + decoded_message)\n\n # prints the following:\n #\n # message: bibbity_bobbity\n # huffman_tree: ['b', [[['_', 'o'], 'y'], ['t', 'i']]]\n # codebook: [('b', '0'), ('_', '1000'), ('o', '1001'),\n # ('y', '101'), ('t', '110'), ('i', '111')]\n # encoded_message: 01110011111010110000100100111110101\n # decoded_message: bibbity_bobbity\n\nif __name__ == '__main__':\n main()\n\nfunction encode(str) {\n const tree = createTree(str);\n const codebook = createCodebook(tree);\n return {\n string: [...str].map(c => codebook[c]).join(\"\"),\n tree,\n codebook\n };\n\n function createTree(str) {\n const chars = [...str];\n const charCounts = chars.reduce((counts, char) => {\n counts[char] = (counts[char] || 0) + 1;\n return counts;\n }, {});\n\n const nodes = Object.entries(charCounts).map(([key, weight]) => ({ key, weight }));\n const priorityQueue = makeQueue(nodes);\n while (priorityQueue.data.length > 1) {\n const left = priorityQueue.dequeue();\n const right = priorityQueue.dequeue();\n priorityQueue.enqueue({ weight: left.weight + right.weight, left, right });\n }\n return priorityQueue.dequeue();\n }\n\n function createCodebook(tree) {\n return recurse(tree, \"\", {});\n\n function recurse(node, bitstring, dict) {\n if (!node.left && !node.right) {\n dict[node.key] = bitstring;\n } else {\n if (node.left) {\n recurse(node.left, bitstring + \"0\", dict);\n }\n\n if (node.right) {\n recurse(node.right, bitstring + \"1\", dict);\n }\n }\n return dict;\n }\n }\n}\n\nfunction decode(bitstring, tree) {\n const result = [];\n let node = tree;\n\n for (const bit of [...bitstring]) {\n node = bit === \"0\" ? node.left : node.right;\n if (!node.left && !node.right) {\n result.push(node.key);\n node = tree;\n }\n }\n\n return result.join(\"\");\n}\n\n// This queue implementation is horribly inefficient, but a proper, heap-based implementation would\n// be longer that the algorithm itself\nfunction makeQueue(iterable) {\n return {\n data: [...iterable].sort((a, b) => a.weight - b.weight),\n enqueue(value) {\n const target = this.data.findIndex(x => x.weight > value.weight);\n if (target === -1) {\n this.data.push(value);\n } else {\n this.data = [...this.data.slice(0, target), value, ...this.data.slice(target)];\n }\n },\n dequeue() {\n return this.data.shift();\n }\n };\n}\n\nconst encoded = encode(\"bibbity bobbity\");\nconst decoded = decode(encoded.string, encoded.tree);\nconsole.log(encoded.string);\nconsole.log(decoded);\n\nimport java.util.*;\n\nclass Huffman {\n public static void main(String[] args) {\n HuffmanTree huffmanTree = new HuffmanTree(\"bibbity_bobbity\");\n huffmanTree.createTree();\n String encoded = huffmanTree.encode();\n System.out.println(\"Encoded String: \" + encoded);\n System.out.println(\"Decoded String: \" + huffmanTree.decode(encoded));\n }\n}\n\nclass TreeNode {\n String letter = \"\";\n int frequency = 0;\n TreeNode left = null, right = null;\n\n public TreeNode(String letter, int frequency) {\n this.letter = letter;\n this.frequency = frequency;\n }\n\n public TreeNode(int frequency, TreeNode left, TreeNode right) {\n this.frequency = frequency;\n this.left = left;\n this.right = right;\n }\n}\n\nclass HuffmanTree {\n private Map frequencyMap = new HashMap<>();\n private Map codeBook = new HashMap<>(), reverseCodeBook = new HashMap<>();\n private TreeNode root;\n private String stringToEncode;\n\n public HuffmanTree(String stringToEncode) {\n this.stringToEncode = stringToEncode;\n }\n\n public void createTree() {\n for (int i = 0; i priorityQueue = new PriorityQueue<>(Comparator.comparingInt(o -> o.frequency));\n for (Map.Entry m : frequencyMap.entrySet()) {\n priorityQueue.add(new TreeNode(m.getKey(), m.getValue()));\n }\n while (priorityQueue.size() > 1) {\n TreeNode left = priorityQueue.remove();\n TreeNode right = priorityQueue.remove();\n priorityQueue.add(new TreeNode(left.frequency + right.frequency, left, right));\n }\n root = priorityQueue.remove();\n }\n\n private void traverse(TreeNode node, StringBuilder code) {\n if (node.left == null && node.right == null) {\n codeBook.put(node.letter, code.toString());\n }\n if (node.left != null) {\n traverse(node.left, code.append(0));\n code.deleteCharAt(code.length() - 1);\n }\n if (node.right != null) {\n traverse(node.right, code.append(1));\n code.deleteCharAt(code.length() - 1);\n }\n }\n\n public void printCodeBook() {\n System.out.println(\"Code Book\");\n for (Map.Entry m : codeBook.entrySet()) {\n System.out.println(m.getKey() + \"\\t\" + m.getValue());\n }\n System.out.println();\n }\n\n private void CodeBookReverse() {\n for (Map.Entry m : codeBook.entrySet()) {\n reverseCodeBook.put(m.getValue(), m.getKey());\n }\n }\n\n public String encode() {\n traverse(root, new StringBuilder());\n StringBuilder encode = new StringBuilder();\n for (int i = 0; i \npackage main\n\nimport (\n \"container/heap\"\n \"fmt\"\n)\n\ntype node struct {\n freq int\n char rune\n left *node\n right *node\n}\n\ntype codebook map[rune]string\ntype nodeHeap []*node\n\nfunc (n nodeHeap) Len() int { return len(n) }\nfunc (n nodeHeap) Less(i, j int) bool { return n[i].freq > n[j].freq }\nfunc (n nodeHeap) Swap(i, j int) { n[i], n[j] = n[j], n[i] }\n\nfunc (n *nodeHeap) Push(x interface{}) {\n if node, ok := x.(*node); ok {\n *n = append(*n, node)\n } else {\n fmt.Printf(\"I got a node of Type %T\\n\", x)\n }\n}\n\nfunc (n *nodeHeap) Pop() interface{} {\n old := *n\n l := len(old)\n x := old[l-1]\n *n = old[0 : l-1]\n return x\n}\n\nfunc buildTree(message string) *node {\n freqMap := make(map[rune]*node)\n h := new(nodeHeap)\n heap.Init(h) // really needed?\n\n for _, char := range message {\n if _, ok := freqMap[char]; ok {\n freqMap[char].freq++\n } else {\n newNode := new(node)\n newNode.freq = 1\n newNode.char = char\n freqMap[char] = newNode\n heap.Push(h, newNode)\n }\n }\n\n for h.Len() > 1 {\n left, right := h.Pop().(*node), h.Pop().(*node)\n branch := new(node)\n branch.freq = right.freq + left.freq\n branch.left = left\n branch.right = right\n heap.Push(h, branch)\n }\n\n root := heap.Pop(h).(*node)\n return root\n}\n\nfunc codebookRecurse(node *node, cb *codebook, code []rune) {\n if node == nil {\n return\n }\n\n if node.left == nil && node.right == nil {\n (*cb)[node.char] = string(code)\n }\n\n code = append(code, '0')\n codebookRecurse(node.left, cb, code)\n code = append(code[:len(code)-1], '1')\n codebookRecurse(node.right, cb, code)\n}\n\nfunc encode(message string) (string, *node, codebook) {\n ret := \"\"\n root := buildTree(message)\n cb := generateCodebook(root)\n for _, char := range message {\n ret += cb[char]\n }\n\n return ret, root, cb\n}\n\nfunc decode(message string, root *node) string {\n cur := root\n ret := \"\"\n\n for _, char := range message {\n if cur == nil {\n return message\n }\n\n switch string(char) {\n case \"0\":\n if cur.left == nil {\n ret += string(cur.char)\n cur = root.left\n } else {\n cur = cur.left\n }\n case \"1\":\n if cur.right == nil {\n ret += string(cur.char)\n cur = root.right\n } else {\n cur = cur.right\n }\n }\n }\n\n if cur.char != 0 {\n ret += string(cur.char)\n }\n\n return ret\n}\n\nfunc generateCodebook(root *node) codebook {\n cb := make(codebook)\n codeArr := make([]rune, 0)\n codebookRecurse(root, &cb, codeArr)\n return cb\n}\n\nfunc main() {\n enc, root, cb := encode(\"bibbity_bobbity\")\n fmt.Println(\"Codebook:\")\n for r, c := range cb {\n fmt.Println(string(r), \"->\", c)\n }\n fmt.Println(\"\\nEncoded:\", enc)\n fmt.Println(\"Decoded:\", decode(enc, root))\n}\n\n.intel_syntax noprefix\n\n# System V calling convention cheatsheet\n# Params: rdi, rsi, rdx, rcx, r8, r9, xmm0-7\n# Return: rax (int 64 bits), rax:rdx (int 128 bits), xmm0 (float)\n# Callee cleanup: rbx, rbp, r12-15\n# Scratch: rax, rdi, rsi, rdx, rcx, r8, r9, r10, r11\n\n.section .rodata\n text: .string \"bibbity bobbity\"\n original: .string \"Original message: %s\\n\"\n encoded: .string \"Encoded message: \"\n decoded: .string \"Decoded message: %s\\n\"\n\n .equ bitstr_len, 32\n .equ bitstr_size, 40\n .equ codebook_size, 256 * bitstr_size\n\n .equ tree_left, 0\n .equ tree_right, 8\n .equ tree_count, 16\n .equ tree_value, 20\n .equ tree_size, 24\n\n .equ heap_len, 0\n .equ heap_data, 4\n .equ heap_size, 512 * 8 + 16 # 512 ptrs + 4 byte length + 12 byte padding\n .equ counts_size, 256 * 4\n\n .equ msg_len, 0\n .equ msg_data, 8\n.section .text\n .global main\n .extern printf, calloc, malloc, memset, puts\n\nmain:\n push r12\n push r13\n sub rsp, codebook_size + 16 # 8 extra bytes for the Huffman-tree ptr, 8 bytes for padding\n\n # Print the original text\n mov rdi, OFFSET original\n mov rsi, OFFSET text\n xor rax, rax\n call printf\n\n # First encode the text. This will also initialize the Huffman-tree and the codebook\n mov rdi, OFFSET text\n mov rsi, rsp\n lea rdx, [rsp + codebook_size]\n call encode\n mov r12, rax # Save the returned message ptr\n\n # Print the codebook and the encoded message\n mov rdi, rsp\n call print_codebook\n mov rdi, OFFSET encoded\n xor rax, rax\n call printf\n mov rdi, r12\n call print_message\n\n # Decode and print the message\n mov rdi, r12\n mov rsi, QWORD PTR [rsp + codebook_size]\n call decode\n mov r13, rax\n mov rdi, OFFSET decoded\n mov rsi, r13\n xor rax, rax\n call printf\n\n # Free allocated resources\n mov rdi, r12\n call free\n mov rdi, r13\n call free\n mov rdi, QWORD PTR [rsp + codebook_size]\n call free_tree\n\n add rsp, codebook_size + 16\n pop r13\n pop r12\n\n # Indiciate success with a 0 exit code\n xor rax, rax\n ret\n\n# rdi - text\n# rsi - codebook ptr\n# rdx - Huffman-tree ptr\n# RET rax - encoded message ptr\nencode:\n push r12\n push r13\n push r14\n mov r12, rdi # Save the original arguments\n mov r13, rsi\n mov r14, rdx\n call generate_tree # The text is already in rdi\n mov QWORD PTR [r14], rax # Save the Huffman-tree's root\n mov rdi, r13 # Set up the parameters for codebook generation: codebook ptr, Huffman-tree root\n mov rsi, rax\n call generate_codebook\n xor rax, rax\n xor r14, r14 # We'll use r14 to keep track of the length of the message\n mov rcx, r12 # Make a copy of the pointer to the message to be encoded\nencode_calculate_length:\n mov al, BYTE PTR [rcx]\n test al, al # If we're at the terminating null character then we're ready to encode\n jz encode_message\n lea rdx, [rax + 4*rax] # We get the codebook entry at the specific index\n lea r8, [r13 + 8*rdx]\n add r14, QWORD PTR [r8 + bitstr_len] # And add the encoded word length to the total\n inc rcx\n jmp encode_calculate_length\nencode_message:\n mov rdi, 1\n lea rsi, [r14 + 7] # Calculate the number of bytes we need to allocate to fit all the bits\n shr rsi, 3 # length % 8 rounded up = (length + 8 - 1) / 8\n lea rsi, [rsi + 8] # Make space for an 8-byte length field\n call calloc # Allocate the necessary memory, the message will be in rax\n mov QWORD PTR [rax], r14 # Save the length of the message\n # Registers:\n # - r12: text\n # - r13: codebook_ptr\n # - rax: message ptr\n # - free to use: rdi, rsi, rcx, rdx, r8, r9, r10, r11, r14\n xor r8, r8 # Bit offset\n lea r9, [rax + 8] # 8-byte message block\nencode_message_bits:\n xor rdi, rdi # We need to clear rdi because moving a single byte to dil doesn't do so\n mov dil, BYTE PTR [r12] # Iterate the message again\n test dil, dil # If we're at the the null terminator we're done\n jz encode_done\n lea rdx, [rdi + 4*rdi] # Get the codebook entry\n lea r10, [r13 + 8*rdx]\n mov r11, QWORD PTR [r10 + bitstr_len] # Load the bitstring length\n lea r14, [r10] # The bitstring qword we're currently processing\nencode_message_bits_qword:\n mov rdi, QWORD PTR [r14] # Calculate the first mask: [code qword] > [64 - bit offset]\n sub rcx, r8\n shr rsi, cl\n mov rcx, r11 # Copy the code length so we can manipulate it without destroying the original value\n sub rcx, 64\n jle encode_message_bits_try_overflow # If the length was less than or equal to 64, check if the code qword would overflow the current message block\n mov r11, rcx # We wanted to subtract 64 from the code length anyway\n lea r9, [r9 + 8] # Load the next message block\n or QWORD PTR [r9], rsi # Save the second mask to the new message block\n jmp encode_message_bits_qword\nencode_message_bits_try_overflow:\n add rcx, r8 # Calculate [code length] + [bit offset] - 64\n jl encode_calculate_new_bit_offset # If the result is less than 0 then we have no remaining bits -> calculate the new bit offset\n mov r8, rcx # Otherwise this also happens to be our new bit offset\n lea r9, [r9 + 8] # Load the next message block\n or QWORD PTR [r9], rsi # Save the second mask to the new message block\n inc r12 # Go to the next character in the input\n jmp encode_message_bits\nencode_calculate_new_bit_offset:\n lea r8, [r8 + r11] # Calculate the bit offset for the next code qword\n inc r12\n jmp encode_message_bits\nencode_done:\n pop r14\n pop r13\n pop r12\n ret\n\n# rdi - encoded message\n# rsi - Huffman-tree root (ptr)\n# RET rax - the decoded message\ndecode:\n push r12\n push r13\n push r14\n mov r12, rdi\n mov r13, rsi\n mov rdi, QWORD PTR [r12] # Load the length of the message\n mov r14, rdi # We'll use the length of the message as a loop counter later\n lea rdi, [rdi + 1] # The null terminator\n call malloc # This will usually be more than enough memory to contain the whole decoded message (we don't handle pathological cases right now)\n mov rdi, r12 # The single-character decoder doesn't touch rdi so we can hoist it before the loop\n xor rcx, rcx\n mov rdx, rax # The current byte in the output string\ndecode_loop:\n cmp rcx, r14 # The encoded message bit counter\n jge decode_done\n mov rsi, r13 # The current node in the Huffman-tree\ndecode_loop_char:\n test rsi, rsi # If the Huffman-tree node is null then we reached a dead-end -> start over\n jz decode_loop\n cmp QWORD PTR [rsi + tree_left], 0 # If the node has either a left or a right child, treat it as a branch\n jnz decode_loop_char_branch\n cmp QWORD PTR [rsi + tree_right], 0\n jnz decode_loop_char_branch\n mov r9d, DWORD PTR [rsi + tree_value] # Load the value in this node in case the next iteration needs it\n mov BYTE PTR [rdx], r9b # And save it to the output\n lea rdx, [rdx + 1] # Advance the output string\n jmp decode_loop\ndecode_loop_char_branch:\n mov r9, rcx # First, load the byte of the message the current bit is in\n shr r9, 3\n mov r10b, BYTE PTR [rdi + r9 + msg_data]\n mov r11, rcx # Save rcx in another register temporarily so we can restore it without push/pop\n and rcx, 7\n shr r10, cl # Get the bit we're interested in to position 0\n lea rcx, [r11 + 1] # Restore rcx and immediately add 1 to get the next bit to decode\n and r10, 0x1 # Zero out all other bits\n mov r8, rsi\n mov rsi, QWORD PTR [r8 + tree_left] # Take the left branch for 0, the right branch for a non-zero bit\n cmovnz rsi, QWORD PTR [r8 + tree_right]\n jmp decode_loop_char\ndecode_done:\n mov BYTE PTR [rdx], 0 # Write the null terminator at the end of the string\n pop r14\n pop r13\n pop r12\n ret\n\n# rdi - The starting address of the codebook we want to generate\n# rsi - Huffman-tree root (ptr)\ngenerate_codebook:\n push r12\n sub rsp, bitstr_size + 16 # 16 extra bytes for alignment\n mov r12, rsi\n xorps xmm0, xmm0 # Create a 0-initialized bitstring. This will be\n movaps XMMWORD PTR [rsp], xmm0 # used in the recursive function calls\n movaps XMMWORD PTR [rsp + 16], xmm0\n mov QWORD PTR [rsp + 32], 0\n xor rsi, rsi\n mov rdx, codebook_size\n call memset\n mov rdi, rax\n mov rsi, r12\n mov rdx, rsp\n call generate_codebook_recurse\n add rsp, bitstr_size + 16\n pop r12\n ret\n\n# rdi - The codebook's starting address\n# rsi - The current Huffman-tree node\n# rdx - The bitstring used for code generation\ngenerate_codebook_recurse:\n push rbp\n push r12\n push r13\n test rsi, rsi # If we reached a null pointer we're done\n jz generate_codebook_recurse_done\n mov r12, rsi\n cmp QWORD PTR [r12 + tree_left], 0 # If at least one of the children is not null\n jnz generate_codebook_branch # then we need to treat the current node as a branch\n cmp QWORD PTR [r12 + tree_right], 0\n jnz generate_codebook_branch\n mov r8d, DWORD PTR [r12 + tree_value] # Get the value of the current node\n movaps xmm0, XMMWORD PTR [rdx] # Get the values of the current bitstring into some registers\n movaps xmm1, XMMWORD PTR [rdx + 16]\n mov r9, QWORD PTR [rdx + 32]\n lea rax, [r8 + 4*r8] # The index calculation needs to add 40 * index. With lea arithmetic this can be represented as\n lea r10, [rdi + 8*rax] # base address + 8 * (5 * index). This is done in two lea instructions\n movups XMMWORD PTR [r10], xmm0 # And copy the data over to it\n movups XMMWORD PTR [r10 + 16], xmm1\n mov QWORD PTR [r10 + 32], r9\n jmp generate_codebook_recurse_done\ngenerate_codebook_branch:\n # First, calculate the necessary indices and bitmask to use for the bitstring\n mov r13, QWORD PTR [rdx + bitstr_len] # Load the current length of the bitstring\n mov rcx, r13 # This will be used to index into the bitstring data. We'll need two copies for it\n shr r13, 6 # We first get which 64 bit chunk of the bitstring we want to modify\n and rcx, 63 # Then the bit we want to change\n mov rbp, 1 # Generate the mask we'll use to set the correct bit\n shl rbp, cl\n # We'll start with the right branch\n or QWORD PTR [rdx + 8*r13], rbp # Set the bit\n inc QWORD PTR [rdx + bitstr_len] # Increase the bitstring length\n mov rsi, QWORD PTR [r12 + tree_right]\n call generate_codebook_recurse\n # Now we move on to the left branch: rbx - left child, r13 - bitstring index, rbp - mask\n not rbp\n and QWORD PTR [rdx + 8*r13], rbp\n mov rsi, QWORD PTR [r12 + tree_left]\n call generate_codebook_recurse\n dec QWORD PTR [rdx + bitstr_len] # Decrease the bitstring length\ngenerate_codebook_recurse_done:\n pop r13\n pop r12\n pop rbp\n ret\n\n# rdi - text\n# RET rax - Huffman-tree root (ptr)\ngenerate_tree:\n push r12\n push r13\n sub rsp, 5128 # 1024 bytes for the char counts, 4 bytes for heap length, 4096 bytes for the heap, 4 byte padding\n mov r12, rdi # Save the original text so it doesn't get clobbered\n mov rdi, rsp # Zero out the character counts and the heap length\n xor rsi, rsi\n mov rdx, 1040\n call memset\n xor rax, rax\ngenerate_tree_count_chars:\n mov al, BYTE PTR [r12]\n test al, al\n jz generate_tree_leaves_setup\n inc DWORD PTR [rsp + 4*rax]\n inc r12\n jmp generate_tree_count_chars\ngenerate_tree_leaves_setup:\n mov r12, 255 # The loop counter. We can only get here if the \"test\" on line 301 resulted in a zero so the next jl instruction will do the right thing\ngenerate_tree_leaves:\n jl generate_tree_one_leaf # If not then it's time to generate the branches\n mov r13d, DWORD PTR [rsp + 4*r12] # Load the count at the ith position\n test r13d, r13d # And check if it's zero\n jz generate_tree_leaves_counters # If it is we can skip this iteration\n mov rdi, 1 # If not, we need to allocate a new leaf node\n mov rsi, tree_size\n call calloc\n mov DWORD PTR [rax + tree_value], r12d # Save the value and the count to the tree\n mov DWORD PTR [rax + tree_count], r13d\n lea rdi, [rsp + counts_size] # Then push it onto the heap\n mov rsi, rax\n call heap_push\ngenerate_tree_leaves_counters:\n dec r12 # Decrement the loop counter and start over\n jmp generate_tree_leaves\ngenerate_tree_one_leaf:\n cmp DWORD PTR [rsp + counts_size], 1 # Check if there is only one element in the heap\n jne generate_tree_branches\n lea rdi, [rsp + counts_size] # Get the element\n call heap_pop\n mov r12, rax\n mov rdi, tree_size # Create the new tree node, the pointer to it will be in rax\n call malloc\n mov QWORD PTR [rax + tree_left], r12 # Save element in the left node\n mov ecx, DWORD PTR [r12 + tree_count] # Save element count in branch\n mov DWORD PTR [rax + tree_count], ecx\n jmp generate_tree_ret # Returning\ngenerate_tree_branches:\n cmp DWORD PTR [rsp + counts_size], 1 # Check if there are still at least two elements in the heap\n jle generate_tree_done # If not, we're done\n lea rdi, [rsp + counts_size] # Get the left child\n call heap_pop\n mov r12, rax\n lea rdi, [rsp + counts_size] # Get the right child\n call heap_pop\n mov r13, rax\n mov rdi, tree_size # Create the new tree node, the pointer to it will be in rax\n call malloc\n mov ecx, DWORD PTR [r12 + tree_count] # The new node's count: left count + right count\n add ecx, DWORD PTR [r13 + tree_count]\n mov QWORD PTR [rax + tree_left], r12 # Save the new node's fields: left, right, count (leave value unititialized, it shouldn't be used with branch nodes)\n mov QWORD PTR [rax + tree_right], r13\n mov DWORD PTR [rax + tree_count], ecx\n lea rdi, [rsp + counts_size] # Add the branch to the heap\n mov rsi, rax\n call heap_push\n jmp generate_tree_branches\ngenerate_tree_done:\n lea rdi, [rsp + counts_size] # The tree's root will be in rax after the pop\n call heap_pop\ngenerate_tree_ret:\n add rsp, 5128\n pop r13\n pop r12\n ret\n\n# rdi - heap ptr\n# rsi - tree ptr\nheap_push:\n lea rax, QWORD PTR [rdi + heap_data] # We load the heap's data ptr and length to the respective registers\n mov ecx, DWORD PTR [rdi + heap_len] # Load the current length\n lea edx, [ecx + 1] # First, calculate the new length (length + 1)\n mov DWORD PTR [rdi + heap_len], edx # Then save it\n mov QWORD PTR [rax + 8*rcx], rsi # And finally add the new value at the end of the array\nheap_push_sift_up:\n test rcx, rcx # Test if we got to the root (index == 0)\n jz heap_push_done\n lea rdx, [rcx - 1] # Calculate the parent index: (index - 1) / 2\n shr rdx, 1\n lea r8, [rax + 8*rcx] # Get the pointer to the current and parent elements\n lea r9, [rax + 8*rdx]\n mov r10, QWORD PTR [r8] # Load the current and the parent elements\n mov r11, QWORD PTR [r9]\n mov esi, DWORD PTR [r10 + tree_count] # Load the current tree's count\n cmp DWORD PTR [r11 + tree_count], esi # If parent count \nimport scala.collection.mutable.{Map, PriorityQueue}\n\nobject HuffmanEncoding {\n\n trait Node {\n var weight: Int\n }\n\n case class Leaf(char: Char, var weight: Int) extends Node\n\n case class Branch(left: Node, right: Node, var weight: Int) extends Node\n\n def createTree(phrase: String): Option[Node] = {\n\n val tree = PriorityQueue[Node]()(Ordering.by(-_.weight))\n tree ++= phrase\n .groupBy(identity)\n .mapValues(_.length)\n .map{\n case (char, count) => Leaf(char, count)\n }\n\n while (tree.size > 1) {\n val node1 = tree.dequeue()\n val node2 = tree.dequeue()\n tree += Branch(node1, node2, node1.weight + node2.weight)\n }\n\n tree.headOption\n }\n\n\n def createCodeBook(maybeRoot: Option[Node]): Map[Char, String] = {\n val codeBook = Map[Char, String]()\n\n def codeBookRecurse(node: Node, code: String): Unit =\n node match {\n case Leaf(symbol, _) => codeBook.put(symbol, code)\n case Branch(left, right, _) => {\n codeBookRecurse(left, code + \"0\")\n codeBookRecurse(right, code + \"1\")\n }\n }\n\n maybeRoot.foreach(c => codeBookRecurse(c, \"\"))\n\n codeBook\n }\n\n\n def encode(phrase: String, codeBook: Map[Char, String]): String = {\n phrase.flatMap(c => codeBook.getOrElse(c, \"?\"))\n }\n\n def decode(encoded: String, maybeRoot: Option[Node]): String = {\n val root = maybeRoot.getOrElse(Leaf('?', 0))\n var currentNode = root\n\n def chooseTreeBranch(bit: Char) =\n currentNode match {\n case Branch(left, right, _) =>\n currentNode = if (bit == '0') left else right\n case _ =>\n }\n\n def maybeGetACharacter =\n currentNode match {\n case Leaf(c, _) => {\n currentNode = root\n Some(c)\n }\n case _ => None\n }\n\n encoded\n .flatMap(bit => {\n chooseTreeBranch(bit)\n maybeGetACharacter\n })\n }\n\n def main(args: Array[String]): Unit = {\n val originalText = \"bibbity_bobbity\"\n println(\"Original Text: \" + originalText)\n\n val tree = createTree(originalText)\n val codeBook = createCodeBook(tree)\n println(\"CodeBook is: \" + codeBook)\n\n val encoded = encode(originalText, codeBook)\n println(\"Encoded text: \" + encoded)\n\n val decoded = decode(encoded, tree)\n println(\"Decoded text: \" + decoded)\n\n }\n\n}\n\nThe code snippet was taken from this scratch project\n\n \nfrom collections import Counter, deque\nfrom bisect import bisect\n\nclass Tree\n\ndata Empty() from Tree\ndata Leaf(char, n is int) from Tree:\n def __str__(self):\n return f'Leaf({self.char}, {self.n})'\n\n __repr__ = __str__\n\ndata Node(left is Tree, right is Tree) from Tree:\n def __str__(self):\n return f'Node({str(self.left)}, {str(self.right)})'\n __repr__ = __str__\n\ndef weight(Tree()) = 0\naddpattern def weight(Leaf(char, n)) = n\naddpattern def weight(Node(left, right)) = weight(left) + weight(right)\n\ndef build_huffman_tree(message):\n\n # get sorted list of character and frequency pairs\n frequencies = Counter(message)\n trees = frequencies.most_common() |> map$(t -> Leaf(*t)) |> reversed |> deque\n\n if not trees:\n return Empty()\n\n # while there is more than one tree\n while len(trees) > 1:\n\n # pop off the two trees of least weight from the trees list\n tree_left = trees.popleft()\n tree_right = trees.popleft()\n\n # combine the nodes and add back to the nodes list\n new_tree = Node(tree_left, tree_right)\n\n # find the first tree that has a weight smaller than new_weight\n # and returns its index in the list.\n # If no such tree can be found, use len(trees) instead to append\n index = bisect(trees |> map$(weight) |> list, weight(new_tree))\n\n # insert the new tree there\n trees.insert(index, new_tree)\n\n huffman_tree = trees[0]\n return huffman_tree\n\n\ndef build_codebook(Empty(), code='') = []\naddpattern def build_codebook(Leaf(char, n), code='') = [(char, code)]\naddpattern def build_codebook(Node(left, right), code='') = \n build_codebook(left, code+'0') + build_codebook(right, code+'1')\n\ndef huffman_encode(codebook, message):\n\n if len(codebook) == 1:\n return '0' * len(message)\n\n # build a char -> code dictionary\n forward_dict = dict(codebook)\n\n return ''.join(message |> map$(forward_dict[]))\n\ndef huffman_decode(codebook, encoded_message):\n\n decoded_message = []\n key = ''\n\n if not codebook:\n return ''\n elif len(codebook) == 1:\n return codebook[0][0] * len(encoded_message)\n\n # build a code -> char dictionary\n inverse_dict = dict((v, k) for k, v in codebook)\n\n # for each bit in the encoding\n # if the bit is in the dictionary, replace the bit with the paired\n # character else look at the bit and the following bits together\n # until a match occurs move to the next bit not yet looked at.\n if encoded_message == '':\n return inverse_dict['']\n\n for bit in encoded_message:\n key += bit\n if key in inverse_dict:\n decoded_message.append(inverse_dict[key])\n key = ''\n\n return ''.join(decoded_message)\n\n\nif __name__ == '__main__':\n # test example\n message = 'bibbity_bobbity'\n tree = build_huffman_tree(message)\n codebook = build_codebook(tree)\n encoded_message = huffman_encode(codebook, message)\n decoded_message = huffman_decode(codebook, encoded_message)\n\n print('message:', message)\n print('huffman tree:', tree)\n print('codebook:', codebook)\n print('encoded message:', encoded_message)\n print('decoded message:', decoded_message)\n\n # prints the following:\n #\n # message: bibbity_bobbity\n # huffman_tree: Node(Leaf(b, 6), Node(Node(Leaf(y, 2), Leaf(t, 2)),\n # Node(Node(Leaf(o, 1), Leaf(_, 1)), Leaf(i, 3))))\n # codebook: [('b', '0'), ('y', '100'), ('t', '101'),\n # ('o', '1100'), ('_', '1101'), ('i', '111')]\n # encoded_message: 01110011110110011010110000111101100\n # decoded_message: bibbity_bobbity\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"huffman_tree\" was created by Julian Schacher and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/computer_graphics/computer_graphics.html":{"url":"contents/computer_graphics/computer_graphics.html","title":"Computer Graphics","keywords":"","body":"Computer Graphics\nOf all areas of computer science research, none have had more of an immediate impact on multimedia than computer graphics.\nThis sub-field is distinctly different than computational science in that it focuses on the appearance of realistic details, instead of computing those details precisely.\nWhere a computational scientist might spend years writing software that runs on the fastest computers known to man to simulate climate, the computer graphics researcher might apply machine learning to create fluid simulations that look good enough to the untrained eye.\nIn the end, the computational scientist will have a plot and the computer graphics researcher will have a beautifully rendered simulation.\nThough I may have painted computer graphics to be a bit hand-wavey, that could not be further from the truth!\nInstead, I would argue that this field of research provides the closest approximation to realistic visualizations that desktop hardware can currently support.\nMany art and video game studios are interested in telling a complete story via computational media, and this simply would not be possible without the rigorous efforts of researchers from around the world.\nThis is why Pixar hires researchers and will actively publish their findings after their movies are released.\nThough the boundary between computer science research fields is a bit vague, for the purposes of the Algorithm Archive, we will broadly classify computer graphics as anything with direct applications to images or fields that can be represented as images.\nConvolutions, for example, would not be considered part of computer graphics because they are used widely in all areas of computer science research; however, Canny edge detection will be.\nWe will also be covering a wide range of applications that are used for rendering high-resolution graphics and computational art.\nAs with all sections to the Algorithm Archive, this is a work in progress and subject to change, so feel free to let me know what you think!\n"},"contents/quantum_information/quantum_information.html":{"url":"contents/quantum_information/quantum_information.html","title":"Quantum Information","keywords":"","body":"Quantum Information\nQuantum information theory is... intense.\nIt requires a strong and fundamental understanding of classical information theory and quantum mechanics.\nIt is not obvious in any way and deserves many textbooks on it's own.\nIn fact, there are numerous textbooks on the subject already.\nThe purpose of this section isn't to outdo any of that fundamental knowledge.\nInstead, we will attempt to distill the knowledge into a short, intuitive summary, with the hopes of helping people to understand more about the topic and pursue it further on their own.\nAt the time of writing, true quantum computers do not exist.\nWe do have some systems that are able to simulate qubits, they are not truly universal quantum computers.\nThe closest market-ready system we currently have is D-WAVE, which boasts an impressive 128 qubits!\nThere are many places to start an introduction to quantum information theory, so we'll go through it one step at a time:\n\nQuantum bitlogic: what is a qubit and how is it different than a classical bit?\nQuantum gates and quantum circuits: How do you fundamentally build a quantum algorithm?\nQuantum computers in the wild: Current experimental techniques to create a quantum computer and what makes them ill-suited as real quantum computers\nA survey of current quantum algorithms: There are a number of algorithms that promise fantastic advantages when performed on quantum computers and should really shake up the industry when they are finally experimentally realized.\n\nAs a note, item 3 might seem out of place for a book on algorithms, and I would tend to agree; however, at this point there is a phenomenal amount of research being done to realize the first truly quantum computer and there are a number of potential systems that could work for this purpose.\nThese systems will change how we think about and interface with quantum computation in the future and it is important to discuss where the field might be heading and when we can expect quantum computers at home.\nNow, there are not too many languages that can compile quantum code.\nA while ago, we tried to make a quantum circuit compiler, which was modeled after the SPICE circuit simulator, but this was far from a computer language.\nAt this point in time, it is impossible to tell what quantum computing languages will look like when we finally have a truly quantum machine, so for the time being, we will not ask for community code for the chapters related to quantum information.\nbasically, it's hard to imagine how to would adequately implement Shor's algorithm in C.\nAs always, this section will be updated as we add more algorithms to the list.\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/stable_marriage_problem/stable_marriage_problem.html":{"url":"contents/stable_marriage_problem/stable_marriage_problem.html","title":"Stable Marriage Problem","keywords":"","body":"The Stable Marriage Problem\nImagine you have two groups, each of size n.\nEach individual within a group has an internal ranking associated with all members of the opposing group.\nThe Stable Matching Problem attempts to unite both groups into stable pairs.\nIn this case, a set of pairs is considered stable if there are no pairs that like each other more than their current partners.\nThis doesn't mean that everyone gets their top choices, but if an individual prefers someone else who also prefers them back, the set of pairs is not stable.\nNow, this is often told as a story.\nOne group is male, the other is female, and everyone gets married, hence the name the Stable Marriage Problem.\nThis problem is solved by the Gale-Shapley algorithm, which can be simply described as follows:\n\nAll the men propose to their top choice of women.\nThe women become tentatively engaged to their top choice of the men who have proposed to them.\nAll rejected men propose to their next choice, and the women again select whichever man they prefer, possibly rejecting the one they were already engaged to.\n\nThis process continues until all individuals are paired, which means that this algorithm guarantees stable matching and also has a \\mathcal{O}(n^2) runtime.\nTo be clear, even though this algorithm seems conceptually simple, it is rather tricky to implement correctly.\nI do not at all claim that the code provided here is efficient and we will definitely be coming back to this problem in the future when we have more tools under our belt.\nI am incredibly interested to see what you guys do and how you implement the algorithm.\nVideo Explanation\nHere is a video describing the stable marriage problem:\n\n\n\n\nExample Code\nclass Person\n def initialize(id, name, prefs)\n @id = id\n @name = name\n @prefs = prefs\n @partner = nil\n @choices = 0\n end\n\n def lonely?\n @partner.nil?\n end\n\n def propose(partners)\n unless self.lonely?\n raise '%s is not lonely!' % self.name\n end\n choice = @prefs[@choices]\n partners[choice].onPropose(self)\n @choices += 1\n end\n\n def to_s\n \"#{@name.rjust(20)}: #{self.lonely? && \"Lonely\" || @partner.name}\"\n end\n\n def self.generate(size, prefix, r)\n Array.new(size){|i|\n Person.new(\n i,\n \"#{prefix} #{i}\",\n (0 ... size).to_a.shuffle(random: r)\n )\n }\n end\n\n protected\n attr_reader :id, :name\n attr_writer :partner\n\n # Acts upon a given Proposal\n def onPropose(partner)\n unless self.lonely?\n offer = score(partner)\n current = score(@partner)\n return unless offer > current \n @partner.partner = nil\n end\n @partner = partner\n partner.partner = self\n end\n\n private\n # Determines the preference of a given partner\n def score(partner)\n return 0 if partner.nil?\n @prefs.size - @prefs.index(partner.id)\n end\nend\n\n# Deterministic Output, feel free to change seed\nr = Random.new(42)\n\n# Determines Output Columns\nmen = Person.generate(4, \"Man\", r)\nwomen = Person.generate(4, \"Woman\", r)\n\n# Assume no Name is longer than 20 characters\nspacer = '-' * (20 * 2 + 2)\n\n# Solve the Problem\n1.step do |round|\n singles = men.select(&:lonely?)\n singles.each do |m|\n m.propose(women)\n end\n\n break if singles.empty?\n\n puts \"Round #{round}\"\n puts spacer\n puts men, women\n puts spacer\nend\n\nusing Random\n\nconst mnames = [\"A\", \"B\", \"C\", \"D\"]\nconst wnames = [\"E\", \"F\", \"G\", \"H\"]\n\nconst Preferences = Dict{String,Vector{String}}\nconst Pairs = Dict{String,String}\n\n# Returns a name => preference list dictionary, in decreasing order of preference\nfunction genpreferences(mannames::Vector{String}, womannames::Vector{String})\n men = Dict(map(m -> (m, shuffle(womannames)), mannames))\n women = Dict(map(w -> (w, shuffle(mannames)), womannames))\n return men, women\nend\n\n# Returns if `person` prefers the `first` candidate over the `second` one.\n# This translates to `first` appearing *sooner* in the preference list\nprefers(prefs, person, first, second) =\n findfirst(m -> m == first, prefs[person]) m == second, prefs[person])\n\nisfree(person, pairs) = !haskey(pairs, person)\n\nfunction galeshapley(men::Preferences, women::Preferences)\n mentowomen = Dict{String,String}()\n womentomen = Dict{String,String}()\n while true\n bachelors = [m for m in keys(men) if isfree(m, mentowomen)]\n if length(bachelors) == 0\n return mentowomen, womentomen\n end\n\n for bachelor in bachelors\n for candidate in men[bachelor]\n if isfree(candidate, womentomen)\n mentowomen[bachelor] = candidate\n womentomen[candidate] = bachelor\n break\n elseif prefers(women, candidate, bachelor, womentomen[candidate])\n delete!(mentowomen, womentomen[candidate])\n mentowomen[bachelor] = candidate\n womentomen[candidate] = bachelor\n break\n end\n end\n end\n end\nend\n\nfunction isstable(men::Preferences, women::Preferences, mentowomen::Pairs, womentoman::Pairs)\n for (husband, wife) in mentowomen\n for candidate in men[husband]\n if candidate != wife &&\n prefers(men, husband, candidate, wife) &&\n prefers(women, candidate, husband, womentoman[candidate])\n return false\n end\n end\n end\n return true\nend\n\nfunction main()\n men, women = genpreferences(mnames, wnames)\n mentowomen, womentomen = galeshapley(men, women)\n println(mentowomen)\n println(isstable(men, women, mentowomen, womentomen) ? \"Stable\" : \"Unstable\")\nend\n\nmain()\n\n# Submitted by Marius Becker\n# Updated by Amaras\n\n\nfrom random import shuffle\nfrom copy import copy\nfrom string import ascii_uppercase, ascii_lowercase\n\n\ndef main():\n # Set this to however many men and women you want, up to 26\n num_pairs = 5\n\n # Create all Person objects\n men = [Person(name) for name in ascii_uppercase[:num_pairs]]\n women = [Person(name) for name in ascii_lowercase[:num_pairs]]\n\n # Set everyone's preferences\n for man in men:\n man.preference = copy(women)\n shuffle(man.preference)\n\n for woman in women:\n woman.preference = copy(men)\n shuffle(woman.preference)\n\n # Run the algorithm\n stable_marriage(men, women)\n\n # Print preferences and the result\n print('Preferences of the men:')\n for man in men:\n print(man)\n\n print()\n\n print('Preferences of the women:')\n for woman in women:\n print(woman)\n\n print('\\n')\n\n print('The algorithm gave this solution:')\n for man in men:\n print(f'{man.name} + {man.partner.name}')\n\n\ndef stable_marriage(men, women):\n \"\"\"Finds pairs with stable marriages\"\"\"\n\n while True:\n # Let every man without a partner propose to a woman\n for man in men:\n if not man.has_partner:\n man.propose_to_next()\n\n # Let the women pick their favorites\n for woman in women:\n woman.pick_preferred()\n\n # Continue only when someone is still left without a partner\n if all((man.has_partner for man in men)):\n return\n\n\nclass Person:\n\n def __init__(self, name):\n self.name = name\n self.preference = []\n self.candidates = []\n self.pref_index = 0\n self._partner = None\n\n @property\n def next_choice(self):\n \"\"\"Return the next person in the own preference list\"\"\"\n try:\n return self.preference[self.pref_index]\n except IndexError:\n return None\n\n def propose_to_next(self):\n \"\"\"Propose to the next person in the own preference list\"\"\"\n person = self.next_choice\n person.candidates.append(self)\n self.pref_index += 1\n\n def pick_preferred(self):\n \"\"\"Pick a new partner or stay with the old one if they are preferred\"\"\"\n # Iterate own preferences in order\n for person in self.preference:\n # Pick the first person that's either a new candidate or the\n # current partner\n if person == self.partner:\n break\n elif person in self.candidates:\n self.partner = person\n break\n\n # Rejected candidates don't get a second chance\n self.candidates.clear()\n\n @property\n def partner(self):\n return self._partner\n\n # The call self.partner = person sets self._partner as person\n # However, since engagement is symmetrical, self._partner._partner\n # (which is then person._partner) also needs to be set to self\n @partner.setter\n def partner(self, person):\n \"\"\"Set a person as the new partner and sets the partner of that\n person as well\"\"\"\n\n # Do nothing if nothing would change\n if person != self._partner:\n # Remove self from current partner\n if self._partner is not None:\n self._partner._partner = None\n\n # Set own and the other person's partner\n self._partner = person\n if self._partner is not None:\n self._partner._partner = self\n\n # This allows use of self.has_partner instead of self.has_partner()\n @property\n def has_partner(self):\n \"\"\"Determine whether this person currently has a partner or not.\"\"\"\n return self.partner is not None\n\n # This allows the preferences to be printed more elegantly\n def __str__(self):\n return f'{self.name}: {\", \".join(p.name for p in self.preference)}'\n\n\nif __name__ == '__main__':\n main()\n\nimport Data.Map as M (Map, (!))\nimport qualified Data.Map as M\nimport Data.List (elemIndex)\nimport Control.Monad.State\n\nstableMatching :: (Ord a, Ord b) => [(a, [b])] -> [(b, [a])] -> [(a, b)]\nstableMatching men women = evalState (propose (M.fromList women) men) M.empty\n\npropose :: (Ord a, Ord b) => Map b [a] ->\n [(a, [b])] ->\n State (Map b (a, [b])) [(a, b)]\npropose _ [] = get >>= return . map (\\(w, (m,_)) -> (m, w)) . M.assocs\npropose women ((man, pref):bachelors) = do\n let theOne = head pref\n couples do\n modify $ M.insert theOne (man, (tail pref))\n propose women bachelors\n Just (boyfriend, planB) -> do\n let rank x = elemIndex x (women!theOne)\n if rank boyfriend \n#include \n#include \n#include \n#include \n#include \n\nstruct person {\n size_t id;\n struct person *partner;\n size_t *prefers;\n size_t index;\n};\n\nvoid shuffle(size_t *array, size_t size) {\n for (size_t i = size - 1; i > 0; --i) {\n size_t j = (size_t)rand() % (i + 1);\n size_t tmp = array[i];\n array[i] = array[j];\n array[j] = tmp;\n }\n}\n\nvoid create_group(struct person *group, size_t size) {\n for (size_t i = 0; i 0) {\n struct person *man = bachelors[bachelors_size - 1];\n struct person *woman = &women[man->prefers[man->index]];\n\n if (!woman->partner) {\n woman->partner = man;\n man->partner = woman;\n bachelors[--bachelors_size] = NULL;\n } else if (!prefers_partner(woman->prefers, woman->partner->id, man->id,\n size)) {\n\n woman->partner->index++;\n bachelors[bachelors_size - 1] = woman->partner;\n woman->partner = man;\n man->partner = woman;\n } else {\n man->index++;\n }\n }\n}\n\nvoid free_group(struct person *group, size_t size) {\n for (size_t i = 0; i id);\n }\n\n free_group(men, 5);\n free_group(women, 5);\n}\n\n#include \n#include \n#include \n#include \n#include \n#include \n\n// this header is so that we can use `not` and `and` on MSVC\n#include \n\n#include \n\nusing std::size_t;\n\n/*\n we use these to generate random numbers in this program.\n this makes the program simpler,\n by not having to pass around random number generators.\n*/\nstatic thread_local std::random_device global_random_device;\nstatic thread_local std::mt19937 global_rng(global_random_device());\n\nstruct person {\n /*\n this is a poor person's std::optional,\n but since we're attempting to be compileable on C++14,\n we won't worry too much about it.\n */\n bool finished;\n size_t preference;\n\n std::vector preference_list;\n};\n\n/*\n this function generates a list of people with size `number_of_partners`.\n\n each person's `preference_list` will be a randomly sorted list of\n the numbers in the range [0, number_of_partners),\n with no duplicates.\n*/\nstd::vector make_person_list(size_t number_of_partners) {\n auto random_pref_list = [&] {\n std::vector ret(number_of_partners);\n std::iota(begin(ret), end(ret), size_t(0));\n std::shuffle(begin(ret), end(ret), global_rng);\n\n return ret;\n };\n\n std::vector ret;\n std::generate_n(std::back_inserter(ret), number_of_partners, [&] {\n return person{false, 0, random_pref_list()};\n });\n\n return ret;\n}\n\ntemplate \nvoid stable_match(LeadIter leads, LeadIter leads_end, FollowIter follows) {\n // for each index in the leads' preference list, we'll go through this\n size_t const number_of_partners = leads_end - leads;\n for (size_t proposal_index = 0; proposal_index > proposals(number_of_partners);\n\n // for each lead, we'll make a proposal to their favorite follow\n for (size_t i = 0; i \nclass Person {\n constructor(name) {\n this.name = name;\n }\n\n get hasFiance() {\n return !!this.fiance;\n }\n\n prefers(other) {\n return this.preferences.indexOf(other) 0) {\n const guy = bachelors.shift();\n for (const girl of guy.preferences) {\n if (!girl.hasFiance) {\n guy.engageTo(girl);\n break;\n } else if (girl.prefers(guy)) {\n bachelors.push(girl.fiance);\n guy.engageTo(girl);\n break;\n }\n }\n }\n}\n\nfunction shuffle(iterable) {\n const array = [...iterable];\n for (let i = array.length - 1; i > 0; i--) {\n const j = Math.floor(Math.random() * (i + 1));\n [array[i], array[j]] = [array[j], array[i]];\n }\n return array;\n}\n\nconst guys = [...\"ABCDE\"].map(name => new Person(name));\nconst girls = [...\"FGHIJ\"].map(name => new Person(name));\n\nconsole.log(\"Guys\");\nfor (const guy of guys) {\n guy.preferences = shuffle(girls);\n console.log(`${guy.name}: ${guy.preferences.map(p => p.name).join()}`)\n}\n\nconsole.log(\"\\nGirls\");\nfor (const girl of girls) {\n girl.preferences = shuffle(guys);\n console.log(`${girl.name}: ${girl.preferences.map(p => p.name).join()}`)\n}\n\nstableMarriage(guys, girls);\n\nconsole.log(\"\\nPairings\");\nfor (const guy of guys) {\n console.log(`${guy.name}: ${guy.fiance.name}`);\n}\n\nGaleShapleyAlgorithm.cs\n// submitted by Julian Schacher (jspp) with great help by gustorn and Marius Becker\nusing System.Collections.Generic;\n\nnamespace StableMarriageProblem\n{\n public static class GaleShapleyAlgorithm\n where TFollow : Person\n where TLead : Person\n {\n public static void RunGaleShapleyAlgorithm(List follows, List leads)\n {\n // All follows are lonely.\n var lonelyFollows = new List(follows);\n\n // Carry on until there are no lonely follows anymore.\n while (lonelyFollows.Count > 0)\n {\n // Let every lonely follow propose to their current top choice.\n foreach (var lonelyFollow in lonelyFollows)\n {\n lonelyFollow.ProposeToNext();\n }\n\n // Look which follows have a partner now and which don't.\n var newLonelyFollows = new List();\n foreach (var follow in follows)\n {\n if (follow.Partner == null)\n newLonelyFollows.Add(follow);\n }\n lonelyFollows = newLonelyFollows;\n }\n }\n }\n}\n\nPerson.cs\n// submitted by Julian Schacher (jspp) with great help by gustorn and Marius Becker\nusing System.Collections.Generic;\n\nnamespace StableMarriageProblem\n{\n public class Person\n where TSelf : Person\n where TPref : Person\n {\n public string Name { get; set; }\n public TPref Partner { get; set; }\n public IList Choices { get; set; }\n // CurrentTopChoice equals the Choice in Choices that is the TopChoice,\n // if already tried women are not counted.\n public int CurrentTopChoiceIndex { get; set; } = 0;\n\n public Person(string name) => Name = name;\n\n public void ProposeToNext()\n {\n var interest = GetNextTopChoice();\n\n // If the interest has no partner or prefers this person,\n // change interest's partner to this person.\n if (interest.Partner == null ||\n interest.Choices.IndexOf(this as TSelf) Choices[CurrentTopChoiceIndex++];\n }\n}\n\nProgram.cs\n// submitted by Julian Schacher (jspp) with great help by gustorn and Marius Becker\nusing System;\nusing System.Collections.Generic;\n\nnamespace StableMarriageProblem\n{\n class Program\n {\n static void Main(string[] args)\n {\n Console.WriteLine(\"GaleShapleyAlgorithm\");\n // Using men and women as an example.\n var men = new List()\n {\n new Man(\"A\"),\n new Man(\"B\"),\n new Man(\"C\"),\n new Man(\"D\"),\n new Man(\"E\")\n };\n var women = new List()\n {\n new Woman(\"F\"),\n new Woman(\"G\"),\n new Woman(\"H\"),\n new Woman(\"I\"),\n new Woman(\"J\"),\n };\n\n var random = new Random();\n\n foreach (var man in men)\n {\n man.Choices = new List(women).Shuffle(random);\n Console.WriteLine(man.Name + \":\");\n foreach (var choice in man.Choices)\n Console.Write(choice.Name);\n Console.WriteLine();\n }\n foreach (var woman in women)\n {\n woman.Choices = new List(men).Shuffle(random);\n Console.WriteLine(woman.Name + \":\");\n foreach (var choice in woman.Choices)\n Console.Write(choice.Name);\n Console.WriteLine();\n }\n\n GaleShapleyAlgorithm.RunGaleShapleyAlgorithm(women, men);\n\n foreach (var woman in women)\n {\n Console.WriteLine(woman.Name + \" : \" + woman?.Partner.Name);\n }\n }\n }\n\n public class Man : Person\n {\n public Man(string name) : base(name) { }\n }\n\n public class Woman : Person\n {\n public Woman(string name) : base(name) { }\n }\n}\n\nListExtensions.cs\nusing System;\nusing System.Collections.Generic;\n\nnamespace StableMarriageProblem\n{\n public static class ListExtensions\n {\n public static IList Shuffle(this IList list, Random rng)\n {\n for (var i = 0; i \nimport java.util.List;\nimport java.util.ArrayList;\nimport java.util.Collections;\n\nclass StableMarriage {\n\n /*\n * Use the stable marriage algorithm to find stable pairs from the\n * lists of men and women.\n */\n public static void findStableMarriages(List women, List men) {\n // We might have more men/women than women/men. In this case, not everybody can\n // get a mate. We should aim to give every member of the less numerous gender a mate,\n // as this is always possible.\n List leastCommonGender = women.size() System.out.println(w + \" married to \" + w.getMate()));\n }\n\n public static void main(String[] args) {\n int nPairs = 5;\n List women = new ArrayList<>();\n List men = new ArrayList<>();\n for (char i = 'A'; i {\n w.receiveOptions(men);\n System.out.println(w + \" prefers \" + w.getPreferredMates());\n });\n men.forEach(m -> {\n m.receiveOptions(women);\n System.out.println(m + \" prefers \" + m.getPreferredMates());\n });\n\n findStableMarriages(women, men);\n }\n\n}\n\nclass Person {\n private final String name;\n protected Person mate;\n protected List preferredMates;\n\n public Person(String name) {\n this.name = name;\n }\n\n public boolean isLonely() {\n return mate == null;\n }\n\n public void setMate(Person mate) {\n // Only set mates if there is a change.\n if (this.mate != mate) {\n // Remove old mates mate.\n if (this.mate != null)\n this.mate.mate = null;\n\n // Set the new mate.\n this.mate = mate;\n\n // If new mate is someone, update their mate.\n if (mate != null)\n mate.mate = this;\n }\n }\n\n public Person getMate() {\n return mate;\n }\n\n public void receiveOptions(List mates) {\n // Preferences are subjective.\n preferredMates = new ArrayList<>(mates);\n Collections.shuffle(preferredMates);\n }\n\n public List getPreferredMates() {\n return preferredMates;\n }\n\n public String toString() {\n return getClass().getName() + \"(\" + name + \")\";\n }\n}\n\nclass Woman extends Person {\n private List suitors = new ArrayList<>();\n\n public Woman(String name) {\n super(name);\n }\n\n public void recieveProposal(Man suitor) {\n suitors.add(suitor);\n }\n\n public void chooseMate() {\n for (Person mostDesired : preferredMates) {\n if (mostDesired == mate || suitors.contains(mostDesired)) {\n setMate(mostDesired);\n break;\n }\n }\n }\n}\n\nclass Man extends Person {\n public Man(String name) {\n super(name);\n }\n\n public void propose() {\n if (!preferredMates.isEmpty()) {\n Woman fiance = (Woman) preferredMates.remove(0);\n fiance.recieveProposal(this);\n }\n }\n}\n\nname = $name;\n }\n\n public function getName(): string\n {\n return $this->name;\n }\n\n public function setPreferences(array $preferences): void\n {\n $this->preferences = $preferences;\n }\n\n public function getMatch(): ?Person\n {\n return $this->match;\n }\n\n public function getPreferences(): array\n {\n return $this->preferences;\n }\n\n public function isSingle(): bool\n {\n return $this->match === null;\n }\n\n public function unmatch(): void\n {\n $this->match = null;\n }\n\n public function setMatch(Person $match): void\n {\n if ($this->match !== $match) {\n if ($this->match !== null) {\n $this->match->unmatch();\n }\n $this->match = $match;\n $match->setMatch($this);\n }\n }\n\n public function propose(): void\n {\n if (!empty($this->preferences)) {\n $fiance = array_shift($this->preferences);\n $fiance->receiveProposal($this);\n }\n }\n\n public function receiveProposal(Person $man): void\n {\n $this->suitors[] = $man;\n }\n\n public function chooseMatch(): void\n {\n foreach ($this->preferences as $preference) {\n if ($preference === $this->match || in_array($preference, $this->suitors)) {\n $this->setMatch($preference);\n break;\n }\n }\n\n $this->suitors = [];\n }\n\n public function __toString(): string\n {\n return $this->name;\n }\n}\n\nfunction stable_marriage(array $men, array $women): void\n{\n do {\n foreach ($men as $man) {\n if ($man->isSingle()) {\n $man->propose();\n }\n }\n\n foreach ($women as $woman) {\n $woman->chooseMatch();\n }\n\n $unmarried = false;\n foreach ($women as $woman) {\n if ($woman->isSingle()) {\n $unmarried = true;\n break;\n }\n }\n\n } while ($unmarried);\n}\n\n$groupSize = 10;\n$men = [];\n$women = [];\n\nfor ($i = 1; $i setPreferences($preferences);\n printf('%s\\'s choices: %s', $man->getName(), implode(',', $man->getPreferences()));\n echo PHP_EOL;\n}\necho PHP_EOL;\nforeach ($women as $woman) {\n $preferences = $men;\n shuffle($preferences);\n $woman->setPreferences($preferences);\n printf('%s\\'s choices: %s', $woman->getName(), implode(',', $woman->getPreferences()));\n echo PHP_EOL;\n}\necho PHP_EOL;\n\nstable_marriage($men, $women);\nforeach ($women as $woman) {\n printf('%s is married to %s', $woman, $woman->getMatch());\n echo PHP_EOL;\n}\n\nimport scala.collection.mutable._\n\nobject StableMarriage {\n\n var bachelors = Queue[Man]()\n\n case class Man(name: String, var preferences: List[Woman] = List()) {\n def propose(): Unit = preferences match {\n case woman :: remainingPreferences => {\n if (woman.prefers(this)) {\n bachelors ++= woman.fiance\n woman.fiance = Some(this)\n }\n else\n bachelors.enqueue(this)\n preferences = remainingPreferences\n }\n case _ =>\n }\n }\n\n case class Woman(name: String, var preferences: List[Man] = List(), var fiance: Option[Man] = None) {\n def prefers(man: Man): Boolean =\n fiance match {\n case Some(otherMan) => preferences.indexOf(man) true //always prefer any man over nobody\n }\n }\n\n def findStableMatches(men: Man*): Unit = {\n bachelors = men.to[Queue]\n while (bachelors.nonEmpty)\n bachelors.dequeue.propose()\n }\n}\n\nobject StableMarriageExample {\n\n val a = StableMarriage.Man(\"Adam\")\n val b = StableMarriage.Man(\"Bart\")\n val c = StableMarriage.Man(\"Colm\")\n val x = StableMarriage.Woman(\"Xena\")\n val y = StableMarriage.Woman(\"Yeva\")\n val z = StableMarriage.Woman(\"Zara\")\n\n a.preferences = List(y, x, z)\n b.preferences = List(y, z, x)\n c.preferences = List(x, z, y)\n x.preferences = List(b, a, c)\n y.preferences = List(c, a, b)\n z.preferences = List(a, c, b)\n\n\n def main(args: Array[String]): Unit = {\n\n StableMarriage.findStableMatches(a, b, c)\n\n List(x, y, z).foreach(\n w => Console.println(\n w.name\n + \" is married to \"\n + w.fiance.getOrElse(StableMarriage.Man(\"Nobody\")).name))\n }\n\n}\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/flood_fill/flood_fill.html":{"url":"contents/flood_fill/flood_fill.html","title":"Flood Fill","keywords":"","body":"Flood Fill\nFlood fill is a method that is surprisingly useful in a large number of different situations and keeps finding me wherever I go.\nWhen I was completing my PhD, I had an idea to track superfluid vortices by using flood fill as a way to help mask out unnecessary features of the simulation.\nWhen I was making a terminal game, I thought of creating an animation that was just flood fill in disguise.\nWhen I decided to play minesweeper or Go with my girlfriend, flood fill was used in both!\nFlood fill is probably most commonly known as the \"Bucket Fill\" application in most art programs [1].\nIt's usually indicated by an icon that looks like a bucket and is known to fill in any enclosed area, as shown below:\n\n \n\n\nBecause flood fill is incredibly common, there are a large number of variations to the method, some of which are more optimal than others.\nFor this chapter, we will cover the basics: how to fill a domain in a quick and dirty way.\nIn subsequent chapters, we will continue our journey by creating more and more efficient flood fill methods, including scanline-based and fixed memory methods [2].\nI have decided to split the chapter up for a few important reasons:\n\nI did not want to flood the Algorithm Archive with flood fill methods all at the same time.\nI feel it's worth letting each chapter sit for a bit while we savor it's unique flavor.\nMany users are implementing versions of each algorithm in their own languages and it is difficult to review and submit code for chapters with a lot of code chunks.\nSeveral sub-chapters with less code is easier for everyone.\nI am kinda under a time-constraint right now and wanted to make sure we regularly get content into the Algorithm Archive.\n\nSo, without further a-do, let's hop right into it!\nWhat does flood fill do?\nFlood fill is essentially composed of 2 parts:\n\nDetermining the extents of the domain to fill\nWalking through all elements within a domain and changing some property\n\nFor the purposes of this chapter, we will be using a set of floating-point values that range from 0 to 1 instead of a color-space like RGB.\nThough bucket fill is always used in art programs in some sort of color space, flood fill is more general and can be used in a space with any type of element.\nAs such, it makes sense to use a simpler element type so we can better understand the method.\nSo how do we go about finding the extents of the domain to fill?\nHere, a domain will be defined as any connected set of elements in an n-dimensional space whose values do not vary beyond a predefined threshold.\nAs an example, if we take a circle embedded into a 2-dimensional grid, we have 3 separate domains:\n\nInside the circle where all elements are 0.\nThe circle, itself, where the elements are set to 0.75.\nOutside the circle where all elements are similarly 0.\n\n\n \n\n\nThough there are some more complicated ways to determine the extents of the domain, we will not focus on this aspect of the flood fill method for the remainder of this chapter and instead leave it for subsequent chapters.\nSo now we will focus on the process of walking through each element in the domain and changing some property.\nDomain traversal\nAs before, the simplest example to work with is that of an image, where each element in our domain is a single pixel.\nHere, we can connect each pixel to all other pixels in its vicinity, like so:\n\n \n\n\nIn this image, a border is shown between each individual pixel and a grid is superimposed to show how each pixel is connected to its neighbors.\nThis means that each element has 4 neighbors: north, south, east, and west.\nWe could also include northeast, southeast, southwest, and northwest if we wanted to do an 8-way fill, but we will restrict the discussion to the 4-way fill for now, as the method is essentially the same and slightly easier to understand with fewer elements to worry about.\nBy connecting each pixel to its neighbors in this way, the flood fill operation becomes a process of graph traversal, not too dissimilar from the tree traversal methods described before.\nThis means that after selecting our initial location, we can then traverse through all elements in either a depth-first or breadth-first fashion.\nWe will be covering the following this chapter:\n\nFinding all neighbors\nDepth-first node traversal\nBreadth-first node traversal and small-scale optimizations\n\nSo let's start by discussing how we might go about finding the neighbors to fill.\nFinding all neighbors\nThe first step of this method is to query the location of all possible neighbors.\nAt first glance, this seems rather straightforward.\nOne simply needs to look up, down, left, and right of the current location and add those elements to the list of neighbors if they are:\n\nOn the canvas\nHave a value close enough to the old value we would like to replace\n\nIn code, this might look like this:\nfunction find_neighbors(canvas, loc::CartesianIndex, old_val, new_val)\n\n # Finding north, south, east, west neighbors\n possible_neighbors = [loc + CartesianIndex(0, 1),\n loc + CartesianIndex(1, 0),\n loc + CartesianIndex(0, -1),\n loc + CartesianIndex(-1, 0)]\n\n # Exclusing neighbors that should not be colored\n neighbors = []\n for possible_neighbor in possible_neighbors\n if inbounds(size(canvas), possible_neighbor) &&\n canvas[possible_neighbor] == old_val\n push!(neighbors, possible_neighbor)\n end\n end\n\n return neighbors\nend\n\nint find_neighbors(struct canvas c, struct point p, int old_val, \n struct point *neighbors) {\n int cnt = 0;\n struct point points[4] = {\n {p.x, p.y + 1},\n {p.x + 1, p.y},\n {p.x, p.y - 1},\n {p.x - 1, p.y}\n };\n\n for (int i = 0; i \nauto find_neighbors(\n std::vector> const& grid,\n CartesianIndex loc,\n float old_value,\n float /* new_value */) {\n\n const std::vector possible_neighbors{\n {loc[0], loc[1] + 1},\n {loc[0] + 1, loc[1]},\n {loc[0], loc[1] - 1},\n {loc[0] - 1, loc[1]}};\n\n std::vector neighbors;\n\n for (auto const& possible_neighbor : possible_neighbors) {\n const auto size = CartesianIndex{\n static_cast(grid[0].size()), static_cast(grid.size())};\n const auto x = static_cast(possible_neighbor[0]);\n const auto y = static_cast(possible_neighbor[1]);\n if (inbounds(size, possible_neighbor) && grid[x][y] == old_value) {\n neighbors.push_back(possible_neighbor);\n }\n }\n\n return neighbors;\n}\n\ndef find_neighbors(canvas, p, old_val, new_val):\n # north, south, east, west neighbors\n possible_neighbors = [\n Point(p.x, p.y+1),\n Point(p.x+1, p.y),\n Point(p.x-1, p.y),\n Point(p.x, p.y-1)\n ]\n\n # exclude the neighbors that go out of bounds and should not be colored\n neighbors = []\n for possible_neighbor in possible_neighbors:\n if inbounds(canvas.shape, possible_neighbor):\n if canvas[possible_neighbor] == old_val:\n neighbors.append(possible_neighbor)\n return neighbors\n\ndef find_neighbours(canvas, location is Point, old_value):\n possible_neighbours = ((Point(0, 1), Point(1, 0), Point(0, -1), Point(-1, 0))\n |> map$(location.__add__))\n\n yield from possible_neighbours |> filter$(x -> (inbounds(canvas.shape, x)\n and canvas[x] == old_value))\n\n\n\n\nThis code is set up to return a vector of elements to then use for subsequent sections.\nDepth-first node traversal\nNow that we have the ability to find all neighboring elements, we can proceed to traverse through those nodes in the most straightforward way: recursion.\nIn code, it might look like this:\nfunction recursive_fill!(canvas, loc::CartesianIndex, old_val, new_val)\n\n if (old_val == new_val)\n return\n end\n\n canvas[loc] = new_val\n\n possible_neighbors = find_neighbors(canvas, loc, old_val, new_val)\n for possible_neighbor in possible_neighbors\n recursive_fill!(canvas, possible_neighbor, old_val, new_val)\n end\nend\n\nvoid recursive_fill(struct canvas c, struct point p, int old_val,\n int new_val) {\n\n if (old_val == new_val) {\n return;\n }\n\n c.data[p.x + c.max_x * p.y] = new_val;\n\n struct point neighbors[4];\n int cnt = find_neighbors(c, p, old_val, neighbors);\n\n for (int i = 0; i \nvoid recursive_fill(\n std::vector>& grid,\n CartesianIndex loc,\n float old_value,\n float new_value) {\n if (old_value == new_value) {\n return;\n }\n\n const auto x = static_cast(loc[0]);\n const auto y = static_cast(loc[1]);\n\n grid[x][y] = new_value;\n\n const auto possible_neighbors = find_neighbors(grid, loc, old_value, new_value);\n for (auto const& possible_neighbor : possible_neighbors) {\n recursive_fill(grid, possible_neighbor, old_value, new_value);\n }\n}\n\ndef recursive_fill(canvas, p, old_val, new_val):\n if old_val == new_val:\n return\n\n canvas[p] = new_val\n\n neighbors = find_neighbors(canvas, p, old_val, new_val)\n for neighbor in neighbors:\n recursive_fill(canvas, neighbor, old_val, new_val)\n\ndef recursive_fill(canvas, location is Point, old_value, new_value):\n if new_value == old_value or not inbounds(canvas.shape, location):\n return\n\n canvas[location] = new_value\n # consume is important here, because otherwise, the recursive function is not called again\n consume(\n find_neighbours(canvas, location, old_value)\n |> map$(recursive_fill$(canvas, ?, old_value, new_value))\n )\n\n\n\nThe above code continues recursing through available neighbors as long as neighbors exist, and this should work so long as we are adding the correct set of neighbors.\nAdditionally, it is possible to do the same type of traversal by managing a stack, like so:\nfunction stack_fill!(canvas, loc::CartesianIndex, old_val, new_val)\n if new_val == old_val\n return\n end\n\n s = Stack{CartesianIndex}()\n push!(s, loc)\n\n while length(s) > 0\n current_loc = pop!(s)\n if canvas[current_loc] == old_val\n canvas[current_loc] = new_val\n possible_neighbors = find_neighbors(canvas, current_loc,\n old_val, new_val)\n for neighbor in possible_neighbors\n push!(s,neighbor)\n end\n end\n\n end\nend\n\nvoid stack_fill(struct canvas c, struct point p, int old_val, int new_val) {\n if (old_val == new_val) {\n return;\n }\n\n struct stack stk = get_stack();\n stack_push(&stk, p);\n\n while (!stack_empty(stk)) {\n struct point cur_loc = stack_pop(&stk);\n if (c.data[cur_loc.x + c.max_x * cur_loc.y] == old_val) {\n c.data[cur_loc.x + c.max_x * cur_loc.y] = new_val;\n\n struct point neighbors[4];\n int cnt = find_neighbors(c, cur_loc, old_val, neighbors);\n\n for (int i = 0; i \nvoid stack_fill(\n std::vector>& grid,\n CartesianIndex loc,\n float old_value,\n float new_value) {\n if (old_value == new_value) {\n return;\n }\n\n auto s = std::stack{};\n s.push(loc);\n\n while (s.size() > 0) {\n const auto current_loc = s.top();\n s.pop();\n\n const auto x = static_cast(current_loc[0]);\n const auto y = static_cast(current_loc[1]);\n\n if (grid[x][y] == old_value) {\n grid[x][y] = new_value;\n const auto possible_neighbors =\n find_neighbors(grid, current_loc, old_value, new_value);\n for (auto const& neighbor : possible_neighbors) {\n s.push(neighbor);\n }\n }\n }\n}\n\ndef stack_fill(canvas, p, old_val, new_val):\n if old_val == new_val:\n return\n\n stack = [p]\n\n while stack:\n cur_loc = stack.pop()\n canvas[cur_loc] = new_val\n stack += find_neighbors(canvas, cur_loc, old_val, new_val)\n\ndef stack_fill(canvas, location is Point, old_value, new_value):\n if new_value == old_value or not inbounds(canvas.shape, location):\n return\n\n stack = [location]\n\n while stack:\n current_location = stack.pop()\n if canvas[current_location] == old_value:\n canvas[current_location] = new_value\n stack.extend(find_neighbours(canvas, current_location, old_value))\n\n\n\nThis is ultimately the same method of traversal as before; however, because we are managing our own data structure, there are a few distinct differences:\n\nThe manually managed stack could be slightly slower and potentially more memory-intensive\nIt is easy to reach the maximum recursion depth on certain hardware with the recursive method, so it is best to use the stack-based implementation in those cases.\n\nIf we were to use either of these methods to fill a circle embedded in a two dimensional domain, we would see the following\n\n\n \nYour browser does not support the video tag.\n\n\n\nHere, we see that these methods will traverse through one direction first before filling from there.\nThis is potentially the easiest method to write, but it is not the most intuitive fill pattern.\nI suspect that if someone was asked to fill the contents of the circle on their own, they would fill it more evenly from the center, like so:\n\n\n \nYour browser does not support the video tag.\n\n\n\nThis is simply another traversal strategy known as breadth-first traversal and comes with its own set of caveats.\nWe will discuss this further in the next subsection\nBreadth-first node traversal and small-scale optimizations\nBreadth-first node traversal is as simple as switching the stack in the depth-first strategy with a queue.\nThe code would look something like this:\nfunction queue_fill!(canvas, loc::CartesianIndex, old_val, new_val)\n if new_val == old_val\n return\n end\n\n q = Queue{CartesianIndex}()\n enqueue!(q, loc)\n\n # Coloring the initial location\n canvas[loc] = new_val\n\n while length(q) > 0\n current_loc = dequeue!(q)\n\n possible_neighbors = find_neighbors(canvas, current_loc,\n old_val, new_val)\n\n # Coloring as we are enqueuing neighbors\n for neighbor in possible_neighbors\n canvas[neighbor] = new_val\n enqueue!(q,neighbor)\n end\n\n end\nend\n\nvoid queue_fill(struct canvas c, struct point p, int old_val, int new_val) {\n if (old_val == new_val) {\n return;\n }\n\n struct queue q = get_queue(sizeof(struct point *));\n enqueue(&q, p);\n\n while (!queue_empty(q)) {\n struct point cur_loc = dequeue(&q);\n if (c.data[cur_loc.x + c.max_x * cur_loc.y] == old_val) {\n c.data[cur_loc.x + c.max_x * cur_loc.y] = new_val;\n\n struct point neighbors[4];\n int cnt = find_neighbors(c, cur_loc, old_val, neighbors);\n\n for (int i = 0; i \nvoid queue_fill(\n std::vector>& grid,\n CartesianIndex loc,\n float old_value,\n float new_value) {\n if (old_value == new_value) {\n return;\n }\n\n auto q = std::queue{};\n q.push(loc);\n const auto x = static_cast(loc[0]);\n const auto y = static_cast(loc[1]);\n grid[x][y] = new_value;\n\n while (q.size() > 0) {\n const auto current_loc = q.front();\n q.pop();\n const auto possible_neighbors =\n find_neighbors(grid, current_loc, old_value, new_value);\n for (auto const& neighbor : possible_neighbors) {\n const auto neighbor_x = static_cast(neighbor[0]);\n const auto neighbor_y = static_cast(neighbor[1]);\n grid[neighbor_x][neighbor_y] = new_value;\n q.push(neighbor);\n }\n }\n}\n\ndef queue_fill(canvas, p, old_val, new_val):\n if old_val == new_val:\n return\n\n q = Queue()\n q.put(p)\n\n canvas[p] = new_val\n\n while not q.empty():\n cur_loc = q.get()\n neighbors = find_neighbors(canvas, cur_loc, old_val, new_val)\n\n for neighbor in neighbors:\n canvas[neighbor] = new_val\n q.put(neighbor)\n\ndef queue_fill(canvas, location is Point, old_value, new_value):\n if new_value == old_value or not inbounds(canvas.shape, location):\n return\n\n queue = deque()\n queue.append(location)\n\n canvas[location] = new_value\n\n while queue:\n current_location = queue.popleft()\n for neighbour in find_neighbours(canvas, current_location, old_value):\n canvas[neighbour] = new_value\n queue.append(neighbour)\n\n\n\nNow, there is a small trick in this code that must be considered to make sure it runs optimally.\nNamely, the nodes must be colored when they are being enqueued, not when visiting the node.\nAt least for me, it was not immediately obvious why this would be the case, but let me try to explain.\nLet's imagine that we decided to write code that colored all neighboring nodes only when visiting them.\nWhen querying all possible neighbors, we will add 4 elements to the queue for the north, south, east, and west neighbors of the initial node, as shown below:\n\n \n\n\nNow let's imagine we travel east first.\nIt then enqueues three more nodes: north, south, and east again.\nThis is shown below:\n\n \n\n\nIt does not enqueue its west neighbor because this has already been colored.\nAt this stage, we will have six nodes ready to be colored and 2 that are already colored.\nNow let's say we travel north next.\nThis node will enqueue three more nodes: west, north, and east, as shown below:\n\n \n\n\nThe problem is that the east element has already been enqueued for coloring by the previous node!.\nThis shared element is colored in red.\nAs we progress through all four initial neighbors, we will find 4 nodes that are doubly enqueued: all directions diagonal to the initial location!\nThis is again shown below:\n\n \n\n\nAs the number of nodes increases, so does the number of duplicate nodes.\nA quick fix is to color the nodes when they are being enqueued like in the example code above.\nWhen doing this, duplicates will not be enqueued with a breadth-first scheme because they will already be colored when other nodes are trying to find their neighbors.\nThis created a node connection pattern like so:\n\n \n\n\nAs some final food for thought: why wasn't this a problem with the depth-first strategy?\nThe simple answer is that it actually was an issue, but it was way less prevalent.\nWith the depth-first strategy, a number of unnecessary nodes are still pushed to the stack, but because we consistently push one direction before spreading out to other directions, it is more likely that the nodes have filled neighbors when they are looking for what to fill around them.\nSimply put: depth-first traversal is slightly more efficient in this case unless you can color as querying for neighbors, in which case breadth-first is more efficient.\nConclusions\nAs stated before, the method discussed in this chapter is just the tip of the iceberg and many other flood fill methods exist that are likely to be more efficient for most purposes.\nThese will all be covered in subsequent chapters which will come out somewhat regularly throughout the next few months, lest we flood that archive with flood fill methods.\nVideo Explanation\nHere is a video describing tree traversal:\n\n\n\n\nExample Code\nThe example code for this chapter will be the simplest application of flood fill that still adequately tests the code to ensure it is stopping at boundaries appropriately.\nFor this, we will create a two dimensional array of floats, all starting at 0.0, and then set a single vertical line of elements at the center to be 1.0.\nAfter, we will fill in the left-hand side of the array to be all ones by choosing any point within the left domain to fill.\nusing DataStructures\nusing Test\n\n# Function to check to make sure we are on the canvas\nfunction inbounds(canvas_size, loc)\n\n # Make sure we are not beneath or to the left of the canvas\n if minimum(Tuple(loc)) canvas_size[2]\n return false\n\n # Make sure we are not above the canvas\n elseif loc[1] > canvas_size[1]\n return false\n else\n return true\n end\nend\n\nfunction find_neighbors(canvas, loc::CartesianIndex, old_val, new_val)\n\n # Finding north, south, east, west neighbors\n possible_neighbors = [loc + CartesianIndex(0, 1),\n loc + CartesianIndex(1, 0),\n loc + CartesianIndex(0, -1),\n loc + CartesianIndex(-1, 0)]\n\n # Exclusing neighbors that should not be colored\n neighbors = []\n for possible_neighbor in possible_neighbors\n if inbounds(size(canvas), possible_neighbor) &&\n canvas[possible_neighbor] == old_val\n push!(neighbors, possible_neighbor)\n end\n end\n\n return neighbors\nend\n\nfunction stack_fill!(canvas, loc::CartesianIndex, old_val, new_val)\n if new_val == old_val\n return\n end\n\n s = Stack{CartesianIndex}()\n push!(s, loc)\n\n while length(s) > 0\n current_loc = pop!(s)\n if canvas[current_loc] == old_val\n canvas[current_loc] = new_val\n possible_neighbors = find_neighbors(canvas, current_loc,\n old_val, new_val)\n for neighbor in possible_neighbors\n push!(s,neighbor)\n end\n end\n\n end\nend\n\n\nfunction queue_fill!(canvas, loc::CartesianIndex, old_val, new_val)\n if new_val == old_val\n return\n end\n\n q = Queue{CartesianIndex}()\n enqueue!(q, loc)\n\n # Coloring the initial location\n canvas[loc] = new_val\n\n while length(q) > 0\n current_loc = dequeue!(q)\n\n possible_neighbors = find_neighbors(canvas, current_loc,\n old_val, new_val)\n\n # Coloring as we are enqueuing neighbors\n for neighbor in possible_neighbors\n canvas[neighbor] = new_val\n enqueue!(q,neighbor)\n end\n\n end\nend\n\nfunction recursive_fill!(canvas, loc::CartesianIndex, old_val, new_val)\n\n if (old_val == new_val)\n return\n end\n\n canvas[loc] = new_val\n\n possible_neighbors = find_neighbors(canvas, loc, old_val, new_val)\n for possible_neighbor in possible_neighbors\n recursive_fill!(canvas, possible_neighbor, old_val, new_val)\n end\nend\n\nfunction main()\n\n # Creation of a 5x5 grid with a single row of 1.0 elements \n grid = zeros(5,5)\n grid[3,:] .= 1\n\n # Create solution grid\n answer_grid = zeros(5,5)\n answer_grid[1:3, :] .= 1\n\n # Start filling at 1,1\n start_loc = CartesianIndex(1,1)\n\n @testset \"Fill Methods\" begin\n # Use recursive method and reinitialize grid\n recursive_fill!(grid, start_loc, 0.0, 1.0)\n @test grid == answer_grid\n\n grid[1:2,:] .= 0\n\n # Use queue method and reinitialize grid\n queue_fill!(grid, start_loc, 0.0, 1.0)\n @test grid == answer_grid\n\n grid[1:2,:] .= 0\n\n # Use stack method and reinitialize grid\n stack_fill!(grid, start_loc, 0.0, 1.0)\n @test grid == answer_grid\n end\n\nend\n\nmain()\n\n#include \n#include \n#include \n\nstruct canvas {\n int max_x, max_y;\n int *data;\n};\n\nstruct point {\n int x, y;\n};\n\nstruct stack {\n size_t top, capacity;\n struct point *data;\n};\n\nstruct queue {\n size_t front, back, capacity;\n struct point *data;\n};\n\nint inbounds(struct point p, struct canvas c) {\n return (p.x = c.max_y || p.x >= c.max_x) ? 0 : 1;\n}\n\nint find_neighbors(struct canvas c, struct point p, int old_val, \n struct point *neighbors) {\n int cnt = 0;\n struct point points[4] = {\n {p.x, p.y + 1},\n {p.x + 1, p.y},\n {p.x, p.y - 1},\n {p.x - 1, p.y}\n };\n\n for (int i = 0; i top == stk->capacity) {\n stk->capacity *= 2;\n stk->data = realloc(stk->data, stk->capacity * sizeof(stk->data[0]));\n }\n\n stk->data[stk->top++] = element;\n}\n\nstruct point stack_pop(struct stack *stk) {\n return stk->data[--stk->top];\n}\n\nvoid free_stack(struct stack stk) {\n free(stk.data);\n}\n\nvoid stack_fill(struct canvas c, struct point p, int old_val, int new_val) {\n if (old_val == new_val) {\n return;\n }\n\n struct stack stk = get_stack();\n stack_push(&stk, p);\n\n while (!stack_empty(stk)) {\n struct point cur_loc = stack_pop(&stk);\n if (c.data[cur_loc.x + c.max_x * cur_loc.y] == old_val) {\n c.data[cur_loc.x + c.max_x * cur_loc.y] = new_val;\n\n struct point neighbors[4];\n int cnt = find_neighbors(c, cur_loc, old_val, neighbors);\n\n for (int i = 0; i front == (q->back + 1) % q->capacity) {\n size_t size = sizeof(q->data[0]);\n struct point *tmp = calloc((q->capacity * 2), size);\n memcpy(tmp, q->data + q->front, (q->capacity - q->front) * size);\n memcpy(tmp + q->capacity - q->front, q->data, (q->front - 1) * size);\n\n free(q->data);\n\n q->data = tmp;\n q->back = q->capacity - 1;\n q->front = 0;\n q->capacity *= 2;\n }\n\n q->data[q->back] = element;\n q->back = (q->back + 1) % q->capacity;\n}\n\nstruct point dequeue(struct queue *q) {\n struct point ret = q->data[q->front];\n q->front = (q->front + 1) % q->capacity;\n\n return ret;\n}\n\nvoid free_queue(struct queue q) {\n free(q.data);\n}\n\nvoid queue_fill(struct canvas c, struct point p, int old_val, int new_val) {\n if (old_val == new_val) {\n return;\n }\n\n struct queue q = get_queue(sizeof(struct point *));\n enqueue(&q, p);\n\n while (!queue_empty(q)) {\n struct point cur_loc = dequeue(&q);\n if (c.data[cur_loc.x + c.max_x * cur_loc.y] == old_val) {\n c.data[cur_loc.x + c.max_x * cur_loc.y] = new_val;\n\n struct point neighbors[4];\n int cnt = find_neighbors(c, cur_loc, old_val, neighbors);\n\n for (int i = 0; i \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing CartesianIndex = std::array;\n\nauto inbounds(CartesianIndex size, CartesianIndex loc) {\n if (loc[0] = size[0] || loc[1] >= size[1]) {\n return false;\n }\n return true;\n}\n\nauto find_neighbors(\n std::vector> const& grid,\n CartesianIndex loc,\n float old_value,\n float /* new_value */) {\n\n const std::vector possible_neighbors{\n {loc[0], loc[1] + 1},\n {loc[0] + 1, loc[1]},\n {loc[0], loc[1] - 1},\n {loc[0] - 1, loc[1]}};\n\n std::vector neighbors;\n\n for (auto const& possible_neighbor : possible_neighbors) {\n const auto size = CartesianIndex{\n static_cast(grid[0].size()), static_cast(grid.size())};\n const auto x = static_cast(possible_neighbor[0]);\n const auto y = static_cast(possible_neighbor[1]);\n if (inbounds(size, possible_neighbor) && grid[x][y] == old_value) {\n neighbors.push_back(possible_neighbor);\n }\n }\n\n return neighbors;\n}\n\nvoid recursive_fill(\n std::vector>& grid,\n CartesianIndex loc,\n float old_value,\n float new_value) {\n if (old_value == new_value) {\n return;\n }\n\n const auto x = static_cast(loc[0]);\n const auto y = static_cast(loc[1]);\n\n grid[x][y] = new_value;\n\n const auto possible_neighbors = find_neighbors(grid, loc, old_value, new_value);\n for (auto const& possible_neighbor : possible_neighbors) {\n recursive_fill(grid, possible_neighbor, old_value, new_value);\n }\n}\n\nvoid queue_fill(\n std::vector>& grid,\n CartesianIndex loc,\n float old_value,\n float new_value) {\n if (old_value == new_value) {\n return;\n }\n\n auto q = std::queue{};\n q.push(loc);\n const auto x = static_cast(loc[0]);\n const auto y = static_cast(loc[1]);\n grid[x][y] = new_value;\n\n while (q.size() > 0) {\n const auto current_loc = q.front();\n q.pop();\n const auto possible_neighbors =\n find_neighbors(grid, current_loc, old_value, new_value);\n for (auto const& neighbor : possible_neighbors) {\n const auto neighbor_x = static_cast(neighbor[0]);\n const auto neighbor_y = static_cast(neighbor[1]);\n grid[neighbor_x][neighbor_y] = new_value;\n q.push(neighbor);\n }\n }\n}\n\nvoid stack_fill(\n std::vector>& grid,\n CartesianIndex loc,\n float old_value,\n float new_value) {\n if (old_value == new_value) {\n return;\n }\n\n auto s = std::stack{};\n s.push(loc);\n\n while (s.size() > 0) {\n const auto current_loc = s.top();\n s.pop();\n\n const auto x = static_cast(current_loc[0]);\n const auto y = static_cast(current_loc[1]);\n\n if (grid[x][y] == old_value) {\n grid[x][y] = new_value;\n const auto possible_neighbors =\n find_neighbors(grid, current_loc, old_value, new_value);\n for (auto const& neighbor : possible_neighbors) {\n s.push(neighbor);\n }\n }\n }\n}\n\nint main() {\n\n const std::vector> grid{\n {0, 0, 1, 0, 0},\n {0, 0, 1, 0, 0},\n {0, 0, 1, 0, 0},\n {0, 0, 1, 0, 0},\n {0, 0, 1, 0, 0}};\n\n const std::vector> solution_grid{\n {1, 1, 1, 0, 0},\n {1, 1, 1, 0, 0},\n {1, 1, 1, 0, 0},\n {1, 1, 1, 0, 0},\n {1, 1, 1, 0, 0}};\n\n const CartesianIndex start_loc{1, 1};\n\n auto test_grid = grid;\n recursive_fill(test_grid, start_loc, 0.0, 1.0);\n assert(test_grid == solution_grid);\n\n test_grid = grid;\n queue_fill(test_grid, start_loc, 0.0, 1.0);\n assert(test_grid == solution_grid);\n\n test_grid = grid;\n stack_fill(test_grid, start_loc, 0.0, 1.0);\n assert(test_grid == solution_grid);\n\n return EXIT_SUCCESS;\n}\n\nfrom collections import namedtuple\nfrom queue import Queue\nimport numpy as np\n\nPoint = namedtuple(\"Point\", \"x y\")\n\ndef inbounds(canvas_shape, p):\n return min(p) >= 0 and p.x \nfrom collections import deque\nimport numpy as np\n\n\ndata Point(x, y):\n def __add__(self, other is Point) = Point(self.x + other.x, self.y + other.y)\n\n\n# This function is necessary, because negative indices wrap around the\n# array in Coconut.\ndef inbounds(canvas_shape, location is Point) =\n min(location) >= 0 and location.x map$(location.__add__))\n\n yield from possible_neighbours |> filter$(x -> (inbounds(canvas.shape, x)\n and canvas[x] == old_value))\n\n\ndef stack_fill(canvas, location is Point, old_value, new_value):\n if new_value == old_value or not inbounds(canvas.shape, location):\n return\n\n stack = [location]\n\n while stack:\n current_location = stack.pop()\n if canvas[current_location] == old_value:\n canvas[current_location] = new_value\n stack.extend(find_neighbours(canvas, current_location, old_value))\n\n\ndef queue_fill(canvas, location is Point, old_value, new_value):\n if new_value == old_value or not inbounds(canvas.shape, location):\n return\n\n queue = deque()\n queue.append(location)\n\n canvas[location] = new_value\n\n while queue:\n current_location = queue.popleft()\n for neighbour in find_neighbours(canvas, current_location, old_value):\n canvas[neighbour] = new_value\n queue.append(neighbour)\n\n\ndef recursive_fill(canvas, location is Point, old_value, new_value):\n if new_value == old_value or not inbounds(canvas.shape, location):\n return\n\n canvas[location] = new_value\n # consume is important here, because otherwise, the recursive function is not called again\n consume(\n find_neighbours(canvas, location, old_value)\n |> map$(recursive_fill$(canvas, ?, old_value, new_value))\n )\n\n\ndef test_grid(initial_canvas, final_canvas, function):\n canvas = initial_canvas.copy() # ensure the initial_canvas is unchanged\n function(canvas)\n return (canvas == final_canvas).all()\n\ndef test():\n from collections import namedtuple\n\n TestResults = namedtuple('TestResults', 'passes failures')\n pass_count = failure_count = 0\n\n grid = np.zeros((5, 5))\n grid[2,:] = 1\n solution_grid = np.zeros((5, 5))\n solution_grid[:3,] = 1\n\n starting_location = Point(0, 0)\n\n recursive_test_func = recursive_fill$(?, starting_location, 0, 1)\n # The following is manual unit testing of the function\n if test_grid(grid, solution_grid, recursive_test_func):\n pass_count += 1\n print('.', end='')\n else:\n failure_count += 1\n print('F', end='')\n\n stack_test_func = stack_fill$(?, starting_location, 0, 1)\n if test_grid(grid, solution_grid, stack_test_func):\n print('.', end='')\n pass_count += 1\n else:\n print('F', end='')\n failure_count += 1\n\n queue_test_func = queue_fill$(?, starting_location, 0, 1)\n if test_grid(grid, solution_grid, queue_test_func):\n print('.', end='')\n pass_count += 1\n else:\n print('F', end='')\n failure_count += 1\n\n print()\n print(TestResults(pass_count, failure_count))\n\nif __name__ == '__main__':\n # Testing setup\n test()\n\n\n\n\nBibliography\n1.Bucket Fill in Gimp, 2020.2.Torbert, Shane, Applied computer science, Springer, 2016.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"Example Bucket Fill\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Circle Domains\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Grid 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Grid 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Grid 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Grid 4\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Grid 5\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Grid 6\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Stack Fill\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Queue Fill\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n"},"contents/jarvis_march/jarvis_march.html":{"url":"contents/jarvis_march/jarvis_march.html","title":"Jarvis March","keywords":"","body":"Jarvis March\nThe first two-dimensional convex hull algorithm was originally developed by R. A. Jarvis in 1973 [1].\nThough other convex hull algorithms exist, this algorithm is often called the gift-wrapping algorithm.\nThe idea behind this algorithm is simple.\nIf we start with a random distribution of points, we can find the convex hull by first starting with the left-most point and using the origin to calculate an angle between every other point in the simulation.\nAs a note, the \"angle\" can be roughly approximated with a cross-product or a dot product, which is common for some implementations here.\nWhichever point has the largest interior angle is chosen as the next point in the convex hull and we draw a line between the two points.\nFrom there, we use the two known points to again calculate the angle between all other points in the simulation.\nWe then choose the point with the largest interior angle and move the simulation forward.\nWe keep repeating this process until we have returned to our original point.\nThe set of points chosen in this simulation will be the convex hull.\nAs we might expect, this algorithm is not incredibly efficient and has a runtime of \\mathcal{O}(nh), where n is the number of points and h is the size of the hull.\nAs a note, the Jarvis March can be generalized to higher dimensions.\nSince this algorithm, there have been many other algorithms that have advanced the field of two-dimensional gift-wrapping forward, including the Graham Scan and Chan's Algorithm, which will be discussed in due time.\nBibliography\n1.Jarvis, Ray A, On the identification of the convex hull of a finite set of points in the plane, Elsevier, 1973.\nExample Code\nJarvisMarch.cs\n// submitted by Julian Schacher (jspp) with great help by gustorn\nusing System;\nusing System.Collections.Generic;\nusing System.Linq;\n\nnamespace JarvisMarch\n{\n public struct Vector\n {\n public readonly int x;\n public readonly int y;\n\n public Vector(int xValue, int yValue)\n {\n this.x = xValue;\n this.y = yValue;\n }\n\n public override bool Equals(object obj) => obj is Vector v && this.x == v.x && this.y == v.y;\n public override int GetHashCode() => (17 * 23 + this.x) * 23 + this.y;\n\n public static bool operator==(Vector a, Vector b) => a.Equals(b);\n public static bool operator!=(Vector a, Vector b) => !(a == b);\n }\n\n public class JarvisMarch\n {\n public List Run(List points)\n {\n var convexHull = new List();\n\n // Set the intial pointOnHull to the point of the list, where the x-position is the lowest.\n var pointOnHull = points.Aggregate((leftmost, current) => leftmost.x \n {\n // Returns true, if potentialNextPointOnHull is equal to the current pointOnHull or if the current point is left of the line defined by pointOnHull and potentialNextPointOnHull.\n if (potentialNextPointOnHull == pointOnHull || IsLeftOf(pointOnHull, potentialNextPointOnHull, current))\n return current;\n return potentialNextPointOnHull;\n });\n\n // Check if the gift wrap is completed.\n } while (pointOnHull != convexHull[0]);\n\n return convexHull;\n }\n\n // Returns true, if p is left of the line defined by a and b.\n private bool IsLeftOf(Vector a, Vector b, Vector p) => (b.x - a.x) * (p.y - a.y) > (p.x - a.x) * (b.y - a.y);\n }\n}\n\nProgram.cs\n// submitted by Julian Schacher (jspp) with great help by gustorn\nusing System;\nusing System.Collections.Generic;\n\nnamespace JarvisMarch\n{\n class Program\n {\n static void Main(string[] args)\n {\n System.Console.WriteLine(\"JarvisMarch\");\n // Example list of points.\n // The points are represented by vectors here, but that doesn't really matter.\n var points = new List()\n {\n new Vector(-5, 2),\n new Vector(5, 7),\n new Vector(-6, -12),\n new Vector(-14, -14),\n new Vector(9, 9),\n new Vector(-1, -1),\n new Vector(-10, 11),\n new Vector(-6, 15),\n new Vector(-6, -8),\n new Vector(15, -9),\n new Vector(7, -7),\n new Vector(-2, -9),\n new Vector(6, -5),\n new Vector(0, 14),\n new Vector(2, 8),\n };\n var jarvisMarch = new JarvisMarch();\n var giftWrap = jarvisMarch.Run(points);\n\n // Print the points of the gift wrap.\n foreach (var point in giftWrap)\n System.Console.WriteLine($\"{point.x}, {point.y}\");\n }\n }\n}\n\nstruct Pos\n x::Float64\n y::Float64\nend\n\nfunction jarvis_cross(point1::Pos, point2::Pos, point3::Pos)\n vec1 = Pos(point2.x - point1.x, point2.y - point1.y)\n vec2 = Pos(point3.x - point2.x, point3.y - point2.y)\n ret_cross = vec1.x*vec2.y - vec1.y*vec2.x\n return ret_cross*ret_cross\nend\n\nfunction jarvis_march(points::Vector{Pos})\n hull = Vector{Pos}()\n\n # sorting array based on leftmost point\n sort!(points, by = item -> item.x)\n push!(hull, points[1])\n\n i = 1\n curr_point = points[2]\n\n # Find cross product between points\n curr_product = jarvis_cross(Pos(0,0), hull[1], curr_point)\n while (curr_point != hull[1])\n for point in points\n product = 0.0\n if (i == 1)\n if (hull[i] != point)\n product = jarvis_cross(Pos(0,0), hull[i], point)\n end\n else\n if (hull[i] != point && hull[i-1] != point)\n product = jarvis_cross(hull[i-1], hull[i], point)\n end\n end\n if (product > curr_product)\n curr_point = point\n curr_product = product\n end\n end\n push!(hull, curr_point)\n curr_product = 0\n i += 1\n end\n\n return hull\nend\n\nfunction main()\n\n points = [Pos(2,1.5), Pos(1, 1), Pos(2, 4), Pos(3, 1)]\n hull = jarvis_march(points)\n println(hull)\nend\n\nmain()\n\nimport Data.List (sort, maximumBy)\nimport Data.Function (on)\n\ntype Point = (Double, Double)\n\nangle :: Point -> Point -> Point -> Double\nangle a@(xa, ya) b@(xb, yb) c@(xc, yc)\n | a==b || c==b = 0\n | theta [Point]\njarvisMarch [] = []\njarvisMarch pts = p0 : wrap (x, y-1) p0\n where p0@(x, y)= minimum pts\n wrap p1 p2\n | pm == p0 = []\n | otherwise = pm : wrap p2 pm\n where pm = maximumBy (compare `on` angle p1 p2) pts\n\nmain = do\n let pts = filter (\\(x,y) -> x^2+y^2\n#include \n#include \n#include \n\nstruct point {\n double x,y;\n};\n\nstruct point left_most_point(struct point *points, size_t num_points) {\n struct point ret = points[0];\n\n for (size_t i = 0; i 0.0) {\n end_point = points[j];\n }\n }\n\n i++;\n hull_point = end_point;\n } while (!equal(end_point, hull_points[0]));\n\n return i;\n}\n\nint main() {\n struct point points[] = {\n { -5.0, 2.0 },\n { 5.0, 7.0 },\n { -6.0, -12.0 },\n { -14.0, -14.0 },\n { 9.0, 9.0 },\n { -1.0, -1.0 },\n { -10.0, 11.0 },\n { -6.0, 15.0 },\n { -6.0, -8.0 },\n { 15.0, -9.0 },\n { 7.0, -7.0 },\n { -2.0, -9.0 },\n { 6.0, -5.0 },\n { 0.0, 14.0 },\n { 2.0, 8.0 }\n };\n struct point hull_points[15];\n\n size_t num_hull_points = jarvis_march(points, hull_points, 15);\n\n printf(\"The Hull points are:\\n\");\n for (size_t i = 0; i \nfunction jarvisMarch(points) {\n const hull = [];\n\n let pointOnHull = points.reduce((leftmost, current) => leftmost.x (p.x - a.x) * (b.y - a.y);\n}\n\nconst points = [\n { x: -5, y: 2 },\n { x: 5, y: 7 },\n { x: -6, y: -12 },\n { x: -14, y: -14 },\n { x: 9, y: 9 },\n { x: -1, y: -1 },\n { x: -10, y: 11 },\n { x: -6, y: 15 },\n { x: -6, y: -8 },\n { x: 15, y: -9 },\n { x: 7, y: -7 },\n { x: -2, y: -9 },\n { x: 6, y: -5 },\n { x: 0, y: 14 },\n { x: 2, y: 8 }\n];\n\nconst convexHull = jarvisMarch(points);\nconvexHull.forEach(p => console.log(`(${p.x}, ${p.y})`));\n\n# Is the turn counter clockwise?\ndef ccw(p1, p2, p3):\n return (p3[1] - p1[1]) * (p2[0] - p1[0]) \\\n >= (p2[1] - p1[1]) * (p3[0] - p1[0])\n\n\ndef jarvis_march(gift):\n n = len(gift) # Number of points in list\n point_on_hull = min(gift) # leftmost point in gift\n hull = [point_on_hull] # leftmost point guaranteed to be in hull\n\n while True:\n # Candidate for next point in hull\n endpoint = gift[0]\n for j in range(1, n):\n if endpoint == point_on_hull \\\n or not ccw(gift[j], hull[-1], endpoint):\n endpoint = gift[j]\n\n point_on_hull = endpoint\n\n # Check if we have completely wrapped gift\n if hull[0] == endpoint:\n break\n else:\n hull.append(point_on_hull)\n\n return hull\n\n\ndef main():\n test_gift = [\n (-5, 2), (5, 7), (-6, -12), (-14, -14), (9, 9),\n (-1, -1), (-10, 11), (-6, 15), (-6, -8), (15, -9),\n (7, -7), (-2, -9), (6, -5), (0, 14), (2, 8)\n ]\n hull = jarvis_march(test_gift)\n\n print(\"The points in the hull are:\")\n for point in hull:\n print(point)\n\n\nif __name__ == \"__main__\":\n main()\n\n#include \n#include \n#include \n\nstruct Point\n{\n double x, y;\n\n bool operator==(const Point& b) const\n {\n return x == b.x && y == b.y;\n }\n\n bool operator!=(const Point& b) const\n {\n return !(*this == b);\n }\n};\n\nstd::vector jarvis_march(const std::vector& points)\n{\n std::vector hull_points;\n\n if(points.empty())\n return hull_points;\n\n // Left most point\n auto first_point_it = std::min_element(points.begin(), points.end(), [](const Point& a, const Point& b){ return a.x (p3.x - p1.x) * (p2.y - p1.y);\n }\n );\n }\n while(*next_point_it != *first_point_it);\n\n return hull_points;\n}\n\nint main() {\n std::vector points = {\n { -5.0, 2.0 },\n { 5.0, 7.0 },\n { -6.0, -12.0 },\n { -14.0, -14.0 },\n { 9.0, 9.0 },\n { -1.0, -1.0 },\n { -10.0, 11.0 },\n { -6.0, 15.0 },\n { -6.0, -8.0 },\n { 15.0, -9.0 },\n { 7.0, -7.0 },\n { -2.0, -9.0 },\n { 6.0, -5.0 },\n { 0.0, 14.0 },\n { 2.0, 8.0 }\n };\n\n auto hull_points = jarvis_march(points);\n\n std::cout \n;;;; Jarvis March implementation\n\n(defstruct (point (:constructor make-point (x y))) x y)\n\n(defun is-left-p (p1 p2 p3)\n \"Checks if the point p3 is to the left of the line p1 -> p2\"\n (>\n (*\n (- (point-y p3) (point-y p1))\n (- (point-x p2) (point-x p1)))\n (*\n (- (point-y p2) (point-y p1))\n (- (point-x p3) (point-x p1)))))\n\n(defun next-point-on-hull (p1 p2 gift)\n \"Finds the next point on the convex hull of a gift\"\n (if (null gift)\n p2\n (if (is-left-p p1 p2 (first gift))\n (next-point-on-hull p1 (first gift) (rest gift))\n (next-point-on-hull p1 p2 (rest gift)))))\n\n(defun leftmost-point (gift)\n \"Returns the lefmost point of a gift\"\n (reduce \n (lambda (p1 p2)\n (if (\nimport java.util.*;\n\npublic class JarvisMarch {\n\n static class Point {\n private double x;\n private double y;\n\n public Point(double a, double b) {\n x = a;\n y = b;\n }\n\n public double getX() {\n return x;\n }\n public double getY() {\n return y;\n }\n\n public boolean equals(Point p) {\n if (p.getX() == x && p.getY() == y) {\n return true;\n } else {\n return false;\n }\n }\n public double magnitude() {\n return Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2));\n }\n }\n\n //find the angle by creating two vectors and then using a property of dot products\n private static double angle(Point a, Point b, Point c) {\n Point ab = new Point(b.getX() - a.getX(), b.getY() - a.getY());\n Point bc = new Point(c.getX() - b.getX(), c.getY() - b.getY());\n return Math.acos(-1 * ((ab.getX() * bc.getX()) + (ab.getY() * bc.getY())) /\n (ab.magnitude() * bc.magnitude()));\n }\n\n public static ArrayList jarvisMarch(ArrayList arr) {\n ArrayList hull = new ArrayList();\n Point pointOnHull = new Point(Double.MAX_VALUE, 0);\n\n //find leftmost point\n for (Point p: arr) {\n if (p.getX() angle(endpoint, pointOnHull, ref)) { //found a point that makes a greater angle\n endpoint = p;\n }\n }\n pointOnHull = endpoint;\n if (pointOnHull.equals(hull.get(0))) { //add next point to hull if not equal to the leftmost point\n break;\n } else {\n hull.add(pointOnHull);\n }\n }\n return hull;\n }\n\n public static void main(String[] args) {\n\n //test array setup\n ArrayList gift = new ArrayList();\n gift.add(new Point(-5, 2));\n gift.add(new Point(5, 7));\n gift.add(new Point(-6, -12));\n gift.add(new Point(-14, -14));\n gift.add(new Point(9, 9));\n gift.add(new Point(-1, -1));\n gift.add(new Point(-10, 11));\n gift.add(new Point(-6, 15));\n gift.add(new Point(-6, -8));\n gift.add(new Point(15, -9));\n gift.add(new Point(7, -7));\n gift.add(new Point(-2, -9));\n gift.add(new Point(6, -5));\n gift.add(new Point(0, 14));\n gift.add(new Point(2, 8));\n\n //print initial array of points\n System.out.println(\"Gift:\");\n for (Point p: gift) {\n System.out.println(\"[\" + p.getX() + \", \" + p.getY() + \"]\");\n }\n\n //find and print the array of points in the hull\n ArrayList hull = jarvisMarch(gift);\n System.out.println(\"Wrapping:\");\n for (Point p: hull) {\n System.out.println(\"[\" + p.getX() + \", \" + p.getY() + \"]\");\n }\n }\n\n}\n\npackage main\n\nimport (\n \"fmt\"\n)\n\ntype point struct {\n x, y float64\n}\n\nfunc leftMostPoint(points []point) point {\n ret := points[0]\n\n for _, p := range points {\n if (p.x = (p2.y-p1.y)*(p3.x-p1.x)\n}\n\nfunc jarvisMarch(points []point) []point {\n hullPoints := make([]point, 0)\n hullPoint := leftMostPoint(points)\n hullPoints = append(hullPoints, hullPoint)\n\n for {\n endPoint := points[0]\n\n for _, p := range points[1:] {\n if endPoint.equal(hullPoint) || !counterClockWise(p, hullPoints[len(hullPoints)-1], endPoint) {\n endPoint = p\n }\n }\n\n hullPoint = endPoint\n\n if endPoint.equal(hullPoints[0]) {\n break\n }\n\n hullPoints = append(hullPoints, hullPoint)\n }\n return hullPoints\n}\n\nfunc main() {\n points := []point{{-5, 2}, {5, 7}, {-6, -12}, {-14, -14}, {9, 9},\n {-1, -1}, {-10, 11}, {-6, 15}, {-6, -8}, {15, -9},\n {7, -7}, {-2, -9}, {6, -5}, {0, 14}, {2, 8},\n }\n\n hullPoints := jarvisMarch(points)\n fmt.Println(\"The hull points are:\")\n\n for _, p := range hullPoints {\n fmt.Printf(\"x=%f y=%f\\n\", p.x, p.y)\n }\n}\n\nstruct Point {\n x int\n y int\n}\n\nfn left_most_point(points []Point) Point {\n mut ret := points[0]\n\n for p in points {\n if (p.x = (p2.y-p1.y) * (p3.x-p1.x)\n}\n\nfn jarvis_march(points []Point) []Point {\n mut hull_point := left_most_point(points)\n mut hull_points := [hull_point]\n\n\n for {\n mut end_point := points[0]\n\n for i := 1; i \n\ntype Point = (i64, i64);\n\n// Is the turn counter clockwise?\nfn turn_counter_clockwise(p1: Point, p2: Point, p3: Point) -> bool {\n (p3.1 - p1.1) * (p2.0 - p1.0) >= (p2.1 - p1.1) * (p3.0 - p1.0)\n}\n\nfn jarvis_march(gift: &[Point]) -> Option> {\n // There can only be a convex hull if there are more than 2 points\n if gift.len() \ndata point(x=0, y=0):\n def __str__(self):\n return f'({self.x}, {self.y})'\n\n# Is the turn counter-clockwise?\ndef counter_clockwise(p1 is point, p2 is point, p3 is point) =\n (p3.y - p1.y) * (p2.x - p1.x) >= (p2.y - p1.y) * (p3.x - p1.x)\n\n\ndef jarvis_march(gift: point[]) -> point[]:\n point_on_hull = min(gift) # The leftmost point in the gift\n hull = [point_on_hull] # It is guaranteed it will be on the hull.\n\n while True:\n # Candidate for the next point in the hull\n endpoint = gift[0]\n for p in gift:\n if (endpoint == point_on_hull\n or not counter_clockwise(p, hull[-1], endpoint)):\n endpoint = p\n\n point_on_hull = endpoint\n\n # Check if the gift is completely covered.\n if hull[0] == endpoint:\n return hull\n hull.append(point_on_hull)\n\n\nif __name__ == '__main__':\n test_gift = [\n (-5, 2), (5, 7), (-6, -12), (-14, -14), (9, 9),\n (-1, -1), (-10, 11), (-6, 15), (-6, -8), (15, -9),\n (7, -7), (-2, -9), (6, -5), (0, 14), (2, 8)\n ] |> map$(t -> point(*t)) |> list\n hull = jarvis_march(test_gift)\n\n print(\"[#] The points in the hull are:\")\n for point in hull:\n print(point)\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/graham_scan/graham_scan.html":{"url":"contents/graham_scan/graham_scan.html","title":"Graham Scan","keywords":"","body":"Graham Scan\nAt around the same time of the Jarvis March, R. L. Graham was also developing an algorithm to find the convex hull of a random set of points [1].\nUnlike the Jarvis March, which is an \\mathcal{O}(nh) operation, the Graham Scan is \\mathcal{O}(n\\log(n)), where n is the number of points and h is the size for the hull.\nThis means that the complexity of the Graham Scan is not output-sensitive; moreover, there are some cases where the Jarvis March is more optimal, depending on the size of the hull and the number of points to wrap.\nRather than starting at the leftmost point like the Jarvis March, the Graham scan starts at the bottom.\nWe then sort the distribution of points based on the angle between the bottom-most point, the origin, and each other point.\nAfter sorting, we go through point-by-point, searching for points that are on the convex hull and throwing out any other points.\nWe do this by looking for counter-clockwise rotations.\nIf an angle between three points turns inward, the shape is obviously not convex, so we can throw that result out.\nWe can find whether a rotation is counter-clockwise with trigonometric functions or by using a cross-product, like so:\nfunction ccw(a::Point, b::Point, c::Point)\n return ((b.x - a.x)*(c.y - a.y) - (b.y - a.y)*(c.x - a.x))\nend\n\nccw :: Point -> Point -> Point -> Double\nccw (xa, ya) (xb, yb) (xc, yc) = (xb - xa) * (yc - ya) - (yb - ya) * (xc - xa)\n\ndouble ccw(struct point a, struct point b, struct point c) {\n return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);\n}\n\nfunction ccw(a, b, c) {\n return (b.x - a.x) * (c.y - a.y) - (c.x - a.x) * (b.y - a.y);\n}\n\ndef counter_clockwise(p1, p2, p3):\n \"\"\"Is the turn counter-clockwise?\"\"\"\n return (p3[1] - p1[1]) * (p2[0] - p1[0]) >= (p2[1] - p1[1]) * (p3[0] - p1[0])\n\nfunc counterClockwise(p1, p2, p3 point) bool {\n return (p3.y-p1.y)*(p2.x-p1.x) >= (p2.y-p1.y)*(p3.x-p1.x)\n}\n\nstatic double ccw(Point a, Point b, Point c) {\n return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);\n}\n\n(defun ccw (p1 p2 p3)\n \"Determines if a turn between three points is counterclockwise\"\n (-\n (*\n (- (point-y p2) (point-y p1))\n (- (point-x p3) (point-x p1)))\n (*\n (- (point-y p3) (point-y p1))\n (- (point-x p2) (point-x p1)))))\n\ndouble ccw(const point& a, const point& b, const point& c) {\n return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);\n}\n\ndata point(x=0, y=0):\n def angle(self, other):\n \"\"\"Computes the angle between the two points\"\"\"\n match point(x1, y1) in other:\n return atan2(y1 - self.y, x1 - self.x)\n\nfn counter_clockwise(a: &Point, b: &Point, c: &Point) -> f64 {\n (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x)\n}\n\n\n\nIf the output of this function is 0, the points are collinear.\nIf the output is positive, then the points form a counter-clockwise \"left\" turn.\nIf the output is negative, then the points form a clockwise \"right\" turn.\nWe basically do not want clockwise rotations, because this means we are at an interior angle.\n\nTo save memory and expensive append() operations, we ultimately look for points that should be on the hull and swap them with the first elements in the array.\nIf there are M elements on the hull, then the first M elements in our output random distribution of points will be the hull.\nIn the end, the code should look something like this:\nfunction graham_scan!(points::Vector{Point})\n N = length(points)\n\n # Place the lowest point at the start of the array\n sort!(points, by = item -> item.y)\n\n # Sort all other points according to angle with that point\n other_points = sort(points[2:end], by = item -> atan(item.y - points[1].y,\n item.x - points[1].x))\n\n # Place points sorted by angle back into points vector\n for i in 1:length(other_points)\n points[i+1] = other_points[i]\n end\n\n # M will be the point on the hull\n M = 2\n for i = 1:N\n while (ccw(points[M-1], points[M], points[i]) 2)\n M -= 1\n # All points are collinear\n elseif (i == N)\n break\n else\n i += 1\n end\n end\n\n # ccw point found, updating hull and swapping points\n M += 1\n points[i], points[M] = points[M], points[i]\n end\n\n return points[1:M]\nend\n\ngrahamScan :: [Point] -> [Point]\ngrahamScan [] = []\ngrahamScan pts = wrap sortedPts [p0]\n where p0@(x, y)= minimumBy (compare `on` snd) pts\n sortedPts = sortOn (\\(px, py) -> atan2 (py-y) (px-x) ) $ filter (/=p0) pts\n wrap [] ps = ps\n wrap (s:ss) [p] = wrap ss [s, p]\n wrap (s:ss) (p1:p2:ps)\n | ccw s p1 p2 > 0 = wrap (s:ss) (p2:ps)\n | otherwise = wrap ss (s:p1:p2:ps)\n\nsize_t graham_scan(struct point *points, size_t size) {\n qsort(points, size, sizeof(struct point), cmp_points);\n polar_angles_sort(points, points[0], size);\n\n struct point tmp_points[size + 1];\n memcpy(tmp_points + 1, points, size * sizeof(struct point));\n tmp_points[0] = tmp_points[size];\n\n size_t m = 1;\n for (size_t i = 2; i 1) {\n m--;\n continue;\n } else if (i == size) {\n break;\n } else {\n i++;\n }\n }\n\n m++;\n struct point tmp = tmp_points[i];\n tmp_points[i] = tmp_points[m];\n tmp_points[m] = tmp;\n }\n\n memcpy(points, tmp_points + 1, size * sizeof(struct point));\n\n return m;\n}\n\nfunction grahamScan(points) {\n // First, sort the points so the one with the lowest y-coordinate comes first (the pivot)\n points = [...points].sort((a, b) => (a.y - b.y));\n const pivot = points[0];\n\n // Then sort all remaining points based on the angle between the pivot and itself\n const hull = points.slice(1).sort((a, b) => polarAngle(a, pivot) - polarAngle(b, pivot));\n\n // The pivot is always on the hull\n hull.unshift(pivot);\n\n let n = hull.length;\n let m = 1;\n for (let i = 2; i 1) {\n m -= 1;\n } else if (m === i) {\n break;\n } else {\n i += 1;\n }\n }\n\n m += 1;\n [hull[i], hull[m]] = [hull[m], hull[i]];\n }\n\n return hull.slice(0, m + 1);\n}\n\ndef graham_scan(gift):\n gift = list(set(gift)) # Remove duplicate points\n start = min(gift, key=lambda p: (p[1], p[0])) # Must be in hull\n gift.remove(start)\n\n s = sorted(gift, key=lambda point: polar_angle(start, point))\n hull = [start, s[0], s[1]]\n\n # Remove points from hull that make the hull concave\n for pt in s[2:]:\n while not counter_clockwise(hull[-2], hull[-1], pt):\n del hull[-1]\n hull.append(pt)\n\n return hull\n\nfunc grahamScan(points []point) []point {\n sort.Slice(points, func(a, b int) bool {\n return points[a].y \nstatic List grahamScan(List gift) {\n gift = gift.stream()\n .distinct()\n .sorted(Comparator.comparingDouble(point -> -point.y))\n .collect(Collectors.toList());\n\n Point pivot = gift.get(0);\n\n // Sort the remaining Points based on the angle between the pivot and itself\n List hull = gift.subList(1, gift.size());\n hull.sort(Comparator.comparingDouble(point -> polarAngle(point, pivot)));\n\n // The pivot is always on the hull\n hull.add(0, pivot);\n\n int n = hull.size();\n int m = 1;\n\n for (int i = 2; i 1) {\n m--;\n } else if (m == 1) {\n break;\n } else {\n i++;\n }\n }\n m++;\n\n Point temp = hull.get(i);\n hull.set(i, hull.get(m));\n hull.set(m, temp);\n }\n return hull.subList(0, m + 1);\n}\n\n(defun atan2 (y x)\n \"Calculates the angle of a point in the euclidean plane in radians\"\n (cond\n ((> x 0) (atan y x))\n ((and (= y 0)) (+ (atan y x) pi))\n ((and ( y 0)) (/ pi 2))\n ((and (eql x 0) ( (length gift) 0)'.\n (if gift\n (labels ((wrap (sorted-points hull)\n (if sorted-points\n ;; This covers the case where the hull has one or more element.\n ;; We aren't concerned about the hull being empty, because then the gift must\n ;; also be empty and this function is never given an empty gift.\n (if (rest hull)\n (if (\nstd::vector graham_scan(std::vector& points) {\n // selecting lowest point as pivot\n size_t low_index = 0;\n for (size_t i = 1; i 1) {\n m--;\n continue;\n } else if (i == points.size()) {\n break;\n } else {\n i++;\n }\n }\n m++;\n std::swap(points[i], points[m]);\n }\n return std::vector(points.begin(), points.begin() + m + 1);\n}\n\ndef graham_scan(gift):\n gift = list(set(gift)) # Remove the duplicate points if any.\n start = min(gift, key=(p -> (p.x, p.y)))\n gift.remove(start)\n\n s = sorted(gift, key=(point -> start.angle(point)))\n hull = [start, s[0], s[1]]\n\n # Remove the hull points that make the hull concave\n for point in s[2:]:\n while not counter_clockwise(hull[-2], hull[-1], point):\n del hull[-1]\n hull.append(point)\n return hull\n\nfn graham_scan(mut points: Vec) -> Vec {\n if points.is_empty() {\n return Vec::new();\n }\n\n // Unwrap is safe because length is > 0\n let start = *points.iter().min().unwrap();\n points.retain(|a| a != &start);\n points.sort_unstable_by(|a, b| polar_angle(&start, a).partial_cmp(&polar_angle(&start, b)).unwrap());\n\n let mut hull: Vec = vec![start, points[0], points[1]];\n\n for pt in points[2..points.len()].iter() {\n while counter_clockwise(&hull[hull.len() - 2], &hull[hull.len() - 1], pt) \n\n\nBibliography\n1.Graham, Ronald L, An efficient algorithm for determining the convex hull of a finite planar set, Elsevier, 1972.\nExample Code\nstruct Point\n x::Float64\n y::Float64\nend\n\nfunction ccw(a::Point, b::Point, c::Point)\n return ((b.x - a.x)*(c.y - a.y) - (b.y - a.y)*(c.x - a.x))\nend\n\nfunction graham_scan!(points::Vector{Point})\n N = length(points)\n\n # Place the lowest point at the start of the array\n sort!(points, by = item -> item.y)\n\n # Sort all other points according to angle with that point\n other_points = sort(points[2:end], by = item -> atan(item.y - points[1].y,\n item.x - points[1].x))\n\n # Place points sorted by angle back into points vector\n for i in 1:length(other_points)\n points[i+1] = other_points[i]\n end\n\n # M will be the point on the hull\n M = 2\n for i = 1:N\n while (ccw(points[M-1], points[M], points[i]) 2)\n M -= 1\n # All points are collinear\n elseif (i == N)\n break\n else\n i += 1\n end\n end\n\n # ccw point found, updating hull and swapping points\n M += 1\n points[i], points[M] = points[M], points[i]\n end\n\n return points[1:M]\nend\n\nfunction main()\n # This hull is just a simple test so we know what the output should be\n points = [\n Point(-5,2), Point(5,7), Point(-6,-12), Point(-14,-14), Point(9,9),\n Point(-1,-1), Point(-10,11), Point(-6,15), Point(-6,-8), Point(15,-9),\n Point(7,-7), Point(-2,-9), Point(6,-5), Point(0,14), Point(2,8)\n ]\n hull = graham_scan!(points)\n println(hull)\nend\n\nmain()\n\nimport Data.List (sortOn, minimumBy)\nimport Data.Function (on)\n\ntype Point = (Double, Double)\n\nccw :: Point -> Point -> Point -> Double\nccw (xa, ya) (xb, yb) (xc, yc) = (xb - xa) * (yc - ya) - (yb - ya) * (xc - xa)\n\ngrahamScan :: [Point] -> [Point]\ngrahamScan [] = []\ngrahamScan pts = wrap sortedPts [p0]\n where p0@(x, y)= minimumBy (compare `on` snd) pts\n sortedPts = sortOn (\\(px, py) -> atan2 (py-y) (px-x) ) $ filter (/=p0) pts\n wrap [] ps = ps\n wrap (s:ss) [p] = wrap ss [s, p]\n wrap (s:ss) (p1:p2:ps)\n | ccw s p1 p2 > 0 = wrap (s:ss) (p2:ps)\n | otherwise = wrap ss (s:p1:p2:ps)\n\nmain = do\n -- We build the set of points of integer coordinates within a circle of radius 5\n let pts = [(x,y) | x\n#include \n#include \n#include \n#include \n#include \n\nstruct point {\n double x, y;\n};\n\nint cmp_points(const void *a, const void *b) {\n struct point* pa = (struct point*) a;\n struct point* pb = (struct point*) b;\n\n if (pa->y > pb->y) {\n return 1;\n } else if (pa->y y) {\n return -1;\n } else {\n return 0;\n }\n}\n\ndouble ccw(struct point a, struct point b, struct point c) {\n return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);\n}\n\ndouble polar_angle(struct point origin, struct point p) {\n return atan2(p.y - origin.y, p.x - origin.x);\n}\n\nvoid polar_angles_sort(struct point *points, struct point origin, size_t size) {\n if (size pivot_angle) {\n j--;\n }\n\n if (i >= j) {\n break;\n }\n\n struct point tmp = points[i];\n points[i] = points[j];\n points[j] = tmp;\n\n i++;\n j--;\n }\n\n polar_angles_sort(points, origin, i);\n polar_angles_sort(points + i, origin, size - i);\n}\n\nsize_t graham_scan(struct point *points, size_t size) {\n qsort(points, size, sizeof(struct point), cmp_points);\n polar_angles_sort(points, points[0], size);\n\n struct point tmp_points[size + 1];\n memcpy(tmp_points + 1, points, size * sizeof(struct point));\n tmp_points[0] = tmp_points[size];\n\n size_t m = 1;\n for (size_t i = 2; i 1) {\n m--;\n continue;\n } else if (i == size) {\n break;\n } else {\n i++;\n }\n }\n\n m++;\n struct point tmp = tmp_points[i];\n tmp_points[i] = tmp_points[m];\n tmp_points[m] = tmp;\n }\n\n memcpy(points, tmp_points + 1, size * sizeof(struct point));\n\n return m;\n}\n\nint main() {\n struct point points[] = {{-5, 2}, {5, 7}, {-6, -12}, {-14, -14}, {9, 9},\n {-1, -1}, {-10, 11}, {-6, 15}, {-6, -8}, {15, -9},\n {7, -7}, {-2, -9}, {6, -5}, {0, 14}, {2, 8}};\n size_t num_initial_points = 15;\n\n printf(\"Points:\\n\");\n for (size_t i = 0; i \nfunction grahamScan(points) {\n // First, sort the points so the one with the lowest y-coordinate comes first (the pivot)\n points = [...points].sort((a, b) => (a.y - b.y));\n const pivot = points[0];\n\n // Then sort all remaining points based on the angle between the pivot and itself\n const hull = points.slice(1).sort((a, b) => polarAngle(a, pivot) - polarAngle(b, pivot));\n\n // The pivot is always on the hull\n hull.unshift(pivot);\n\n let n = hull.length;\n let m = 1;\n for (let i = 2; i 1) {\n m -= 1;\n } else if (m === i) {\n break;\n } else {\n i += 1;\n }\n }\n\n m += 1;\n [hull[i], hull[m]] = [hull[m], hull[i]];\n }\n\n return hull.slice(0, m + 1);\n}\n\nfunction polarAngle(a, b) {\n return Math.atan2(a.y - b.y, a.x - b.x);\n}\n\nfunction ccw(a, b, c) {\n return (b.x - a.x) * (c.y - a.y) - (c.x - a.x) * (b.y - a.y);\n}\n\nconst points = [\n { x: -5, y: 2 },\n { x: 5, y: 7 },\n { x: -6, y: -12 },\n { x: -14, y: -14 },\n { x: 9, y: 9 },\n { x: -1, y: -1 },\n { x: -10, y: 11 },\n { x: -6, y: 15 },\n { x: -6, y: -8 },\n { x: 15, y: -9 },\n { x: 7, y: -7 },\n { x: -2, y: -9 },\n { x: 6, y: -5 },\n { x: 0, y: 14 },\n { x: 2, y: 8 },\n];\n\nconst convexHull = grahamScan(points);\nconsole.log(\"The points in the hull are:\");\nconvexHull.forEach(p => console.log(`(${p.x}, ${p.y})`));\n\nfrom math import atan2\n\n\ndef counter_clockwise(p1, p2, p3):\n \"\"\"Is the turn counter-clockwise?\"\"\"\n return (p3[1] - p1[1]) * (p2[0] - p1[0]) >= (p2[1] - p1[1]) * (p3[0] - p1[0])\n\n\ndef polar_angle(ref, point):\n \"\"\"Find the polar angle of a point relative to a reference point\"\"\"\n return atan2(point[1] - ref[1], point[0] - ref[0])\n\n\ndef graham_scan(gift):\n gift = list(set(gift)) # Remove duplicate points\n start = min(gift, key=lambda p: (p[1], p[0])) # Must be in hull\n gift.remove(start)\n\n s = sorted(gift, key=lambda point: polar_angle(start, point))\n hull = [start, s[0], s[1]]\n\n # Remove points from hull that make the hull concave\n for pt in s[2:]:\n while not counter_clockwise(hull[-2], hull[-1], pt):\n del hull[-1]\n hull.append(pt)\n\n return hull\n\n\ndef main():\n test_gift = [\n (-5, 2),\n (5, 7),\n (-6, -12),\n (-14, -14),\n (9, 9),\n (-1, -1),\n (-10, 11),\n (-6, 15),\n (-6, -8),\n (15, -9),\n (7, -7),\n (-2, -9),\n (6, -5),\n (0, 14),\n (2, 8),\n ]\n hull = graham_scan(test_gift)\n\n print(\"The points in the hull are:\")\n for point in hull:\n print(point)\n\n\nmain()\n\npackage main\n\nimport (\n \"fmt\"\n \"math\"\n \"sort\"\n)\n\ntype point struct {\n x, y int\n}\n\nfunc counterClockwise(p1, p2, p3 point) bool {\n return (p3.y-p1.y)*(p2.x-p1.x) >= (p2.y-p1.y)*(p3.x-p1.x)\n}\n\nfunc polarAngle(ref, point point) float64 {\n return math.Atan2(float64(point.y-ref.y), float64(point.x-ref.x))\n}\n\nfunc grahamScan(points []point) []point {\n sort.Slice(points, func(a, b int) bool {\n return points[a].y \nimport java.util.ArrayList;\nimport java.util.Comparator;\nimport java.util.List;\nimport java.util.stream.Collectors;\n\npublic class GrahamScan {\n\n static class Point {\n public double x;\n public double y;\n\n public Point(double x, double y) {\n this.x = x;\n this.y = y;\n }\n\n @Override\n public boolean equals(Object o) {\n if (o == null) return false;\n if (o == this) return true;\n if (!(o instanceof Point)) return false;\n Point p = (Point)o;\n return p.x == this.x && p.y == this.y;\n }\n }\n\n static double ccw(Point a, Point b, Point c) {\n return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);\n }\n\n static double polarAngle(Point origin, Point p) {\n return Math.atan2(p.y - origin.y, p.x - origin.x);\n }\n\n static List grahamScan(List gift) {\n gift = gift.stream()\n .distinct()\n .sorted(Comparator.comparingDouble(point -> -point.y))\n .collect(Collectors.toList());\n\n Point pivot = gift.get(0);\n\n // Sort the remaining Points based on the angle between the pivot and itself\n List hull = gift.subList(1, gift.size());\n hull.sort(Comparator.comparingDouble(point -> polarAngle(point, pivot)));\n\n // The pivot is always on the hull\n hull.add(0, pivot);\n\n int n = hull.size();\n int m = 1;\n\n for (int i = 2; i 1) {\n m--;\n } else if (m == 1) {\n break;\n } else {\n i++;\n }\n }\n m++;\n\n Point temp = hull.get(i);\n hull.set(i, hull.get(m));\n hull.set(m, temp);\n }\n return hull.subList(0, m + 1);\n }\n\n public static void main(String[] args) {\n ArrayList points = new ArrayList<>();\n\n points.add(new Point(-5, 2));\n points.add(new Point(5, 7));\n points.add(new Point(-6, -12));\n points.add(new Point(-14, -14));\n points.add(new Point(9, 9));\n points.add(new Point(-1, -1));\n points.add(new Point(-10, 11));\n points.add(new Point(-6, 15));\n points.add(new Point(-6, -8));\n points.add(new Point(15, -9));\n points.add(new Point(7, -7));\n points.add(new Point(-2, -9));\n points.add(new Point(6, -5));\n points.add(new Point(0, 14));\n points.add(new Point(2, 8));\n\n List convexHull = grahamScan(points);\n\n convexHull.forEach(p -> System.out.printf(\"% 1.0f, % 1.0f\\n\", p.x, p.y));\n }\n}\n\n;;;; Graham scan implementation in Common Lisp\n\n(defstruct (point (:constructor make-point (x y))) x y)\n\n(defun ccw (p1 p2 p3)\n \"Determines if a turn between three points is counterclockwise\"\n (-\n (*\n (- (point-y p2) (point-y p1))\n (- (point-x p3) (point-x p1)))\n (*\n (- (point-y p3) (point-y p1))\n (- (point-x p2) (point-x p1)))))\n\n(defun atan2 (y x)\n \"Calculates the angle of a point in the euclidean plane in radians\"\n (cond\n ((> x 0) (atan y x))\n ((and (= y 0)) (+ (atan y x) pi))\n ((and ( y 0)) (/ pi 2))\n ((and (eql x 0) ( (length gift) 0)'.\n (if gift\n (labels ((wrap (sorted-points hull)\n (if sorted-points\n ;; This covers the case where the hull has one or more element.\n ;; We aren't concerned about the hull being empty, because then the gift must\n ;; also be empty and this function is never given an empty gift.\n (if (rest hull)\n (if (\n#include \n#include \n#include \n#include \n\nstruct point {\n double x;\n double y;\n};\n\nstd::ostream& operator& points) {\n for (auto p : points) {\n os graham_scan(std::vector& points) {\n // selecting lowest point as pivot\n size_t low_index = 0;\n for (size_t i = 1; i 1) {\n m--;\n continue;\n } else if (i == points.size()) {\n break;\n } else {\n i++;\n }\n }\n m++;\n std::swap(points[i], points[m]);\n }\n return std::vector(points.begin(), points.begin() + m + 1);\n}\n\nint main() {\n std::vector points = {{-5, 2},\n {5, 7},\n {-6, -12},\n {-14, -14},\n {9, 9},\n {-1, -1},\n {-10, 11},\n {-6, 15},\n {-6, -8},\n {15, -9},\n {7, -7},\n {-2, -9},\n {6, -5},\n {0, 14},\n {2, 8}};\n std::cout hull = graham_scan(points);\n std::cout \nfrom math import atan2\n\n\ndata point(x=0, y=0):\n def angle(self, other):\n \"\"\"Computes the angle between the two points\"\"\"\n match point(x1, y1) in other:\n return atan2(y1 - self.y, x1 - self.x)\n def __str__(self):\n return f'({self.x}, {self.y})'\n\n# Is the turn counter-clockwise?\ndef counter_clockwise(p1, p2, p3) =\n (p3.y - p1.y) * (p2.x - p1.x) >= (p2.y - p1.y) * (p3.x - p1.x)\n\n\ndef graham_scan(gift):\n gift = list(set(gift)) # Remove the duplicate points if any.\n start = min(gift, key=(p -> (p.x, p.y)))\n gift.remove(start)\n\n s = sorted(gift, key=(point -> start.angle(point)))\n hull = [start, s[0], s[1]]\n\n # Remove the hull points that make the hull concave\n for point in s[2:]:\n while not counter_clockwise(hull[-2], hull[-1], point):\n del hull[-1]\n hull.append(point)\n return hull\n\n\nif __name__ == '__main__':\n test_gift = [\n (-5, 2),\n (5, 7),\n (-6, -12),\n (-14, -14),\n (9, 9),\n (-1, -1),\n (-10, 11),\n (-6, 15),\n (-6, -8),\n (15, -9),\n (7, -7),\n (-2, -9),\n (6, -5),\n (0, 14),\n (2, 8),\n ] |> map$(p -> point(*p)) |> list\n hull = graham_scan(test_gift)\n \"The points in the hull are:\" |> print\n \"\\n\".join(map(str, hull)) |> print\n\nuse std::cmp::Ordering;\n\n#[derive(Debug, PartialEq, Copy, Clone)]\nstruct Point {\n x: f64,\n y: f64,\n}\n\nimpl Eq for Point {}\n\nimpl PartialOrd for Point {\n fn partial_cmp(&self, other: &Self) -> Option {\n if self.y == other.y {\n self.x.partial_cmp(&other.x)\n } else {\n self.y.partial_cmp(&other.y)\n }\n }\n}\n\n// Defines an order for Points so they can be sorted\nimpl Ord for Point {\n fn cmp(&self, other: &Self) -> Ordering {\n // Neither field of Point will be NaN, so this is safe\n self.partial_cmp(other).unwrap()\n }\n}\n\n// Determines whether the angle abc is clockwise, counter-clockwise or colinear\n// result > 0 : counter-clockwise\n// result = 0 : colinear\n// result f64 {\n (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x)\n}\n\n// Calculate the polar angle of a point relative to a reference point.\nfn polar_angle(reference: &Point, point: &Point) -> f64 {\n (point.y - reference.y).atan2(point.x - reference.x)\n}\n\nfn graham_scan(mut points: Vec) -> Vec {\n if points.is_empty() {\n return Vec::new();\n }\n\n // Unwrap is safe because length is > 0\n let start = *points.iter().min().unwrap();\n points.retain(|a| a != &start);\n points.sort_unstable_by(|a, b| polar_angle(&start, a).partial_cmp(&polar_angle(&start, b)).unwrap());\n\n let mut hull: Vec = vec![start, points[0], points[1]];\n\n for pt in points[2..points.len()].iter() {\n while counter_clockwise(&hull[hull.len() - 2], &hull[hull.len() - 1], pt) \n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/data_compression/data_compression.html":{"url":"contents/data_compression/data_compression.html","title":"Data Compression","keywords":"","body":"Data Compression\nI'll be honest, data compression used to be an incredibly hot topic, but kids these days usually have incredibly powerful devices that do not seem to be memory-limited at all.\nBecause of this, it seems odd to talk about data compression as a field of intense debate and development.\nIt would naively seem that better hardware means that there are less restrictions on programmers and less of a need to search for new and unique ways to compress their data; however, this is far from the case.\nThat said, there will always be new devices on the market that require minimizing data storage.\nIn fact, some of the most revolutionary algorithms and methods in existence today fall in the category of data compression.\nFrom lossless data compression with Huffman encoding to genetic compression algorithms and machine learning, there is a lot to learn about this field, and we'll go through it piece-by-piece.\nAll that said, no discussion about data compression is complete without first discussing the information, itself -- specifically how information is represented in computer systems.\nNow, we've discussed this in some depth before with bitlogic, but there is much more to the story than what we let on before.\nLet's start with a working definition of information:\nInformation is a representation of certainty.\nThis might seem like a silly, hand-wavey definition, but hear me out.\nIf I am uncertain about something, I will ask a question.\nThe answer to this question could be any number of things, but it will contain information from an individual with some level of certainty.\nFor example, let's pretend you have been furiously coding for months in your mother's basement (it happens).\nAt some point, you realize you haven't gone outside and are completely unaware of the day, month, or even year!\nAs your mother slips food under your door one day, you reach out to her and ask, \"What's it like outside today?\"\nOverjoyed at the prospect of her child finally leaving their room, your mother might say, \"It's bright, sunny and warm. A perfect day to go outside and relax!\"\nThis provides you a lot of information, and to some degree of certainty you can conclude it is summer.\nOf course, after this interaction you do not acknowledge your mother's existence after her answer and go back to coding.\nYou have the information you need.\nNo reason to overcomplicate things with further human contact.\nSee, information is defined in a number of different places for a number of different reasons, so for our purposes, we will define the unit of information to be the bit, a simple binary 1 or 0.\nTaking the example mentioned before (assuming you can take your mother at face-value), you were provided 3 true statements:\n\nIt is bright\nIt is sunny\nIt is warm\n\nWith this information, you assumed that it was probably summer.\nUnfortunately, your assumption about it being summer is not information.\nIt might be a logical conclusion, but it was not provided as a \"fact.\"\nThis is an important distinction between what we might colloquially describe as information and what information theory requires.\nInformation theory works with measurements -- binary absolutes.\nNow, we can clearly say that with some probability it is summer, but this is a different story altogether, which we will undoubtedly discuss in the future.\nFor now, let's talk about a simple representation of information on computer systems.\nImagine you have a simple alphabet with only 2 characters in it, a and b.\nIn this case, there are plenty of ways you can represent these characters in bits, but the most obvious way might look like this:\n\n\n\nCharacter\nBit Representation\n\n\n\n\na\n0\n\n\nb\n1\n\n\n\nSo long as you don't add any new characters to the mix, this is a perfectly valid set of codewords.\nIf you get the bitstring 0111101, you can easily decode it as abbbbab.\nBut what if you wanted to add a third character, c?\nWell, it's clear that c cannot be either 0 or 1, but because of the way we have defined the set of codewords above, it actually cannot be any combination of 0 or 1 either.\nFor example, if we defined c to be 01 and we were provided the bitstring 0111101, we could interpret this string as either abbbbab or cbbbc!\nNow, we could use context or other information provided to distinguish these two possible cases, but it is clear that we need to think more deeply about our set of codewords in this case.\nFirst, let's think a bit about decoding.\nFor our purposes, we do not want to think when decoding.\nNo matter what the bitstring is that we need to decode, we want to be able to read bit-by-bit until we find a match in our set of codewords and move on.\nBasically, we do not want any ambiguity in our set of codewords.\nThe code for c should not contain the code for a or b!\nIn this way, our set of codewords should be prefix-free.\nNo word should appear as a prefix to another word.\nIf we wanted a good, prefix-free set of codewords for 4 characters (a, b, c, and d), it might look like this:\n\n\n\nCharacter\nBit Representation\n\n\n\n\na\n00\n\n\nb\n01\n\n\nc\n10\n\n\nd\n11\n\n\n\nWe can decode any even bitstring with this set.\n0100101010110100 is bacccdba.\nThis is great, but now we have another question: given a string of characters, can we construct a set of codewords that minimizes the number of bits in its corresponding bitstring?\nThis is the heart of data compression!\nFirst things first, let's define a simple measure for how compressed the data is.\nLet's take the following set of characters: abbcccdddd.\nIf we were to put all the letters in a bag and pull one out at random, we would have the following probabilities of pulling out any of the letters:\n\n\n\nCharacter\nProbability\n\n\n\n\na\n.1\n\n\nb\n.2\n\n\nc\n.3\n\n\nd\n.4\n\n\n\nThis basically means that we are far more likely to pull out a d than an a, and if we are trying to minimize the length of our encoded bitstring, the length of the bit representation for d should probably be shorter than the bit representation for a.\nUltimately, to compress our encoded bitstring, we want to minimize the following quantity:\n\nL(C(W)) = \\sum_{i=0}^{n}w_i\\times \\text{length}(c_i)\n\nWhere C is the characters of our alphabet and c_i is codeword for a single character, W is related to the probability of pulling that character out of a bag and w_i is an individual probability of getting a specific character, and L is a vague, unitless quantity to determine the overall length and is usually used to determine compression ratios.\nTo show how this works, let's consider encoding the word abbcccdddd with two different alphabets:\n\n\n\nCharacter\nProbability\nBit Representation 1\nBit Representation 2\n\n\n\n\na\n.1\n00\n000\n\n\nb\n.2\n01\n001\n\n\nc\n.3\n10\n01\n\n\nd\n.4\n11\n1\n\n\n\nIn this case:\n\n\\begin{align}\nL_1 &= 0.1\\times 2 + 0.2 \\times 2 + 0.3 \\times 2 + 0.4 \\times 2 = 2 \\\\\nL_2 &= 0.1\\times 3 + 0.2 \\times 3 + 0.3 \\times 2 + 0.4 \\times 1 = 1.9\n\\end{align}\n\nHere, it's clear that L_2 , and thus the second set of codewords compresses our data more than the first.\nThis measure can be used as a direct test of certain simple data compression techniques, notably those created by Shannon, Fano, and Huffman, which will be covered soon!\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/cryptography/cryptography.html":{"url":"contents/cryptography/cryptography.html","title":"Cryptography","keywords":"","body":"Cryptography\nHumans have almost always been interested in sending secret messages that only the sender and receiver understand.\nThe reason for this is obvious: secret messages should remain secret.\nThe easiest way for this to happen is to talk behind closed doors, but that simply doesn't work if the sender and receiver are separated by a significant distance.\nIn this case, they need to rely on a messenger or mailman to send the message.\nFor simplicity, let's assume they are sending a written letter for the purpose of negotiating war tactics in ancient Greece or Rome.\nObviously, the message can remain secret if both the sender and receiver also trust the messenger; however, what if the messenger is actually an evil spy?\nWhat if the messenger is killed and the letter is stolen?\nWhat if (in an elaborate ruse), some third party slips into the messenger's tent in the dead-of-night and replaces the letter with another one entirely different?\nThese are all important questions cryptography addresses.\nThe idea is simple: we procedurally scramble the message we are sending and only provide the unscrambling procedure to trusted parties.\nIn this way, the message would seem like utter gobbledygook to anyone other than the sender and receiver.\nIt doesn't matter if the messenger is evil.\nThey cannot read the message anyway.\nIt's also fine if the message is replaced, because then the receiver won't be able to properly decode the message and can just ask for another message to be sent (probably on another path with a different messenger).\nUnsurprisingly, a very early method of encryption was supposedly developed by Julius Caeser and called the \"Caesar Cipher\" [1].\nHere, every character in the message is replaced by another character based on some pre-defined table or chart that only the sender and receiver have.\nThe table is created by simply rotating the alphabet by n spaces, where n is chosen in a discussion between the sender and receiver before-hand.\n\n\n\nn\n0\n2\n14\n18\n21\n24\n\n\n\n\na\na\nc\no\ns\nv\ny\n\n\nb\nb\nd\np\nt\nw\nz\n\n\nc\nc\ne\nq\nu\nx\na\n\n\nd\nd\nf\nr\nv\ny\nb\n\n\ne\ne\ng\ns\nw\nz\nc\n\n\nf\nf\nh\nt\nx\na\nd\n\n\ng\ng\ni\nu\ny\nb\ne\n\n\nh\nh\nj\nv\nz\nc\nf\n\n\ni\ni\nk\nw\na\nd\ng\n\n\nj\nj\nl\nx\nb\ne\nh\n\n\nk\nk\nm\ny\nc\nf\ni\n\n\nl\nl\nn\nz\nd\ng\nj\n\n\nm\nm\no\na\ne\nh\nk\n\n\nn\nn\np\nb\nf\ni\nl\n\n\no\no\nq\nc\ng\nj\nm\n\n\np\np\nr\nd\nh\nk\nn\n\n\nq\nq\ns\ne\ni\nl\no\n\n\nr\nr\nt\nf\nj\nm\np\n\n\ns\ns\nu\ng\nk\nn\nq\n\n\nt\nt\nv\nh\nl\no\nr\n\n\nu\nu\nw\ni\nm\np\ns\n\n\nv\nv\nx\nj\nn\nq\nt\n\n\nw\nw\ny\nk\no\nr\nu\n\n\nx\nx\nz\nl\np\ns\nv\n\n\ny\ny\na\nm\nq\nt\nw\n\n\nz\nz\nb\nn\nr\nu\nx\n\n\n\nIt is certainly not the most complicated scheme out there, but it is generally the first encryption scheme people come up with when trying to encode secret messages to one another.\nHonestly, I remember sending messages back and forth to friends in elementary school, but we would never provide the necessary table to decode the message.\nInstead, we would provide enough text that they could find the table themselves from context.\nIf a bunch of elementary school kids can figure out how to break this encryption scheme, it cannot be too robust.\nIn fact, it's interesting to see how the field of cryptography has grown since the Caesar cipher was developed.\nIn the cryptographic literature, there is always a sender, receiver, and eavesdropper.\nFor some reason beyond my own comprehension, the first two people are almost always given the names Alice (sender) and Bob (receiver).\nMeanwhile, the attacker or eavesdropper is usually called either Eve or Charlie\nThese names are consistent even with quantum cryptography, so they are here to stay.\nIn general, there are two different types of encryption: symmetric and asymmetric.\nBoth of which are described in the following sections.\nCryptographic systems are a cornerstone to modern information technology and lie at the heart of everything from WiFi to online banking.\nIf an attacker manages to crack modern cryptographic algorithms, they could cause serious damage.\nFor this reason, it is important to keep a few things in mind:\n\nBecause cryptography has become such an advanced field cryptographic systems should be analyzed by trained professionals and have undergo extensive testing and vetting.\n This means that whenever possible, one should use a widely accepted cryptography library instead of writing their own cypher.\nKerckhoffs's principle says that when determining the robustness of a cryptographic system it should be assumed that the attacker knows the encryption and decryption algorithm [2].\n This does not include any pre-shared or secret keys.\nWith the advances in technology, cryptography often hits its limits.\n Many formerly state-of-the-art hashing algorithms have become obsolete because the computers used to crack them have gotten faster and better.\n Another field that cryptography will have to face is quantum computing.\n Quantum computers will have a big impact on cryptography and especially asymmetric cryptography.\n This whole set of problems is summarized in the field of post-quantum cryptography [3].\n\nSymmetric Cryptography\nSymmetric cryptography is called symmetric because the key that is used is the same for encrypting and decrypting. \nFor this to work Alice and Bob both need the same key, which they have to share before communicating. \nSome examples for symmetric cryptography are:\n\nCeasar Cipher: Alice and Bob rotate the alphabet by n characters and use that as a table to encode and decode their message [1].\nRot13: This is a special case of the Caeser Cipher where the alphabet is rotated by 13, hence the name \"Rot13\" [4]\nPermutation Cipher: Here we choose a permutation \\pi (i.e. \\pi=(3,1,2,4)) and reorder the the letters according to that \\pi which is the key [5].\nXOR encryption: This method works on bit strings and combines the message and a key of equal bit length with the XOR operator [6].\n To decrypt, simply XOR again with the same key.\nDES or Data Encryption Standard: This is a newer encryption algorithm which was standardized in 1977 [7]. \n It has since been deemed insecure and is superseded by AES.\nAES or Advanced Encryption Standard: The actual algorithm is called \"Rijndael\" [8]. \n Like with XOR or DES we generate a bit string (depending on which AES you use 128/192 or 256 bit long) which is your key.\nBlowfish: This algorithm was also a good contender for the AES but lost to Rijndael [9].\n\nThis section is currently a work-in-progress, and all of these methods will have corresponding chapters in the near future.\nAsymmetric Cryptography\nAsymmetric cryptography is sometimes called \"public key cryptography\" (or PK cryptography in short) because Bob and Alice both need a shared public key and a private key they keep to themselves.\nThese algorithms are called asymmetric because what is encrypted with the public key can only be decrypted with the private key and vice versa. \nThis can be used for a number of different applications, like digital signing, encrypted communication, or secretly sharing keys.\nFor example, if Alice wants to send a message to Bob and this message has to be kept private, Alice will encrypt the message with Bob's public key.\nNow only Bob can decrypt the message again and read it.\nIf Charlie were to alter Alice's message, Bob couldn't decrypt it anymore.\nIf Bob wants to make sure the message is actually from Alice, Alice can encrypt the already encrypted message with her private key again.\nThis is to keep Charlie from sending forged or altered messages since Bob couldn't decrypt that layer with Alice's public key.\nSome examples for public key cryptography:\n\nRSA: This algorithm calculates a public and a private key from two very large primes [10]. \n It is (hopefully) near impossible to factor the product of two such primes in a feasible amount of time.\nECC or Elliptic-curve cryptography: Here you calculate the private and public key from two points on an elliptic curve [11]. \n This has the positive side effect that you need smaller numbers than non-ECC algorithms like RSA to achieve the same level of security.\n\nThis section is currently a work-in-progress. These methods will also have corresponding chapters in the near future.\nBibliography\n1.Wikipedia: Ceasar Cipher, 2022.2.Wikipedia: Kerckhoffs's principle, 2022.3.Wikipedia: Post-quantum Cryptography, 2022.4.Wikipedia: ROT13, 2022.5.Crypto Corner: Permutation Cipher, 2022.6.Wikipedia: XOR cipher, 2022.7.Wikipedia: Data Encryption Standard, 2022.8.Wikipedia: Advanced Encryption Standard, 2022.9.Wikipedia: Blowfish (cipher), 2022.10.Wikipedia: RSA (cryptosystem), 2022.11.Wikipedia: Elliptic-curve cryptography, 2022.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nThe text of this chapter was written by Liikt and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by Liikt and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n"},"contents/taylor_series_expansion/taylor_series_expansion.html":{"url":"contents/taylor_series_expansion/taylor_series_expansion.html","title":"Taylor Series","keywords":"","body":"NOTE: Incomplete!\nTaylor Series Expansion\nI have been formally trained as a physicist. In my mind, there are several mathematical topics that blur the boundary between mathematics and physics. Taylor Series Expansions are one of those topics.\nOn the one hand, I can see how the expansion could be considered purely mathematical. I mean, here is the definition:\n\nf(x) \\simeq \\sum_{n=0}^{\\infty} \\frac{f^{(n)}(a)}{n!}(x-a)^n\n\nwhere f(x) is some function along real or complex space, a is the point that we are expanding from, and f^{(n)}(x) denotes the n^{\\text{th}} derivative of f(x).\nFrom this perspective, the expansion just looks like a bunch of derivatives strung together! Where's the physics? Well, let's expand this series for the first few derivatives:\n\nf(x) \\simeq f(a) + \\frac{df(a)}{dx}(x-a)\n + \\frac{1}{2}\\frac{d^2f(a)}{dx^2}(x-a)^2\n\nIf we substitute the derivatives for their physical quantities with f(x) \\rightarrow x(t), expanding from 0, and set\n\n\\begin{align}\n\\frac{dx(t)}{dt} &= \\text{velocity} = v(t) \\\\\n\\frac{d^2x(t)}{dt^2} &= \\text{acceleration} = a \\\\\n\\end{align}\n\nThe Taylor series expansion turns into one of the most common formulas in classical physics, the kinematic equation!\n\nx(t) \\simeq x_0 + v_0t\n + \\frac{1}{2}at^2\n\nNote that here, we assume the acceleration to be constant, but it could technically have higher order terms.\nTruth be told, the Taylor Series Expansion can be found in the most unusual places and is used as the foundation of many different algorithms throughout this book. At first, it might not seem obvious why, but we can approximate almost any smooth function with a Taylor Series Expansion, and the more terms we include, the better our approximation becomes! For example, take Figure 1. Any function can be approximated as a sum of all the derivatives for that function. If we evaluate these derivatives at any point, we closely approximate the actual function.\n\n \n\n\nThis shows the true power of the Taylor Series Expansion. It allows us to more easily tackle complicated functions by approximating them as functions we can actually use and imagine!\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"Taylor Approximation\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/convolutions/convolutions.html":{"url":"contents/convolutions/convolutions.html","title":"Convolutions","keywords":"","body":"Convolutions\nTo put it bluntly, convolutions can be confusing.\nSome might even call them convoluted!\n(Get it? Because we are talking about convolutions? A wise man once told me that all good jokes need additional clarification.)\nNot only are convolutions hard to describe, but if they are not used in practice, it is hard to understand why they would ever be needed.\nI am going to do what I can to describe them in an intuitive way; however, I may need to come back to this in the future.\nLet me know if there is anything here that is unclear, and I will do what I can to clear it up.\nAs always, we should start at the start.\nIf you take two functions f and g, there are a number of ways you can combine them.\nAll basic operations can do this (addition, subtraction, multiplication, and division), but there are also special operations that only work with functions and do not work on standard variables or numbers.\nFor example, f \\circ g is a composition of the two functions, where you plug g(x) into f.\nA convolution is another function-related operation, and is often notated with a star (*) operator, where\n\nf*g=c\n\nprovides a third function, c, that is a blended version of f and g.\nAs a rather important side-note: there is an incredibly similar operation known as a correlation which will be discussed in the near future.\nNow we are left with a rather vague question: how do we blend functions?\nTo answer this question, we will need to show off a few simple graphics and animations in the Convolutions in 1D section while also discussing the mathematical definition of convolutions.\nAfter, there will be a brief discussion on an interesting application of one dimensional convolutions in integer multiplication in the Multiplication as a Convolution section.\nWe will then move on to the most stereotypical application of convolutions in the Convolutions of Images section, where we will also discuss two important filters: the Gaussian kernel and the Sobel operator.\nAs a note: convolutions can be extended to n-dimensions, but after seeing how they are extended to two dimensions, it should be possible for the reader to extend it to three dimensions and beyond if that is needed, so we will not cover that in great detail here unless is is useful for another algorithm.\nIn addition, we will be touching on a rather difficult but powerful topic with the Convolutional Theorem section where convolutions can be computed by using Fourier transforms.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/convolutions/1d/1d.html":{"url":"contents/convolutions/1d/1d.html","title":"Convolutions in 1D","keywords":"","body":"Convolutions in 1D\nAs mentioned in the introductory section for convolutions, convolutions allow mathematicians to \"blend\" two seemingly unrelated functions; however, this definition is not very rigorous, so it might be better to think of a convolution as a method to apply a filter to a signal or image.\nThis, of course, brings up more questions: what is a filter? What is a signal? How is this all related to images?\nFor this, we will start with some predefined signal.\nIt does not matter too much what it is, so we will pick a square wave where everything is set to zero except for a few elements at the center, which will be set to one.\nThis signal can be treated as an array, or a black and white, one-dimensional image where everything is black except for a white strip at the center.\nWe will also introduce a filter, which will be a simple triangle wave that goes to 1.\nBoth of these are shown below:\n\n \n \n\n\nSo now we have a signal and a filter.\nHow do we apply the filter to the signal?\nThe easiest way to do this is to iterate through every point in the signal and blend it with neighboring elements, where each neighboring element is weighted based on the filter value.\nSo in the case where the triangle wave is only 3 elements ([0.5, 1, 0.5]), the output at each point would be\n\nC_n = \\frac{A_{n-1}}{2} + A_{n} + \\frac{A_{n+1}}{2},\n\nwhere C is the output value, A is the input array (a signal or image), and n is an iterable element through that signal.\nIn this way, the \"application of a filter,\" is simply a multiplication of the triangle wave centered around each point of the input array, followed by in integral or sum of the output.\nIn some sense, this means we will shift the filter, then multiply and sum every step.\nThis can be seen in the following animation:\n\n\n \nYour browser does not support the video tag.\n\n\n\nHere, the purple, dashed line is the output convolution C, the vertical line is the iteration n, the blue line is the original signal, the red line is the filter, and the green area is the signal multiplied by the filter at that location.\nThe convolution at each point is the integral (sum) of the green area for each point.\nIf we extend this concept into the entirety of discrete space, it might look like this:\n(f*g)[n] = \\sum_{m = -\\infty}^{\\infty}f[m]g[n-m] = \\sum_{m = -\\infty}^{\\infty}f[n-m]g[m]\nWhere f[n] and g[n] are arrays of some form.\nThis means that the convolution can calculated by shifting either the filter along the signal or the signal along the filter.\nThis can be read as we said before: every step, we shift the filter, multiply, and sum.\nThere is, of course, a small caveat here.\nWhy are we subtracting m?\nCertainly, if we wanted to \"shift the filter along the signal,\" we could also do so by adding m instead, but that is actually an entirely separate operation known as a correlation, which will be discussed at a later time.\nThe simplest interpretation for this equation is the same as the animation: we reverse the second array, and move it through the first array one step at a time, performing a simple element-wise multiplication and summation at each step.\nWith this in mind, we can almost directly transcribe the discrete equation into code like so:\nfunction convolve_linear(signal::Array{T, 1}, filter::Array{T, 1},\n output_size) where {T \nstatic double[] ConvolveLinear(double[] signal, double[] filter, int outputSize)\n{\n // Convolutional output.\n var output = new double[outputSize];\n var sum = 0.0;\n\n for (var i = 0; i \ndef convolve_linear(signal, filter_array, output_size):\n out = np.zeros(output_size)\n s = 0\n\n for i in range(output_size):\n for j in range(max(0, i - len(filter_array)), i + 1):\n if j \n\n\nThe easiest way to reason about this code is to read it as you might read a textbook.\nFor each element in the output domain, we are summing a certain subsets of elements from i-length(filter) to i after multiplying it by the reversed filter (filter[i-j]).\nIn this way, it is precisely the same as the mathematical notation mentioned before.\nIn contrast to the animation, where the filter continuously reappears on the left edge of the screen, the code we have written for this part of the chapter requires the user to specify what they expect the output array length to be.\nDetermining what should happen at the edges of the convolution is a somewhat hotly debated topic and differs depending on what the user actually wants, so we will be discussing this in greater detail later in this chapter.\nAs an important note, if we were to extend the convolution into continuous space, we might write something like:\n(f*g)(x) = \\int_{-\\infty}^{\\infty}f(\\xi)g(x-\\xi)d\\xi = \\int_{-\\infty}^{\\infty}f(x-\\xi)g(\\xi)d\\xi\nNote that in this case, x and \\xi are not necessarily spatial elements, but the interpretation is otherwise the same as before.\nAt this stage, the mathematics and code might still be a little opaque, so it is a good idea to play around a bit and think about how this operation might be used in practice with a few different filters.\nPlaying with filters\nHonestly, the best way to learn how convolutions work is by using them for a number of different signals and filters, so\nlet us extend the previous triangle filter a bit further by convolving a square wave with a relatively sharp Gaussian, which can be seen in the following animation:\n\n\n \nYour browser does not support the video tag.\n\n\n\nIn practice, the convolutional output here is very similar to the triangle wave we showed before.\nThe final convolved image looks a lot like the square, except that its boundaries have been smoothed out or \"blurred.\"\nIn practice whenever a Gaussian filter is used, it will always blur the other convolved signal, which is why a convolution with a Gaussian is also called a blurring operation.\nThis operation is used very often when dealing with two-dimensional images, and we will discuss common kernels found in the wild in the next section.\nStill, it is interesting to see the blurring operation in action by convolving a random distribution with a larger Gaussian filter:\n\n\n \nYour browser does not support the video tag.\n\n\n\nIn this animation, the final convolution is so blurred that it does not seem related to the random input signal at all!\nIn fact, this animation seems to blend much more when compared to the previous Gaussian and the triangle wave animations.\nThis is because the Gaussian is wider than the previous to filters.\nIn general, the wider the filter, the stronger the blurring effect.\nSo what happens if we convolve a Gaussian with another Gaussian?\nWell, that is shown below:\n\n\n \nYour browser does not support the video tag.\n\n\n\nAs one might expect, the output is a blurrier Gaussian, which is essentially just wider.\nIf you were paying particularly close attention to the visualization, you might have noticed that the green area inside this visualization does not properly line up with the overlap of the two arrays.\nDon't worry!\nThis is exactly what should happen!\nRemember that the convolution requires a multiplication of the signal and filter, which was the same as the overlap when the signal was a square wave; however, in the case of two distinct signals, we should expect the multiplied output to look somewhat distinct.\nLet us extend this concept to one final example of a square wave convolved with a triangular, sawtooth function that looks like this:\n\n \n\n\nThis is the first non-symmetric filter of this chapter, and its convolution would look like this:\n\n\n \nYour browser does not support the video tag.\n\n\n\nNon-symmetric filters are useful for testing convolutions to ensure that the output is correct, so it might be worthwhile to linger on this animation for a bit longer.\nNotice how the convolution has an accelerating, positive slope when the reversed sawtooth function interacts with the square.\nThis makes sense as the smallest part of the triangle interacts first.\nSimilarly, there is a negatively accelerating slope when the sawtooth function leaves the square.\nDealing with boundaries\nIn all of the animations, we have shown the filter constantly reappearing on the left edge of the screen, which is not always the best thing to do at the boundaries.\nIn fact, these boundary conditions are somewhat non-trivial to code, so for this section, we will start with relatively simple boundary conditions that were introduced in the previous code example.\nSimple boundaries\nIn general, if a user wants to see a full convolution between two signals, the output size must be the size of the two signals put together, otherwise, we cannot iterate through the entire convolutional output domain.\nFor example, here is random noise again convolved with a Gaussian function, but with non-periodic boundaries:\n\n\n \nYour browser does not support the video tag.\n\n\n\nThis shows the full, unbounded convolution of the two signals, where\nwe clearly see a \"ramp up\" and \"ramp down\" phase at the start and end of the animation.\nThat said, there are many applications where the user actually needs to specify the output domain to be another length, such as the size of one of the input signals.\nIn this case, the simplest boundary would be to assume that whenever the filter hits the end of the image, it simply disappears.\nAnother way to think about this is that the signal only exists for the domain we specify it over, and is all 0s outside of this domain; therefore, the filter does not sum any signal from elements beyond its scope.\nAs an example, let's take the same example as before:\n\n\n \nYour browser does not support the video tag.\n\n\n\nSimilar to the case without boundary conditions, this convolution needs to \"ramp up,\" but it does not need to \"ramp down.\"\nThis is because the convolution output no longer extends past the bounds of the original signal so the bounded convolution is a subset of the full convolution.\nMore than that, the convolution does not go all the way to 0 on the right side.\nThis means that we are actually ignoring a rather important part of the convolution!\nThis is 100% true; however, if the signal is large and the filter is small (as is the case with most of image processing), we do not really care that much about the bits of the convolution we missed.\nIn addition, there is a way to center the convolution by modifying the location where the filter starts.\nFor example, we could have half of the filter already existing and overlapping with the signal for the very first computed point of the convolution.\nFor this reason, simple bounds are used frequently when performing convolutions on an image.\nIn the previous code snippet, we were able to perform both a bounded and unbounded convolution.\nHere it is again for clarity:\nfunction convolve_linear(signal::Array{T, 1}, filter::Array{T, 1},\n output_size) where {T \nstatic double[] ConvolveLinear(double[] signal, double[] filter, int outputSize)\n{\n // Convolutional output.\n var output = new double[outputSize];\n var sum = 0.0;\n\n for (var i = 0; i \ndef convolve_linear(signal, filter_array, output_size):\n out = np.zeros(output_size)\n s = 0\n\n for i in range(output_size):\n for j in range(max(0, i - len(filter_array)), i + 1):\n if j \n\n\nHere, the main difference between the bounded and unbounded versions is that the output array size is smaller in the bounded case.\nFor an unbounded convolution, the function would be called with a the output array size specified to be the size of both signals put together:\n# full convolution, output will be the size of x + y - 1\nfull_linear_output = convolve_linear(x, y, length(x) + length(y) - 1)\n\n// Full convolution, output will be the size of x + y - 1.\nvar fullLinearOutput = ConvolveLinear(x, y, x.Length + y.Length - 1);\n\n# full convolution, output will be the size of x + y - 1\nfull_linear_output = convolve_linear(x, y, len(x) + len(y) - 1)\n\n\n\nOn the other hand, the bounded call would set the output array size to simply be the length of the signal\n# simple boundaries\nsimple_linear_output = convolve_linear(x, y, length(x))\n\n// Simple boundaries.\nvar simpleLinearOutput = ConvolveLinear(x, y, x.Length);\n\n# simple boundaries\nsimple_linear_output = convolve_linear(x, y, len(x))\n\n\n\nFinally, as we mentioned before, it is possible to center bounded convolutions by changing the location where we calculate the each point along the filter.\nThis can be done by modifying the following line:\nfor j = max(1, i-length(filter)):i\n\nfor (var j = Math.Max(0, i - filter.Length); j \nfor j in range(max(0, i - len(filter_array)), i + 1):\n\n\n\nHere, j counts from i-length(filter) to i.\nTo center the convolution, it would need to count from i-(length(filter)/2) to i+(length(filter)/2) instead.\nI think this is a good place to stop discussions on simple boundary conditions.\nNow let us talk a bit more in detail about the case where we want the filter to continuously reappear every loop.\nThis case is known as the \"periodic boundary condition\" and was used for the visualizations at the start of this chapter.\nPeriodic boundary conditions\nThough periodic boundary conditions are more complicated that those mentioned in the previous section, they are still relatively straightforward to implement.\nWith these conditions, the filter will wrap itself around to the other end of the signal whenever it hits a boundary.\nIn this way, the signal is periodic, with an identical copy of itself acting as left and right neighbors.\nThose neighbors then have other neighbors, and those then have more neighbors, creating a sea of signals extending to infinity and beyond in both directions.\nFor us, this means that when the filter leaves one edge of the domain, it simply appears on the other, opposite edge.\nThis particular convolution is known as a cyclic convolution and is also the most common output of convolutions that work via the convolutional theorem, which will be discussed in another section.\nFor clarity: here is the same cyclic visualization we showed above with a random distribution and a Gaussian signal.\n\n\n \nYour browser does not support the video tag.\n\n\n\nIn code, this typically amounts to using some form of modulus operation, as shown here:\nfunction convolve_cyclic(signal::Array{T, 1},\n filter::Array{T, 1}) where {T \nstatic double[] ConvolveCyclic(double[] signal, double[] filter)\n{\n var outputSize = Math.Max(signal.Length, filter.Length);\n\n // Convolutional output.\n var output = new double[outputSize];\n var sum = 0.0;\n\n for (var i = 0; i \ndef convolve_cyclic(signal, filter_array):\n output_size = max(len(signal), len(filter_array))\n out = np.zeros(output_size)\n s = 0\n\n for i in range(output_size):\n for j in range(output_size):\n if(mod1(i - j, output_size) \n\n\nThis is essentially the same as before, except for the modulus operations, which allow us to work on a periodic domain.\nAs a final note before continuing: dealing with boundaries is tricky business and can dramatically change the behavior of the output convolution.\nFor this reason, it is important to think about what types of boundaries will work best for what you, the programmer, actually need.\nThe selection of boundary conditions will be a common trope for a large portion of computer graphics and physics algorithms where researchers often need to present and simulate data on an array of some sort.\nExample Code\nFor the code associated with this chapter, we have used the convolution to generate a few files for the full convolution, along with the periodic and simple boundary conditions discussed in this chapter.\nusing DelimitedFiles\nusing LinearAlgebra\n\nfunction convolve_cyclic(signal::Array{T, 1},\n filter::Array{T, 1}) where {T \nusing System;\nusing System.IO;\n\nnamespace Convolution1D\n{\n public class Convolution1D\n {\n // Creates a sawtooth function with the given length.\n static double[] CreateSawtooth(int length)\n {\n var array = new double[length];\n for (var i = 0; i = 0.\n static int Mod(int x, int y) => ((x % y) + y) % y;\n\n static double[] ConvolveCyclic(double[] signal, double[] filter)\n {\n var outputSize = Math.Max(signal.Length, filter.Length);\n\n // Convolutional output.\n var output = new double[outputSize];\n var sum = 0.0;\n\n for (var i = 0; i \nimport numpy as np\n\ndef mod1(x, y): return ((x % y) + y) % y\n\ndef convolve_cyclic(signal, filter_array):\n output_size = max(len(signal), len(filter_array))\n out = np.zeros(output_size)\n s = 0\n\n for i in range(output_size):\n for j in range(output_size):\n if(mod1(i - j, output_size) \n\n\nAt a test case, we have chosen to use two sawtooth functions, which should produce the following images:\n\n\n\nDescription\nImage\n\n\n\n\nSimple Boundaries\n\n\n\nFull\n\n\n\nCyclic\n\n\n\n\nAs a sanity check, make sure that the bounded convolution is a subset of the full convolution.\nIn this example, the bounded convolution is the start of the full convolution, but it is entirely possible it could be the middle or somewhere else entirely depending on how you counted within the inner, summation loop for the convolution.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nImages/Graphics\n\nThe image \"Square Wave\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Triangle Wave\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Triangle Square Convolution\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Gaussian Square Convolution\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Gaussian Random Convolution\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Double Convolution\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Sawtooth Wave\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Sawtooth Square Convolution\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Full Random Convolution\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Simple Random Convolution\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Simple Linear\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Full Linear\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Cyclic\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/convolutions/multiplication/multiplication.html":{"url":"contents/convolutions/multiplication/multiplication.html","title":"Multiplication as a Convolution","keywords":"","body":"Multiplication as a convolution\nAs a brief aside, we will touch on a rather interesting side topic: the relation between integer multiplication and convolutions\nAs an example, let us consider the following multiplication: 123 \\times 456 = 56088.\nIn this case, we might line up the numbers, like so:\n\n\\begin{matrix}\n&&1&2&3 \\\\\n&\\times &4&5&6 \\\\\n\\hline\n5 & 6 & 0 & 8 & 8\n\\end{matrix}\n\nHere, each column represents another power of 10, such that in the number 123, there is 1 100, 2 10s, and 3 1s.\nSo let us use a similar notation to perform the convolution, by reversing the second set of numbers and moving it to the right, performing an element-wise multiplication at each step:\n\n\\begin{matrix}\n&&&\\color{red}1&2&3 \\\\\n\\times &6&5&\\color{red}4&& \\\\\n\\hline\n\\end{matrix}\\\\\n\\color{red}{1}\\times\\color{red}{4} = 4\n\n\n\\begin{matrix}\n&&&\\color{red}1&\\color{green}2&3 \\\\\n\\times &&6&\\color{red}5&\\color{green}4& \\\\\n\\hline\n\\end{matrix}\\\\\n\\color{red}1\\times\\color{red}5+\\color{green}2\\times\\color{green}4=13\n\n\n\\begin{matrix}\n&&&\\color{red}1&\\color{green}2&\\color{blue}3 \\\\\n\\times &&&\\color{red}6&\\color{green}5&\\color{blue}4 \\\\\n\\hline\n\\end{matrix}\\\\\n\\color{red}1\\times\\color{red}6+\\color{green}2\\times\\color{green}5+\\color{blue}3\\times\\color{blue}4=28\n\n\n\\begin{matrix}\n&&1&\\color{green}2&\\color{blue}3& \\\\\n\\times &&&\\color{green}6&\\color{blue}5&4 \\\\\n\\hline\n\\end{matrix}\\\\\n\\color{green}2\\times\\color{green}6+\\color{blue}3\\times\\color{blue}5=27\n\n\n\\begin{matrix}\n&1&2&\\color{blue}3&& \\\\\n\\times &&&\\color{blue}6&5&4 \\\\\n\\hline\n\\end{matrix}\\\\\n\\color{blue}3\\times\\color{blue}6=18\n\nFor these operations, any blank space should be considered a 0.\nIn the end, we will have a new set of numbers:\n\n\\begin{matrix}\n&&1&2&3 \\\\\n&\\times &4&5&6 \\\\\n\\hline\n4 & 13 & 28 & 27 & 18\n\\end{matrix}\n\nNow all that is left is to perform the carrying operation by moving any number in the 10s digit to its left-bound neighbor.\nFor example, the numbers [4, 18]=[4+1, 8]=[5,8] or 58.\nFor these numbers, \n\n\\begin{matrix}\n&4 & 13 & 28 & 27 & 18\\\\\n=&4+1 & 3+2 & 8+2 & 7+1 & 8\\\\\n=&5 & 5 & 10 & 8 & 8\\\\\n=&5 & 5+1 & 0 & 8 & 8\\\\\n=&5 & 6 & 0 & 8 & 8\n\\end{matrix}\n\nWhich give us 123\\times456=56088, the correct answer for integer multiplication.\nI am not suggesting that we teach elementary school students to learn convolutions, but I do feel this is an interesting fact that most people do not know: integer multiplication can be performed with a convolution.\nThis will be discussed in further detail when we talk about the Schonhage-Strassen algorithm, which uses this fact to perform multiplications for incredibly large integers.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"url":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","title":"Convolutional Theorem","keywords":"","body":"Convolutional Theorem\nImportant note: this particular section will be expanded upon after the Fourier transform and Fast Fourier Transform (FFT) chapters have been revised.\nNow, let me tell you about a bit of computational magic:\nConvolutions can be performed with Fourier Transforms!\nThis is crazy, but it is also incredibly hard to explain, so let me do my best.\nAs described in the chapter on Fourier Transforms, Fourier Transforms allow programmers to move from real space to frequency space.\nWhen we transform a wave into frequency space, we can see a single peak in frequency space related to the frequency of that wave.\nNo matter what function we send into a Fourier Transform, the frequency-space image can be interpreted as a series of different waves with a specified frequency.\nEach of these waves is parameterized by another e^{2\\pi i k n / N} term, where k is the element's value in the frequency domain, n is its value in the time domain, and N is the overall length of the signal.\nIn this way, each wave can be seen as a complex exponential.\nSo here's the idea: if we take two functions f(x) and g(x) and move them to frequency space to be \\hat f(\\xi) and \\hat g(\\xi), we can then multiply those two functions and transform them back into to blend the signals together.\nIn this way, we will have a third function that relates the frequency-space images of the two input functions.\nThis is known as the convolution theorem which looks something like this:\n\\mathcal{F}(f*g) = \\mathcal{F}(f) \\cdot \\mathcal{F}(g)\nWhere \\mathcal{F} denotes the Fourier Transform.\nAt first, this might not seem particularly intuitive, but remember that frequency space is essentially composed of a set of exponentials.\nAs mentioned in the section about Multiplication as a Convolution, multiplication in base 10 space is also a convolution.\nThe convolutional theorem extends this concept into multiplication with any set of exponentials, not just base 10.\nObviously, this description is still lacking a bit of explanation, but I promise we will add more when revising the Fourier transform sections!\nBy using a Fast Fourier Transform (FFT) in code, this can take a standard convolution on two arrays of length n, which is an \\mathcal{O}(n^2) process, to \\mathcal{O}(n\\log(n)).\nThis means that the convolution theorem is fundamental to creating fast convolutional methods for certain large inputs.\n# using the convolutional theorem\nfunction convolve_fft(signal1::Array{T}, signal2::Array{T}) where {T \n\n\nThis method also has the added advantage that it will always output an array of the size of your signal; however, if your signals are not of equal size, we need to pad the smaller signal with zeros.\nAlso note that the Fourier Transform is a periodic or cyclic operation, so there are no real edges in this method, instead the arrays \"wrap around\" to the other side, creating a cyclic convolution like we showed in the periodic boundary condition case for the one-dimensional convolution.\nExample Code\nFor this example code, we will be using two sawtooth functions as we did in the chapter on one-dimensional convolutions:\nusing FFTW\nusing LinearAlgebra\nusing DelimitedFiles\n\n# using the convolutional theorem\nfunction convolve_fft(signal1::Array{T}, signal2::Array{T}) where {T \nfrom scipy.fft import fft, ifft\nimport numpy as np\n\n# using the convolutional theorem\ndef convolve_fft(signal1, signal2):\n return ifft(np.multiply(fft(signal1),fft(signal2)))\n\n# Sawtooth functions\nx = [float(i)/200 for i in range(1,101)]\ny = [float(i)/200 for i in range(1,101)]\n\nx /= np.linalg.norm(x)\ny /= np.linalg.norm(y)\n\n# Convolving the two signals\nfft_output = convolve_fft(x, y)\n\nnp.savetxt(\"fft.dat\", np.real(fft_output))\n\n\n\nThis should produce the following output:\n\n \n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nImages/Graphics\n\nThe image \"Cyclic\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/plotting/plotting.html":{"url":"contents/plotting/plotting.html","title":"Plotting","keywords":"","body":"Plotting\nPlotting is an essential tool for visualizing and understanding important details of several algorithms and methods and is necessary for studies in various areas of computational science.\nFor many languages, such as python, julia, and matlab, it is relatively straightforward to create simple plots for various types of data; however, for several other languages, like Fortran, C/C++, and java, plotting can be a chore.\nBecause the Algorithm Archive strives to be language agnostic, we do not want to favor any particular set of languages and have decided instead to output all data that needs plotting into a file format that can easily be read in by various plotting scripts separate from the algorithm implementations.\nIf you are implementing any algorithm in a language found on this page, you should be able to modify your existing code to allow for on-the-fly plotting.\nOtherwise, please use the language of your choice to write the initial implementation and output the data to a file before using one of the scripts available here for plotting.\nThis chapter aims to explain how to plot several different types of data and will be updated as more algorithms require more complex plotting schemes.\nThough many complex file formats exist, we will be mainly storing data for plotting in simple ASCII text.\nIf you wish to use these plotting scripts for other file formats or projects unrelated to the Algorithm Archive, some modification will be necessary.\nIn addition, each plotting language used in this chapter will likely have many features we are not currently using, so there may be methods to create stunning visualizations that we are ignoring here.\nPlotting a series of functions\nTo begin, let's write a simple script that allows for plotting a sine wave\nplot sin(x) with lines\n\nWhere x is a range from negative to positive 10.\nTo plot from the terminal, you can either:\n\nenter the gnuplot REPL (Read, Evaluate, Print, Loop -- the gnuplot shell) by using the gnuplot command and type the above command manually.\nwrite the command in an external script (let's call it script.gp) and run it with gnuplot script.gp -. The - will keep the terminal open in the background so the image stays up. If your plotting script outputs a .png file, the - is unnecessary.\n\nThis command will create a plot that looks like this:\n\n \n\n\nFor most gnuplot scripts, this command is written in short-hand.\nThe phrase with lines is abbreviated to simply w l and plot is sometimes written as simply p, so the following command would also work:\np sin(x) w l\n\n\nFrom here, it is rather straightforward to add more plots.\nFor example, let's add in a cosine function.\nIn this case, we need to add the following line to our script:\nplot sin(x) with lines\nreplot cos(x) with lines\n\nWhich will create an image that looks like this:\n\n \n\n\nIf you would prefer to plot everything on a single line (which will become more relevant when plotting directly to an image file), then you can use the following command:\np sin(x) w l, cos(x) w l\n\n\nIn some sense, this chapter is meant as a guide so users can better understand plotting in their language of choice.\nAs such, it is important to first understand how to perform a few basic tasks:\n\nChanging auxiliary features of the plot such as: title, axis, labels, x/ytic values, and plot dimensions\nPlotting multiple functions at the same time\nOutputting the plot to file\n\nAt the end of this chapter, we will discuss the scatter plot; however, additional plotting techniques may be covered in the near future for specific algorithms and methods.\nChanging auxiliary features\nBeauty is in the eye of the beholder, but it is rare for people to call plots \"beautiful.\"\nThat said, there are plenty of things you can do to more clearly represent your data, and if your data is beautiful, so be it!\nIn this section, we'll show you some small-scale modifications you can make to the plot we have already generated to make it little cleaner, but there are plenty of other ways to spruce up your plot that we are not covering here.\nBe sure to look at the documentation [1] for plotting in your language of choice if you want to do anything more complicated.\nx and y range\nAll data that can be plotted has a scope at which the important features are more clear.\nIt is sometimes important to zoom in or zoom out to highlight particular facets of the data available.\nThis can be simply done by modifying the x and y ranges in your plotter of choice, like so:\nset xrange [0:10]\nset yrange [0:1]\nplot sin(x) w l, cos(x) w l\nHere, the keywords xrange and yrange are known by gnuplot and take a range from [n:m], where n and m are real units in the plot, itself.\nFor this script, we generate a plot that looks like this:\n\n \n\n\nx and y tics\nIn addition to changing the plot scales, it is also important to notify your audience of what these scales actually mean.\nTo help guide the reader's eye and better understand what the plot represents, plotters provide tics (little notches) on the x and y axes.\nAs such, it is important to update the x and y tics with appropriate scales and labels.\nFirstly, to remove x and y tics, use\nunset xtics\nunset ytics\nThis will create a plot that looks like this:\n\n \n\n\nIf you want to set particular x or y tic values, use\nset xtics 0, 5, 10\nset ytics (\"bottom\" 0 , \"top\" 1)\nwhich creates a plot that looks like this:\n\n \n\n\nHere, we are selecting 3 values to use for the x-axis and using words or phrases for the \"bottom\" and \"top\" of the y-axis.\nTo be clear: we are not condoning the behavior of having mismatched x and y tic values by using words or phrases along the y axis and numbers along the x axis.\nThis is simply meant as a showcase for using gnuplot in this way.\nAs a note: there is a lot of information here we missed, specifically format specifiers, which allow users to modify the format of the numbers in their plots (to be in floating point, scientific notation, or something else).\nThis can be found in the documentation, along with anything else that is missed here.\n\n\nlogscale\nIn addition to changing the values of the x and y tics, we can also change the axes to plot in log-scale by using the following command:\nset logscale x\nset logscale y\n\n\nAs a simple example, let's take the exp(x) function.\nIn gnuplot, we can plot this by using p exp(x) w l, which will create the following:\n\n \n\n\nNow let's plot the same function with log-scale along the y axis:\n\n \n\n\nHere, we see what we expect: exp(x) is a straight line when the y axis is in log-scale.\nWhen we use log-scale on the sine and cosine waves from before, we get the following:\n\n \n\n\nThis is an awful plot, so it is only fitting that we use it as out example for the a few more plots in this chapter.\nlabels, titles, and legends\nMany researchers are very particular about labels.\nLabels need to be in the right spot, say the right stuff, and be interpreted in the right way.\nAs such, most plotters have a lot of options for labels, including LaTeX-like formatting for academic journals and such.\nThere are also multiple labels associated with each plot.\nEvery line has a label, often held in a box called a legend, and the plot, itself, has a title.\nlabels\nFirst, let's change the labels associated with each data set or function.\np sin(x) w l title \"sine wave\", cos(x) w l title \"cos(x)\"\n\n \n\n\nHere, we show that we can modify the data labels to be whatever we want.\nNote that for LaTeX-like math in the label, we might need to change the output to TeX, which will be shown later.\nFor now, let's move on to discuss what we can to with all of the labels in the legend\nlegend\nFirst things first, you should probably use a legend, unless you are a legend yourself and don't need one... In which case you can use the following:\nset nokey\nwhich will produce a plot that looks like this:\n\n \n\n\nAdmittedly, you are probably not important enough to remove the legend and doing so will prevent readers from understanding the data you are plotting, so this should be used sparingly.\nInstead, you should probably try to move the legend out of the way of the data, which can be done in a number of ways.\nIn gnuplot, it is possible to specify where we place the legend by using certain keywords, like top, bottom, left, right, and center, like so:\nset key top left\nwhich will produce a plot that looks like this:\n\n \n\n\nIn addition, we can specify exact coordinates in the plot to place the legend.\nFor example, if we wanted the legend to be at the position (1,0.5), then we would use the following command:\nset key at 1, 0.5\nwhich will produce a plot that looks like this:\n\n \n\n\nThis is certainly an awful place to put a legend for this plot, but this command could be useful for other plots.\n\n\ntitles\nObviously, in addition to labels, we can also provide a title for the entire plot, like so:\nset title \"Gnuplot Test\"\n\n \n\n\nsquare output\nMany times, plotting data in a 6:9 (or worse, 16:9) aspect ratio can feel like a misrepresentation of the data.\nFor whatever reason, I was told time and time again as a fledgling researcher that there is no need for widescreen plots and that I should set the output to square whenever possible.\nThat can be done by using\nset size square\nwhich will output the following plot:\n\n \n\n\nline and point types\nFinally, it's important to show your individuality by choosing your own point and line types.\nTo find all the point or line types available in gnuplot, simply open the REPL and run the test command, which outputs something that looks like this:\n\n \n\n\nAs a note, changing the line color is not mentioned in the test image above, this can be done with the linecolor command, which takes an argument in a color space like rgb.\nIf we would like to use a dashed black line for the sine function and purple crosses for cosine, we would use something like this:\np sin(x) with lines dashtype 2 linecolor rgb \"black\" title \"sin(x)\"\nrep cos(x) w p pt 17 lc rgb \"purple\" t \"cos(x)\"\nThis will create a plot that looks like this:\n\n \n\n\nWith this script, we are using a bunch of aliases, which can be found in the following section.\nFor now, it is clear that you can make your plot look however you like without too much trouble.\nThere are also a bunch of cool features that you can learn by looking up examples on the gnuplot site.\n\n\ngnuplot aliases\nAs we have seen in this chapter, it is common to use several aliases with gnuplot, and I have tried to introduce these slowly in the above text.\nHere are all the aliases stated explicitly:\n\n\n\ncommand\nalias\n\n\n\n\nplot\np\n\n\nreplot\nrep\n\n\nwith lines\nw l\n\n\nwith points\nw p\n\n\nlinecolor\nlc\n\n\npointtype\npt\n\n\ntitle\nt\n\n\n\nWe will add more aliases to this table as they are used in the Algorithm Archive.\n\n\nOutputting the plot to file\nAt this point, all the scripts have shown so far will output an image directly to your computer screen; however, it is important to note that you can use any of the above methods when outputting to a file as well.\nFor the most part, if you want to output any of the above scripts to a file, you simply need to run the following commands:\nset terminal pngcairo\nset output \"check.png\"\nIn this case, we are changing the REPL type to work with png images with the Cairo back-end, which is a vector drawing library in C.\nWe are also setting the output to \"check.png\".\nIf we would like to set the resolution of the output image, we could do the following:\nset terminal pngcairo size 640, 480\nAs an example, here is the script for the image we generated above:\nset terminal pngcairo size 640, 480\nset output \"sine_cosine_plot.png\"\nset xrange [0:10]\nset yrange [0:1]\nset logscale x\nset logscale y\nset key at 1,0.5\nset title \"Gnuplot Test\"\nset size square\n\nplot sin(x) with lines dashtype 2 linecolor rgb \"black\" title \"sin(x)\", \\\n cos(x) w p pt 17 lc rgb \"purple\" t \"cos(x)\"\n\nAs mentioned above, for a lot of scientific papers and articles, it is worth outputting images into a format that is used commonly for typesetting, such as LaTeX.\nThere are multiple ways to create TeX output with gnuplot by using different REPL modes like epslatex.\nThe easiest method to generate a pdf output with gnuplot that uses LaTeX would be to create a standalone TeX file, like so\nset terminal epslatex standalone size 10cm, 10cm\nset output \"check.tex\"\nThis can be quickly turned into a pdf with the pdflatex check.tex command.\nFor example, if we run the following script:\nset terminal epslatex standalone size 12cm, 8cm\nset output \"out.tex\"\n\np exp(x)\n\nand then run\ngnuplot file.gp\npdflatex out.tex\nWe will have a standalone pdf that uses LaTeX features in the file out.pdf.\nThis file should look like this:\n\n \n\n\nNote that in this process, we create auxiliary files like *.eps and *.aux, which are expected with LaTeX.\nIf you would like to directly read the output .tex file from gnuplot into another LaTeX document, you can use the same command as above without the standalone option, like so:\nset terminal epslatex size 10cm, 10cm\nset output \"check.tex\"\nThis will output another \"check.tex\" file that can be used by other LaTeX documents, and here is an example tex file to do that:\n\\documentclass[11pt]{article}\n\n\\usepackage{gnuplottex}\n\\begin{document}\n\n\\input{out}\n\n\\end{document}\n\nAs a note, the units for the epslatex terminal are real units in terms of cm, inches, or whatever other measurement LaTeX takes.\nAs such, you will probably want to make sure the size of the output image from gnuplot actually fits in the document you want to create.\n\n\nPlotting data from a file\nEach algorithm in the Algorithm Archive that requires plotting will also output a data file to use for this purpose.\nEven though there are plenty of complex data formats to write to and read from, for the purposes of this text, we will focus on simple ASCII data.\nThis is not preferred for any data-intensive task and there are a large number of different storage formats and file types available to choose from for your specific purposes; however, the Algorithm Archive intends to provide the simplest explanation of algorithms and methods and we do not want to over-complicate the process with file input and output.\nIf multiple data sets are required to be plotted, they will also be provided a new file, usually with a zero-padded name such as file_0000.dat, file_0001.dat, file_0002.dat, and so on.\nWe will assume that your plotter of choice has limited three dimensional capabilities and will instead focus on the data format for one and two-dimensional data here\nOne-dimensional output\nIn the case of one-dimensional output, the data file will have all numbers separated by a newline, such as in this case:\n0.5877852522924731\n0.9510565162951535\n0.9510565162951536\n0.5877852522924732\n1.2246467991473532e-16\n-0.587785252292473\n-0.9510565162951535\n-0.9510565162951536\n-0.5877852522924734\n-2.4492935982947064e-16\nFor the purposes of the Algorithm Archive, we will call these data files .dat files; however, the file extension does not matter and you can just as well name the files .tsv or .csv depending on your tastes.\nGnuplot can read in this file in the same way it can plot functions above.\nSo we can use the following command:\nplot \"sample_data.dat\" with lines\nWhich will provide the following output:\n\n \n\n\nTwo-dimensional image output\nIn the case of two-dimensional image output, the data file be similar, but this time, each number will be separated by a tab for different column entries and a newline for rows, as shown here:\n1.0 2.0 3.0\n4.0 5.0 6.0\n7.0 8.0 9.0\nIt is expected that the number of columns does not vary in each row and that we are working with an n \\times m matrix which can be simply plotted as a series of pixels that scale in color according to some defined color bar.\nTo create 2 dimensional plots in Gnuplot, we need to set the view to 2 dimensional and then do a 3 dimensional plot with the splot function that we set to a matrix image, like so:\nset view map\nsplot \"sample_data.dat\" matrix with image\n\n \n\n\nchanging the color bar\nFor plotting images from data files, we will often need to specify how we color the image by setting a custom color bar\nIn Gnuplot, there are not many predefined themes, but it is fairly easy to set your own theme for coloring a 2 dimensional image.\nThis is done by setting a palette and there are repositories online that have a number of palettes to choose from.\nSimply put, a palette is a number line where you can set a color to be associated with whatever value you like, like in this example:\nset view map\nset palette defined (0 0 0 1, 1 'red', 2 '#00FF00')\nsplot \"2d_sample_low_res.dat\" matrix with image\nThe integer value corresponds to the location of the color on the color bar and the color can be set as either a recognized word (blue, red, green, etc.), HTML notation ('#FF0000', '#00FF00', '#0000FF', etc.), or RGB colors (1 0 0, 0 1 0, 0 0 1, etc.).\nThis example will output the following plot:\n\n \n\n\n\nScatter Plots\nThe scatter plot is another useful method for visualizing data that plots each point in an n -dimensional space.\nFor the purposes of the Algorithm Archive, this space is mainly two-dimensional; however, scatter plots in three-dimensions may also be used for visualizing three-dimensional datasets.\nWe will update this section if three-dimensional scatter plots are required.\nFor the purposes of the Algorithm Archive, scatter plot data will be output as a series of x and y pairs, where each row has an x and a y value, separated by a tab character.\nFor example, a data file might look like this:\n0.7972009737623846 0.3548405553754319\n0.8661873069668018 0.13307711243511333\n0.7605752608745506 0.8686860241215444\n0.7796784902862803 0.35589625594005647\n0.23842162678327328 0.18541942067815853\n0.23648916187439406 0.6351126027850458\n0.6075688534409027 0.789554555806735\n0.361307926046027 0.6338943724188091\n0.3692102429804389 0.40610861857701597\n0.30699091691896263 0.27999628668153087\nFor three-dimensional scatter plots, there might be a third, z dimension.\nIn gnuplot, scatter plots are easy to generate with the provided data format, for example, you could use the following command:\np \"scatterplot_data.dat\" pt 7\nWhich will create the following image\n\n \n\n\nHere, we have chosen pointtype 7, simply because it is easier to see when compared to the default crosses.\n\n\nHistograms\nMany different algorithms will output data as a series of points that must be organized into separate bins before anyone can make sense of the data.\nFor example, here are 10 values from a set of 100 randomly generated integers between 1 and 9:\n2\n5\n5\n5\n1\n3\n2\n6\n3\n1\n6\nSomeone might ask, \"How many 1s show up in this string of numbers?\"\nSimilarly, someone might want to know how many 1s we have in comparison to the number of 2s (or 3s or 4s, etc).\nTo do this, we would create a set of bins and then iterate through the data, adding one to a bin every time we find a corresponding number.\nNote that the bins do not necessarily need to be sequential integer values and that for floating point numbers, the input might need to be rounded.\nYou can even histograms objects or anything that else that can be categorized.\nFor the data that we have shown above, we might create a histogram that looks like this:\n\n \n\n\nAnd here is a plotting script to generate it:\n# This is the size of each bin\nbin_width = 1;\n\n# This takes the data and determins which bin id it should fall into\nbin_id(x) = floor(x/bin_width)\n\n# This modifies each bin to be the correct width and also centers it over the \n# correct number\nbin(x) = bin_width * ( bin_id(x) + 0.5 )\n\n# Starts the y-axis at 0\nset yrange [0:]\n\n# Removes legend\nunset key\n\n# Sets a fill style for \"fillsteps\"\nset style fill solid 1.00 border\n\n# The column number to be histogrammed is 1, change $1 to another number if \n# you want to plot another column\nplot '../../data/rand.dat' u (bin($1)):(1) t 'data' smooth frequency w fillsteps\n\nFor this, we are using a fill style to use with fillsteps so the histogram is colored, but if you just want a line, you could remove the fill style and use histeps instead.\nAs another note, we are using t 'data' smooth frequency, which essentially turns the input numbers into a small, binned array to plot.\n\n\nNote that this code rounds the input in the case of floating point numbers.\nIf you are interested in seeing this type of plot generate fractal patterns, please look at the chapter on iterated function systems.\nConclusions\nPlotting is a powerful tool that is essential for most of computational science.\nHere, we have provided all of the essential skills to plot any data that comes from the Algorithm Archive, and we will strive to provide the plotting scripts we used whenever possible.\nBibliography\n1.Williams, T and Kelley, C, Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation, 2015.\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"gnuplot_sine_wave\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_wave\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_wave_range\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_notics\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_customtics\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"exp_fn\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"exp_fn_log\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_log\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_label\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_nokey\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_movekey\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_movekey2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_title\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_square\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_test\" was created by the gnuplot test command, and gnuplot has this copyright.\nThe image \"gnuplot_sine_cosine_linetype\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_exp_tex\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_1d_sample\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_2d_sample\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_2d_sample_colorbar\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_scatterplot\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_histogram\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n\n\nPull Requests\nThe following pull requests have modified the text or graphics of this chapter:\n\n622: Initial PR for chapter\n\n"},"contents/monte_carlo_integration/monte_carlo_integration.html":{"url":"contents/monte_carlo_integration/monte_carlo_integration.html","title":"Monte Carlo","keywords":"","body":"Monte Carlo Integration\nMonte Carlo methods were some of the first methods I ever used for research, and when I learned about them, they seemed like some sort of magic.\nTheir premise is simple: random numbers can be used to integrate arbitrary shapes embedded into other objects.\nNowadays, \"Monte Carlo\" has become a bit of a catch-all term for methods that use random numbers to produce real results, but it all started as a straightforward method to integrate objects.\nNo matter how you slice it, the idea seems a bit crazy at first.\nAfter all, random numbers are random.\nHow could they possibly be used to find non-random values?\nWell, imagine you have a square.\nThe area of the square is simple, \\text{Area}_{\\text{square}} = \\text{length} \\times \\text{width}.\nSince it's a square, the \\text{length} and \\text{width} are the same, so the formula is technically just \\text{Area}_{\\text{square}} = \\text{length}^2.\nIf we embed a circle into the square with a radius r = \\tfrac{length}{2} (shown below), then its area is \\text{Area}_{\\text{circle}}=\\pi r^2.\nFor simplicity, we can also say that \\text{Area}_{\\text{square}}=4r^2.\n\n \n\n\nNow, let's say we want to find the area of the circle without an equation.\nAs we said before, it's embedded in the square, so we should be able to find some ratio of the area of the square to the area of the circle:\n\n\\text{Ratio} = \\frac{\\text{Area}_{\\text{circle}}}{\\text{Area}_{\\text{square}}}\n\nThis means,\n\n\\text{Area}_{\\text{circle}} = \\text{Area}_{\\text{square}}\\times\\text{Ratio} = 4r^2 \\times \\text{ratio}\n\nSo, if we can find the \\text{Ratio} and we know r, we should be able to easily find the \\text{Area}_{\\text{circle}}.\nThe question is, \"How do we easily find the \\text{Ratio}?\"\nWell, one way is with random sampling.\nWe basically just pick a bunch of points randomly in the square, and\neach point is tested to see whether it's in the circle or not:\nfunction in_circle(x_pos::Float64, y_pos::Float64)\n\n # Setting radius to 1 for unit circle\n radius = 1\n return x_pos^2 + y_pos^2 \n(defn in-circle? [pv r]\n \"take a vector representing point and radius return true if the\n point is inside the circle\"\n (>\n pv\n (map #(* % %))\n (reduce +))\n (* r r)))\n\nbool in_circle(double x, double y) {\n return x * x + y * y \n/**\n * Check if the point (x, y) is within a circle of a given radius.\n * @param x coordinate one\n * @param y coordinate two\n * @param r radius of the circle (optional)\n * @return true if (x, y) is within the circle.\n */\ninline bool in_circle(double x, double y, double r = 1) {\n return x * x + y * y \nfunction inCircle(xPos, yPos) {\n // Setting radius to 1 for unit circle\n let radius = 1;\n return xPos * xPos + yPos * yPos \ninCircle (x, y) = x^2 + y^2 \nfn in_circle(x: f64, y: f64, radius: f64) -> bool {\n x * x + y * y \nbool inCircle(real x, real y)\n{\n return x ^^ 2 + y ^^ 2 \nfunc inCircle(x, y float64) bool {\n return x*x+y*y \nin_circle \nprivate static boolean inCircle(double x, double y) {\n return x * x + y * y \nfunc inCircle(x: Double, y: Double, radius: Double) -> Bool {\n return (x*x) + (y*y) \ndef in_circle(x, y, radius = 1):\n \"\"\"Return True if the point is in the circle and False otherwise.\"\"\"\n return (x*x + y*y) \npublic bool IsInMe(Point point) => Math.Pow(point.X, 2) + Math.Pow(point.Y, 2) \nproc in_circle(x, y, radius: float): bool =\n return x * x + y * y \ndef in_circle(x, y, radius=1)\n # Check if coords are in circle via Pythagorean Thm\n return (x*x + y*y) \nFUNCTION in_circle(pos_x, pos_y, r)\n IMPLICIT NONE\n REAL(16), INTENT(IN) :: pos_x, pos_y, r\n LOGICAL :: in_circle\n\n in_circle = (pos_x ** 2 + pos_y ** 2) \n[ ! in-circle check\n [ 2 ^ ] bi@ + ! get the distance from the center\n 1 \n❗️ 📥 point ☝️ ➡️ 👌 🍇\n 📪 point❗️ ➡️ point_x\n 📫 point❗️ ➡️ point_y\n ↩️ 🤜point_x ✖️ point_x ➕ point_y ✖️ point_y🤛 ◀️ 🤜radius ✖️ radius🤛\n🍉\n\nfunction in_circle(float $positionX, float $positionY, float $radius = 1): bool\n{\n return pow($positionX, 2) + pow($positionY, 2) \nlocal function in_circle(x, y)\n return x*x + y*y \n(define (in-circle x y)\n \"Checks if a point is in a unit circle\"\n (\ndef inCircle(x: Double, y: Double) = x * x + y * y \n(defun in-circle-p (x y)\n \"Checks if a point is in a unit circle\"\n (\n# xmm0 - x\n# xmm1 - y\n# RET rax - bool\nin_circle:\n mulsd xmm0, xmm0 # Calculate x * x + y * y\n mulsd xmm1, xmm1\n addsd xmm0, xmm1\n movsd xmm1, one # Set circle radius to 1\n xor rax, rax\n comisd xmm1, xmm0 # Return bool xmm0 \ninCircle() {\n local ret\n local mag\n ((ret = 0))\n if (($1 ** 2 + $2 ** 2 \nprivate fun inCircle(x: Double, y: Double, radius: Double = 1.0) = (x * x + y * y) \n% a 2 by n array, rows are xs and ys\nxy_array = rand(2, n); \n\n% square every element in the array\nsquares_array = xy_array.^2; \n\n% sum the xs and ys and check if it's in the quarter circle\nincircle_array = sum(squares_array)\n\n \ndata point(x, y):\n def __abs__(self) = (self.x, self.y) |> map$(pow$(?, 2)) |> sum |> math.sqrt\n\ndef in_circle(p is point, radius = 1):\n \"\"\"Return True if the point is in the circle and False otherwise.\"\"\"\n return abs(p) \nfunction Is-InCircle($x, $y, $radius=1) {\n return ([Math]::Pow($x, 2) + [Math]::Pow($y, 2)) -lt [Math]::Pow($radius, 2)\n}\n\n\n\nIf it's in the circle, we increase an internal count by one, and in the end,\n\n\\text{Ratio} = \\frac{\\text{count in circle}}{\\text{total number of points used}}\n\nIf we use a small number of points, this will only give us a rough approximation, but as we start adding more and more points, the approximation becomes much, much better (as shown below)!\n\n \n\n\nThe true power of Monte Carlo comes from the fact that it can be used to integrate literally any object that can be embedded into the square.\nAs long as you can write some function to tell whether the provided point is inside the shape you want (like in_circle() in this case), you can use Monte Carlo integration!\nThis is obviously an incredibly powerful tool and has been used time and time again for many different areas of physics and engineering.\nI can guarantee that we will see similar methods crop up all over the place in the future!\nVideo Explanation\nHere is a video describing Monte Carlo integration:\n\n\n\n\nExample Code\nMonte Carlo methods are famous for their simplicity.\nIt doesn't take too many lines to get something simple going.\nHere, we are just integrating a circle, like we described above; however, there is a small twist and trick.\nInstead of calculating the area of the circle, we are instead trying to find the value of \\pi, and\nrather than integrating the entire circle, we are only integrating the upper right quadrant of the circle from 0 .\nThis saves a bit of computation time, but also requires us to multiply our output by 4.\nThat's all there is to it!\nFeel free to submit your version via pull request, and thanks for reading!\n# function to determine whether an x, y point is in the unit circle\nfunction in_circle(x_pos::Float64, y_pos::Float64)\n\n # Setting radius to 1 for unit circle\n radius = 1\n return x_pos^2 + y_pos^2 \n(ns monte-carlo.core)\n\n(defn in-circle? [pv r]\n \"take a vector representing point and radius return true if the\n point is inside the circle\"\n (>\n pv\n (map #(* % %))\n (reduce +))\n (* r r)))\n\n(defn rand-point [r]\n \"return a random point from (0,0) inclusive to (r,r) exclusive\"\n (repeatedly 2 #(rand r)))\n\n(defn monte-carlo [n r]\n \"take the number of random points and radius return an estimate to\npi\"\n (*' 4 (/ n)\n (loop [i n count 0]\n (if (zero? i)\n count\n (recur (dec i)\n (if (in-circle? (rand-point r) r)\n (inc count)\n count))))))\n\n(defn -main []\n (let [constant-pi Math/PI\n computed-pi (monte-carlo 10000000 2) ;; this may take some time on lower end machines\n difference (Math/abs (- constant-pi computed-pi))\n error (* 100 (/ difference constant-pi))]\n (println \"world's PI: \" constant-pi\n \",our PI: \" (double computed-pi)\n \",error: \" error)))\n\n#include \n#include \n#include \n#include \n#include \n\nbool in_circle(double x, double y) {\n return x * x + y * y \n#include \n#include \n#include \n\nconstexpr double PI = 3.14159265358979323846264338;\n\n/**\n * Check if the point (x, y) is within a circle of a given radius.\n * @param x coordinate one\n * @param y coordinate two\n * @param r radius of the circle (optional)\n * @return true if (x, y) is within the circle.\n */\ninline bool in_circle(double x, double y, double r = 1) {\n return x * x + y * y dist(0, 1);\n\n unsigned count = 0;\n for (unsigned i = 0; i \n// submitted by xam4lor\nfunction inCircle(xPos, yPos) {\n // Setting radius to 1 for unit circle\n let radius = 1;\n return xPos * xPos + yPos * yPos \nimport System.Random\n\nmonteCarloPi :: RandomGen g => g -> Int -> Float\nmonteCarloPi g n = count $ filter inCircle $ makePairs\n where makePairs = take n $ toPair (randomRs (0, 1) g :: [Float])\n toPair (x:y:rest) = (x, y) : toPair rest\n inCircle (x, y) = x^2 + y^2 \n// Submitted by jess 3jane\n\nextern crate rand;\n\nuse std::f64::consts::PI;\n\nfn in_circle(x: f64, y: f64, radius: f64) -> bool {\n x * x + y * y f64 {\n let mut count = 0;\n\n for _ in 0..n {\n let x = rand::random();\n let y = rand::random();\n if in_circle(x, y, 1.0) {\n count += 1;\n }\n }\n\n // return our pi estimate\n (4 * count) as f64 / n as f64\n}\n\nfn main() {\n let pi_estimate = monte_carlo(10000000);\n\n println!(\n \"Percent error is {:.3}%\",\n (100.0 * (pi_estimate - PI).abs() / PI)\n );\n}\n\n///Returns true if a point (x, y) is in the circle with radius r\nbool inCircle(real x, real y)\n{\n return x ^^ 2 + y ^^ 2 tuple!(\"x\", \"y\")(uniform01, uniform01))\n .take(n)\n .count!(a => inCircle(a.x, a.y));\n return piCount * 4.0 / n;\n}\n\nvoid main()\n{\n import std.math : abs, PI;\n import std.stdio : writeln;\n\n auto p = monteCarloPI(100_000);\n writeln(\"Estimated pi: \", p);\n writeln(\"Percent error: \", abs(p - PI) * 100 / PI);\n}\n\n// Submitted by Chinmaya Mahesh (chin123)\n\npackage main\n\nimport (\n \"fmt\"\n \"math\"\n \"math/rand\"\n \"time\"\n)\n\nfunc inCircle(x, y float64) bool {\n return x*x+y*y \n\nin_circle \nimport java.util.Random;\n\npublic class MonteCarlo {\n\n public static void main(String[] args) {\n double piEstimation = monteCarlo(1000);\n System.out.println(\"Estimated pi value: \" + piEstimation);\n System.out.printf(\"Percent error: \" + 100 * Math.abs(piEstimation - Math.PI) / Math.PI);\n }\n\n // function to check whether point (x,y) is in unit circle\n private static boolean inCircle(double x, double y) {\n return x * x + y * y \nfunc inCircle(x: Double, y: Double, radius: Double) -> Bool {\n return (x*x) + (y*y) Double {\n let radius: Double = 1\n var piCount = 0\n var randX: Double\n var randY: Double\n\n for _ in 0...n {\n randX = Double.random(in: 0..\nimport math\nimport random\n\n\ndef in_circle(x, y, radius = 1):\n \"\"\"Return True if the point is in the circle and False otherwise.\"\"\"\n return (x*x + y*y) \nMonteCarlo.cs\nusing System;\n\nnamespace MonteCarloIntegration\n{\n public class MonteCarlo\n {\n public double Run(int samples)\n {\n var circle = new Circle(1.0);\n var count = 0;\n var random = new Random();\n\n for (int i = 0; i \nCircle.cs\nusing System;\n\nnamespace MonteCarloIntegration\n{\n public struct Point\n {\n public double X { get; set; }\n public double Y { get; set; }\n\n public Point(double x, double y)\n {\n this.X = x;\n this.Y = y;\n }\n }\n\n public class Circle\n {\n public double Radius { get; private set; }\n\n public Circle(double radius) => this.Radius = Math.Abs(radius);\n\n public bool IsInMe(Point point) => Math.Pow(point.X, 2) + Math.Pow(point.Y, 2) \nProgram.cs\nusing System;\n\nnamespace MonteCarloIntegration\n{\n class Program\n {\n static void Main(string[] args)\n {\n var monteCarlo = new MonteCarlo();\n System.Console.WriteLine(\"Running with 10,000,000 samples.\");\n var piEstimate = monteCarlo.Run(10000000);\n System.Console.WriteLine($\"The estimate of pi is: {piEstimate}\");\n System.Console.WriteLine($\"The percent error is: {Math.Abs(piEstimate - Math.PI) / Math.PI * 100}%\");\n }\n }\n}\n\nimport random\nimport math\n\nrandomize()\n\nproc in_circle(x, y, radius: float): bool =\n return x * x + y * y \ndef in_circle(x, y, radius=1)\n # Check if coords are in circle via Pythagorean Thm\n return (x*x + y*y) \nFUNCTION in_circle(pos_x, pos_y, r)\n IMPLICIT NONE\n REAL(16), INTENT(IN) :: pos_x, pos_y, r\n LOGICAL :: in_circle\n\n in_circle = (pos_x ** 2 + pos_y ** 2) \nUSING: locals random math.ranges math.functions ;\n\n:: monte-carlo ( n in-shape?: ( x y -- ? ) -- % )\n n [ drop random-unit random-unit in-shape? call ] count n /\n; inline\n\n! Use the monte-carlo approximation to calculate pi\n: monte-carlo-pi ( n -- pi-approx )\n [ ! in-circle check\n [ 2 ^ ] bi@ + ! get the distance from the center\n 1 float\n;\n\nUSING: math.constants ;\n10000000 monte-carlo-pi ! Approximate pi\ndup . ! Print the approximation\npi - pi / 100 * >float abs . ! And the error margin\n\n🐇 ☝️ 🍇\n 🖍🆕 x 💯\n 🖍🆕 y 💯\n\n 🆕 🍼 x 💯 🍼 y 💯 🍇 🍉\n\n ❗️ 📪 ➡️ 💯 🍇\n ↩️ x\n 🍉\n\n ❗️ 📫 ➡️ 💯 🍇\n ↩️ y\n 🍉\n🍉\n\n🐇 🌕 🍇\n 🖍🆕 radius 💯\n\n 🆕 given_radius 💯 🍇\n 🏧 given_radius❗️ ➡️ 🖍radius\n 🍉\n\n ❗️ 📥 point ☝️ ➡️ 👌 🍇\n 📪 point❗️ ➡️ point_x\n 📫 point❗️ ➡️ point_y\n ↩️ 🤜point_x ✖️ point_x ➕ point_y ✖️ point_y🤛 ◀️ 🤜radius ✖️ radius🤛\n 🍉\n🍉\n\n🐇 🤡 🍇\n 🐇 ❗️ 🏃‍♀️ samples 🔢 ➡️ 💯 🍇\n 🆕🌕🆕 1.0 ❗️ ➡️ circle\n 0 ➡️ 🖍🆕 count\n\n 🆕🎰🆕 ❗️ ➡️ random\n\n 🔂 i 🆕⏩⏩ 0 samples❗️ 🍇\n 🆕☝️🆕 💯 random❗️ 💯 random❗️❗️ ➡️ point\n ↪️ 📥 circle point❗️ 🍇\n count ⬅️ ➕ 1\n 🍉\n 🍉\n\n ↩️ 4.0 ✖️ 💯 count❗️ ➗ 💯samples❗️\n 🍉\n🍉\n\n🏁 🍇\n 😀 🔤Running with 10,000,000 samples.🔤❗️\n 🏃‍♀️🐇🤡 10000000❗️ ➡️ pi_estimate\n 😀 🍪🔤The estimate of pi is: 🔤 🔡 pi_estimate 10❗🍪❗️\n 🏧 🤜pi_estimate ➖ 🥧🕊💯 ❗️🤛❗️ ➗ 🥧🕊💯 ❗️ ✖️ 100 ➡️ percent_error\n 😀 🍪🔤The percent error is: 🔤 🔡 percent_error 10❗ 🔤%🔤🍪❗️\n🍉\n\n\n-- function to determine whether an x, y point is in the unit circle\nlocal function in_circle(x, y)\n return x*x + y*y \n#lang racket/base\n\n(require racket/local)\n(require racket/math)\n\n(define (in-circle x y)\n \"Checks if a point is in a unit circle\"\n (string pi-estimate)))\n(displayln (string-append \"Estimate (float): \" (number->string (real->single-flonum pi-estimate))))\n(displayln (string-append \"Error:\" (number->string (* (/ (abs (- pi-estimate pi)) pi) 100))))\n\nobject MonteCarlo {\n\n def inCircle(x: Double, y: Double) = x * x + y * y \n;;;; Monte carlo integration to approximate pi\n\n(defun in-circle-p (x y)\n \"Checks if a point is in a unit circle\"\n (\n.intel_syntax noprefix\n\n.section .rodata\n pi: .double 3.141592653589793\n one: .double 1.0\n four: .double 4.0\n hundred: .double 100.0\n rand_max: .long 4290772992\n .long 1105199103\n fabs_const: .long 4294967295\n .long 2147483647\n .long 0\n .long 0\n estimate_fmt: .string \"The estaimate of pi is %lf\\n\"\n error_fmt: .string \"Percentage error: %0.2f\\n\"\n\n.section .text\n .global main\n .extern printf, srand, time, rand\n\n# xmm0 - x\n# xmm1 - y\n# RET rax - bool\nin_circle:\n mulsd xmm0, xmm0 # Calculate x * x + y * y\n mulsd xmm1, xmm1\n addsd xmm0, xmm1\n movsd xmm1, one # Set circle radius to 1\n xor rax, rax\n comisd xmm1, xmm0 # Return bool xmm0 \n#!/usr/bin/env bash\ninCircle() {\n local ret\n local mag\n ((ret = 0))\n if (($1 ** 2 + $2 ** 2 \nimport java.util.Random\n\nprivate fun inCircle(x: Double, y: Double, radius: Double = 1.0) = (x * x + y * y) ) {\n val piEstimate = monteCarlo(100000)\n println(\"Estimated pi value: $piEstimate\")\n val percentError = 100 * Math.abs(piEstimate - Math.PI) / Math.PI\n println(\"Percent error: $percentError\")\n}\n\npi_estimate = monte_carlo(10000000);\n\nfprintf(\"The pi estimate is: %f\\n\", pi_estimate);\nfprintf(\"Percent error is: %f%%\\n\", 100 * abs(pi_estimate - pi) / pi);\n\nfunction pi_estimate=monte_carlo(n)\n\n % a 2 by n array, rows are xs and ys\n xy_array = rand(2, n); \n\n % square every element in the array\n squares_array = xy_array.^2; \n\n % sum the xs and ys and check if it's in the quarter circle\n incircle_array = sum(squares_array)\nThe code snippets were taken from this scratch project\n\n \nimport math\nimport random\n\ndata point(x, y):\n def __abs__(self) = (self.x, self.y) |> map$(pow$(?, 2)) |> sum |> math.sqrt\n\ndef in_circle(p is point, radius = 1):\n \"\"\"Return True if the point is in the circle and False otherwise.\"\"\"\n return abs(p) map$(-> point(random.uniform(0, radius), random.uniform(0, radius)))\n |> filter$(in_circle$(?, radius))\n |> tuple\n |> len) * 4 / n_samples\n\nif __name__ == '__main__':\n\n samples = 100_000\n\n print(f\"Using {samples:_} samples.\")\n\n pi_estimate = monte_carlo(samples)\n percent_error = 100*abs(math.pi - pi_estimate)/math.pi\n\n print(\"The estimate of pi is: {:.3f}\".format(pi_estimate))\n print(\"The percent error is: {:.3f}\".format(percent_error))\n\nfunction Is-InCircle($x, $y, $radius=1) {\n return ([Math]::Pow($x, 2) + [Math]::Pow($y, 2)) -lt [Math]::Pow($radius, 2)\n}\n\nfunction Monte-Carlo([int]$n) {\n $PiCount = 0;\n for ($i = 0; $i -lt $n; $i++) {\n $x = Get-Random -Minimum 0.0 -Maximum 1.0\n $y = Get-Random -Minimum 0.0 -Maximum 1.0\n\n if (Is-InCircle $x $y) {\n $PiCount++\n }\n }\n return 4.0 * $PiCount / $n\n}\n\n# This could take some time\n$PiEstimate = Monte-Carlo 10000000\nWrite-Host \"The pi estimate is: $PiEstimate\"\nWrite-Host \"Percent error is: $(100 * [Math]::Abs($PiEstimate - ([Math]::PI)) / ([Math]::PI))\"\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"squarecircle\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe animation \"simplemontecarlo\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/bitlogic/bitlogic.html":{"url":"contents/bitlogic/bitlogic.html","title":"Bit Logic","keywords":"","body":"Bit Logic\nWe write code in a language that makes a little sense to us, but does not make sense at all to our computer without a compiler to transform the code we write into a language the computer can understand.\nIn the end, whenever we write code, all of the data structures we write are transformed into binary strings of 1's and 0's to be interpreted by our computer.\nThat said, it's not always obvious how this happens, so let's start the simple case of integer numbers.\nIntegers\nFor integer numbers, 0 is still 0 and 1 is still 1; however, for 2, we need to use 2 digits because binary only has 0's and 1's. When we get to 4, we'll need 3 digits and when we get to 8, we'll need 4. Every time we cross a power of 2, we'll need to add a new digit. Here's a table of the first 10 integers in binary:\n\n\n\nInteger Number\nBinary Number\n\n\n\n\n0\n0000\n\n\n1\n0001\n\n\n2\n0010\n\n\n3\n0011\n\n\n4\n0100\n\n\n5\n0101\n\n\n6\n0110\n\n\n7\n0111\n\n\n8\n1000\n\n\n9\n1001\n\n\n\nThe easiest way to interpret a binary string is to imagine that each digit is a power of 2 and add them together. For example, take the number 13, with a bitstring 1101:\n\n\n\n1\n1\n0\n1\n\n\n\n\n2^3\n2^2\n2^1\n2^0\n\n\n8\n4\n2\n1\n\n\n\nWe have 1 2^3 = 8, 1 2^2 = 4, 0 2^1 = 2 and 1 2^0 = 1, adding together to 13.\nThough this might seem straightforward, it is essential to understanding several operations that will be done on bits later.\nFor now, let's talk about the only trick to integer values: negative numbers!\nThere are a few ways to represent negative numbers.\nFor example, if we are using 8 bits, we might use the first of the 8 bits to be a sign bit, whose only purpose is telling the computer whether the number is positive or negative.\nAnother method is to \"roll over\" to negative numbers when the bit count gets too high, for example:\n\n\n\nInteger Number\nBinary Number\n\n\n\n\n126\n01111110\n\n\n127\n01111111\n\n\n-128\n10000000\n\n\n-127\n10000001\n\n\n\nUltimately, integer numbers are not that difficult to deal with in binary, so let's move onto something more complicated: floating-point numbers!\nFloating-point Numbers\nFloats are numbers with a decimal point.\n9.125 is a float. 9.000 is a float. 9 is an integer.\nHere are a few floats and their integer representations:\n\n\n\nFloating-point Number\nBinary Number\n\n\n\n\n9.125\n1001.001\n\n\n10.25\n1010.01\n\n\n1.00\n1\n\n\n\nThe idea is similar to before: Each digit represents a power of 2; however, this time any digit after the decimal point counts negative.\nSo for 9.125, we have 1 2^3 = 8, 1 2^0 = 1, and 1 2^{-3} = \\frac{1}{8}.\nNow, how is this actually implemented on your computer?\nWell, one way is with the IEEE 754 Floating-point Arithmetic Standard.\nFor 32 bits, the first bit is the sign bit, the next 8 bits tell us about the number's exponent, and the next 23 are called the mantissa and hold the binary string, itself. Now, there are a few points to keep in mind:\n\nBecause the exponent is being represented in 8 bits, we only have 256 values to play with. This means that the largest exponent we can represent (in single precision) is 128 and the smallest is -127. For this reason, we will add 127 to the power of every floating-point number. So, 1 = 1 \\times 2^{0}. The exponent stored is 0+127 = 127.\n\nWe normalize every bitstring to the first 1 available. For example: 9.125 = 1.001001 \\times 2^{3} and the biased exponent is 3+127=130, 8.25 = 1.00001 \\times 2^{130}, 0.5 = 1 \\times 2^{126} \\ldots This means that there will always be a leading 1 in our bitstring. This means that the first 1 is redundant and can be removed from the mantissa.\n\n\nSo here are a few floating-point numbers and their corresponding bitstrings:\n\n\n\nFloat\nSign\nExponent\nMantissa\n\n\n\n\n9.125\n0\n10000010\n00100100000000000000000\n\n\n- 5.25\n1\n10000001\n01010000000000000000000\n\n\n- 4096.625\n1\n10001011\n00000000000010100000000\n\n\n\nNow that we know how to represent integers and floating-point numbers, let's move on to operations, starting with bitshift operators\nBitshift Operators: >\nBitshift operators do what their name implies: they shift a string of bits one digit to the left (>).\nThis has the somewhat profound effect of multiplying or dividing the value by 2, which makes sense when you consider that each digit represents a power of 2.\nBecause of the somewhat complicated nature of floating-point numbers, bitshift operators usually only work on integer numbers, like so:\n\n\n\nOperation\nInteger\nBitstring\n\n\n\n\nNone\n10\n00001010\n\n\nBitshift left, \n20\n00010100\n\n\nBitshift right, >>\n5\n00000101\n\n\n\nThere are more complicated things that can be done with the bitshift operators; however, we'll leave that discussion for another day!\nLogic gates\nIn addition to the bitshift operations, there are a number of logical operations that can be performed on one or two bits together.\nThese operations are called gates, and follow somewhat straightforward logic.\nThe AND gate, for example, reads in 2 bits and will only output a 1 value if both inputs are 1. This can be seen in the corresponding truth table:\n\n \n\n\nThe OR gate will output 1 if either input bits are 1:\n\n \n\n\nThe exclusive OR or XOR gate is the same as the OR gate, but will not output 1 if both bits are 1:\n\n \n\n\nThe NOT gate simply flips the input bit:\n\n \n\n\nBy combining the NOT and AND gates, we get the NAND gate:\n\n \n\n\nAnd NOT and OR create NOR:\n\n \n\n\nThere are a few other gates, but this is enough for most things. We'll add more as the need arises!\nThat's about it for bitlogic. I realize it was a bit long, but this is absolutely essential to understanding how computers think and how to use programming as an effective tool!\nVideo Explanation\nHere is a video describing the contents of this chapter:\n\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"ANDgate\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"ORgate\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"XORgate\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"NOTgate\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"NANDgate\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"NORgate\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/box_muller/box_muller_rejection.html":{"url":"contents/box_muller/box_muller_rejection.html","title":"How costly is rejection sampling?","keywords":"","body":"Just how costly is rejection sampling anyway?\nLet's imagine we want to have a final Gaussian distribution with n particles in it.\nWith the Cartesian Box—Muller method, this is easy: start the initial distribution(s) with n particles and then do the transform.\nThings can be just as easy with the Polar Box—Muller method as well, so long as we start with a uniformly distributed circle instead of a uniformly distributed square.\nThat is to say, so long as we do the rejection sampling before-hand, the Polar Box—Muller method will always be more efficient.\nTo be fair, there are methods to generate a uniform distribution of points within a circle without rejection sampling, but let's assume that we require rejection sampling for this example\nThis means that someone somehow needs to do the rejection sampling for the Polar method, which is sometimes a painful process.\nThis also means that the Box—Muller method can be used to teach some of the fundamentals of General-Purpose GPU computing.\nNote that because of the specificity of this problem, all the code in this subsection will be in Julia and using the package KernelAbstractions.jl, which allows us to execute the same kernels on either CPU or GPU hardware depending on how we configure things.\nLet's first consider the case where we do the rejection sampling as a part of the polar Box—Muller kernel instead of as a pre-processing step.\nIn this case, we can imagine 2 separate ways of writing our kernel:\n\nWith replacement: In this case, we absolutely require the final number of points in our Gaussian distribution to be n, so if we find a point outside of the unit circle while running the kernel, we will \"re-roll\" again for a new point that is within the circle.\nWithout replacement: This means that we will start with a uniform distribution of n points, but end with a Gaussian of m points. In this case, if we find a point outside of the unit circle while running the kernel, we just ignore it by setting the output values to NaNs (or something similar).\n\nOK, so first with replacement:\n@kernel function polar_muller_replacement!(input_pts, output_pts, sigma, mu)\n tid = @index(Global, Linear)\n @inbounds r_0 = input_pts[tid, 1]^2 + input_pts[tid, 2]^2\n\n while r_0 > 1 || r_0 == 0\n p1 = rand()*2-1\n p2 = rand()*2-1\n r_0 = p1^2 + p2^2\n end\n\n @inbounds output_pts[tid,1] = sigma * input_pts[tid,1] *\n sqrt(-2 * log(r_0) / r_0) + mu\n @inbounds output_pts[tid,2] = sigma * input_pts[tid, 2] *\n sqrt(-2 * log(r_0) / r_0) + mu\nend\n\nThis is an awful idea for a number of reasons.\nHere are a few:\n\nIf we find a point outside of the unit circle, we have to continually look for new points until we do find one inside of the circle. Because we are running this program in parallel, where each thread transforms one point at a time, some threads might take literally forever to find a new point (if we are really unlucky).\nTo generate new points, we need to re-generate a uniform distribution, but what if our uniform distribution is not random? What if it's a grid (or something similar) instead? In this case, we really shouldn't look for a new point on the inside of the circle as all those points have already been accounted for.\nThe rand() function is kinda tricky on some parallel platforms (like GPUs) and might not work out of the box. In fact, the implementation shown above can only be run on the CPU.\n\nOK, fine.\nI don't think anyone expected a kernel with a while loop inside of it to be fast.\nSo what about a method without replacement?\nSurely there is no problem if we just ignore the while loop altogether!\nWell, the problem with this approach is a bit less straightforward, but first, code:\n@kernel function polar_muller_noreplacement!(input_pts, output_pts, sigma, mu)\n tid = @index(Global, Linear)\n @inbounds r_0 = input_pts[tid, 1]^2 + input_pts[tid, 2]^2\n\n # this method is only valid for points within the unit circle\n if r_0 == 0 || r_0 > 1\n @inbounds output_pts[tid,1] = NaN\n @inbounds output_pts[tid,2] = NaN\n else\n @inbounds output_pts[tid,1] = sigma * input_pts[tid,1] *\n sqrt(-2 * log(r_0) / r_0) + mu\n @inbounds output_pts[tid,2] = sigma * input_pts[tid, 2] *\n sqrt(-2 * log(r_0) / r_0) + mu\n end\n\nend\n\nTo start discussing why a polar kernel without replacement is also a bad idea, let's go back to the Monte Carlo chapter, where we calculated the value of \\pi by embedding it into a circle.\nThere, we found that the probability of a randomly chosen point falling within the unit circle to be \\frac{\\pi r^2}{(2r)^2} = \\frac{pi}{4} \\sim 78.54\\%, shown in the visual below:\n\n \n\n\nThis means that a uniform distribution of points within a circle will reject \\sim 21.46\\% of points on the square.\nThis also means that if we have a specific n value we want for the final distribution, we will need \\frac{1}{0.7853} \\sim 1.273 \\times more input values on average!\nNo problem!\nIn this hypothetical case, we don't need exactly n points, so we can just start the initial distributions with 1.273 \\times n points, right?\nRight.\nThat will work well on parallel CPU hardware, but on the GPU this will still have an issue.\nOn the GPU, computation is all done in parallel, but there is a minimum unit of parallelism called a warp.\nThe warp is the smallest number of threads that can execute something in parallel and is usually about 32.\nThis means that if an operation is queued, all 32 threads will do it at the same time.\nIf 16 threads need to execute something and the other 16 threads need to execute something else, this will lead to warp divergence where 2 actions need to be performed instead of 1:\n\n \n\n\nIn this image, every odd thread needs to perform the pink action, while the even threads need to perform the blue action.\nThis means that 2 separate parallel tasks will be performed, one for the even threads, another for the odd threads.\nThis means that if \\ell separate operations are queued, it could take \\ell\\times as long for all the threads to do their work!\nThis is why if statements in a kernel can be dangerous!\nIf used improperly, they can cause certain threads in a warp to do different things!\nSo let's imagine that the above image is part of a larger array of values, such that there are a bunch of warps with the same divergence issue.\nIn this case, we could sort the array before-hand so that all even elements come before all odd elements.\nThis would mean that the warps will almost certainly not diverge because the elements queued will all be of the same type and require the same operations.\nUnfortunately, this comes at the cost of a sorting operation which is prohibitively expensive.\nIf we look at the above kernel, we are essentially asking 21.47\\% of our threads to do something different than everyone else, and because we are usually inputting a uniform random distribution, this means that most warps will have to queue up 2 parallel actions instead of 1.\nEssentially, we need to pick our poison:\n\nSlow \\sin and \\cos operations with the Cartesian method\nWarp divergence with the Polar method\n\nThe only way to know which is better is to perform benchmarks, which we will show in a bit, but there is one final scenario we should consider: what about doing the rejection sampling as a pre-processing step?\nThis would mean that we pre-initialize the polar kernel with a uniform distribution of points in the unit circle.\nThis means no warp divergence, so we can get the best of both worlds, right?\nWell, not exactly.\nThe polar Box—Muller method will definitely be faster, but again: someone somewhere needed to do rejection sampling and if we include that step into the process, things become complicated again.\nThe truth is that this pre-processing step is difficult to get right, so it might require a chapter in it's own right.\nIn many cases, it's worth spending a little time before-hand to make sure subsequent operations are fast, but in this case, we only have a single operation, not a set of operations.\nThe Box—Muller method will usually only be used once at the start of the simulation, which means that the pre-processing step of rejection sampling might end up being overkill.\nNo matter the case, benchmarks will show the true nature of what we are dealing with here:\n\n\n\nMethod\nCPU\nGPU\n\n\n\n\nCartesian\n385.819 \\pm 1.9ms\n19.347 \\pm 0.618ms\n\n\nPolar without replacement\n273.308 \\pm 2.81ms\n26.712 \\pm 0.592ms\n\n\nPolar with replacement\n433.644 \\pm 2.64ms\nNA\n\n\n\nThese were run with an Nvidia GTX 970 GPU and a Ryzen 3700X 16 core CPU.\nFor those interested, the code can be found below.\nFor these benchmarks, we used Julia's inbuilt benchmarking suite from BenchmarkTools, making sure to sync the GPU kernels with CUDA.@sync.\nWe also ran with 4096^2 input points.\nHere, we see an interesting divergence in the results.\nOn the CPU, the polar method is always faster, but on the GPU, both methods are comparable.\nI believe this is the most important lesson to be learned from the Box—Muller method: sometimes, no matter how hard you try to optimize your code, different hardware can provide radically different results!\nIt's incredibly important to benchmark code to make sure it is actually is as performant as you think it is!\nFull Script\nusing KernelAbstractions\nusing CUDA\n\nif has_cuda_gpu()\n using CUDAKernels\nend\n\nfunction create_grid(n, endpoints; AT = Array)\n\n grid_extents = endpoints[2] - endpoints[1]\n\n # number of points along any given axis\n # For 2D, we take the sqrt(n) and then round up\n axis_num = ceil(Int, sqrt(n))\n\n # we are now rounding n up to the nearest square if it was not already one\n if sqrt(n) != axis_num\n n = axis_num^2\n end \n\n # Distance between each point\n dx = grid_extents / (axis_num)\n\n # This is warning in the case that we do not have a square number\n if sqrt(n) != axis_num\n println(\"Cannot evenly divide \", n, \" into 2 dimensions!\")\n end \n\n # Initializing the array, particles along the column, dimensions along rows\n a = AT(zeros(n, 2))\n\n # This works by firxt generating an N dimensional tuple with the number\n # of particles to be places along each dimension ((10,10) for 2D and n=100)\n # Then we generate the list of all CartesianIndices and cast that onto a\n # grid by multiplying by dx and subtracting grid_extents/2\n for i = 1:axis_num\n for j = 1:axis_num\n a[(i - 1) * axis_num + j, 1] = i * dx + endpoints[1]\n a[(i - 1) * axis_num + j, 2] = j * dx + endpoints[1]\n end\n end\n\n return a\nend\n\nfunction create_rand_dist(n, endpoints; AT = Array)\n grid_extents = endpoints[2] - endpoints[1]\n return(AT(rand(n,2)) * grid_extents .+ endpoints[1]) \nend\n\n# This function reads in a pair of input points and performs the Cartesian\n# Box--Muller transform\n@kernel function polar_muller_noreplacement!(input_pts, output_pts, sigma, mu)\n tid = @index(Global, Linear)\n @inbounds r_0 = input_pts[tid, 1]^2 + input_pts[tid, 2]^2\n\n # this method is only valid for points within the unit circle\n if r_0 == 0 || r_0 > 1\n @inbounds output_pts[tid,1] = NaN\n @inbounds output_pts[tid,2] = NaN\n else\n @inbounds output_pts[tid,1] = sigma * input_pts[tid,1] *\n sqrt(-2 * log(r_0) / r_0) + mu\n @inbounds output_pts[tid,2] = sigma * input_pts[tid, 2] *\n sqrt(-2 * log(r_0) / r_0) + mu\n end\n\nend\n\n@kernel function polar_muller_replacement!(input_pts, output_pts, sigma, mu)\n tid = @index(Global, Linear)\n @inbounds r_0 = input_pts[tid, 1]^2 + input_pts[tid, 2]^2\n\n while r_0 > 1 || r_0 == 0\n p1 = rand()*2-1\n p2 = rand()*2-1\n r_0 = p1^2 + p2^2\n end\n\n @inbounds output_pts[tid,1] = sigma * input_pts[tid,1] *\n sqrt(-2 * log(r_0) / r_0) + mu\n @inbounds output_pts[tid,2] = sigma * input_pts[tid, 2] *\n sqrt(-2 * log(r_0) / r_0) + mu\nend\n\n\nfunction polar_box_muller!(input_pts, output_pts, sigma, mu;\n numthreads = 256, numcores = 4,\n f = polar_muller_noreplacement!)\n if isa(input_pts, Array)\n kernel! = f(CPU(), numcores)\n else\n kernel! = f(CUDADevice(), numthreads)\n end\n kernel!(input_pts, output_pts, sigma, mu, ndrange=size(input_pts)[1])\nend\n\n\n@kernel function cartesian_kernel!(input_pts, output_pts, sigma, mu)\n tid = @index(Global, Linear)\n\n @inbounds r = sqrt(-2 * log(input_pts[tid,1]))\n @inbounds theta = 2 * pi * input_pts[tid, 2]\n\n @inbounds output_pts[tid,1] = sigma * r * cos(theta) + mu\n @inbounds output_pts[tid,2] = sigma * r * sin(theta) + mu\nend\n\nfunction cartesian_box_muller!(input_pts, output_pts, sigma, mu;\n numthreads = 256, numcores = 4)\n if isa(input_pts, Array)\n kernel! = cartesian_kernel!(CPU(), numcores)\n else\n kernel! = cartesian_kernel!(CUDADevice(), numthreads)\n end\n\n kernel!(input_pts, output_pts, sigma, mu, ndrange=size(input_pts)[1])\nend\n\nfunction main()\n\n input_pts = create_rand_dist(4096^2,[0,1])\n output_pts = create_rand_dist(4096^2,[0,1])\n\n wait(cartesian_box_muller!(input_pts, output_pts, 1, 0))\n @time wait(cartesian_box_muller!(input_pts, output_pts, 1, 0))\n wait(polar_box_muller!(input_pts, output_pts, 1, 0))\n @time wait(polar_box_muller!(input_pts, output_pts, 1, 0))\n\n if has_cuda_gpu()\n input_pts = create_rand_dist(4096^2,[0,1], AT = CuArray)\n output_pts = create_rand_dist(4096^2,[0,1], AT = CuArray)\n\n wait(cartesian_box_muller!(input_pts, output_pts, 1, 0))\n CUDA.@time wait(cartesian_box_muller!(input_pts, output_pts, 1, 0))\n wait(polar_box_muller!(input_pts, output_pts, 1, 0))\n CUDA.@time wait(polar_box_muller!(input_pts, output_pts, 1, 0))\n end\n\nend\n\nmain()\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n"},"contents/convolutions/2d/2d.html":{"url":"contents/convolutions/2d/2d.html","title":"Convolutions of Images (2D)","keywords":"","body":"Convolutions on Images\nFor this section, we will no longer be focusing on signals, but instead images (arrays filled with elements of red, green, and blue values).\nThat said, for the code examples, greyscale images may be used such that each array element is composed of some floating-point value instead of color.\nIn addition, we will not be discussing boundary conditions too much in this chapter and will instead be using the simple boundaries introduced in the section on one-dimensional convolutions.\nThe extension of one-dimensional convolutions to two dimensions requires a little thought about indexing and the like, but is ultimately the same operation.\nHere is an animation of a convolution for a two-dimensional image:\n\n\n \nYour browser does not support the video tag.\n\n\n\nIn this case, we convolved the image with a 3x3 square filter, all filled with values of \\frac{1}{9}.\nThis created a simple blurring effect, which is somewhat expected from the discussion in the previous section.\nIn code, a two-dimensional convolution might look like this:\nfunction convolve_linear(signal::Array{T, 2}, filter::Array{T, 2},\n output_size) where {T \ndef convolve_linear(signal, filter, output_size):\n out = np.zeros(output_size)\n sum = 0\n\n for i in range(output_size[0]):\n for j in range(output_size[1]):\n for k in range(max(0, i-filter.shape[0]), i+1):\n for l in range(max(0, j-filter.shape[1]), j+1):\n with suppress(IndexError):\n sum += signal[k, l] * filter[i-k, j-l]\n out[i, j] = sum\n sum = 0\n\n return out\n\n\n\nThis is very similar to what we have shown in previous sections; however, it essentially requires four iterable dimensions because we need to iterate through each axis of the output domain and the filter.\nAt this stage, it is worth highlighting common filters used for convolutions of images.\nIn particular, we will further discuss the Gaussian filter introduced in the previous section, and then introduce another set of kernels known as Sobel operators, which are used for naïve edge detection or image derivatives.\nThe Gaussian kernel\nThe Gaussian kernel serves as an effective blurring operation for images.\nAs a reminder, the formula for any Gaussian distribution is\n\ng(x,y) = \\frac{1}{2\\pi\\sigma^2}e^{-\\frac{x^2+y^2}{2\\sigma^2}},\n\nwhere \\sigma is the standard deviation and is a measure of the width of the Gaussian.\nA larger \\sigma means a larger Gaussian; however, remember that the Gaussian must fit onto the filter, otherwise it will be cut off!\nFor example, if you are using a 3\\times 3 filter, you should not be using \\sigma = 10.\nSome definitions of \\sigma allow users to have a separate deviation in x and y to create an ellipsoid Gaussian, but for the purposes of this chapter, we will assume \\sigma_x = \\sigma_y.\nAs a general rule of thumb, the larger the filter and standard deviation, the more \"smeared\" the final convolution will be.\nAt this stage, it is important to write some code, so we will generate a simple function that returns a Gaussian kernel with a specified standard deviation and filter size.\nfunction create_gaussian_kernel(kernel_size)\n\n kernel = zeros(kernel_size, kernel_size)\n\n # The center must be offset by 0.5 to find the correct index\n center = kernel_size * 0.5 + 0.5\n\n sigma = sqrt(0.1*kernel_size)\n\n for i = 1:kernel_size\n for j = 1:kernel_size\n kernel[i,j] = exp(-((i-center)^2 + (j-center)^2) / (2*sigma^2))\n end\n end\n\n return normalize(kernel)\n\nend\n\ndef create_gaussian_kernel(kernel_size):\n kernel = np.zeros((kernel_size, kernel_size))\n\n # The center must be offset by 0.5 to find the correct index\n center = kernel_size*0.5 + 0.5\n\n sigma = np.sqrt(0.1*kernel_size)\n\n def kernel_function(x, y):\n return np.exp(-((x-center+1)**2 + (y-center+1)**2)/(2*sigma**2))\n\n kernel = np.fromfunction(kernel_function, (kernel_size, kernel_size))\n return kernel / np.linalg.norm(kernel)\n\n\n\nThough it is entirely possible to create a Gaussian kernel whose standard deviation is independent on the kernel size, we have decided to enforce a relation between the two in this chapter.\nAs always, we encourage you to play with the code and create your own Gaussian kernels any way you want!\nAs a note, all the kernels will be scaled (normalized) at the end by the sum of all internal elements.\nThis ensures that the output of the convolution will not have an obnoxious scale factor associated with it.\nBelow are a few images generated by applying a kernel generated with the code above to a black and white image of a circle.\n\n \n\n\n\nIn (a), we show the original image, which is just a white circle at the center of a 50\\times 50 grid.\nIn (b), we show the image after convolution with a 3\\times 3 kernel.\nIn (c), we show the image after convolution with a 20\\times 20 kernel.\nHere, we see that (c) is significantly fuzzier than (b), which is a direct consequence of the kernel size.\nThere is a lot more that we could talk about, but now is a good time to move on to a slightly more complicated convolutional method: the Sobel operator.\nThe Sobel operator\nThe Sobel operator effectively performs a gradient operation on an image by highlighting areas where a large change has been made.\nIn essence, this means that this operation can be thought of as a naïve edge detector.\nEssentially, the n-dimensional Sobel operator is composed of n separate gradient convolutions (one for each dimension) that are then combined together into a final output array.\nAgain, for the purposes of this chapter, we will stick to two dimensions, which will be composed of two separate gradients along the x and y directions.\nEach gradient will be created by convolving our image with their corresponding Sobel operator:\n\n\\begin{align}\nS_x &= \\left(\\begin{bmatrix}\n1 \\\\\n2 \\\\\n1 \\\\\n\\end{bmatrix} \\otimes [1~0~-1]\n\\right) = \\begin{bmatrix}\n1 & 0 & -1 \\\\\n2 & 0 & -2 \\\\\n1 & 0 & -1 \\\\\n\\end{bmatrix}\\\\\n\nS_y &= \\left(\n\\begin{bmatrix}\n1 \\\\\n0 \\\\\n-1 \\\\\n\\end{bmatrix} \\otimes [1~2~1]\n\\right) = \\begin{bmatrix}\n1 & 2 & 1 \\\\\n0 & 0 & 0 \\\\\n-1 & -2 & -1 \\\\\n\\end{bmatrix}.\n\\end{align}\n\nThe gradients can then be found with a convolution, such that:\n\n\\begin{align}\nG_x &= S_x*A \\\\\nG_y &= S_y*A.\n\\end{align}\n\nHere, A is the input array or image.\nFinally, these gradients can be summed in quadrature to find the total Sobel operator or image gradient:\n\nG_{\\text{total}} = \\sqrt{G_x^2 + G_y^2}\n\nSo let us now show what it does in practice:\n\n \n\n\nIn this diagram, we start with the circle image on the right, and then convolve it with the S_x and S_y operators to find the gradients along x and y before summing them in quadrature to get the final image gradient.\nHere, we see that the edges of our input image have been highlighted, showing outline of our circle.\nThis is why the Sobel operator is also known as naïve edge detection and is an integral component to many more sophisticated edge detection methods like one proposed by Canny [1].\nIn code, the Sobel operator involves first finding the operators in x and y and then applying them with a traditional convolution:\nfunction create_sobel_operators()\n Sx = [1.0, 2.0, 1.0]*[-1.0 0.0 1.0] / 9\n Sy = [-1.0, 0.0, 1.0]*[1.0 2.0 1.0] / 9\n\n return Sx, Sy\nend\n\nfunction compute_sobel(signal)\n Sx, Sy = create_sobel_operators()\n\n Gx = convolve_linear(signal, Sx, size(signal) .+ size(Sx))\n Gy = convolve_linear(signal, Sy, size(signal) .+ size(Sy))\n\n return sqrt.(Gx.^2 .+ Gy.^2)\nend\n\ndef create_sobel_operators():\n Sx = np.dot([[1.0], [2.0], [1.0]], [[-1.0, 0.0, 1.0]]) / 9\n Sy = np.dot([[-1.0], [0.0], [1.0]], [[1.0, 2.0, 1.0]]) / 9\n\n return Sx, Sy\n\ndef sum_matrix_dimensions(mat1, mat2):\n return (mat1.shape[0] + mat2.shape[0], \n mat1.shape[1] + mat2.shape[1])\n\ndef compute_sobel(signal):\n Sx, Sy = create_sobel_operators()\n\n Gx = convolve_linear(signal, Sx, sum_matrix_dimensions(signal, Sx))\n Gy = convolve_linear(signal, Sy, sum_matrix_dimensions(signal, Sy))\n\n return np.sqrt(np.power(Gx, 2) + np.power(Gy, 2))\n\n\n\nWith that, I believe we are at a good place to stop discussions on two-dimensional convolutions.\nWe will definitely return to this topic in the future as new algorithms require more information.\nExample Code\nFor the code in this section, we have modified the visualizations from the one-dimensional convolution chapter to add a two-dimensional variant for blurring an image of random white noise.\nWe have also added code to create the Gaussian kernel and Sobel operator and apply it to the circle, as shown in the text.\nusing DelimitedFiles\nusing LinearAlgebra\n\nfunction convolve_linear(signal::Array{T, 2}, filter::Array{T, 2},\n output_size) where {T \nimport numpy as np\nfrom contextlib import suppress\n\n\ndef convolve_linear(signal, filter, output_size):\n out = np.zeros(output_size)\n sum = 0\n\n for i in range(output_size[0]):\n for j in range(output_size[1]):\n for k in range(max(0, i-filter.shape[0]), i+1):\n for l in range(max(0, j-filter.shape[1]), j+1):\n with suppress(IndexError):\n sum += signal[k, l] * filter[i-k, j-l]\n out[i, j] = sum\n sum = 0\n\n return out\n\n\ndef create_gaussian_kernel(kernel_size):\n kernel = np.zeros((kernel_size, kernel_size))\n\n # The center must be offset by 0.5 to find the correct index\n center = kernel_size*0.5 + 0.5\n\n sigma = np.sqrt(0.1*kernel_size)\n\n def kernel_function(x, y):\n return np.exp(-((x-center+1)**2 + (y-center+1)**2)/(2*sigma**2))\n\n kernel = np.fromfunction(kernel_function, (kernel_size, kernel_size))\n return kernel / np.linalg.norm(kernel)\n\n\ndef create_sobel_operators():\n Sx = np.dot([[1.0], [2.0], [1.0]], [[-1.0, 0.0, 1.0]]) / 9\n Sy = np.dot([[-1.0], [0.0], [1.0]], [[1.0, 2.0, 1.0]]) / 9\n\n return Sx, Sy\n\ndef sum_matrix_dimensions(mat1, mat2):\n return (mat1.shape[0] + mat2.shape[0], \n mat1.shape[1] + mat2.shape[1])\n\ndef compute_sobel(signal):\n Sx, Sy = create_sobel_operators()\n\n Gx = convolve_linear(signal, Sx, sum_matrix_dimensions(signal, Sx))\n Gy = convolve_linear(signal, Sy, sum_matrix_dimensions(signal, Sy))\n\n return np.sqrt(np.power(Gx, 2) + np.power(Gy, 2))\n\n\ndef create_circle(image_resolution, grid_extents, radius):\n out = np.zeros((image_resolution, image_resolution))\n\n for i in range(image_resolution):\n x_position = ((i * grid_extents / image_resolution)\n - 0.5 * grid_extents)\n for j in range(image_resolution):\n y_position = ((j * grid_extents / image_resolution)\n - 0.5 * grid_extents)\n if x_position ** 2 + y_position ** 2 \n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nBibliography\n1.Canny, John, A computational approach to edge detection, Ieee, 1986.\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nImages/Graphics\n\nThe image \"8bit Heart\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Circle Blur\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Sobel Filters\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"2D Convolution\" was created by James Schloss and Grant Sanderson and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/cooley_tukey/cooley_tukey.html":{"url":"contents/cooley_tukey/cooley_tukey.html","title":"FFT","keywords":"","body":"What Makes a Fourier Transform Fast?\nIf there were ever an algorithm to radically change the landscape of computer science and engineering by making seemingly impossible problems possible, it would be the Fast Fourier Transform (FFT).\nOn the surface, the algorithm seems like a simple application of recursion, and in principle, that is exactly what it is; however, the Fourier Transform is no ordinary transform -- it allows researchers and engineers to easily bounce back and forth between real space and frequency space and is the heart of many physics and engineering applications.\nFrom calculating superfluid vortex positions to super-resolution imaging, Fourier Transforms lay at the heart of many scientific disciplines and are essential to many algorithms we will cover later in this book.\nSimply put, the Fourier Transform is a beautiful application of complex number systems; however, it would rarely be used today if not for the ability to quickly perform the operation with Fast Fourier Transform, first introduced by the great Frederick Gauss in 1805 and later independently discovered by James Cooley and John Tukey in 1965 [1].\nGauss (of course) already had too many things named after him and Cooley and Tukey both had cooler names, so the most common algorithm for FFTs today is known as the Cooley-Tukey algorithm.\nWhat is a Fourier Transform?\nTo an outsider, the Fourier Transform looks like a mathematical mess -- certainly a far cry from the heroic portal between two domains I have depicted it to be; however, like most things, it's not as bad as it initially appears to be.\nSo, here it is in all it's glory!\nF(\\xi) = \\int_{-\\infty} ^\\infty f(x) e^{-2 \\pi i x \\xi} dx\nand\nf(x) = \\int_{-\\infty} ^\\infty F(\\xi) e^{2 \\pi i \\xi x} d\\xi\nWhere F(\\xi) represents a function in frequency space, \\xi represents a value in frequency space, f(x) represents a function in real space, and x represents a value in the real space.\nNote here that the only difference between the two exponential terms is a minus sign in the transformation to frequency space.\nAs I mentioned, this is not intuitive syntax, so please allow me to explain a bit.\nFirstly, what does the Fourier Transform do?\nIf we take a sum sinusoidal functions (like \\sin(\\omega t) or \\cos(\\omega t)), we might find a complicated mess of waves between \\pm 1.\nEach constituent wave can be described by only one value: \\omega.\nSo, instead of representing these curves as seen above, we could instead describe them as peaks in frequency space, as shown below.\n\n \n\n\nThis is what the Fourier Transform does!\nAfter performing the transform, it is now much, much easier to understand precisely which frequencies are in our waveform, which is essential to most areas of signal processing.\nNow, how does this relate to the transformations above?\nWell, the easiest way is to substitute in the Euler's formula:\ne^{2 \\pi i \\theta} = \\cos(2 \\pi \\theta) + i \\sin(2 \\pi \\theta)\nThis clearly turns our function in frequency space into:\nF(\\xi) = \\int_{-\\infty} ^\\infty f(x) (\\cos(-2 \\pi x \\xi) + i \\sin(-2 \\pi x \\xi))dx\nand our function in real space into:\nf(x) = \\int_{-\\infty} ^\\infty F(\\xi) (\\cos(2 \\pi \\xi x) + i \\sin(2 \\pi \\xi x)) d\\xi\nHere, the \\sin and \\cos functions are clearly written in the formulas, so it looks much friendlier, right?\nThis means that a point in real space is defined by the integral over all space of it's corresponding frequency function multiplied by sinusoidal oscillations.\nTruth be told, even after seeing this math, I still didn't understand Fourier Transforms.\nTruth be told, I didn't understand it fully until I discretized real and frequency space to create the Discrete Fourier Transform (DFT), which is the only way to implement Fourier Transforms in code.\nWhat is a Discrete Fourier Transform?\nIn principle, the Discrete Fourier Transform (DFT) is simply the Fourier transform with summations instead of integrals:\nX_k = \\sum_{n=0}^{N-1} x_n \\cdot e^{-2 \\pi i k n / N}\nand\nx_n = \\frac{1}{N} \\sum_{k=0}^{N-1} X_k \\cdot e^{2 \\pi i k n / N}\nWhere X_n and x_n are sequences of N numbers in frequency and real space, respectively.\nIn principle, this is no easier to understand than the previous case!\nFor some reason, though, putting code to this transformation really helped me figure out what was actually going on.\nfunction DFT(x)\n N = length(x)\n\n # We want two vectors here for real space (n) and frequency space (k)\n n = 0:N-1\n k = n'\n transform_matrix = exp.(-2im*pi*n*k/N)\n return transform_matrix*x\n\nend\n\nvoid dft(double complex *X, const size_t N) {\n double complex tmp[N];\n for (size_t i = 0; i \n(defn dft\n \"take a vector of real numbers and return a vector of frequency\n space\"\n [vx]\n (let [len (count vx)]\n (matrix-mult\n (partition len\n (for [n (range len)\n k (range len)]\n ;; expresion below is\n ;; e^(n*k*2*pi*(1/len)*(-i))\n (c/exp (c/* n k\n 2 Math/PI\n (/ len)\n (c/complex 0 -1)))))\n vx)))\n\ntemplate \nvoid dft(Iter X, Iter last) {\n const auto N = last - X;\n std::vector tmp(N);\n for (auto i = 0; i \ndft :: [Complex Double] -> [Complex Double]\ndft x = matMult dftMat x\n where\n n = length x\n w = exp $ (-2) * pi * (0 :+ 1) / fromIntegral n\n dftMat = [[w ^ (j * k) | j \ndef dft(X):\n N = len(X)\n temp = [0] * N\n for i in range(N):\n for k in range(N):\n temp[i] += X[k] * exp(-2.0j * pi * i * k / N)\n return temp\n\n# rdi - array ptr\n# rsi - array size\ndft:\n push rbx\n push r12\n push r13\n push r14\n push r15\n mov r12, rdi # Save parameters\n mov r13, rsi\n sub rsp, r13 # Make a double complex array\n xor r14, r14 # Set index to 0\ndft_loop_i:\n cmp r14, r13 # Check if index is equal to array size\n je dft_end_i\n lea rax, [rsp + r14] # Set tmp array to zero at r14\n mov QWORD PTR [rax], 0\n mov QWORD PTR [rax + 8], 0\n xor r15, r15 # Set second index to 0\ndft_loop_j:\n cmp r15, r13 # Check if the index is equal to array size\n je dft_end_j\n movsd xmm1, two_pi # Calculate xmm1 = -2pi * i * j / N\n mov rax, r14\n imul rax, r15\n shr rax, 4\n cvtsi2sdq xmm2, rax\n mulsd xmm1, xmm2\n cvtsi2sdq xmm2, r13\n divsd xmm1, xmm2\n pxor xmm0, xmm0 # Set xmm0 to 0\n call cexp\n lea rax, [r12 + r15] # Calculate X[i] * cexp(-2pi * i * j / N)\n movsd xmm2, QWORD PTR [rax]\n movsd xmm3, QWORD PTR [rax + 8]\n call __muldc3\n lea rax, [rsp + r14]\n movsd xmm6, QWORD PTR [rax] # Sum to tmp array\n movsd xmm7, QWORD PTR [rax + 8]\n addsd xmm6, xmm0\n addsd xmm7, xmm1\n movsd QWORD PTR [rax], xmm6 # Save to tmp array\n movsd QWORD PTR [rax + 8], xmm7\n add r15, 16\n jmp dft_loop_j\ndft_end_j:\n add r14, 16\n jmp dft_loop_i\ndft_end_i:\n mov rdi, r12 # Move tmp array to array ptr\n mov rsi, rsp\n mov rdx, r13\n call memcpy\n add rsp, r13\n pop r15\n pop r14\n pop r13\n pop r12\n pop rbx\n ret\n\nfunction dft(x) {\n const N = x.length;\n\n // Initialize an array with N elements, filled with 0s\n return Array(N)\n .fill(new Complex(0, 0))\n .map((temp, i) => {\n // Reduce x into the sum of x_k * exp(-2*sqrt(-1)*pi*i*k/N)\n return x.reduce((a, b, k) => {\n return a.add(b.mul(new Complex(0, (-2 * Math.PI * i * k) / N).exp()));\n }, new Complex(0, 0)); // Start accumulating from 0\n });\n}\n\nfn dft(x: &[Complex]) -> Vec> {\n let n = x.len();\n (0..n)\n .map(|i| {\n (0..n)\n .map(|k| {\n x[k] * (Complex::new(0.0_f64, -2.0_f64) * PI * (i as f64) * (k as f64)\n / (n as f64))\n .exp()\n })\n .sum()\n })\n .collect()\n}\n\n(defun coefficient (time-index freq-index dft-len)\n \"Calculates a single twiddle factor for the Fourier Transform.\"\n (exp (- (/ (* #c(0 1) 2.0 pi time-index freq-index)\n dft-len))))\n\n(defun dft (data)\n \"Performs the Discrete Fourier Transform\"\n (let ((dft-len (length data)))\n (loop for freq-index from 0 below dft-len collect\n (loop for time-index from 0 below dft-len sum\n (* (coefficient time-index freq-index dft-len) (elt data time-index))))))\n\n\n\nIn this function, we define n to be a set of integers from 0 \\rightarrow N-1 and arrange them to be a column.\nWe then set k to be the same thing, but in a row.\nThis means that when we multiply them together, we get a matrix, but not just any matrix!\nThis matrix is the heart to the transformation itself!\nM = [1.0+0.0im 1.0+0.0im 1.0+0.0im 1.0+0.0im;\n 1.0+0.0im 6.12323e-17-1.0im -1.0-1.22465e-16im -1.83697e-16+1.0im;\n 1.0+0.0im -1.0-1.22465e-16im 1.0+2.44929e-16im -1.0-3.67394e-16im;\n 1.0+0.0im -1.83697e-16+1.0im -1.0-3.67394e-16im 5.51091e-16-1.0im]\nIt was amazing to me when I saw the transform for what it truly was: an actual transformation matrix!\nThat said, the Discrete Fourier Transform is slow -- primarily because matrix multiplication is slow, and as mentioned before, slow code is not particularly useful.\nSo what was the trick that everyone used to go from a Discrete Fourier Transform to a Fast Fourier Transform?\nRecursion!\nThe Cooley-Tukey Algorithm\nThe problem with using a standard DFT is that it requires a large matrix multiplications and sums over all elements, which are prohibitively complex operations.\nThe Cooley-Tukey algorithm calculates the DFT directly with fewer summations and without matrix multiplications.\nIf necessary, DFTs can still be calculated directly at the early stages of the FFT calculation.\nThe trick to the Cooley-Tukey algorithm is recursion.\nIn particular, we split the matrix we wish to perform the FFT on into two parts: one for all elements with even indices and another for all odd indices.\nWe then proceed to split the array again and again until we have a manageable array size to perform a DFT (or similar FFT) on.\nWe can also perform a similar re-ordering by using a bit reversal scheme, where we output each array index's integer value in binary and flip it to find the new location of that element.\nWith recursion, we can reduce the complexity to \\sim \\mathcal{O}(n \\log n), which is a feasible operation.\nIn the end, the code looks like:\nfunction cooley_tukey(x)\n N = length(x)\n\n if (N > 2)\n x_odd = cooley_tukey(x[1:2:N])\n x_even = cooley_tukey(x[2:2:N])\n else\n x_odd = x[1]\n x_even = x[2]\n end\n n = 0:N-1\n half = div(N,2)\n factor = exp.(-2im*pi*n/N)\n return vcat(x_odd .+ x_even .* factor[1:half],\n x_odd .- x_even .* factor[1:half])\n\nend\n\nvoid cooley_tukey(double complex *X, const size_t N) {\n if (N >= 2) {\n double complex tmp [N / 2];\n for (size_t i = 0; i \n(defn fft [vx]\n (let [len (count vx)]\n (if (= len 1)\n vx\n ;;else\n (let [;; take values of vx in the even indices\n even-indices (keep-indexed #(if (even? %1) %2) vx)\n ;; take values in the odd indices\n odd-indices (keep-indexed #(if (odd? %1) %2) vx)\n ;; recursion\n even-fft (fft even-indices)\n odd-fft (fft odd-indices)\n ;; make a sequence of e^(-2pi*i*k/N) where N is the length\n ;; vx and k range from 0 to N/2\n omegas-half (map\n (comp c/exp\n (partial c/*\n (/ len)\n 2 Math/PI\n (c/complex 0 -1)))\n (range 0 (quot len 2)))\n ;; take the negative of the first sequence because\n ;; e^(-2pi*i*(k+N/2)/N=-e^(-2pi*i*k/N) where k ranges from\n ;; 0 to N/2 \n omegas-2half (map c/- omegas-half)\n mult-add (partial map #(c/+ %3 (c/* %1 %2)))]\n (concat (mult-add omegas-half odd-fft even-fft)\n (mult-add omegas-2half odd-fft even-fft))))))\n\ntemplate \nvoid cooley_tukey(Iter first, Iter last) {\n auto size = last - first;\n if (size >= 2) {\n // split the range, with even indices going in the first half,\n // and odd indices going in the last half.\n auto temp = std::vector(size / 2);\n for (int i = 0; i (size)));\n\n auto& bottom = first[k];\n auto& top = first[k + size / 2];\n top = bottom - w * top;\n bottom -= top - bottom;\n }\n }\n}\n\nfft :: [Complex Double] -> [Complex Double]\nfft x = fft' x\n where\n n = length x\n w0 = exp ((-2) * pi * (0 :+ 1) / fromIntegral n)\n w = M.fromList [(k % n, w0 ^ k) | k e + o * w ! (k %n)) e o [0 ..]\n x2 = zipWith3 (\\e o k -> e - o * w ! (k %n)) e o [0 ..]\n in x1 ++ x2\n\ndef cooley_tukey(X):\n N = len(X)\n if N \n# rdi - array ptr\n# rsi - array size\ncooley_tukey:\n cmp rsi, 16 # Check if size if greater then 1\n jle cooley_tukey_return\n push rbx\n push r12\n push r13\n push r14\n push r15\n mov r12, rdi # Save parameters\n mov r13, rsi\n mov r14, rsi # Save N / 2\n shr r14, 1\n sub rsp, r14 # Make a tmp array\n xor r15, r15\n mov rbx, r12\ncooley_tukey_spliting:\n cmp r15, r14\n je cooley_tukey_split\n lea rax, [r12 + 2 * r15] # Moving all odd entries to the front of the array\n movaps xmm0, XMMWORD PTR [rax + 16]\n movaps xmm1, XMMWORD PTR [rax]\n movaps XMMWORD PTR [rsp + r15], xmm0\n movaps XMMWORD PTR [rbx], xmm1\n add rbx, 16\n add r15, 16\n jmp cooley_tukey_spliting\ncooley_tukey_split:\n mov rax, rsp\n lea rdi, [r12 + r13]\ncooley_tukey_mov_data:\n cmp rbx, rdi\n je cooley_tukey_moved\n movaps xmm0, XMMWORD PTR [rax]\n movaps XMMWORD PTR [rbx], xmm0\n add rbx, 16\n add rax, 16\n jmp cooley_tukey_mov_data\ncooley_tukey_moved:\n add rsp, r14\n mov rdi, r12 # Makking a recursive call\n mov rsi, r14\n call cooley_tukey\n lea rdi, [r12 + r14] # Makking a recursive call\n mov rsi, r14\n call cooley_tukey\n lea rbx, [r12 + r14]\n mov r14, rbx\n mov r15, r12\ncooley_tukey_loop:\n cmp r15, rbx\n je cooley_tukey_end\n pxor xmm0, xmm0 # Calculate cexp(-2.0 * I * M_PI * i / N)\n movsd xmm1, two_pi\n mov rax, r14\n sub rax, rbx\n cvtsi2sdq xmm2, rax\n cvtsi2sdq xmm3, r13\n divsd xmm2, xmm3\n mulsd xmm1, xmm2\n call cexp\n movq xmm2, QWORD PTR [r14] # Calculating X[i] - cexp() * X[i + N / 2]\n movq xmm3, QWORD PTR [r14 + 8]\n call __muldc3\n movq xmm2, QWORD PTR [r15]\n movq xmm3, QWORD PTR [r15 + 8]\n subsd xmm2, xmm0\n subsd xmm3, xmm1\n movq QWORD PTR [r14], xmm2 # Save value in X[i + N / 2]\n movq QWORD PTR [r14 + 8], xmm3\n movq xmm0, QWORD PTR [r15] # Calculating X[i] -= X[i + N / 2] - X[i]\n movq xmm1, QWORD PTR [r15 + 8]\n subsd xmm2, xmm0\n subsd xmm3, xmm1\n subsd xmm0, xmm2\n subsd xmm1, xmm3\n movq QWORD PTR [r15], xmm0\n movq QWORD PTR [r15 + 8], xmm1\n add r14, 16\n add r15, 16\n jmp cooley_tukey_loop\ncooley_tukey_end:\n pop r15\n pop r14\n pop r13\n pop r12\n pop rbx\ncooley_tukey_return:\n ret\n\nfunction cooley_tukey(x) {\n const N = x.length;\n const half = Math.floor(N / 2);\n if (N !(idx % 2)));\n const odds = cooley_tukey(x.filter((_, idx) => idx % 2));\n\n // Fill an array with null values\n let temp = Array(N).fill(null);\n\n for (let i = 0; i \nfn cooley_tukey(x: &[Complex]) -> Vec> {\n let n = x.len();\n if n >());\n let odd = cooley_tukey(&x.iter().skip(1).step_by(2).cloned().collect::>());\n\n let mut temp = vec![Complex::new(0.0_f64, 0.0_f64); n];\n for k in 0..(n / 2) {\n temp[k] = even[k]\n + (Complex::new(0.0_f64, -2.0_f64) * PI * (k as f64) / (n as f64)).exp() * odd[k];\n temp[k + n / 2] = even[k]\n - (Complex::new(0.0_f64, -2.0_f64) * PI * (k as f64) / (n as f64)).exp() * odd[k];\n }\n temp\n}\n\n(defun merge-sub-ffts (evens odds)\n \"Combines the FFTs of the even and odd indices.\"\n (let* ((fft-length (+ (length evens) (length odds)))\n ;; Calculate coefficients for the odd indices.\n (twiddle-factors (loop for i from 0 below (length odds)\n collect (coefficient 1.0 i fft-length)))\n ;; Multiply values with coefficients.\n (odd-terms (mapcar #'* odds twiddle-factors)))\n ;; Combine the two FFTs.\n (concatenate 'list \n (mapcar #'+ evens odd-terms)\n (mapcar #'- evens odd-terms))))\n\n(defun cooley-tukey-rec (data)\n \"Performs the Fourier Transform using the recursive Cooley-Tukey method.\"\n (if (\n\n\nAs a side note, we are enforcing that the array must be a power of 2 for the operation to work.\nThis is a limitation of the fact that we are using recursion and dividing the array in 2 every time; however, if your array is not a power of 2, you can simply pad the leftover space with 0's until your array is a power of 2.\nThe above method is a perfectly valid FFT; however, it is missing the pictorial heart and soul of the Cooley-Tukey algorithm: Butterfly Diagrams.\nButterfly Diagrams\nButterfly Diagrams show where each element in the array goes before, during, and after the FFT.\nAs mentioned, the FFT must perform a DFT.\nThis means that even though we need to be careful about how we add elements together, we are still ultimately performing the following operation:\nX_k = \\sum_{n=0}^{N-1} x_n \\cdot e^{-2 \\pi i k n / N}\nHowever, after shuffling the initial array (by bit reversing or recursive subdivision), we perform the matrix multiplication of the e^{-2 \\pi k n / N} terms in pieces.\nBasically, we split the array into a series of omega values:\n\\omega_N^k = e^{-2 \\pi i k / N}\nAnd at each step, we use the appropriate term.\nFor example, imagine we need to perform an FFT of an array of only 2 elements.\nWe can represent this addition with the following (radix-2) butterfly:\n\n \n\n\nHere, the diagram means the following:\n\nb_0 = a_0 + \\omega_2^0 a_1 \\\\\n\nb_1 = a_0 + \\omega_2^1 a_1\n\nHowever, it turns out that the second half of our array of \\omega values is always the negative of the first half, so \\omega_2^0 = -\\omega_2^1, so we can use the following butterfly diagram:\n\n \n\n\nWith the following equations:\n\nb_0 = a_0 + \\omega_2^0 a_1 \\\\\n\nb_1 = a_0 - \\omega_2^0 a_1\n\nBy swapping out the second \\omega value in this way, we can save a good amount of space.\nNow imagine we need to combine more elements.\nIn this case, we start with simple butterflies, as shown above, and then sum butterflies of butterflies.\nFor example, if we have 8 elements, this might look like this:\n\n \n\n\nNote that we can perform a DFT directly before using any butterflies, if we so desire, but we need to be careful with how we shuffle our array if that's the case.\nIn the code snippet provided in the previous section, the subdivision was performed in the same function as the concatenation, so the ordering was always correct; however, if we were to re-order with bit-reversal, this might not be the case.\nFor example, take a look at the ordering of FFT (found on wikipedia) that performs the DFT shortcut:\n\n \n\n\nHere, the ordering of the array was simply divided into even and odd elements once, but they did not recursively divide the arrays of even and odd elements again because they knew they would perform a DFT soon thereafter.\nUltimately, that's all I want to say about Fourier Transforms for now, but this chapter still needs a good amount of work!\nI'll definitely come back to this at some point, so let me know what you liked and didn't like and we can go from there!\nBibliography\n1.Cooley, James W and Tukey, John W, An algorithm for the machine calculation of complex Fourier series, JSTOR, 1965.\nExample Code\nTo be clear, the example code this time will be complicated and requires the following functions:\n\nAn FFT library (either in-built or something like FFTW)\nAn approximation function to tell if two arrays are similar\n\nAs mentioned in the text, the Cooley-Tukey algorithm may be implemented either recursively or non-recursively, with the recursive method being much easier to implement.\nI would ask that you implement either the recursive or non-recursive methods (or both, if you feel so inclined).\nIf the language you want to write your implementation in is already used, please append your code to the already existing codebase.\nAs before, pull requests are favored.\nNote: I implemented this in Julia because the code seems more straightforward in Julia; however, if you wish to write better Julia code or better code in your own language, please feel free to do so!\nI do not claim that this is the most efficient way to implement the Cooley-Tukey method, so if you have a better way to do it, feel free to implement it that way!\nusing FFTW\n\n#simple DFT function\nfunction DFT(x)\n N = length(x)\n\n # We want two vectors here for real space (n) and frequency space (k)\n n = 0:N-1\n k = n'\n transform_matrix = exp.(-2im*pi*n*k/N)\n return transform_matrix*x\n\nend\n\n# Implementing the Cooley-Tukey Algorithm\nfunction cooley_tukey(x)\n N = length(x)\n\n if (N > 2)\n x_odd = cooley_tukey(x[1:2:N])\n x_even = cooley_tukey(x[2:2:N])\n else\n x_odd = x[1]\n x_even = x[2]\n end\n n = 0:N-1\n half = div(N,2)\n factor = exp.(-2im*pi*n/N)\n return vcat(x_odd .+ x_even .* factor[1:half],\n x_odd .- x_even .* factor[1:half])\n\nend\n\nfunction bitreverse(a::Array)\n # First, we need to find the necessary number of bits\n digits = convert(Int,ceil(log2(length(a))))\n\n indices = [i for i = 0:length(a)-1]\n\n bit_indices = []\n for i = 1:length(indices)\n push!(bit_indices, bitstring(indices[i]))\n end\n\n # Now stripping the unnecessary numbers\n for i = 1:length(bit_indices)\n bit_indices[i] = bit_indices[i][end-digits:end]\n end\n\n # Flipping the bits\n for i =1:length(bit_indices)\n bit_indices[i] = reverse(bit_indices[i])\n end\n\n # Replacing indices\n for i = 1:length(indices)\n indices[i] = 0\n for j = 1:digits\n indices[i] += 2^(j-1) * parse(Int, string(bit_indices[i][end-j]))\n end\n indices[i] += 1\n end\n\n b = [float(i) for i = 1:length(a)]\n for i = 1:length(indices)\n b[i] = a[indices[i]]\n end\n\n return b\nend\n\nfunction iterative_cooley_tukey(x)\n N = length(x)\n logN = convert(Int,ceil(log2(length(x))))\n bnum = div(N,2)\n stride = 0;\n\n x = bitreverse(x)\n\n z = [Complex(x[i]) for i = 1:length(x)]\n for i = 1:logN\n stride = div(N, bnum)\n for j = 0:bnum-1\n start_index = j*stride + 1\n y = butterfly(z[start_index:start_index + stride - 1])\n for k = 1:length(y)\n z[start_index+k-1] = y[k]\n end\n end\n bnum = div(bnum,2)\n end\n\n return z\nend\n\nfunction butterfly(x)\n N = length(x)\n half = div(N,2)\n n = [i for i = 0:N-1]\n half = div(N,2)\n factor = exp.(-2im*pi*n/N)\n\n y = [0 + 0.0im for i = 1:length(x)]\n\n for i = 1:half\n y[i] = x[i] + x[half+i]*factor[i]\n y[half+i] = x[i] - x[half+i]*factor[i]\n end\n\n return y\nend\n\nfunction main()\n x = rand(128)\n y = cooley_tukey(x)\n z = iterative_cooley_tukey(x)\n w = fft(x)\n if(isapprox(y, w))\n println(\"Recursive Cooley Tukey matches fft() from FFTW package.\")\n end\n if(isapprox(z, w))\n println(\"Iterative Cooley Tukey matches fft() from FFTW package.\")\n end\nend\n\nmain()\n\n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nvoid fft(double complex *x, size_t n) {\n double complex y[n];\n memset(y, 0, sizeof(y));\n fftw_plan p;\n\n p = fftw_plan_dft_1d((int)n, (fftw_complex*)x, (fftw_complex*)y,\n FFTW_FORWARD, FFTW_ESTIMATE);\n\n fftw_execute(p);\n fftw_destroy_plan(p);\n\n for (size_t i = 0; i = 2) {\n double complex tmp [N / 2];\n for (size_t i = 0; i >= 1;\n while (n > 0) {\n a = (a >= 1;\n }\n n = (a i) {\n double complex tmp = X[i];\n X[i] = X[n];\n X[n] = tmp;\n }\n }\n}\n\nvoid iterative_cooley_tukey(double complex *X, size_t N) {\n bit_reverse(X, N);\n\n for (int i = 1; i 1E-5) {\n printf(\"This is not approximate.\\n\");\n return;\n }\n }\n printf(\"This is approximate.\\n\");\n}\n\nint main() {\n srand((unsigned int)time(NULL));\n double complex x[64], y[64], z[64];\n for (size_t i = 0; i \n(ns fft.core\n (:require [complex.core :as c]))\n;; complex is a jar for complex numbers\n;; https://github.com/alanforr/complex\n;; add [complex \"0.1.11\"] to :dependencies in your project.clj\n;; and run lein repl or lein deps in the terminal\n(defn matrix-mult\n \"take a matrix m and a vector v which length is number of columns\n ,return a vector of applying dot-product between v and each row of\n m. the returned vector's length is the number of rows of m\"\n [m v]\n (mapv (comp (partial apply c/+)\n (partial map c/* v))\n m))\n(defn dft\n \"take a vector of real numbers and return a vector of frequency\n space\"\n [vx]\n (let [len (count vx)]\n (matrix-mult\n (partition len\n (for [n (range len)\n k (range len)]\n ;; expresion below is\n ;; e^(n*k*2*pi*(1/len)*(-i))\n (c/exp (c/* n k\n 2 Math/PI\n (/ len)\n (c/complex 0 -1)))))\n vx)))\n(defn fft [vx]\n (let [len (count vx)]\n (if (= len 1)\n vx\n ;;else\n (let [;; take values of vx in the even indices\n even-indices (keep-indexed #(if (even? %1) %2) vx)\n ;; take values in the odd indices\n odd-indices (keep-indexed #(if (odd? %1) %2) vx)\n ;; recursion\n even-fft (fft even-indices)\n odd-fft (fft odd-indices)\n ;; make a sequence of e^(-2pi*i*k/N) where N is the length\n ;; vx and k range from 0 to N/2\n omegas-half (map\n (comp c/exp\n (partial c/*\n (/ len)\n 2 Math/PI\n (c/complex 0 -1)))\n (range 0 (quot len 2)))\n ;; take the negative of the first sequence because\n ;; e^(-2pi*i*(k+N/2)/N=-e^(-2pi*i*k/N) where k ranges from\n ;; 0 to N/2 \n omegas-2half (map c/- omegas-half)\n mult-add (partial map #(c/+ %3 (c/* %1 %2)))]\n (concat (mult-add omegas-half odd-fft even-fft)\n (mult-add omegas-2half odd-fft even-fft))))))\n(defn -main [& args]\n (let [vx [0 1 2 3]\n len (count vx)\n ;; calculate the next power of 2 after len\n ;; the reason behind this is to fill them with zeros for fft\n next-len (->>\n [len 2]\n (map #(Math/log %))\n (apply /)\n Math/ceil\n (Math/pow 2)\n int)\n ;; add zeros at the end of vx\n complete-vx (into vx (repeat (- next-len len) 0))\n fft-cvx (fft complete-vx)\n dft-cvx (dft complete-vx)\n diffv (mapv c/- fft-cvx dft-cvx)]\n (println \"vx:\" vx)\n (println \"complete-vx:\" complete-vx)\n (println \"result from fft:\" (map c/stringify fft-cvx))\n (println \"result from dft:\" (map c/stringify dft-cvx))\n (println \"difference: \" (map c/stringify diffv))))\n\n// written by Gathros, modernized by Nicole Mazzuca.\n\n#include \n#include \n#include \n#include \n#include \n\n// These headers are for presentation not for the algorithm.\n#include \n#include \n#include \n\nusing std::begin;\nusing std::end;\nusing std::swap;\n\nusing std::size_t;\n\nusing complex = std::complex;\nstatic const double pi = 3.14159265358979323846264338327950288419716;\n\ntemplate \nvoid dft(Iter X, Iter last) {\n const auto N = last - X;\n std::vector tmp(N);\n for (auto i = 0; i \nvoid cooley_tukey(Iter first, Iter last) {\n auto size = last - first;\n if (size >= 2) {\n // split the range, with even indices going in the first half,\n // and odd indices going in the last half.\n auto temp = std::vector(size / 2);\n for (int i = 0; i (size)));\n\n auto& bottom = first[k];\n auto& top = first[k + size / 2];\n top = bottom - w * top;\n bottom -= top - bottom;\n }\n }\n}\n\n// note: (last - first) must be less than 2**32 - 1\ntemplate \nvoid sort_by_bit_reverse(Iter first, Iter last) {\n // sorts the range [first, last) in bit-reversed order,\n // by the method suggested by the FFT\n auto size = last - first;\n\n for (std::uint32_t i = 0; i > 1) | ((b & 0x55555555) > 2) | ((b & 0x33333333) > 4) | ((b & 0x0f0f0f0f) > 8) | ((b & 0x00ff00ff) > 16) | (b > (32 - std::uint32_t(log2(static_cast(size))));\n if (b > i) {\n swap(first[b], first[i]);\n }\n }\n}\n\n// `iterative_cooley_tukey` does the cooley-tukey algorithm iteratively\ntemplate \nvoid iterative_cooley_tukey(Iter first, Iter last) {\n sort_by_bit_reverse(first, last);\n\n // perform the butterfly on the range\n auto size = last - first;\n for (int stride = 2; stride distribution(0.0, 1.0);\n\n std::array initial;\n std::generate(\n begin(initial), end(initial), [&] { return distribution(rng); });\n\n auto recursive = initial;\n auto iterative = initial;\n\n // Preform an FFT on the arrays.\n cooley_tukey(begin(recursive), end(recursive));\n iterative_cooley_tukey(begin(iterative), end(iterative));\n\n // Check if the arrays are approximately equivalent\n std::cout \nimport Data.Complex\nimport Data.List (partition)\nimport Data.Map ((!))\nimport qualified Data.Map as M\nimport Data.Ratio\n\ndft :: [Complex Double] -> [Complex Double]\ndft x = matMult dftMat x\n where\n n = length x\n w = exp $ (-2) * pi * (0 :+ 1) / fromIntegral n\n dftMat = [[w ^ (j * k) | j [Complex Double]\nfft x = fft' x\n where\n n = length x\n w0 = exp ((-2) * pi * (0 :+ 1) / fromIntegral n)\n w = M.fromList [(k % n, w0 ^ k) | k e + o * w ! (k %n)) e o [0 ..]\n x2 = zipWith3 (\\e o k -> e - o * w ! (k %n)) e o [0 ..]\n in x1 ++ x2\n\nmain = do\n print $ dft [0, 1, 2, 3]\n print $ fft [0, 1, 2, 3]\n\nfrom random import random\nfrom cmath import exp, pi\nfrom math import log2\n\n\ndef dft(X):\n N = len(X)\n temp = [0] * N\n for i in range(N):\n for k in range(N):\n temp[i] += X[k] * exp(-2.0j * pi * i * k / N)\n return temp\n\n\ndef cooley_tukey(X):\n N = len(X)\n if N > i & 1)\n temp[k] = X[b]\n temp[b] = X[k]\n return temp\n\n\ndef iterative_cooley_tukey(X):\n N = len(X)\n\n X = bit_reverse(X)\n\n for i in range(1, int(log2(N)) + 1):\n stride = 2 ** i\n w = exp(-2.0j * pi / stride)\n for j in range(0, N, stride):\n v = 1\n for k in range(stride // 2):\n X[k + j + stride // 2] = X[k + j] - v * X[k + j + stride // 2]\n X[k + j] -= X[k + j + stride // 2] - X[k + j]\n v *= w\n return X\n\n\nX = []\n\nfor i in range(64):\n X.append(random())\n\nY = cooley_tukey(X)\nZ = iterative_cooley_tukey(X)\nT = dft(X)\n\nprint(all(abs([Y[i] - Z[i] for i in range(64)][j]) \n.intel_syntax noprefix\n\n.section .rodata\n two: .double 2.0\n one: .double 1.0\n two_pi: .double -6.28318530718\n rand_max: .long 4290772992\n .long 1105199103\n fmt: .string \"%g\\n\"\n\n.section .text\n .global main\n .extern printf, memset, memcpy, srand, rand, time, cexp, __muldc3, cabs, log2\n\n# rdi - array ptr\n# rsi - array size\ndft:\n push rbx\n push r12\n push r13\n push r14\n push r15\n mov r12, rdi # Save parameters\n mov r13, rsi\n sub rsp, r13 # Make a double complex array\n xor r14, r14 # Set index to 0\ndft_loop_i:\n cmp r14, r13 # Check if index is equal to array size\n je dft_end_i\n lea rax, [rsp + r14] # Set tmp array to zero at r14\n mov QWORD PTR [rax], 0\n mov QWORD PTR [rax + 8], 0\n xor r15, r15 # Set second index to 0\ndft_loop_j:\n cmp r15, r13 # Check if the index is equal to array size\n je dft_end_j\n movsd xmm1, two_pi # Calculate xmm1 = -2pi * i * j / N\n mov rax, r14\n imul rax, r15\n shr rax, 4\n cvtsi2sdq xmm2, rax\n mulsd xmm1, xmm2\n cvtsi2sdq xmm2, r13\n divsd xmm1, xmm2\n pxor xmm0, xmm0 # Set xmm0 to 0\n call cexp\n lea rax, [r12 + r15] # Calculate X[i] * cexp(-2pi * i * j / N)\n movsd xmm2, QWORD PTR [rax]\n movsd xmm3, QWORD PTR [rax + 8]\n call __muldc3\n lea rax, [rsp + r14]\n movsd xmm6, QWORD PTR [rax] # Sum to tmp array\n movsd xmm7, QWORD PTR [rax + 8]\n addsd xmm6, xmm0\n addsd xmm7, xmm1\n movsd QWORD PTR [rax], xmm6 # Save to tmp array\n movsd QWORD PTR [rax + 8], xmm7\n add r15, 16\n jmp dft_loop_j\ndft_end_j:\n add r14, 16\n jmp dft_loop_i\ndft_end_i:\n mov rdi, r12 # Move tmp array to array ptr\n mov rsi, rsp\n mov rdx, r13\n call memcpy\n add rsp, r13\n pop r15\n pop r14\n pop r13\n pop r12\n pop rbx\n ret\n\n# rdi - array ptr\n# rsi - array size\ncooley_tukey:\n cmp rsi, 16 # Check if size if greater then 1\n jle cooley_tukey_return\n push rbx\n push r12\n push r13\n push r14\n push r15\n mov r12, rdi # Save parameters\n mov r13, rsi\n mov r14, rsi # Save N / 2\n shr r14, 1\n sub rsp, r14 # Make a tmp array\n xor r15, r15\n mov rbx, r12\ncooley_tukey_spliting:\n cmp r15, r14\n je cooley_tukey_split\n lea rax, [r12 + 2 * r15] # Moving all odd entries to the front of the array\n movaps xmm0, XMMWORD PTR [rax + 16]\n movaps xmm1, XMMWORD PTR [rax]\n movaps XMMWORD PTR [rsp + r15], xmm0\n movaps XMMWORD PTR [rbx], xmm1\n add rbx, 16\n add r15, 16\n jmp cooley_tukey_spliting\ncooley_tukey_split:\n mov rax, rsp\n lea rdi, [r12 + r13]\ncooley_tukey_mov_data:\n cmp rbx, rdi\n je cooley_tukey_moved\n movaps xmm0, XMMWORD PTR [rax]\n movaps XMMWORD PTR [rbx], xmm0\n add rbx, 16\n add rax, 16\n jmp cooley_tukey_mov_data\ncooley_tukey_moved:\n add rsp, r14\n mov rdi, r12 # Makking a recursive call\n mov rsi, r14\n call cooley_tukey\n lea rdi, [r12 + r14] # Makking a recursive call\n mov rsi, r14\n call cooley_tukey\n lea rbx, [r12 + r14]\n mov r14, rbx\n mov r15, r12\ncooley_tukey_loop:\n cmp r15, rbx\n je cooley_tukey_end\n pxor xmm0, xmm0 # Calculate cexp(-2.0 * I * M_PI * i / N)\n movsd xmm1, two_pi\n mov rax, r14\n sub rax, rbx\n cvtsi2sdq xmm2, rax\n cvtsi2sdq xmm3, r13\n divsd xmm2, xmm3\n mulsd xmm1, xmm2\n call cexp\n movq xmm2, QWORD PTR [r14] # Calculating X[i] - cexp() * X[i + N / 2]\n movq xmm3, QWORD PTR [r14 + 8]\n call __muldc3\n movq xmm2, QWORD PTR [r15]\n movq xmm3, QWORD PTR [r15 + 8]\n subsd xmm2, xmm0\n subsd xmm3, xmm1\n movq QWORD PTR [r14], xmm2 # Save value in X[i + N / 2]\n movq QWORD PTR [r14 + 8], xmm3\n movq xmm0, QWORD PTR [r15] # Calculating X[i] -= X[i + N / 2] - X[i]\n movq xmm1, QWORD PTR [r15 + 8]\n subsd xmm2, xmm0\n subsd xmm3, xmm1\n subsd xmm0, xmm2\n subsd xmm1, xmm3\n movq QWORD PTR [r15], xmm0\n movq QWORD PTR [r15 + 8], xmm1\n add r14, 16\n add r15, 16\n jmp cooley_tukey_loop\ncooley_tukey_end:\n pop r15\n pop r14\n pop r13\n pop r12\n pop rbx\ncooley_tukey_return:\n ret\n\n# rdi - array ptr\n# rsi - array size\nbit_reverse:\n push rbx\n push r12\n push r13\n push r14\n push r15\n mov r12, rdi # Save parameters\n mov r13, rsi\n shr r13, 4\n xor r14, r14 # Loop through all entries\nbit_reverse_entries:\n cmp r14, r13\n je bit_reverse_return\n cvtsi2sdq xmm0, r13 # Calculating the number of bit in N\n call log2\n cvttsd2si rcx, xmm0\n mov rdi, 1 # Calculating (1 \nconst Complex = require(\"complex.js\");\n\nfunction dft(x) {\n const N = x.length;\n\n // Initialize an array with N elements, filled with 0s\n return Array(N)\n .fill(new Complex(0, 0))\n .map((temp, i) => {\n // Reduce x into the sum of x_k * exp(-2*sqrt(-1)*pi*i*k/N)\n return x.reduce((a, b, k) => {\n return a.add(b.mul(new Complex(0, (-2 * Math.PI * i * k) / N).exp()));\n }, new Complex(0, 0)); // Start accumulating from 0\n });\n}\n\nfunction cooley_tukey(x) {\n const N = x.length;\n const half = Math.floor(N / 2);\n if (N !(idx % 2)));\n const odds = cooley_tukey(x.filter((_, idx) => idx % 2));\n\n // Fill an array with null values\n let temp = Array(N).fill(null);\n\n for (let i = 0; i 2 * x);\n return twice.concat(twice.map(x => x + 1));\n }\n}\n\nfunction bit_reverse(x) {\n const N = x.length;\n const indexes = bit_reverse_idxs(Math.log2(N));\n return x.map((_, i) => x[indexes[i]]);\n}\n\n// Assumes log_2(N) is an integer\nfunction iterative_cooley_tukey(x) {\n const N = x.length;\n\n x = bit_reverse(x);\n\n for (let i = 1; i new Complex(Math.random(), 0));\nconst Y = cooley_tukey(X);\nconst Z = iterative_cooley_tukey(X);\nconst T = dft(X);\n\n// Check if the calculations are correct within a small tolerance\nconsole.log(\"Cooley tukey approximation is accurate: \", approx(Y, T));\nconsole.log(\"Iterative cooley tukey approximation is accurate: \", approx(Z, T));\n\nextern crate rand;\nextern crate rustfft;\n\nuse rand::prelude::*;\nuse rustfft::num_complex::Complex;\nuse rustfft::FFTplanner;\nuse std::f64::consts::PI;\n\n// This is based on the Python and C implementations.\n\nfn fft(x: &[Complex]) -> Vec> {\n let n = x.len();\n let mut new_x = x.to_vec();\n let mut y = vec![Complex::new(0.0_f64, 0.0_f64); n];\n\n let mut planner = FFTplanner::new(false);\n let this_fft = planner.plan_fft(n);\n this_fft.process(new_x.as_mut_slice(), y.as_mut_slice());\n\n // y.into_iter().map(|i| i / (n as f64).sqrt()).collect()\n y\n}\n\nfn dft(x: &[Complex]) -> Vec> {\n let n = x.len();\n (0..n)\n .map(|i| {\n (0..n)\n .map(|k| {\n x[k] * (Complex::new(0.0_f64, -2.0_f64) * PI * (i as f64) * (k as f64)\n / (n as f64))\n .exp()\n })\n .sum()\n })\n .collect()\n}\n\nfn cooley_tukey(x: &[Complex]) -> Vec> {\n let n = x.len();\n if n >());\n let odd = cooley_tukey(&x.iter().skip(1).step_by(2).cloned().collect::>());\n\n let mut temp = vec![Complex::new(0.0_f64, 0.0_f64); n];\n for k in 0..(n / 2) {\n temp[k] = even[k]\n + (Complex::new(0.0_f64, -2.0_f64) * PI * (k as f64) / (n as f64)).exp() * odd[k];\n temp[k + n / 2] = even[k]\n - (Complex::new(0.0_f64, -2.0_f64) * PI * (k as f64) / (n as f64)).exp() * odd[k];\n }\n temp\n}\n\nfn bit_reverse(x: &[Complex]) -> Vec> {\n let n = x.len();\n let mut temp = vec![Complex::new(0.0_f64, 0.0_f64); n];\n for k in 0..n {\n let b: usize = (0..((n as f64).log2() as usize))\n .filter(|i| k >> i & 1 != 0)\n .map(|i| 1 ]) -> Vec> {\n let n = x.len();\n\n let mut new_x = bit_reverse(x);\n\n for i in 1..=((n as f64).log2() as usize) {\n let stride = 2_u128.pow(i as u32);\n let w = (Complex::new(0.0_f64, -2.0_f64) * PI / (stride as f64)).exp();\n for j in (0..n).step_by(stride as usize) {\n let mut v = Complex::new(1.0_f64, 0.0_f64);\n for k in 0..((stride / 2) as usize) {\n new_x[k + j + ((stride / 2) as usize)] =\n new_x[k + j] - v * new_x[k + j + ((stride / 2) as usize)];\n new_x[k + j] =\n new_x[k + j] - (new_x[k + j + ((stride / 2) as usize)] - new_x[k + j]);\n v *= w;\n }\n }\n }\n\n new_x\n}\n\nfn main() {\n let mut x = Vec::with_capacity(64);\n let mut rng = thread_rng();\n for _i in 0..64 {\n let real = rng.gen_range(0.0_f64, 1.0_f64);\n x.push(Complex::new(real, 0.0_f64));\n }\n let v = fft(&x);\n let y = cooley_tukey(&x);\n let z = iterative_cooley_tukey(&x);\n let t = dft(&x);\n\n println!(\n \"{}\",\n v.iter().zip(y.iter()).all(|i| (i.0 - i.1).norm() \n\n(defun coefficient (time-index freq-index dft-len)\n \"Calculates a single twiddle factor for the Fourier Transform.\"\n (exp (- (/ (* #c(0 1) 2.0 pi time-index freq-index)\n dft-len))))\n\n(defun dft (data)\n \"Performs the Discrete Fourier Transform\"\n (let ((dft-len (length data)))\n (loop for freq-index from 0 below dft-len collect\n (loop for time-index from 0 below dft-len sum\n (* (coefficient time-index freq-index dft-len) (elt data time-index))))))\n\n(defun merge-sub-ffts (evens odds)\n \"Combines the FFTs of the even and odd indices.\"\n (let* ((fft-length (+ (length evens) (length odds)))\n ;; Calculate coefficients for the odd indices.\n (twiddle-factors (loop for i from 0 below (length odds)\n collect (coefficient 1.0 i fft-length)))\n ;; Multiply values with coefficients.\n (odd-terms (mapcar #'* odds twiddle-factors)))\n ;; Combine the two FFTs.\n (concatenate 'list \n (mapcar #'+ evens odd-terms)\n (mapcar #'- evens odd-terms))))\n\n(defun cooley-tukey-rec (data)\n \"Performs the Fourier Transform using the recursive Cooley-Tukey method.\"\n (if (\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"FTexample\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"radix2positive\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"radix2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"radix8\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"DIT-FFT-butterfly\" was created by Virens and is licensed under the Creative Commons Attribution 3.0 Unported License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/notation/notation.html":{"url":"contents/notation/notation.html","title":"Complexity Notation","keywords":"","body":"Complexity Notation\nAlgorithms are designed to solve problems.\nOver time, new algorithms are created to solve problems that old algorithms have already solved.\nIn some cases, the new algorithms are not intrinsically better than the older ones.\nIn other cases, these new algorithms breathe life into areas of research and engineering that could not exist without them.\nThe question is: what makes an algorithm \"better\" than another one?\nObviously, there is no good answer to this question.\nIf you write an algorithm to solve a problem, whatever you come up with will probably work just fine for small problems.\nThat said, if you need to use the algorithm for a larger system, you might find yourself waiting for longer and longer on your code to run.\nIn these cases, it's obvious that if you are working on a large system, you need an algorithm that scales well with a large size.\nIdeally, an algorithm that works well for a large system will also work with a smaller one; however, this is not always the case.\nIn order to determine the best algorithm for your system, it's often best to consult a tool computer scientists use to describe how algorithms scale with system size: complexity theory.\nHere's the idea: algorithms operate on data.\nComplexity theory uses different notations to describe how many operations an algorithm will need.\nIn this way, computational complexity measures runtime in terms of the number of operations an algorithm takes to complete its task.\nTo be clear, the notations used are not at all exact, but they roughly describe the run-time of code and can be used to estimate how long an algorithm should take to run.\nIn addition, there are many different notations depending on who you ask, but for now we'll focus on the big 3: O, \\Omega, and \\Theta.\nBig O assumes the worst, which is the often the most useful description of an algorithm.\nOn the other hand, \\Omega assumes the best and \\Theta is used when the best and worst cases are the same.\nIt may seems like strange that an algorithm can run in different time, but let me explain a while:\nfunction constant(a::UInt64, b::UInt64)\n println(b)\n for i=0:18446744073709551615\n if(a \nIf we calculates the big 3 in b, it will be \\Omega(1) and O(b), Obviously not the same.\nThe best-case runtime will be 1 println statement if a > b, the worst-case runtime will be b println statement if a = 1.\nSo that's the explanation, and let's move on.\nOf the three Big O is used the most, and is used in conversation to mean that the algorithm will take \"on the order of\" n operations.\nUnfortunately, at this point, these notations might be a little vague.\nIn fact, it was incredibly vague for me for a long time, and it wasn't until I saw the notations in action that it all started to make sense, so that's what this section is about: providing concrete examples to better understand computational complexity notation.\nIn algorithms below, let us consider that the slowest statement is println, and we always talk about all the println in the function.\nConstant Time\nLet's write some code that reads in an array of length n and runs with constant time:\nfunction constant(a::Array{Float64})\n println(a[1])\nend\n\nObviously, no matter how large a is, this function will not take any longer to run.\nBecause of this, we say it has a constant runtime and notate it with O(1) = \\Omega(1) = \\Theta(1).\nBasically, we are saying that this function will run with 1 operation total (a single print).\nThe best-case runtime will be 1 operation, the worst-case runtime will be 1 operation, and because they are both the same, we can use \\Theta to notate that.\nNow imagine the following function:\nfunction constant(a::Array{Float64})\n if (length(a) >= 3)\n println(a[1])\n println(a[2])\n println(a[3])\n end\nend\n\nThis function has 3 print statements, so it has 3 operations total.\nBecause of this, it's tempting to say that the runtime would be O(3) = \\Omega(3) = \\Theta(3), and you would not be wrong; however, complexity notations often make a big assumption: we don't care about constants!\nWhat does this mean? Well, it means that we get rid of all constants that are not 1!\nIn this case, that means we set O(3) = O(1).\nNow, I know what you are thinking, That's stupid! It's clear that the second function will take 3 times as long to run, shouldn't we notate that?\nYou're not wrong; however, complexity notation is mostly interested in how algorithms scale with larger and larger inputs.\nBecause we are talking about constant run-time, there is no scaling with larger inputs. No matter what array you read in to the above functions, they will always take a constant number of operations to finish.\nWhether that constant time is 1 operation or 3 operations doesn't really matter because different machines will have different runtimes anyway.\nNow, here's the thing: as we move on to more complicated examples, we will continue to ignore constants and extra terms to make the notation easier to understand.\nJust because this is common practice does not mean it's the best practice.\nI have run into several situation where knowing the constants has saved me hours of run-time, so keep in mind that all of these notations are somewhat vague and dependent on a number of auxiliary factors.\nStill, that doesn't mean the notation is completely useless. For now, let's keep moving forward with some more complicated (and useful) examples!\nLinear Time\nNow we are moving into interesting territory!\nLet's consider the following function:\nfunction linear(a::Array{Float64})\n for i = 1:length(a)\n println(a[i])\n end\nend\n\nHere, it's clear that if we increase a by one element, we will need to do another operation.\nThat is, with an array of size n, we will need to do n operations, which means that our complexity is O(n) = \\Omega(n) = \\Theta(n).\nAs before, adding more operations into the for loop will change the constant in front of n in our complexity notation, but we'll continue to ignore those constants.\nFor example:\nfunction linear(a::Array{Float64})\n println(\"The first element in our array is: \", a[1])\n\n println(\"The sum of all pairs of elements in our array are...\")\n for i = 1:length(a)/2\n println(\"a is: \", a[2*i])\n println(\"b is: \", a[2*i+1])\n println(\"The sum of a and b is: \", a[2*i] + a[2*i+1])\n end\n\n println(\"The last element in our array is: \", a[end])\nend\n\nTechnically has a complexity of \\Theta(\\frac{3n}{2} + 2), but we'll just call it \\Theta(n).\nRegardless of the notation, if you see something that is O(n), you know that at worst it will run at the speed of a for loop, which is pretty good!\nPolynomial Time\nA promise of O(n) is not bad in terms of run-time; however, it is unlikely that you will run into too many straightforward algorithms that are O(n).\nFor example, let's say you have a square, 2D image and want to iterate through all of its points.\nWell, to do this, we might write code that looks something like:\n# Here, size is the length of a single side of the image\nfunction access_image(img::Array{Float64}, size::Int64)\n for i = 1:size\n for j = 1:size\n index = j + i*size\n println(img[index])\n end\n end\nend\n\nThis is a simple case where a nested for loop is perfectly acceptable, and it's obvious geometrically that we need to access \\mathrm{size}\\times\\mathrm{size} number of elements (because we are working with a square).\nThis means that this example has \\Theta(n^2) complexity. This is not great.\nIf you have to access 3D space, this might require \\Theta(n^3), which is even worse! Don't even get me started on 4D!\nIntuitively, if you see anything that has a polynomial runtime, it's easy to think of it as a bunch of nested for loops.\nThat said, there have been several cases throughout the history of algorithms where polynomial runtimes have inhibited certain algorithms from being used entirely, simply because it takes too long to run!\nFor this reason, if you can avoid writing nested for loops, you certainly should!\nHowever, there are several cases where this cannot be avoided, so don't spend too much time worrying about it unless runtime becomes an issue!\nExponential and Logarithmic Time\nThese are two more cases that come up all the time and often require a common theme: recursion.\nGenerally speaking, logarithmic algorithms are some of the fastest algorithms out there, while exponential algorithms are some of the slowest.\nUnfortunately, this means that recursion can be either the most useful tool in existence for realizing certain algorithms or the most harmful one, depending on your problem.\nHere is a simple example of a function with exponential runtime:\n# Here, n is the number of iterations\nfunction exponential(value::Int64, n::Int64)\n println(value)\n if(n >= 0)\n value += 1\n exponential(value, n-1)\n exponential(value, n-1)\nend\n\nHere, we read in the maximum number n we are iterating through and recursively call the exponential function, decrementing the number of iterations left each time.\nBecause we are calling the exponential function twice, this has a complexity of \\Theta(2^n), which is not great, but if it's the only way to get a job done, it's the only way to get a job done.\nLogarithmic algorithms can be thought of as the opposite of exponential ones.\nInstead of taking a value and computing more and more values each time, a good example of a logarithmic algorithm is one that takes an array and recursively divides it up, like so:\n# Here, cutoff is an arbitrary variable to know when to stop recursing\nfunction logarithmic(a::Array{Float64}, cutoff::Int64)\n if (length(a) > cutoff)\n logarithmic(a[length(a)/2+1:end], cutoff)\n end\n println(length(a))\nend\n\nTo be honest, it is not obvious that the provided logarithmic function should operate in \\Theta(\\log(n)) time, where n is the size of a.\nThat said, I encourage you to think about an array of size 8.\nFirst, we split it in half and run the algorithm on one of them, creating an array of 4 elements.\nIf we split the new array and run it on 1 of them, we have an array of 2, and if we split it by two and run on 1 we have an array of 1 element each.\nThis is as far as we can go, and we ended up dividing the array 3 times to get to this point.\n3 = \\log_2(8), so this function runs with a logarithmic number of operations.\nPutting it all together\nWe've outlined the most common complexity cases of different algorithms here, but at this point things might still be unclear.\nWhich is better: O(n^2) or O(log(n))?\nWell, let's plot all the different cases out, and the answer should become obvious.\n\n \n\n\nHere, we see each of the complexity cases as n increases.\nClearly, linear time is not bad when compared to polynomial or exponential time; however, if you can manage something in logarithmic or constant time, do it!\nNow, there is a lot more to say about computational complexity and we'll definitely cover it at some point, but I can only move so fast!\nIn particular, I would love to have a discussion on the P=NP issue that has been rustling the jimmies of a few computer scientists for a while, but we'll get to that in due time.\nFinal Warning\nThis is a book about algorithms.\nIt would be nearly impossible to talk about most algorithms without touching on complexity theory and explaining why certain algorithms are faster than others.\nThat said, just because an algorithm runs in O(\\log n) does not mean it will always be faster than one that runs in O(n^2).\nBecause complexity notation often ignores constants, there could be a crazy constant that we are missing that actually makes a huge difference in runtime.\nIn addition, in order to use an algorithm that seems faster based on complexity notation, you may need to use a library that massively increases runtime due to a plethora of other reasons.\nBasically, take complexity notation with a grain of salt.\nIt is a useful descriptor of how fast algorithms should run in an ideal world; however, ideal worlds do not exist.\nWhen it comes to programming, there may be hundreds of other factors that need to be considered before implementing anything.\nThat said, complexity notation should not be ignored.\nIf you can easily implement an algorithm that is notationally faster with no repercussions, go for it!\nJust be sure you do not waste time trying to optimize code you haven't written yet.\nIn general, my advice would be the following:\nwrite code first and optimize what you can on the first run-through without going too far out of your way.\nIf the runtime is awful, go back and see about implementing algorithms that are faster based on complexity notation.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"Complexity Scaling\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/thomas_algorithm/thomas_algorithm.html":{"url":"contents/thomas_algorithm/thomas_algorithm.html","title":"Thomas Algorithm","keywords":"","body":"Thomas Algorithm\nAs alluded to in the Gaussian Elimination chapter, the Thomas Algorithm (or TDMA, Tri-Diagonal Matrix Algorithm) allows for programmers to massively cut the computational cost of their code from O(n^3) to O(n) in certain cases!\nThis is done by exploiting a particular case of Gaussian Elimination where the matrix looks like this:\n\n\\left[\n \\begin{array}{ccccc|c}\n b_0 & c_0 & & & & d_0 \\\\\n a_1 & b_1 & c_1 & & & d_1 \\\\\n & a_2 & \\ddots & & & \\vdots \\\\\n & & & & c_{n-1}& d_{n-1} \\\\\n & & & a_n & b_n & d_n\n \\end{array}\n\\right]\n\nThis matrix shape is called Tri-Diagonal (excluding the right-hand side of our system of equations, of course!).\nNow, at first, it might not be obvious how this helps. Well, firstly, it makes the system easier to encode: we may divide it into four separate vectors corresponding to a, b, c, and d (in some implementations, you will see the missing a_0 and c_n set to zero to get four vectors of the same size).\nSecondly, and most importantly, equations this short and regular are easy to solve analytically.\nWe'll start by applying mechanisms familiar to those who have read the Gaussian Elimination chapter.\nOur first goal is to eliminate the a_i terms and set the diagonal values b_i to 1. The c_i and d_i terms will be transformed into c'_i and d'_i.\nThe first row is particularly easy to transform since there is no a_0, we simply need to divide the row by b_0:\n\n\\left\\{\n\\begin{align}\nc'_0 &= \\frac{c_0}{b_0} \\\\\nd'_0 &= \\frac{d_0}{b_0}\n\\end{align}\n\\right.\n\nLet's assume that we found a way to transform the first i-1 rows. How would we transform the next one? We have\n\n\\begin{array}{ccccccc|c}\n & & \\ddots & & & & & \\\\\n(i-1) & & 0 & 1 & c'_{i-1} & & & d'_{i-1} \\\\\n(i) & & & a_i & b_i & c_i & & d_i \\\\\n & & & & & \\ddots & &\n\\end{array}\n\nLet's transform row (i) in two steps.\nStep one: eliminate a_i with the transformation (i)^* = (i) - a_i \\times (i-1):\n\n\\left\\{\n\\begin{align}\na^*_i &= 0 \\\\\nb^*_i &= b_i - a_i \\times c'_{i-1} \\\\\nc^*_i &= c_i \\\\\nd^*_i &= d_i - a_i \\times d'_{i-1}\n\\end{align}\n\\right.\n\nStep two: get b'_i=1 with the transformation (i)' = (i)^* / b^*_i :\n\n\\left\\{\n\\begin{align}\na'_i &= 0 \\\\\nb'_i &= 1 \\\\\nc'_i &= \\frac{c_i}{b_i - a_i \\times c'_{i-1}} \\\\\nd'_i &= \\frac{d_i - a_i \\times d'_{i-1}}{b_i - a_i \\times c'_{i-1}}\n\\end{align}\n\\right.\n\nBrilliant! With the last two formula, we can calculate all the c'_i and d'_i in a single pass, starting from row 1, since we already know the values of c'_0 and d'_0.\nOf course, what we really need are the solutions x_i. It's back substitution time!\nIf we express our system in terms of equations instead of a matrix, we get\n\nx_i + c'_i \\times x_{i+1} = d'_i\n\nplus the last row that is even simpler: x_n = d'_n. One solution for free!\nMaybe we can backtrack from the last solution? Let's (barely) transform the above equation:\n\nx_i = d'_i - c'_i \\times x_{i+1}\n\nand that's all there is to it. We can calculate all the x_i in a single pass starting from the end.\nOverall, we only need two passes, and that's why our algorithm is O(n)!\nThe transformations are quite easy too, isn't that neat?\nExample Code\nfunction thomas(a::Vector{Float64}, b::Vector{Float64}, c::Vector{Float64},\n d::Vector{Float64}, n::Int64)\n\n x = copy(d)\n c_prime = copy(c)\n\n # Setting initial elements\n c_prime[1] /= b[1]\n x[1] /= b[1]\n\n for i = 2:n\n # Scale factor is for c_prime and x\n scale = 1.0 / (b[i] - c_prime[i-1]*a[i])\n c_prime[i] *= scale\n x[i] = (x[i] - a[i] * x[i-1]) * scale\n end\n\n # Back-substitution\n for i = n-1:-1:1\n x[i] -= (c_prime[i] * x[i+1])\n end\n\n return x\n\nend\n\nfunction main()\n a = [0.0, 2.0, 3.0]\n b = [1.0, 3.0, 6.0]\n c = [4.0, 5.0, 0.0]\n d = [7.0, 5.0, 3.0]\n\n println(\n \"\"\"The system\n $(join((b[1], c[1], \"\", \"|\", d[1]), \"\\t\"))\n $(join((a[2], b[2], c[2], \"|\", d[2]), \"\\t\"))\n $(join((\"\", a[3], b[3], \"|\", d[3]), \"\\t\"))\n Has the solution:\"\"\"\n )\n\n soln = thomas(a, b, c, d, 3)\n\n println(soln)\nend\n\nmain()\n\n#include \n#include \n\nvoid thomas(double * const a, double * const b, double * const c,\n double * const x, const size_t size) {\n\n double y[size];\n memset(y, 0, size * sizeof(double));\n\n y[0] = c[0] / b[0];\n x[0] = x[0] / b[0];\n\n for (size_t i = 1; i \n# Author: gammison\n\n# note this example is inplace and destructive\ndef thomas(a, b, c, d):\n\n # set the initial elements\n c[0] = c[0] / b[0]\n d[0] = d[0] / b[0]\n\n n = len(d) # number of equations to solve\n for i in range(1, n):\n # scale factor for c and d\n scale = 1 / (b[i] - c[i-1] * a[i])\n\n c[i] *= scale\n d[i] = (d[i] - a[i] * d[i-1]) * scale\n\n\n # do the back substitution\n for i in range(n-2, -1, -1):\n d[i] -= c[i] * d[i+1]\n\n return d\n\ndef main():\n # example for matrix\n # [1 4 0][x] [7]\n # [2 3 5][y] = [5]\n # [0 3 6][z] [3]\n\n # [.8666]\n # soln will equal [1.533]\n # [-.266]\n # note we index a from 1 and c from 0\n a = [0, 2, 3]\n b = [1, 3, 6]\n c = [4, 5, 0]\n d = [7, 5, 3]\n\n soln = thomas(a, b, c, d)\n print(soln)\n\nif __name__ == '__main__':\n main()\n\nYou will find this algorithm implemented in this project.\n\n \npublic class Thomas {\n private static double[] thomasAlgorithm(double[] a, double[] b, double[] c, double[] x) {\n int size = a.length;\n double[] y = new double[size]; // This is needed so that we don't have to modify c\n double[] solution = new double[size];\n\n // Set initial elements\n y[0] = c[0] / b[0];\n solution[0] = x[0] / b[0];\n\n for (int i = 1; i = 0; --i) {\n solution[i] -= y[i] * solution[i + 1];\n }\n\n return solution;\n }\n\n public static void main(String[] args) {\n double[] a = {0.0, 2.0, 3.0};\n double[] b = {1.0, 3.0, 6.0};\n double[] c = {4.0, 5.0, 0.0};\n double[] x = {7.0, 5.0, 3.0};\n double[] solution = thomasAlgorithm(a, b, c, x);\n\n System.out.format(\"The system,\\n\");\n System.out.format(\"[%.1f, %.1f, %.1f][x] = [%.1f]\\n\", b[0], c[0], 0f, x[0]);\n System.out.format(\"[%.1f, %.1f, %.1f][y] = [%.1f]\\n\", a[1], b[1], c[1], x[1]);\n System.out.format(\"[%.1f, %.1f, %.1f][z] = [%.1f]\\n\", 0f, a[2], b[2], x[2]);\n System.out.format(\"has the solution:\\n\");\n\n for (int i = 0; i \nimport Data.List (zip4)\nimport Data.Ratio\n\nthomas :: Fractional a => [a] -> [a] -> [a] -> [a] -> [a]\nthomas a b c = init . scanr back 0 . tail . scanl forward (0, 0) . zip4 a b c\n where\n forward (c', d') (a, b, c, d) =\n let denominator = b - a * c'\n in (c / denominator, (d - a * d') / denominator)\n back (c, d) x = d - c * x\n\nmain :: IO ()\nmain = do\n let a = [0, 2, 3] :: [Ratio Int]\n b = [1, 3, 6]\n c = [4, 5, 0]\n d = [7, 5, 3]\n print $ thomas a b c d\n\npackage main\n\nimport \"fmt\"\n\nfunc thomas(a, b, c, d []float64) []float64 {\n c[0] = c[0] / b[0]\n d[0] = d[0] / b[0]\n\n for i := 1; i = 0; i-- {\n d[i] -= c[i] * d[i+1]\n }\n\n return d\n}\n\nfunc main() {\n a := []float64{0., 2., 3.}\n b := []float64{1., 3., 6.}\n c := []float64{4., 5., 0.}\n d := []float64{7., 5., 3.}\n\n fmt.Println(\"The system,\")\n fmt.Println(\"[1.0 4.0 0.0][x] = [7.0]\")\n fmt.Println(\"[2.0 3.0 5.0][y] = [5.0]\")\n fmt.Println(\"[0.0 3.0 6.0][z] = [3.0]\")\n fmt.Println(\"has the solution:\")\n solve := thomas(a, b, c, d)\n for _, i := range solve {\n fmt.Printf(\"[%f]\\n\", i)\n }\n}\n\nfn thomas(a []f32, b []f32, c []f32, d []f32) []f32 {\n mut new_c := c\n mut new_d := d\n new_c[0] = new_c[0] / b[0]\n new_d[0] = new_d[0] / b[0]\n\n for i := 1; i = 0; i-- {\n new_d[i] -= new_c[i] * new_d[i+1]\n }\n\n return new_d\n}\n\nfn main() {\n a := [0.0, 2.0, 3.0]\n b := [1.0, 3.0, 6.0]\n c := [4.0, 5.0, 0.0]\n d := [7.0, 5.0, 3.0]\n\n println(\"The system,\")\n println(\"[1.0 4.0 0.0][x] = [7.0]\")\n println(\"[2.0 3.0 5.0][y] = [5.0]\")\n println(\"[0.0 3.0 6.0][z] = [3.0]\")\n println(\"has the solution:\")\n solution := thomas(a, b, c, d)\n for i in solution {\n println(\"[$i]\")\n }\n}\n\nfunc thomas(a: [Double], b: [Double], c: [Double], d: [Double]) -> [Double] {\n var a = a\n var b = b\n var c = c\n var d = d\n\n // set the initial elements\n c[0] = c[0] / b[0]\n d[0] = d[0] / b[0]\n\n let n = d.count // number of equations to solve\n for i in 1..\n= 0; --$i)\n $x[$i] -= $y[$i] & $x[$i + 1];\n\n return $x;\n}\n\n\n$a = [0.0, 2.0, 3.0];\n$b = [1.0, 3.0, 6.0];\n$c = [4.0, 5.0, 0.0];\n$x = [7.0, 5.0, 3.0];\n\nprintf('The system,%s', PHP_EOL);\nprintf(' [%s, %s, %s][x] = [%s]%s', $b[0], $c[0], 0, $x[0], PHP_EOL);\nprintf(' [%s, %s, %s][y] = [%s]%s', $a[1], $b[1], $c[1], $x[1], PHP_EOL);\nprintf(' [%s, %s, %s][z] = [%s]%s', 0, $a[2], $b[2], $x[2], PHP_EOL);\nprintf('has the solution:%s', PHP_EOL);\n\n$solution = thomas_algorithm($a, $a, $c, $x, count($x));\nfor ($i = 0; $i \nproc thomas_algorithm(a, b, c_in, d_in: seq[float]): seq[float] = \n\n let n: int = len(d_in)\n\n var c: seq[float] = c_in\n var d: seq[float] = d_in\n\n c[0] /= b[0]\n d[0] /= b[0]\n\n for i in 1..n - 1:\n let scale: float = (1 / (b[i] - c[i - 1] * a[i]))\n\n c[i] *= scale\n d[i] = (d[i] - a[i] * d[i - 1]) * scale\n\n for i in countdown(n - 2,0):\n d[i] -= c[i] * d[i + 1]\n\n\n return d\n\n\nconst x: seq[float] = @[0.0, 2.0, 3.0]\nconst y: seq[float] = @[1.0, 3.0, 6.0]\nconst z: seq[float] = @[4.0, 5.0, 0.0]\nconst w: seq[float] = @[7.0, 5.0, 3.0] \n\necho \"The system,\"\necho \"[1.0 4.0 0.0][x] = [7.0]\"\necho \"[2.0 3.0 5.0][y] = [5.0]\"\necho \"[0.0 3.0 6.0][z] = [3.0]\"\n\necho \"has the solution:\"\n\nconst soln: seq[float] = thomas_algorithm(x, y, z, w)\n\nfor i in 0..len(w) - 1:\n echo soln[i]\n\n#include \n#include \n#include \n\nvoid thomas(\n std::vector const& a,\n std::vector const& b,\n std::vector const& c,\n std::vector& x) {\n auto y = std::vector(a.size(), 0.0);\n\n y[0] = c[0] / b[0];\n x[0] = x[0] / b[0];\n\n for (std::size_t i = 1; i a = {0.0, 2.0, 3.0};\n const std::vector b = {1.0, 3.0, 6.0};\n const std::vector c = {4.0, 5.0, 0.0};\n std::vector x = {7.0, 5.0, 3.0};\n\n std::cout \nlocal function thomas(a, b, c, d)\n\n -- Create tables and set initial elements\n local c_prime = {c[1] / b[1]}\n local result = {d[1] / b[1]}\n\n for i = 2, #a do\n -- Scale factor is for c_prime and result\n local scale = 1.0 / (b[i] - a[i] * c_prime[i - 1])\n c_prime[i] = c[i] * scale\n result[i] = (d[i] - a[i] * result[i - 1]) * scale\n end\n\n -- Back-substitution\n for i = #a-1, 1, -1 do\n result[i] = result[i] - (c_prime[i] * result [i + 1])\n end\n\n return result\nend\n\nlocal a = {0.0, 2.0, 3.0}\nlocal b = {1.0, 3.0, 6.0}\nlocal c = {4.0, 5.0, 0.0}\nlocal d = {7.0, 5.0, 3.0}\n\nprint(\"The system\")\nprint(b[1], c[1], \"\", \"|\", d[1])\nprint(a[2], b[2], c[2], \"|\", d[2])\nprint(\"\", a[3], b[3], \"|\", d[3])\nprint(\"Has the solution:\")\n\nlocal solution = thomas(a, b, c, d)\n\nprint(table.unpack(solution))\n\ndef thomas(a, b, c, d)\n c_prime = c.dup\n x = d.dup\n\n # Setting initial elements\n c_prime[0] /= b[0]\n x[0] /= b[0]\n\n 1.upto(a.size - 1) do |i|\n # Scale factor is for c_prime and x\n scale = 1.0 / (b[i] - c_prime[i - 1]*a[i])\n c_prime[i] *= scale\n x[i] = (x[i] - a[i] * x[i - 1]) * scale\n end\n\n # Back-substitution\n (a.size - 2).downto(0) do |i|\n x[i] -= (c_prime[i] * x[i + 1])\n end\n\n x\nend\n\ndef main\n a = [0.0, 2.0, 3.0]\n b = [1.0, 3.0, 6.0]\n c = [4.0, 5.0, 0.0]\n d = [7.0, 5.0, 3.0]\n\n puts \"The system\"\n puts [b[0], c[0], \"\", \"|\", d[0]].join(\"\\t\")\n puts [a[1], b[1], c[1], \"|\", d[1]].join(\"\\t\")\n puts [\"\", a[2], b[2], \"|\", d[2]].join(\"\\t\")\n puts \"Has the solution:\"\n\n soln = thomas(a, b, c, d)\n\n puts soln.join(\"\\t\")\nend\n\nmain\n\nprivate fun thomas(a: DoubleArray, b: DoubleArray, c: DoubleArray, d: DoubleArray): DoubleArray {\n val cPrime = c.clone()\n val x = d.clone()\n val size = a.size\n cPrime[0] /= b[0]\n x[0] /= b[0]\n for (i in 1 until size) {\n val scale = 1.0 / (b[i] - cPrime[i - 1] * a[i])\n cPrime[i] *= scale\n x[i] = (x[i] - a[i] * x[i - 1]) * scale\n }\n for (i in (size - 2) downTo 0) {\n x[i] -= cPrime[i] * x[i + 1]\n }\n return x\n}\n\nfun main(args: Array) {\n val a = doubleArrayOf(0.0, 2.0, 3.0)\n val b = doubleArrayOf(1.0, 3.0, 6.0)\n val c = doubleArrayOf(4.0, 5.0, 0.0)\n val x = doubleArrayOf(7.0, 5.0, 3.0)\n val solution = thomas(a, b, c, x)\n\n println(\"System:\")\n println(\"[%.1f, %.1f, %.1f][x] = [%.1f]\".format(b[0], c[0], 0f, x[0]))\n println(\"[%.1f, %.1f, %.1f][y] = [%.1f]\".format(a[1], b[1], c[1], x[1]))\n println(\"[%.1f, %.1f, %.1f][z] = [%.1f]\\n\".format(0f, a[2], b[2], x[2]))\n println(\"Solution:\")\n for (i in solution.indices) {\n println(\"[% .5f]\".format(solution[i]))\n }\n}\n\n;;;; Thomas algorithm implementation in Common Lisp\n\n(defmacro divf (place divisor)\n \"Divides the value at place by divisor\"\n `(setf ,place (/ ,place ,divisor)))\n\n(defun helper (v1 v2 v3 row)\n (- (svref v1 row) (* (svref v2 row) (svref v3 (1- row)))))\n\n(defun thomas (diagonal-a diagonal-b diagonal-c last-column)\n \"Returns the solutions to a tri-diagonal matrix non-destructively\"\n ;; We have to copy the inputs to ensure non-destructiveness\n (let ((a (copy-seq diagonal-a))\n (b (copy-seq diagonal-b))\n (c (copy-seq diagonal-c))\n (d (copy-seq last-column)))\n (divf (svref c 0) (svref b 0))\n (divf (svref d 0) (svref b 0))\n (loop\n for i from 1 upto (1- (length a)) do\n (divf (svref c i) (helper b a c i))\n (setf (svref d i) (/ (helper d a d i) (helper b a c i))))\n (loop\n for i from (- (length a) 2) downto 0 do\n (decf (svref d i) (* (svref c i) (svref d (1+ i)))))\n d))\n\n(defparameter diagonal-a #(0 2 3))\n(defparameter diagonal-b #(1 3 6))\n(defparameter diagonal-c #(4 5 0))\n(defparameter last-column #(7 5 3))\n\n;; should print 0.8666667 1.5333333 -0.26666668\n(format t \"~{~f ~}~%\" (coerce (thomas diagonal-a diagonal-b diagonal-c last-column) 'list))\n\n# note this example is inplace and destructive\ndef thomas(a, b, c, d)\n # set the initial elements\n c[0] = c[0] / b[0]\n d[0] = d[0] / b[0]\n\n n = d.length # number of equations to solve\n (1...n).each do |i|\n scale = 1 / (b[i] - c[i - 1] * a[i]) # scale factor for c and d\n c[i] *= scale\n d[i] = (d[i] - a[i] * d[i - 1]) * scale\n end\n\n # do the back substitution\n (n - 2).downto(0).each do |j|\n d[j] -= c[j] * d[j + 1]\n end\n\n d\nend\n\n# example for matrix\n# [1 4 0][x] [7]\n# [2 3 5][y] = [5]\n# [0 3 6][z] [3]\n\n# [.8666]\n# soln will equal [1.533]\n# [-.266]\n# note we index a from 1 and c from 0\n\na = [0.0, 2.0, 3.0]\nb = [1.0, 3.0, 6.0]\nc = [4.0, 5.0, 0.0]\nd = [7.0, 5.0, 3.0]\n\nsoln = thomas(a, b, c, d)\nputs soln\n\nfunction thomas(a, b, c, x) {\n const y = [];\n\n y[0] = c[0] / b[0];\n x[0] = x[0] / b[0];\n\n for (let i = 1; i = 0; i--)\n x[i] -= y[i] * x[i + 1];\n}\n\nlet a = [0.0, 2.0, 3.0];\nlet b = [1.0, 3.0, 6.0];\nlet c = [4.0, 5.0, 0.0];\nlet x = [7.0, 5.0, 3.0];\n\nconsole.log(\"The system,\");\nconsole.log(\"[1.0 4.0 0.0][x] = [7.0]\");\nconsole.log(\"[2.0 3.0 5.0][y] = [5.0]\");\nconsole.log(\"[0.0 3.0 6.0][z] = [3.0]\");\nconsole.log(\"has the solution:\\n\");\n\nthomas(a, b, c, x);\n\nfor (let i = 0; i \nfn thomas(a: &[f64], b: &[f64], c: &[f64], x: &[f64]) -> Vec {\n let size = a.len();\n let mut y = vec![0.0; size];\n let mut z = Vec::from(x);\n\n y[0] = c[0] / b[0];\n z[0] = x[0] / b[0];\n\n for i in 1..size {\n let scale = 1.0 / (b[i] - a[i] * y[i - 1]);\n y[i] = c[i] * scale;\n z[i] = (z[i] - a[i] * z[i - 1]) * scale;\n }\n\n for i in (0..(size - 1)).rev() {\n z[i] -= y[i] * z[i + 1];\n }\n\n z\n}\n\nfn main() {\n let a = vec![0.0, 2.0, 3.0];\n let b = vec![1.0, 3.0, 6.0];\n let c = vec![4.0, 5.0, 0.0];\n let x = vec![7.0, 5.0, 3.0];\n\n println!(\"The system\");\n println!(\"[{:?} {:?} {:?}][x] = [{:?}]\", a[0], b[0], c[0], &x[0]);\n println!(\"[{:?} {:?} {:?}][x] = [{:?}]\", a[1], b[1], c[1], &x[1]);\n println!(\"[{:?} {:?} {:?}][x] = [{:?}]\", a[2], b[2], c[2], &x[2]);\n println!(\"has the solution\");\n\n let y = thomas(&a, &b, &c, &x);\n\n y.iter()\n .for_each(|i| println!(\"[{:>19}]\", format!(\"{:18}\", format!(\"{:?}\", i))));\n}\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/IFS/IFS.html":{"url":"contents/IFS/IFS.html","title":"Iterated Function Systems","keywords":"","body":"Iterated Function Systems\nA few quick notes before we start:\n\nFor this chapter, we will be following the methodology set by the plotting chapter.\nThat is to say that the code presented in this chapter will output another file that can be easily plotted by an external plotter.\nIf you like to use a plotter provided by your language of choice, please modify the code provided to do so.\n\nThis chapter is currently a subsection to the plotting chapter, but we may extend the algorithm archive in the future with other fractal generation methods, which would require creating a new section on fractals, in particular.\nThis would include a chapter with more rigorous definitions on fractals, which is largely missing from the following discussion.\nPlease let us know if you are interested!\n\n\nIn this chapter, we will show you how to make one of the most famous fractals, the Sierpinski triangle, via Iterated Function Systems (IFSs).\nWe will also introduce a number of interesting concepts for further exploration, such as chaos games, Hutchinson operators, and attractors.\nThe Sierpinski Triangle\nTo begin the discussion of Iterated Function Systems (IFSs), we will first discuss what might be one of the most famous fractals currently known: the Sierpinski triangle (shown below):\n\nThis image is clearly a set of triangles embedded in a larger triangle in such a way that it can be continually cut into three identical pieces and still retain its internal structure.\nThis idea is known as self-similarity [1], and it is usually the first aspect of fractals to catch an audience's attention.\nIn fact, there are plenty of uses of fractals and their mathematical underpinnings, such as estimating the coastline of Britain [2], identifying fingerprints [3], and image compression [4][5].\nIn many more rigorous definitions, a fractal can be described as any system that has a non-integer Hausdorff dimension [6][7][8].\nThough this is an incredibly interesting concept, the discussion of this chapter will instead focus on methods to generate fractal patterns through iterated function systems.\nTo start, imagine creating a triangle from three points, A, B, and C.\nThese points can be arbitrarily chosen, but for this conversation, we will constrict them to the vertices of an equilateral triangle, as shown below:\n\nNow let's create three separate functions that can act on a 2-dimensional space:\n\n\\begin{align}\nf_1(P) &= \\frac{P + A}{2}\\\\\nf_2(P) &= \\frac{P + B}{2}\\\\\nf_3(P) &= \\frac{P + C}{2}\\\\\n\\end{align}\n\nEach function will read in a particular location in space (here, P \\in \\mathbb{R}^2) and output a new location that is the midpoint between the input location and A, B, or C for f_1, f_2, and f_3 respectively.\nThe union of all of these functions (the set of all possible functions available for use) is often notated as the Hutchinson operator [9][10], and for this case it would look like this:\n\nH(P) = \\bigcup_{i=1}^3f_i(P)\n\nBy iteratively using this operator, we can traverse through all possible movements in the set.\nFor example, let's generate 3 new points that are halfway between A and B, B and C, and A and C, which will be called D, E, and F respectively.\nThis is shown below:\n\nFrom here, each new point (D, E, and F) will spawn 3 children, and each child will move according to one of the three possible functions in the Hutchinson operator, as shown below:\n\n\n \n \n\n\n\nHere, all red children come from D, green children come from E and blue children come from F.\nAt this stage, the children will then spawn 3 more children, each of which will move according to a different function.\nThose children will then spawn more children, who act accordingly.\nAs this process continues on and on, we begin to see an interesting pattern form:\n\n\n \n \n\n\n\nThis is the Sierpinski triangle.\nAt first, it might seem like mathematical magic that a simple set of 3 functions can create such a pattern.\nAfter all, why aren't any of the children migrating to the empty spaces in the structure?\nThis will require some thought, but the simplest answer is that no function within the Hutchinson operator allows for children to enter those spaces; therefore, none of the children can enter them.\nWhat about a square?\nWhen I learned about how the Sierpinski triangle could be generated from 3 simple functions, I began to wonder about other shapes.\nCould we create fractal squares? Hexagons? Circles?\nSuch shapes seem like natural extensions to the triangular Hutchinson operator provided above, but there's a bit of a hitch...\nFirst, let's take 4 points, A, B, C, and D, this time located at the four vertices of a square, like so:\n\nIn a similar fashion, we'll create 4 functions with H(P) = \\bigcup_{i=1}^4f_i(P), and P \\in \\mathbb{R}^2 such that:\n\n\\begin{align}\nf_1(P) &= \\frac{P + A}{2}\\\\\nf_2(P) &= \\frac{P + B}{2}\\\\\nf_3(P) &= \\frac{P + C}{2}\\\\\nf_4(P) &= \\frac{P + D}{2}\\\\\n\\end{align}\n\nIf we then create 5 initial points located between all the vertices and allow these points to continually spawn children like before, something peculiar happens:\n\n\n \n \n\n\n\nWe essentially see a square of squares.\nWhat happened to the self-similar structure we were getting before?\nWhy isn't this more interesting?\nThe best answer I have for now is that some Hutchinson operators are interesting and some are not.\nStill, this square is a bit more interesting than it first appears, but to see why, we need to use the Hutchinson operator in a slightly different way.\nChaos games and attractors\nUntil now, our visualizations for both the Sierpinski triangle and the square have been computationally costly.\nEvery iteration, we generate 3 or 4 new children per child per step of the simulation.\nThis scales exponentially and means that we will quickly have millions of children to keep track of!\nIn fact, to deal with this, we developed our own method of counting through the tree to more efficiently keep track of everything, but that is a story for another day.\nThe question for now is whether there is a more computationally feasible way of iterating through our Hutchinson operator.\nAs it turns out, there is!\nRather than keeping track of every possible movement within the Hutchinson operator to draw out a shape, it's actually possible to randomly sample the function set instead through a process known as a chaos game [11][12]..\nHere, instead of tracking children of children, we track a single individual that chooses randomly between the Hutchinson functions, as shown here:\nfunction chaos_game(n::Int, shape_points)\n\n # Initializing the output array and the initial point\n output_points = zeros(n,2)\n point = [rand(), rand()]\n\n for i = 1:n\n output_points[i,:] .= point\n point = 0.5*(rand(shape_points) .+ point)\n end\n\n return output_points\n\nend\n\nchaosGame :: RandomGen g => g -> Int -> Array Int (Point -> Point) -> [Point]\nchaosGame g n hutchinson = take n points\n where\n (x, g') = random g\n (y, g'') = random g'\n choices = randomRs (bounds hutchinson) g''\n points = Point x y : zipWith (hutchinson !) choices points\n\n// This is a function to simulate a \"chaos game\"\nPointVector chaosGame(int numOutputPoints, const PointVector& inputPoints) {\n // Choose first point randomly\n Point curPoint = {drand(), drand()};\n\n // For each output point, compute midpoint to random input point\n PointVector outputPoints(numOutputPoints);\n for (auto& outPoint : outputPoints) {\n outPoint = curPoint;\n curPoint = 0.5 * (curPoint + choose(inputPoints));\n }\n\n return outputPoints;\n}\n\ndef chaos_game(n, shape_points):\n # Initialize the starting point\n point = [random(), random()]\n\n for _ in range(n):\n # Update the point position and yield the result\n point = [(p + s) / 2 for p, s in zip(point, choice(shape_points))]\n yield point\n\nvoid chaos_game(struct point *in, size_t in_n, struct point *out,\n size_t out_n) {\n\n struct point cur_point = {drand(), drand()};\n\n for (size_t i = 0; i \n(defun chaos-game (iterations shape-points)\n \"Plays a chaos game with a certain shape for a determined amount of iterations\"\n (loop\n repeat iterations\n for rand-point = (svref shape-points (random (length shape-points)))\n for point = (make-point (random 1.0) (random 1.0)) ; starting point\n then (make-point\n (* 0.5 (+ (point-x rand-point) (point-x point)))\n (* 0.5 (+ (point-y rand-point) (point-y point)))) ; every subsequent point\n collect point))\n\ndata point(x=0, y=0):\n def __add__(self, other):\n return point(self.x + other.x, self.y + other.y)\n\n def __rmul__(self, other):\n return point(self.x * other, self.y * other)\n\ndef chaos_game(n, shape_points):\n p = point(random(), random())\n\n for _ in range(n):\n p = (1/2) * (p + choice(shape_points))\n yield p\n\nfn chaos_game(iters: usize, shapes: Vec) -> Vec {\n let mut rng = rand::thread_rng();\n let mut p = Point{x: rng.gen(), y: rng.gen()};\n\n (0..iters).into_iter().map(|_| {\n let old_point = p;\n let tmp = shapes[rng.gen_range(0..shapes.len())];\n p.x = 0.5 * (p.x + tmp.x);\n p.y = 0.5 * (p.y + tmp.y);\n old_point\n }).collect()\n}\n\npublic static Point[] chaosGame(int n, Point[] shapePoints) {\n Random rng = new Random();\n\n // Initialize output vector\n Point[] outputPoints = new Point[n];\n\n // Choose first point randomly\n Point point = new Point(rng.nextDouble(), rng.nextDouble());\n\n for (int i = 0; i \nfunction Simulate-ChaosGame($n, $shapePoints) {\n $outputPoints = New-Object System.Collections.ArrayList\n\n # Initialize the starting point\n $point = @($(Get-Random -Minimum 0.0 -Maximum 1.0), $(Get-Random -Minimum 0.0 -Maximum 1.0))\n\n for ($i = 0; $i -lt $n; $i++) {\n $outputPoints.add($point) | Out-Null\n $temp = $shapePoints[$(Get-Random -Maximum $shapePoints.Count)]\n\n $point = @(\n 0.5 * ($point[0] + $temp[0])\n 0.5 * ($point[1] + $temp[1])\n )\n }\n\n return $outputPoints\n}\n\n\n\nIf we set the initial point to the on the equilateral triangle we saw before, we can see the Sierpinski triangle again after a few thousand iterations, as shown below:\n\n\n \n \n\n\n\nHere, we are plotting 200,000 point locations in sets of 1000, and every set becomes successively more blue as the visualization continues.\nAt first glance, this visualization seems bewildering.\nAfter all, it appears as if the entire triangle just magically comes into view in a few seconds.\nThe important thing to remember here is that each of these 200,000 dots is another location that our initial point decided to visit.\nThat said, there is something peculiar about the way the chaos game starts.\nWe are actually allowed to start the simulation off of the Sierpinski triangle.\nAs we mentioned earlier, none of the functions for the Sierpinski visualization allow children to enter the empty spaces of the triangle, so let's see what happens if we start the point off at the center of the triangle:\n\n\n \n \n\n\n\nHere, I have plotted the first 20 steps of the chaos game, and it is clear that the point gets closer and closer to the triangle each iteration.\nOnce it lands on the triangle, it can no longer escape and every movement from then on will be on the triangle.\nIn a sense, the wanderin point is attracted to the Sierpinski triangle with this set of functions, and that is actually the case!\nThe truth is that the word attractor is a very loaded term in the literature, but for the purposes of our discussion here, an attractor is any shape defined by the iteration through Hutchinson operator functions.\nSo let's go back to the example with the 4 points along the square and generate the attractor via a chaos game instead of going through every branch of the Hutchinson operator.\nIf we do this, we get what seems to be a random distribution of points:\n\nThis kinda boggled my mind a bit when I looked at it for the first time.\nWhat does a random distribution of points mean in this context?\nWell, firstly, it's only a random distribution between the square vertices of A, B, C, and D, but nothing exists outside of these points.\nThis means that it's not actually a random distribution of points, but instead an attractive plane that our lone wandering point can exist happily within.\nThis really helped me understand how attractors present themselves in different dimensions.\nThe Sierpinski triangle seems like a series of lines (one-dimensional objects) in two-dimensional space, but the square is a truly two-dimensional object.\nIn general, this means that an attractor embedded within \\mathbb{R}^N can be any shape of dimension N or lower.\nThe next obvious question is whether a square can create any more interesting fractally patterns, and the answer is \"yes, but only if we restrict the movement a bit.\"\nWhich brings us to another topic entirely: restricted chaos games.\nDiscussing restricted chaos games in more detail is a chapter in its own right, so I will forego the discussion here.\nIf you are interested, please let me know and I will be more than willing to add the chapter in the future!\nVideo Explanation\nHere is a video describing iterated function systems:\n\n\n\n\nExample Code\nFor the code in this chapter, we have decided to write it specifically for the Chaos game, not the hutchinson animations shown at the start of the chapter.\nThis is because that animation is slightly tricky to create and distracts from the overall purpose of this chapter.\nIn addition, we have written the chaos game code to take in a set of points so that it is not hard-coded for the Sierpinski triangle and can be easily extended to other shapes like the square or restricted chaos games, as we mentioned before!\nusing DelimitedFiles\n\n# This is a function to simulate a \"chaos game\"\nfunction chaos_game(n::Int, shape_points)\n\n # Initializing the output array and the initial point\n output_points = zeros(n,2)\n point = [rand(), rand()]\n\n for i = 1:n\n output_points[i,:] .= point\n point = 0.5*(rand(shape_points) .+ point)\n end\n\n return output_points\n\nend\n\n# This will generate a Sierpinski triangle with a chaos game of n points for an \n# initial triangle with three points on the vertices of an equilateral triangle:\n# A = (0.0, 0.0)\n# B = (0.5, sqrt(0.75))\n# C = (1.0, 0.0)\n# It will output the file sierpinski.dat, which can be plotted after\nshape_points = [[0.0, 0.0],\n [0.5, sqrt(0.75)],\n [1.0, 0.0]]\noutput_points = chaos_game(10000, shape_points)\nwritedlm(\"sierpinski.dat\", output_points)\n\nimport Data.Array ((!), Array, bounds, listArray)\nimport Data.List (intercalate)\nimport System.Random\n\ndata Point = Point Double Double\n\nchaosGame :: RandomGen g => g -> Int -> Array Int (Point -> Point) -> [Point]\nchaosGame g n hutchinson = take n points\n where\n (x, g') = random g\n (y, g'') = random g'\n choices = randomRs (bounds hutchinson) g''\n points = Point x y : zipWith (hutchinson !) choices points\n\nmain :: IO ()\nmain = do\n g \n#include \n#include \n#include \n#include \n\n// Simple X-Y point structure, along with some operators\nstruct Point {\n double x, y;\n};\n\nPoint operator+(Point lhs, Point rhs) { return {lhs.x + rhs.x, lhs.y + rhs.y}; }\nPoint operator*(double k, Point pt) { return {k * pt.x, k * pt.y}; }\nPoint operator*(Point pt, double k) { return k * pt; }\n\nusing PointVector = std::vector;\n\n// Returns a pseudo-random number generator\nstd::default_random_engine& rng() {\n // Initialize static pseudo-random engine with non-deterministic random seed\n static std::default_random_engine randEngine(std::random_device{}());\n return randEngine;\n}\n\n// Returns a random double in [0, 1)\ndouble drand() {\n return std::uniform_real_distribution(0.0, 1.0)(rng());\n}\n\n// Returns a random integer in [0, numElems-1]\nstd::size_t randrange(std::size_t numElems) {\n return std::uniform_int_distribution(0, numElems - 1)(rng());\n}\n\n// Return a random point from the non-empty PointVector\nPoint choose(const PointVector& points) {\n return points[randrange(points.size())];\n}\n\n// This is a function to simulate a \"chaos game\"\nPointVector chaosGame(int numOutputPoints, const PointVector& inputPoints) {\n // Choose first point randomly\n Point curPoint = {drand(), drand()};\n\n // For each output point, compute midpoint to random input point\n PointVector outputPoints(numOutputPoints);\n for (auto& outPoint : outputPoints) {\n outPoint = curPoint;\n curPoint = 0.5 * (curPoint + choose(inputPoints));\n }\n\n return outputPoints;\n}\n\nint main() {\n // This will generate a Sierpinski triangle with a chaos game of n points for\n // an initial triangle with three points on the vertices of an equilateral\n // triangle.\n PointVector inputPoints = {{0.0, 0.0}, {0.5, std::sqrt(0.75)}, {1.0, 0.0}};\n auto outputPoints = chaosGame(10000, inputPoints);\n\n // It will output the file sierpinski.dat, which can be plotted after\n std::ofstream ofs(\"sierpinski.dat\");\n for (auto pt : outputPoints)\n ofs \nfrom random import random, choice\nfrom math import sqrt\n\n# This generator simulates a \"chaos game\"\ndef chaos_game(n, shape_points):\n # Initialize the starting point\n point = [random(), random()]\n\n for _ in range(n):\n # Update the point position and yield the result\n point = [(p + s) / 2 for p, s in zip(point, choice(shape_points))]\n yield point\n\n# This will generate a Sierpinski triangle with a chaos game of n points for an\n# initial triangle with three points on the vertices of an equilateral triangle:\n# A = (0.0, 0.0)\n# B = (0.5, sqrt(0.75))\n# C = (1.0, 0.0)\n# It will output the file sierpinski.dat, which can be plotted after\nshape_points = [[0.0, 0.0],\n [0.5, sqrt(0.75)],\n [1.0, 0.0]]\nwith open(\"sierpinski.dat\", \"w\") as f:\n for point in chaos_game(10000, shape_points):\n f.write(\"{0}\\t{1}\\n\".format(*point))\n\n#include \n#include \n#include \n#include \n\nstruct point {\n double x, y;\n};\n\ndouble drand() {\n return ((double) rand() / (RAND_MAX));\n}\n\nstruct point random_element(struct point *array, size_t n) {\n return array[rand() % (int)n];\n}\n\nvoid chaos_game(struct point *in, size_t in_n, struct point *out,\n size_t out_n) {\n\n struct point cur_point = {drand(), drand()};\n\n for (size_t i = 0; i \n;;;; Iterated Function System implementation\n\n(defstruct (point (:constructor make-point (x y))) x y)\n\n(defun chaos-game (iterations shape-points)\n \"Plays a chaos game with a certain shape for a determined amount of iterations\"\n (loop\n repeat iterations\n for rand-point = (svref shape-points (random (length shape-points)))\n for point = (make-point (random 1.0) (random 1.0)) ; starting point\n then (make-point\n (* 0.5 (+ (point-x rand-point) (point-x point)))\n (* 0.5 (+ (point-y rand-point) (point-y point)))) ; every subsequent point\n collect point))\n\n(defparameter *shape-points*\n (map\n 'vector\n (lambda (e) (apply #'make-point e))\n ;; the backquote allows us to selectively evaluate (sqrt 0.75) with the comma\n `((0 0) (0.5 ,(sqrt 0.75)) (1 0))))\n\n;; output the data to the \"out.dat\" file\n(with-open-file (out \"sierpinski.dat\" :direction :output :if-exists :supersede)\n (flet ((format-point (p)\n ;; this is not very clean, but it's the simplest way to insert a tab into a string.\n (format nil \"~f~c~f\" (point-x p) #\\tab (point-y p))))\n (format out \"~{~a~%~}\" (map 'list #'format-point (chaos-game 10000 *shape-points*)))))\n\nfrom math import sqrt\nfrom random import random, choice\n\ndata point(x=0, y=0):\n def __add__(self, other):\n return point(self.x + other.x, self.y + other.y)\n\n def __rmul__(self, other):\n return point(self.x * other, self.y * other)\n\ndef chaos_game(n, shape_points):\n p = point(random(), random())\n\n for _ in range(n):\n p = (1/2) * (p + choice(shape_points))\n yield p\n\n\n# This will generate a Sierpinski triangle with a chaos game of n points for an\n# initial triangle with three points on the vertices of an equilateral triangle:\n# A = (0.0, 0.0)\n# B = (0.5, sqrt(0.75))\n# C = (1.0, 0.0)\n# It will output the file sierpinski.dat, which can be plotted after\nshape_points = [point(0.0, 0.0),\n point(0.5, sqrt(0.75)),\n point(1.0, 0.0)]\nwith open(\"sierpinski.dat\", \"w\") as f:\n for p in chaos_game(10000, shape_points):\n f.write(\"{0}\\t{1}\\n\".format(p.x, p.y))\n\nuse rand::*;\n\n#[derive(Clone, Copy)]\nstruct Point {\n x: f64,\n y: f64,\n}\n\nfn chaos_game(iters: usize, shapes: Vec) -> Vec {\n let mut rng = rand::thread_rng();\n let mut p = Point{x: rng.gen(), y: rng.gen()};\n\n (0..iters).into_iter().map(|_| {\n let old_point = p;\n let tmp = shapes[rng.gen_range(0..shapes.len())];\n p.x = 0.5 * (p.x + tmp.x);\n p.y = 0.5 * (p.y + tmp.y);\n old_point\n }).collect()\n}\n\nfn main() {\n let shapes = vec![\n Point{x: 0., y: 0.},\n Point{x: 0.5, y: 0.75_f64.sqrt()},\n Point{x: 1., y: 0.},\n ];\n\n let mut out = String::new();\n\n for point in chaos_game(10_000, shapes) {\n out += format!(\"{}\\t{}\\n\", point.x, point.y).as_str();\n }\n\n std::fs::write(\"./sierpinski.dat\", out).unwrap();\n}\n\nimport java.io.FileWriter;\nimport java.util.Random;\n\npublic class IFS {\n\n private static class Point {\n double x, y;\n\n public Point(double x, double y) {\n this.x = x;\n this.y = y;\n }\n }\n\n // This is a function to simulate a \"chaos game\"\n public static Point[] chaosGame(int n, Point[] shapePoints) {\n Random rng = new Random();\n\n // Initialize output vector\n Point[] outputPoints = new Point[n];\n\n // Choose first point randomly\n Point point = new Point(rng.nextDouble(), rng.nextDouble());\n\n for (int i = 0; i \n# This function simulates a \"chaos game\"\nfunction Simulate-ChaosGame($n, $shapePoints) {\n $outputPoints = New-Object System.Collections.ArrayList\n\n # Initialize the starting point\n $point = @($(Get-Random -Minimum 0.0 -Maximum 1.0), $(Get-Random -Minimum 0.0 -Maximum 1.0))\n\n for ($i = 0; $i -lt $n; $i++) {\n $outputPoints.add($point) | Out-Null\n $temp = $shapePoints[$(Get-Random -Maximum $shapePoints.Count)]\n\n $point = @(\n 0.5 * ($point[0] + $temp[0])\n 0.5 * ($point[1] + $temp[1])\n )\n }\n\n return $outputPoints\n}\n\n\n# This will generate a Sierpinski triangle with a chaos game of n points for an\n# initial triangle with three points on the vertices of an equilateral triangle:\n# A = (0.0, 0.0)\n# B = (0.5, sqrt(0.75))\n# C = (1.0, 0.0)\n# It will output the file sierpinski.dat, which can be plotted after\n$shapePoints = @(\n @(0.0, 0.0),\n @(0.5, [math]::sqrt(0.75)),\n @(1.0, 0.0)\n)\n\nSimulate-ChaosGame -n 10000 -shapePoints $shapePoints | % { \"$($_[0])`t$($_[1])\" } | Out-File -Path \"sierpinski.dat\"\n\n\n\nBibliography\n1.Wikipedia: Self-similarity, 2019.2.Mandelbrot, Benoit, How long is the coast of Britain? Statistical self-similarity and fractional dimension, American Association for the Advancement of Science, 1967.3.Jampour, Mahdi et al., A new fast technique for fingerprint identification with fractal and chaos game theory, World Scientific, 2010.4.Wikipedia: Fractal Compression, 2019.5.Saupe, Dietmar and Hamzaoui, Raouf, A review of the fractal image compression literature, ACM, 1994.6.Sanderson, G, 3blue1brown: Fractals are typically not self-similar, 2017.7.Wikipedia: Hausdorff dimension, 2019.8.Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B, Estimators of fractal dimension: Assessing the roughness of time series and spatial data, JSTOR, 2012.9.Wikipedia: Hutchinson Operator, 2019.10.Hutchinson, John E, Fractals and self similarity, JSTOR, 1981.11.Wikipedia: Chaos Game, 2019.12.Wolfram: Chaos Game, 2019.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"IFS triangle 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"IFS triangle 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"IFS triangle 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"IFS triangle 4\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"IFS triangle 5\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"IFS square 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"IFS square 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"IFS square 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Chaos 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Chaos 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"IFS triangle video 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"IFS triangle video 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"IFS square video 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Chaos video 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Chaos video 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n"},"contents/verlet_integration/verlet_integration.html":{"url":"contents/verlet_integration/verlet_integration.html","title":"Verlet Integration","keywords":"","body":"Verlet Integration\nVerlet integration is essentially a solution to the kinematic equation for the motion of any object,\n\nx = x_0 + v_0t + \\frac{1}{2}at^2 + \\frac{1}{6}bt^3 + \\cdots\n\nwhere x is the position, v is the velocity, a is the acceleration, b is the often forgotten jerk term, and t is time. This equation is a central equation to almost every Newtonian physics solver and brings up a class of algorithms known as force integrators. One of the first force integrators to work with is Verlet Integration.\nSo, let's say we want to solve for the next timestep in x. To a close approximation (actually performing a Taylor Series Expansion about x(t\\pm \\Delta t)), that might look like this:\n\nx(t+\\Delta t) = x(t) + v(t)\\Delta t + \\frac{1}{2}a(t)\\Delta t^2 + \\frac{1}{6}b(t) \\Delta t^3 + \\mathcal{O}(\\Delta t^4)\n\nThis means that if we need to find the next x, we need the current x, v, a, etc. However, because few people calculate the jerk term, our error is typically \\mathcal{O}(\\Delta t^3). That said, we can calculate x with less knowledge and higher accuracy if we play a trick! Let's say we want to calculate x of the previous timestep. Again, to a close approximation, that might look like this:\n\nx(t-\\Delta t) = x(t) - v(t)\\Delta t + \\frac{1}{2}a(t)\\Delta t^2 - \\frac{1}{6}b(t) \\Delta t^3 + \\mathcal{O}(\\Delta t^4)\n\nNow, we have two equations to solve for two different timesteps in x, one of which we already have. If we add the two equations together and solve for x(t+\\Delta t), we find that\n\nx(t+ \\Delta t) = 2x(t) - x(t-\\Delta t) + a(t)\\Delta t^2 + \\mathcal{O}(\\Delta t^4)\n\nSo, this means we can find our next x simply by knowing our current x, the x before that, and the acceleration! No velocity necessary! In addition, this drops the error to \\mathcal{O}(\\Delta t^4), which is great!\nHere is what it looks like in code:\nfunction verlet(pos::Float64, acc::Float64, dt::Float64)\n prev_pos = pos\n time = 0.0\n\n while (pos > 0)\n time += dt\n temp_pos = pos\n pos = pos * 2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n end\n\n return time\nend\n\ndouble verlet(double pos, double acc, double dt) {\n\n double prev_pos = pos;\n double time = 0;\n\n while (pos > 0) {\n time += dt;\n double next_pos = pos * 2 - prev_pos + acc * dt * dt;\n prev_pos = pos;\n pos = next_pos;\n }\n\n return time;\n}\n\nvoid verlet(double *time, double pos, double acc, double dt) {\n double prev_pos, temp_pos;\n prev_pos = pos;\n *time = 0.0;\n\n while (pos > 0) {\n *time += dt;\n temp_pos = pos;\n pos = pos * 2 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n }\n}\n\nstatic double verlet(double pos, double acc, double dt) {\n\n // Note that we are using a temp variable for the previous position\n double prev_pos, temp_pos, time;\n prev_pos = pos;\n time = 0;\n\n while (pos > 0) {\n time += dt;\n temp_pos = pos;\n pos = pos*2 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n }\n\n return time;\n}\n\ndef verlet(pos, acc, dt):\n prev_pos = pos\n time = 0\n\n while pos > 0:\n time += dt\n next_pos = pos * 2 - prev_pos + acc * dt * dt\n prev_pos, pos = pos, next_pos\n\n return time\n\ntype Method = Model -> Time -> Particle -> Particle -> Particle\n\nverlet :: Method\nverlet acc dt (xOld, _, _, _) (x, _, a, t) = (x', v', a', t + dt)\n where\n x' = 2 * x - xOld + a * dt ^ 2\n v' = 0\n a' = acc (x', v', a, t + dt)\n\nfunction verlet(pos, acc, dt) {\n let prevPos = pos;\n let time = 0;\n let tempPos;\n\n while (pos > 0) {\n time += dt;\n tempPos = pos;\n pos = pos * 2 - prevPos + acc * dt * dt;\n prevPos = tempPos;\n }\n\n return time;\n}\n\nfn verlet(mut pos: f64, acc: f64, dt: f64) -> f64 {\n let mut prev_pos = pos;\n let mut time = 0.0;\n\n while pos > 0.0 {\n time += dt;\n let temp_pos = pos;\n pos = pos * 2.0 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n }\n\n time\n}\n\nfunc verlet(pos: Double, acc: Double, dt: Double) -> Double {\n var pos = pos\n var temp_pos, time: Double\n var prev_pos = pos\n time = 0.0\n\n while (pos > 0) {\n time += dt\n temp_pos = pos\n pos = pos*2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n }\n\n return time\n}\n\nSUBROUTINE verlet(pos, acc, dt, time) \n IMPLICIT NONE\n REAL(8), INTENT(INOUT) :: pos, acc, dt, time\n REAL(8) :: prev_pos, next_pos\n\n\n prev_pos = pos\n time = 0d0\n\n DO\n IF (pos > 0d0) THEN\n time = time + dt\n next_pos = pos * 2d0 - prev_pos + acc * dt ** 2\n prev_pos = pos\n pos = next_pos\n ELSE\n EXIT\n END IF\n END DO\nEND SUBROUTINE verlet\n\ndef verlet(pos, acc, dt)\n\n prev_pos = pos\n time = 0\n while pos > 0 do\n time += dt\n temp_pos = pos\n pos = pos*2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n end\n\n return time\n\nend\n\nfunc verlet(pos, acc, dt float64) (time float64) {\n prevPos := pos\n time = 0\n\n for pos > 0 {\n time += dt\n nextPos := pos*2 - prevPos + acc*dt*dt\n prevPos, pos = pos, nextPos\n }\n\n return\n}\n\n# xmm0 - pos\n# xmm1 - acc\n# xmm2 - dt\n# RET xmm0 - time\nverlet:\n pxor xmm7, xmm7 # Holds 0 for comparisons\n pxor xmm3, xmm3 # Holds time value\n comisd xmm0, xmm7 # Check if pos is greater then 0.0\n jbe verlet_return\n movsd xmm6, xmm1 # xmm6 = acc * dt * dt\n mulsd xmm6, xmm2\n mulsd xmm6, xmm2\n movsd xmm5, xmm0 # Holds previous position\nverlet_loop:\n addsd xmm3, xmm2 # Adding dt to time\n movsd xmm4, xmm0 # Hold old value of posistion\n addsd xmm0, xmm0 # Calculating new position\n subsd xmm0, xmm5\n addsd xmm0, xmm6\n movsd xmm5, xmm4\n comisd xmm0, xmm7 # Check if position is greater then 0.0\n ja verlet_loop\nverlet_return:\n movsd xmm0, xmm3 # Saving time value\n ret\n\nfun verlet(_pos: Double, acc: Double, dt: Double): Double {\n var pos = _pos // Since function parameter are val and can't be modified\n var prevPos = pos\n var time = 0.0\n\n while (pos > 0) {\n time += dt\n val nextPos = pos * 2 - prevPos + acc * dt * dt\n prevPos = pos\n pos = nextPos\n }\n return time\n}\n\nfunc verlet(pos_in, acc, dt: float): float =\n var\n pos: float = pos_in\n prevPos: float = pos\n time: float = 0.0\n tempPos: float\n\n while pos > 0.0:\n time += dt\n tempPos = pos\n pos = pos * 2 - prevPos + acc * dt * dt\n prevPos = tempPos\n\n time\n\n(defun verlet (pos acc dt)\n \"Integrates Newton's equation for motion while pos > 0 using Verlet integration.\"\n (loop\n with prev-pos = pos\n for time = 0 then (incf time dt)\n while (> pos 0)\n ;; The starting speed is assumed to be zero.\n do (psetf\n pos (+ (* pos 2) (- prev-pos) (* acc dt dt))\n prev-pos pos)\n finally (return time)))\n\n\n\nNow, obviously this poses a problem; what if we want to calculate a term that requires velocity, like the kinetic energy, \\frac{1}{2}mv^2? In this case, we certainly cannot get rid of the velocity! Well, we can find the velocity to \\mathcal{O}(\\Delta t^2) accuracy by using the Stormer-Verlet method.\nWe have the equations for x(t+\\Delta t) and x(t-\\Delta t) above, so let's start there.\nIf we subtract the latter from the former, we get the following:\n\nx(t+\\Delta t) - x(t - \\Delta t) = 2v(t)\\Delta t + \\frac{1}{3}b(t)\\Delta t^3.\n\nWhen we solve for v(t), we get\n\n\\begin{align}\nv(t) &= \\frac{x(t+\\Delta t) - x(t-\\Delta t)}{2\\Delta t} + \\frac{b(t) \\Delta t^3}{3 \\Delta t} \\\\ \nv(t) &= \\frac{x(t+\\Delta t) - x(t-\\Delta t)}{2\\Delta t} + \\mathcal{O}(\\Delta t^2).\n\\end{align}\n\nNote that the 2 in the denominator makes sense because we are going over 2 timesteps. It's essentially solving v=\\frac{\\Delta x}{\\Delta t}. In addition, we can calculate the velocity of the next timestep like so\n\nv(t+\\Delta t) = \\frac{x(t+\\Delta t) - x(t)}{\\Delta t} + \\mathcal{O}(\\Delta t)\n\nHowever, the error for this is \\mathcal{O}(\\Delta t), which is quite poor, but it gets the job done in a pinch. Here's what it looks like in code:\nfunction stormer_verlet(pos::Float64, acc::Float64, dt::Float64)\n prev_pos = pos\n time = 0.0\n vel = 0.0\n\n while (pos > 0.0)\n time += dt\n temp_pos = pos\n pos = pos * 2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n\n # Because acceleration is constant, velocity is straightforward\n vel += acc * dt\n end\n\n return time, vel\nend\n\ntimestep stormer_verlet(double pos, double acc, double dt) {\n\n double prev_pos = pos;\n double time = 0;\n double vel = 0;\n while (pos > 0) {\n time += dt;\n double next_pos = pos * 2 - prev_pos + acc * dt * dt;\n prev_pos = pos;\n pos = next_pos;\n\n // The acceleration is constant, so the velocity is\n // straightforward\n vel += acc * dt;\n }\n\n return timestep { time, vel };\n}\n\nvoid stormer_verlet(double *time, double *vel,\n double pos, double acc, double dt) {\n double prev_pos, temp_pos;\n prev_pos = pos;\n *vel = 0.0;\n *time = 0.0;\n\n while (pos > 0) {\n *time += dt;\n temp_pos = pos;\n pos = pos * 2 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n\n *vel += acc * dt;\n }\n}\n\nstatic VerletValues stormer_verlet(double pos, double acc, double dt) {\n\n // Note that we are using a temp variable for the previous position\n double prev_pos, temp_pos, time, vel;\n prev_pos = pos;\n vel = 0;\n time = 0;\n while (pos > 0) {\n time += dt;\n temp_pos = pos;\n pos = pos*2 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n\n // The acceleration is constant, so the velocity is straightforward\n vel += acc*dt;\n }\n\n return new VerletValues(time, vel);\n}\n\ndef stormer_verlet(pos, acc, dt):\n prev_pos = pos\n time = 0\n vel = 0\n\n while pos > 0:\n time += dt\n next_pos = pos * 2 - prev_pos + acc * dt * dt\n prev_pos, pos = pos, next_pos\n vel += acc * dt\n\n return time, vel\n\nstormerVerlet :: Method\nstormerVerlet acc dt (xOld, _, _, _) (x, _, a, t) = (x', v', a', t + dt)\n where\n x' = 2 * x - xOld + a * dt ^ 2\n v' = (x' - x) / dt\n a' = acc (x', v', a, t + dt)\n\nfunction stormerVerlet(pos, acc, dt) {\n let prevPos = pos;\n let time = 0;\n let vel = 0;\n let tempPos;\n\n while (pos > 0) {\n time += dt;\n tempPos = pos;\n pos = pos * 2 - prevPos + acc * dt * dt;\n prevPos = tempPos;\n\n vel += acc * dt;\n }\n\n return { time, vel };\n}\n\nfn stormer_verlet(mut pos: f64, acc: f64, dt: f64) -> (f64, f64) {\n let mut prev_pos = pos;\n let mut time = 0.0;\n let mut vel = 0.0;\n\n while pos > 0.0 {\n time += dt;\n let temp_pos = pos;\n pos = pos * 2.0 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n\n // Because acceleration is constant, velocity is\n // straightforward\n vel += acc * dt;\n }\n\n (time, vel)\n}\n\nfunc stormerVerlet(pos: Double, acc: Double, dt: Double) -> (time: Double, vel: Double) {\n var pos = pos\n var temp_pos, time, vel: Double\n var prev_pos = pos\n vel = 0\n time = 0\n\n while (pos > 0) {\n time += dt\n temp_pos = pos\n pos = pos*2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n\n vel += acc*dt\n }\n\n return (time:time, vel:vel)\n}\n\nSUBROUTINE stormer_verlet(pos, acc, dt, time, vel) \n IMPLICIT NONE\n REAL(8), INTENT(INOUT) :: pos, acc, dt, time, vel\n REAL(8) :: prev_pos, next_pos\n\n prev_pos = pos \n time = 0d0\n vel = 0d0\n\n DO\n IF (pos > 0d0) THEN\n time = time + dt\n next_pos = pos * 2 - prev_pos + acc * dt ** 2\n prev_pos = pos\n pos = next_pos\n vel = vel + acc * dt\n ELSE\n EXIT\n END IF\n END DO\nEND SUBROUTINE stormer_verlet\n\ndef stormer_verlet(pos, acc, dt)\n\n prev_pos = pos\n vel = 0\n time = 0\n while pos > 0 do\n time += dt\n temp_pos = pos\n pos = pos*2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n\n vel += acc*dt\n end\n\n return time, vel\n\nend\n\nfunc stormerVerlet(pos, acc, dt float64) (time, vel float64) {\n prevPos := pos\n time, vel = 0, 0\n\n for pos > 0 {\n time += dt\n vel += acc * dt\n nextPos := pos*2 - prevPos + acc*dt*dt\n prevPos, pos = pos, nextPos\n }\n\n return\n}\n\n# xmm0 - pos\n# xmm1 - acc\n# xmm2 - dt\n# RET xmm0 - time\n# RET xmm1 - velocity\nstormer_verlet:\n pxor xmm7, xmm7 # Holds 0 for comparisons\n pxor xmm3, xmm3 # Holds time value\n comisd xmm0, xmm7 # Check if pos is greater then 0.0\n jbe stormer_verlet_return\n movsd xmm6, xmm1 # xmm6 = acc * dt * dt\n mulsd xmm6, xmm2\n mulsd xmm6, xmm2\n movsd xmm5, xmm0 # Holds previous position\nstormer_verlet_loop:\n addsd xmm3, xmm2 # Adding dt to time\n movsd xmm4, xmm0 # Hold old value of posistion\n addsd xmm0, xmm0 # Calculating new position\n subsd xmm0, xmm5\n addsd xmm0, xmm6\n movsd xmm5, xmm4\n comisd xmm0, xmm7 # Check if position is greater then 0.0\n ja stormer_verlet_loop\nstormer_verlet_return:\n movsd xmm0, xmm3 # Saving time and velocity\n mulsd xmm3, xmm1\n movsd xmm1, xmm3\n ret\n\nfun stormerVerlet(_pos: Double, acc: Double, dt: Double): VerletValues {\n var pos = _pos\n var prevPos = pos\n var time = 0.0\n var vel = 0.0\n while (pos > 0) {\n time += dt\n val nextPos = pos * 2 - prevPos + acc * dt * dt\n prevPos = pos\n pos = nextPos\n vel += acc * dt\n }\n return VerletValues(time, vel)\n}\n\nfunc stormerVerlet(pos_in, acc, dt: float): (float, float) =\n var\n pos: float = pos_in\n prevPos: float = pos\n time: float = 0.0\n vel: float = 0.0\n tempPos: float\n\n while pos > 0.0:\n time += dt\n tempPos = pos\n pos = pos * 2 - prevPos + acc * dt * dt\n prevPos = tempPos\n\n vel += acc * dt\n\n (time, vel)\n\n(defun stormer-verlet (pos acc dt)\n \"Integrates Newton's equation for motion while pos > 0 using the Stormer-Verlet method.\"\n (loop\n with prev-pos = pos\n for time = 0 then (incf time dt)\n for vel = 0 then (incf vel (* acc dt))\n while (> pos 0)\n ;; Variables are changed simultaneously by 'psetf', so there's no need for a temporary variable.\n do (psetf\n pos (+ (* pos 2) (- prev-pos) (* acc dt dt))\n prev-pos pos)\n finally (return (list time vel))))\n\n\n\n\nNow, let's say we actually need the velocity to calculate out next timestep. Well, in this case, we simply cannot use the above approximation and instead need to use the Velocity Verlet algorithm.\nVelocity Verlet\nIn some ways, this algorithm is even simpler than above. We can calculate everything like\n\n\\begin{align}\nx(t+\\Delta t) &=x(t) + v(t)\\Delta t + \\frac{1}{2}a(t)\\Delta t^2 \\\\\na(t+\\Delta t) &= f(x(t+\\Delta t)) \\\\\nv(t+\\Delta t) &= v(t) + \\frac{1}{2}(a(t) + a(t+\\Delta t))\\Delta t\n\\end{align}\n\nwhich is literally the kinematic equation above, solving for x, v, and a every timestep. You can also split up the equations like so\n\n\\begin{align}\nv(t+\\frac{1}{2}\\Delta t) &= v(t) + \\frac{1}{2}a(t)\\Delta t \\\\\nx(t+\\Delta t) &=x(t) + v(t+\\frac{1}{2}\\Delta t)\\Delta t \\\\\na(t+\\Delta t) &= f(x(t+\\Delta t)) \\\\\nv(t+\\Delta t) &= v(t+\\frac{1}{2}\\Delta t) + \\frac{1}{2}a(t+\\Delta t)\\Delta t\n\\end{align}\n\nHere is the velocity Verlet method in code:\nfunction velocity_verlet(pos::Float64, acc::Float64, dt::Float64)\n prev_pos = pos\n time = 0.0\n vel = 0.0\n\n while (pos > 0.0)\n time += dt\n pos += vel * dt + 0.5 * acc * dt * dt;\n vel += acc * dt;\n end\n\n return time, vel\nend\n\ntimestep velocity_verlet(double pos, double acc, double dt) {\n\n double time = 0;\n double vel = 0;\n while (pos > 0) {\n time += dt;\n pos += vel * dt + 0.5 * acc * dt * dt;\n vel += acc * dt;\n }\n\n return timestep { time, vel };\n}\n\nvoid velocity_verlet(double *time, double *vel,\n double pos, double acc, double dt) {\n *vel = 0.0;\n *time = 0.0;\n\n while (pos > 0) {\n *time += dt;\n pos += (*vel) * dt + 0.5 * acc * dt * dt;\n *vel += acc * dt;\n }\n}\n\nstatic VerletValues velocity_verlet(double pos, double acc, double dt) {\n\n // Note that we are using a temp variable for the previous position\n double time, vel;\n vel = 0;\n time = 0;\n while (pos > 0) {\n time += dt;\n pos += vel*dt + 0.5*acc * dt * dt;\n vel += acc*dt;\n }\n return new VerletValues(time, vel);\n}\n\ndef velocity_verlet(pos, acc, dt):\n time = 0\n vel = 0\n\n while pos > 0:\n time += dt\n pos += vel * dt + 0.5 * acc * dt * dt\n vel += acc * dt\n\n return time, vel\n\nvelocityVerlet :: Method\nvelocityVerlet acc dt (xOld, _, aOld, _) (x, v, a, t) = (x', v', a', t + dt)\n where\n x' = 2 * x - xOld + a * dt ^ 2\n v' = v + 0.5 * (aOld + a) * dt\n a' = acc (x', v', a, t + dt)\n\nfunction velocityVerlet(pos, acc, dt) {\n let time = 0;\n let vel = 0;\n\n while (pos > 0) {\n time += dt;\n pos += vel * dt + 0.5 * acc * dt * dt;\n vel += acc * dt;\n }\n\n return { time, vel };\n}\n\nfn velocity_verlet(mut pos: f64, acc: f64, dt: f64) -> (f64, f64) {\n let mut time = 0.0;\n let mut vel = 0.0;\n\n while pos > 0.0 {\n time += dt;\n pos += vel * dt + 0.5 * acc * dt * dt;\n vel += acc * dt;\n }\n\n (time, vel)\n}\n\nfunc velocityVerlet(pos: Double, acc: Double, dt: Double) -> (time: Double, vel: Double) {\n var pos = pos\n var time, vel : Double\n vel = 0\n time = 0\n\n while (pos > 0) {\n time += dt\n pos += vel*dt + 0.5*acc * dt * dt\n vel += acc*dt\n }\n\n return (time:time, vel:vel)\n}\n\nSUBROUTINE velocity_verlet(pos, acc, dt, time, vel) \n IMPLICIT NONE\n REAL(8), INTENT(INOUT) :: pos, acc, dt, time, vel\n\n time = 0d0\n vel = 0d0\n\n DO\n IF (pos > 0d0) THEN\n time = time + dt\n pos = pos + vel * dt + 0.5d0 * acc * dt ** 2 \n vel = vel + acc * dt\n ELSE\n EXIT\n END IF\n END DO\nEND SUBROUTINE velocity_verlet\n\ndef velocity_verlet(pos, acc, dt)\n\n vel = 0\n time = 0\n while pos > 0 do\n time += dt\n pos += vel*dt + 0.5*acc * dt * dt\n vel += acc*dt\n end\n\n return time, vel\n\nend\n\nfunc velocityVerlet(pos, acc, dt float64) (time, vel float64) {\n time, vel = 0, 0\n\n for pos > 0 {\n time += dt\n pos += vel*dt + .5*acc*dt*dt\n vel += acc * dt\n }\n\n return\n}\n\n# xmm0 - pos\n# xmm1 - acc\n# xmm2 - dt\n# RET xmm0 - time\n# RET xmm1 - velocity\nvelocity_verlet:\n pxor xmm7, xmm7 # Holds 0 for comparisons\n pxor xmm3, xmm3 # Holds the velocity value\n pxor xmm4, xmm4 # Holds the time value\n comisd xmm0, xmm7 # Check if pos is greater then 0.0\n jbe velocity_verlet_return\n movsd xmm5, half # xmm5 = 0.5 * dt * dt * acc\n mulsd xmm5, xmm2\n mulsd xmm5, xmm2\n mulsd xmm5, xmm1\nvelocity_verlet_loop:\n movsd xmm6, xmm3 # Move velocity into register\n mulsd xmm6, xmm2 # Calculate new position\n addsd xmm6, xmm5\n addsd xmm0, xmm6\n addsd xmm4, xmm2 # Incrementing time\n movsd xmm3, xmm4 # Updating velocity\n mulsd xmm3, xmm1\n comisd xmm0, xmm7\n ja velocity_verlet_loop\nvelocity_verlet_return:\n movsd xmm0, xmm4 # Saving time and velocity\n movsd xmm1, xmm3\n ret\n\nfun velocityVerlet(_pos: Double, acc: Double, dt: Double): VerletValues {\n var pos = _pos\n var time = 0.0\n var vel = 0.0\n while (pos > 0) {\n time += dt\n pos += vel * dt + 0.5 * acc * dt * dt\n vel += acc * dt\n }\n return VerletValues(time, vel)\n}\n\nfunc velocityVerlet(pos_in, acc, dt: float): (float, float) =\n var\n pos: float = pos_in\n time: float = 0.0\n vel: float = 0.0\n\n while pos > 0.0:\n time += dt\n pos += vel * dt + 0.5 * acc * dt * dt\n vel += acc * dt\n\n (time, vel)\n\n(defun velocity-verlet (pos acc dt)\n \"Integrates Newton's equation for motion while pos > 0 using the velocity in calculations.\"\n (loop\n for time = 0 then (incf time dt)\n for vel = 0 then (incf vel (* acc dt))\n for p = pos then (incf p (+ (* vel dt) (* 0.5 acc dt dt)))\n while (> p 0)\n finally (return (list time vel))))\n\n\n\nEven though this method is more widely used than the simple Verlet method mentioned above, it unfortunately has an error term of \\mathcal{O}(\\Delta t^2), which is two orders of magnitude worse. That said, if you want to have a simulation with many objects that depend on one another --- like a gravity simulation --- the Velocity Verlet algorithm is a handy choice; however, you may have to play further tricks to allow everything to scale appropriately. These types of simulations are sometimes called n-body simulations and one such trick is the Barnes-Hut algorithm, which cuts the complexity of n-body simulations from \\sim \\mathcal{O}(n^2) to \\sim \\mathcal{O}(n\\log(n)).\nVideo Explanation\nHere is a video describing Verlet integration:\n\n\n\n\nExample Code\nBoth of these methods work simply by iterating timestep-by-timestep and can be written straightforwardly in any language. For reference, here are snippets of code that use both the classic and velocity Verlet methods to find the time it takes for a ball to hit the ground after being dropped from a given height.\nfunction verlet(pos::Float64, acc::Float64, dt::Float64)\n prev_pos = pos\n time = 0.0\n\n while (pos > 0)\n time += dt\n temp_pos = pos\n pos = pos * 2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n end\n\n return time\nend\n\nfunction stormer_verlet(pos::Float64, acc::Float64, dt::Float64)\n prev_pos = pos\n time = 0.0\n vel = 0.0\n\n while (pos > 0.0)\n time += dt\n temp_pos = pos\n pos = pos * 2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n\n # Because acceleration is constant, velocity is straightforward\n vel += acc * dt\n end\n\n return time, vel\nend\n\nfunction velocity_verlet(pos::Float64, acc::Float64, dt::Float64)\n prev_pos = pos\n time = 0.0\n vel = 0.0\n\n while (pos > 0.0)\n time += dt\n pos += vel * dt + 0.5 * acc * dt * dt;\n vel += acc * dt;\n end\n\n return time, vel\nend\n\nfunction main()\n time = verlet(5.0, -10.0, 0.01);\n println(\"[#]\\nTime for Verlet integration is:\")\n println(\"$(time)\")\n\n time, vel = stormer_verlet(5.0, -10.0, 0.01);\n println(\"[#]\\nTime for Stormer Verlet integration is:\")\n println(\"$(time)\")\n println(\"[#]\\nVelocity for Stormer Verlet integration is:\")\n println(\"$(vel)\")\n\n time, vel = velocity_verlet(5.0, -10.0, 0.01);\n println(\"[#]\\nTime for velocity Verlet integration is:\")\n println(\"$(time)\")\n println(\"[#]\\nVelocity for velocity Verlet integration is:\")\n println(\"$(vel)\")\n\nend\n\nmain()\n\n#include \n#include \n\nstruct timestep {\n double time;\n double vel;\n};\n\ndouble verlet(double pos, double acc, double dt) {\n\n double prev_pos = pos;\n double time = 0;\n\n while (pos > 0) {\n time += dt;\n double next_pos = pos * 2 - prev_pos + acc * dt * dt;\n prev_pos = pos;\n pos = next_pos;\n }\n\n return time;\n}\n\ntimestep stormer_verlet(double pos, double acc, double dt) {\n\n double prev_pos = pos;\n double time = 0;\n double vel = 0;\n while (pos > 0) {\n time += dt;\n double next_pos = pos * 2 - prev_pos + acc * dt * dt;\n prev_pos = pos;\n pos = next_pos;\n\n // The acceleration is constant, so the velocity is\n // straightforward\n vel += acc * dt;\n }\n\n return timestep { time, vel };\n}\n\ntimestep velocity_verlet(double pos, double acc, double dt) {\n\n double time = 0;\n double vel = 0;\n while (pos > 0) {\n time += dt;\n pos += vel * dt + 0.5 * acc * dt * dt;\n vel += acc * dt;\n }\n\n return timestep { time, vel };\n}\n\nint main() {\n std::cout \n#include \n\nvoid verlet(double *time, double pos, double acc, double dt) {\n double prev_pos, temp_pos;\n prev_pos = pos;\n *time = 0.0;\n\n while (pos > 0) {\n *time += dt;\n temp_pos = pos;\n pos = pos * 2 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n }\n}\n\nvoid stormer_verlet(double *time, double *vel,\n double pos, double acc, double dt) {\n double prev_pos, temp_pos;\n prev_pos = pos;\n *vel = 0.0;\n *time = 0.0;\n\n while (pos > 0) {\n *time += dt;\n temp_pos = pos;\n pos = pos * 2 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n\n *vel += acc * dt;\n }\n}\n\nvoid velocity_verlet(double *time, double *vel,\n double pos, double acc, double dt) {\n *vel = 0.0;\n *time = 0.0;\n\n while (pos > 0) {\n *time += dt;\n pos += (*vel) * dt + 0.5 * acc * dt * dt;\n *vel += acc * dt;\n }\n}\n\nint main() {\n double time, vel;\n\n verlet(&time, 5.0, -10, 0.01);\n printf(\"[#]\\nTime for Verlet integration is:\\n\");\n printf(\"%lf\\n\", time);\n\n stormer_verlet(&time, &vel, 5.0, -10, 0.01);\n printf(\"[#]\\nTime for Stormer Verlet integration is:\\n\");\n printf(\"%lf\\n\", time);\n printf(\"[#]\\nVelocity for Stormer Verlet integration is:\\n\");\n printf(\"%lf\\n\", vel);\n\n velocity_verlet(&time, &vel, 5.0, -10, 0.01);\n printf(\"[#]\\nTime for velocity Verlet integration is:\\n\");\n printf(\"%lf\\n\", time);\n printf(\"[#]\\nVelocity for Stormer Verlet integration is:\\n\");\n printf(\"%lf\\n\", vel);\n\n return 0;\n}\n\npublic class Verlet {\n\n private static class VerletValues {\n public double time;\n public double vel;\n\n public VerletValues(double time, double vel) {\n this.time = time;\n this.vel = vel;\n }\n }\n\n\n static double verlet(double pos, double acc, double dt) {\n\n // Note that we are using a temp variable for the previous position\n double prev_pos, temp_pos, time;\n prev_pos = pos;\n time = 0;\n\n while (pos > 0) {\n time += dt;\n temp_pos = pos;\n pos = pos*2 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n }\n\n return time;\n }\n\n static VerletValues stormer_verlet(double pos, double acc, double dt) {\n\n // Note that we are using a temp variable for the previous position\n double prev_pos, temp_pos, time, vel;\n prev_pos = pos;\n vel = 0;\n time = 0;\n while (pos > 0) {\n time += dt;\n temp_pos = pos;\n pos = pos*2 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n\n // The acceleration is constant, so the velocity is straightforward\n vel += acc*dt;\n }\n\n return new VerletValues(time, vel);\n }\n\n static VerletValues velocity_verlet(double pos, double acc, double dt) {\n\n // Note that we are using a temp variable for the previous position\n double time, vel;\n vel = 0;\n time = 0;\n while (pos > 0) {\n time += dt;\n pos += vel*dt + 0.5*acc * dt * dt;\n vel += acc*dt;\n }\n return new VerletValues(time, vel);\n }\n\n public static void main(String[] args) {\n\n double verletTime = verlet(5.0, -10, 0.01);\n System.out.println(\"[#]\\nTime for Verlet integration is:\");\n System.out.println(verletTime);\n\n VerletValues stormerVerlet = stormer_verlet(5.0, -10, 0.01);\n System.out.println(\"[#]\\nTime for Stormer Verlet integration is:\");\n System.out.println(stormerVerlet.time);\n System.out.println(\"[#]\\nVelocity for Stormer Verlet integration is:\");\n System.out.println(stormerVerlet.vel);\n\n VerletValues velocityVerlet = velocity_verlet(5.0, -10, 0.01);\n System.out.println(\"[#]\\nTime for velocity Verlet integration is:\");\n System.out.println(velocityVerlet.time);\n System.out.println(\"[#]\\nVelocity for velocity Verlet integration is:\");\n System.out.println(velocityVerlet.vel);\n\n }\n}\n\ndef verlet(pos, acc, dt):\n prev_pos = pos\n time = 0\n\n while pos > 0:\n time += dt\n next_pos = pos * 2 - prev_pos + acc * dt * dt\n prev_pos, pos = pos, next_pos\n\n return time\n\ndef stormer_verlet(pos, acc, dt):\n prev_pos = pos\n time = 0\n vel = 0\n\n while pos > 0:\n time += dt\n next_pos = pos * 2 - prev_pos + acc * dt * dt\n prev_pos, pos = pos, next_pos\n vel += acc * dt\n\n return time, vel\n\ndef velocity_verlet(pos, acc, dt):\n time = 0\n vel = 0\n\n while pos > 0:\n time += dt\n pos += vel * dt + 0.5 * acc * dt * dt\n vel += acc * dt\n\n return time, vel\n\ndef main():\n time = verlet(5, -10, 0.01)\n print(\"[#]\\nTime for Verlet integration is:\")\n print(\"{:.10f}\".format(time))\n\n time, vel = stormer_verlet(5, -10, 0.01)\n print(\"[#]\\nTime for Stormer Verlet integration is:\")\n print(\"{:.10f}\".format(time))\n print(\"[#]\\nVelocity for Stormer Verlet integration is:\")\n print(\"{:.10f}\".format(vel))\n\n time, vel = velocity_verlet(5, -10, 0.01)\n print(\"[#]\\nTime for velocity Verlet integration is:\")\n print(\"{:.10f}\".format(time))\n print(\"[#]\\nVelocity for velocity Verlet integration is:\")\n print(\"{:.10f}\".format(vel))\n\n\nif __name__ == '__main__':\n main()\n\n-- submitted by Jie\ntype Time = Double\n\ntype Position = Double\n\ntype Speed = Double\n\ntype Acceleration = Double\n\ntype Particle = (Position, Speed, Acceleration, Time)\n\ntype Model = Particle -> Acceleration\n\ntype Method = Model -> Time -> Particle -> Particle -> Particle\n\nverlet :: Method\nverlet acc dt (xOld, _, _, _) (x, _, a, t) = (x', v', a', t + dt)\n where\n x' = 2 * x - xOld + a * dt ^ 2\n v' = 0\n a' = acc (x', v', a, t + dt)\n\nstormerVerlet :: Method\nstormerVerlet acc dt (xOld, _, _, _) (x, _, a, t) = (x', v', a', t + dt)\n where\n x' = 2 * x - xOld + a * dt ^ 2\n v' = (x' - x) / dt\n a' = acc (x', v', a, t + dt)\n\nvelocityVerlet :: Method\nvelocityVerlet acc dt (xOld, _, aOld, _) (x, v, a, t) = (x', v', a', t + dt)\n where\n x' = 2 * x - xOld + a * dt ^ 2\n v' = v + 0.5 * (aOld + a) * dt\n a' = acc (x', v', a, t + dt)\n\ntrajectory :: Method -> Model -> Time -> Particle -> [Particle]\ntrajectory method acc dt p0@(x, v, a, t0) = traj\n where\n traj = p0 : p1 : zipWith (method acc dt) traj (tail traj)\n p1 = (x', v', acc (x', v', a, t0 + dt), t0 + dt)\n x' = x + v * dt + 0.5 * a * dt ^ 2\n v' = v + a * dt\n\nmain :: IO ()\nmain = do\n let p0 = (5, 0, -10, 0)\n dt = 0.001\n freefall _ = -10\n aboveGround (x, _, _, _) = x > 0\n timeVelocity m =\n let (_, v, _, t) = last $ takeWhile aboveGround $ trajectory m freefall dt p0\n in (show t, show v)\n\n putStrLn \"[#]\\nTime for Verlet integration is:\"\n putStrLn $ fst $ timeVelocity verlet\n putStrLn \"[#]\\nTime for Stormer Verlet integration is:\"\n putStrLn $ fst $ timeVelocity stormerVerlet\n putStrLn \"[#]\\nVelocity for Stormer Verlet integration is:\"\n putStrLn $ snd $ timeVelocity stormerVerlet\n putStrLn \"[#]\\nTime for velocity Verlet integration is:\"\n putStrLn $ fst $ timeVelocity velocityVerlet\n putStrLn \"[#]\\nVelocity for velocity Verlet integration is:\"\n putStrLn $ snd $ timeVelocity velocityVerlet\n\nfunction verlet(pos, acc, dt) {\n let prevPos = pos;\n let time = 0;\n let tempPos;\n\n while (pos > 0) {\n time += dt;\n tempPos = pos;\n pos = pos * 2 - prevPos + acc * dt * dt;\n prevPos = tempPos;\n }\n\n return time;\n}\n\nfunction stormerVerlet(pos, acc, dt) {\n let prevPos = pos;\n let time = 0;\n let vel = 0;\n let tempPos;\n\n while (pos > 0) {\n time += dt;\n tempPos = pos;\n pos = pos * 2 - prevPos + acc * dt * dt;\n prevPos = tempPos;\n\n vel += acc * dt;\n }\n\n return { time, vel };\n}\n\nfunction velocityVerlet(pos, acc, dt) {\n let time = 0;\n let vel = 0;\n\n while (pos > 0) {\n time += dt;\n pos += vel * dt + 0.5 * acc * dt * dt;\n vel += acc * dt;\n }\n\n return { time, vel };\n}\n\nconst time = verlet(5, -10, 0.01);\nconsole.log(`[#]\\nTime for Verlet integration is:`);\nconsole.log(`${time}`);\n\nconst stormer = stormerVerlet(5, -10, 0.01);\nconsole.log(`[#]\\nTime for Stormer Verlet integration is:`);\nconsole.log(`${stormer.time}`);\nconsole.log(`[#]\\nVelocity for Stormer Verlet integration is:`);\nconsole.log(`${stormer.vel}`);\n\nconst velocity = velocityVerlet(5, -10, 0.01);\nconsole.log(`[#]\\nTime for velocity Verlet integration is:`);\nconsole.log(`${velocity.time}`);\nconsole.log(`[#]\\nVelocity for velocity Verlet integration is:`);\nconsole.log(`${velocity.vel}`);\n\nfn verlet(mut pos: f64, acc: f64, dt: f64) -> f64 {\n let mut prev_pos = pos;\n let mut time = 0.0;\n\n while pos > 0.0 {\n time += dt;\n let temp_pos = pos;\n pos = pos * 2.0 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n }\n\n time\n}\n\nfn stormer_verlet(mut pos: f64, acc: f64, dt: f64) -> (f64, f64) {\n let mut prev_pos = pos;\n let mut time = 0.0;\n let mut vel = 0.0;\n\n while pos > 0.0 {\n time += dt;\n let temp_pos = pos;\n pos = pos * 2.0 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n\n // Because acceleration is constant, velocity is\n // straightforward\n vel += acc * dt;\n }\n\n (time, vel)\n}\n\nfn velocity_verlet(mut pos: f64, acc: f64, dt: f64) -> (f64, f64) {\n let mut time = 0.0;\n let mut vel = 0.0;\n\n while pos > 0.0 {\n time += dt;\n pos += vel * dt + 0.5 * acc * dt * dt;\n vel += acc * dt;\n }\n\n (time, vel)\n}\n\nfn main() {\n let time_v = verlet(5.0, -10.0, 0.01);\n let (time_sv, vel_sv) = stormer_verlet(5.0, -10.0, 0.01);\n let (time_vv, vel_vv) = velocity_verlet(5.0, -10.0, 0.01);\n\n println!(\"[#]\\nTime for Verlet integration is:\");\n println!(\"{}\", time_v);\n\n println!(\"[#]\\nTime for Stormer Verlet integration is:\");\n println!(\"{}\", time_sv);\n println!(\"[#]\\nVelocity for Stormer Verlet integration is:\");\n println!(\"{}\", vel_sv);\n\n println!(\"[#]\\nTime for velocity Verlet integration is:\");\n println!(\"{}\", time_vv);\n println!(\"[#]\\nVelocity for velocity Verlet integration is:\");\n println!(\"{}\", vel_vv);\n}\n\nfunc verlet(pos: Double, acc: Double, dt: Double) -> Double {\n var pos = pos\n var temp_pos, time: Double\n var prev_pos = pos\n time = 0.0\n\n while (pos > 0) {\n time += dt\n temp_pos = pos\n pos = pos*2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n }\n\n return time\n}\n\nfunc stormerVerlet(pos: Double, acc: Double, dt: Double) -> (time: Double, vel: Double) {\n var pos = pos\n var temp_pos, time, vel: Double\n var prev_pos = pos\n vel = 0\n time = 0\n\n while (pos > 0) {\n time += dt\n temp_pos = pos\n pos = pos*2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n\n vel += acc*dt\n }\n\n return (time:time, vel:vel)\n}\n\nfunc velocityVerlet(pos: Double, acc: Double, dt: Double) -> (time: Double, vel: Double) {\n var pos = pos\n var time, vel : Double\n vel = 0\n time = 0\n\n while (pos > 0) {\n time += dt\n pos += vel*dt + 0.5*acc * dt * dt\n vel += acc*dt\n }\n\n return (time:time, vel:vel)\n}\n\nfunc main() {\n let verletTime = verlet(pos: 5.0, acc: -10.0, dt: 0.01)\n print(\"[#]\\nTime for Verlet integration is:\")\n print(\"\\(verletTime)\")\n\n let stormer = stormerVerlet(pos: 5.0, acc: -10.0, dt: 0.01);\n print(\"[#]\\nTime for Stormer Verlet integration is:\")\n print(\"\\(stormer.time)\")\n print(\"[#]\\nVelocity for Stormer Verlet integration is:\")\n print(\"\\(stormer.vel)\")\n\n let velVerlet = velocityVerlet(pos: 5.0, acc: -10, dt: 0.01)\n print(\"[#]\\nTime for velocity Verlet integration is:\")\n print(\"\\(velVerlet.time)\")\n print(\"[#]\\nVelocity for velocity Verlet integration is:\")\n print(\"\\(velVerlet.vel)\")\n}\n\nmain()\n\nSUBROUTINE verlet(pos, acc, dt, time) \n IMPLICIT NONE\n REAL(8), INTENT(INOUT) :: pos, acc, dt, time\n REAL(8) :: prev_pos, next_pos\n\n\n prev_pos = pos\n time = 0d0\n\n DO\n IF (pos > 0d0) THEN\n time = time + dt\n next_pos = pos * 2d0 - prev_pos + acc * dt ** 2\n prev_pos = pos\n pos = next_pos\n ELSE\n EXIT\n END IF\n END DO\nEND SUBROUTINE verlet\n\nSUBROUTINE stormer_verlet(pos, acc, dt, time, vel) \n IMPLICIT NONE\n REAL(8), INTENT(INOUT) :: pos, acc, dt, time, vel\n REAL(8) :: prev_pos, next_pos\n\n prev_pos = pos \n time = 0d0\n vel = 0d0\n\n DO\n IF (pos > 0d0) THEN\n time = time + dt\n next_pos = pos * 2 - prev_pos + acc * dt ** 2\n prev_pos = pos\n pos = next_pos\n vel = vel + acc * dt\n ELSE\n EXIT\n END IF\n END DO\nEND SUBROUTINE stormer_verlet \n\nSUBROUTINE velocity_verlet(pos, acc, dt, time, vel) \n IMPLICIT NONE\n REAL(8), INTENT(INOUT) :: pos, acc, dt, time, vel\n\n time = 0d0\n vel = 0d0\n\n DO\n IF (pos > 0d0) THEN\n time = time + dt\n pos = pos + vel * dt + 0.5d0 * acc * dt ** 2 \n vel = vel + acc * dt\n ELSE\n EXIT\n END IF\n END DO\nEND SUBROUTINE velocity_verlet \n\nPROGRAM verlet_integration\n\n IMPLICIT NONE \n REAL(8) :: pos,acc, dt, time, vel\n\n INTERFACE\n SUBROUTINE verlet(pos, acc, dt, time)\n REAL(8), INTENT(INOUT) :: pos, acc, dt, time\n REAL(8) :: prev_pos, next_pos\n END SUBROUTINE\n END INTERFACE \n\n INTERFACE \n SUBROUTINE stormer_verlet(pos, acc, dt, time, vel) \n REAL(8), INTENT(INOUT) :: pos, acc, dt, time, vel\n REAL(8) :: prev_pos, next_pos\n END SUBROUTINE \n END INTERFACE \n\n INTERFACE \n SUBROUTINE velocity_verlet(pos, acc, dt, time, vel) \n REAL(8), INTENT(INOUT) :: pos, acc, dt, time, vel\n REAL(8) :: prev_pos, next_pos \n END SUBROUTINE \n END INTERFACE \n\n pos = 5d0\n acc = -10d0\n dt = 0.01d0\n ! Verlet \n CALL verlet(pos, acc, dt, time)\n\n WRITE(*,*) '[#]'\n WRITE(*,*) 'Time for Verlet integration:'\n WRITE(*,*) time \n\n ! stormer Verlet \n pos = 5d0\n CALL stormer_verlet(pos, acc, dt, time, vel)\n\n WRITE(*,*) '[#]'\n WRITE(*,*) 'Time for Stormer Verlet integration:'\n WRITE(*,*) time\n WRITE(*,*) '[#]'\n WRITE(*,*) 'Velocity for Stormer Verlet integration:'\n WRITE(*,*) vel\n\n\n\n ! Velocity Verlet\n pos = 5d0\n CALL velocity_verlet(pos, acc, dt, time, vel)\n\n WRITE(*,*) '[#]'\n WRITE(*,*) 'Time for velocity Verlet integration:'\n WRITE(*,*) time\n WRITE(*,*) '[#]'\n WRITE(*,*) 'Velocity for velocity Verlet integration:'\n WRITE(*,*) vel\n\nEND PROGRAM verlet_integration\n\ndef verlet(pos, acc, dt)\n\n prev_pos = pos\n time = 0\n while pos > 0 do\n time += dt\n temp_pos = pos\n pos = pos*2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n end\n\n return time\n\nend\n\ndef stormer_verlet(pos, acc, dt)\n\n prev_pos = pos\n vel = 0\n time = 0\n while pos > 0 do\n time += dt\n temp_pos = pos\n pos = pos*2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n\n vel += acc*dt\n end\n\n return time, vel\n\nend\n\ndef velocity_verlet(pos, acc, dt)\n\n vel = 0\n time = 0\n while pos > 0 do\n time += dt\n pos += vel*dt + 0.5*acc * dt * dt\n vel += acc*dt\n end\n\n return time, vel\n\nend\n\nputs \"[#]\\nTime for Verlet integration is:\"\np verlet(5.0, -10, 0.01)\n\ntime, vel = stormer_verlet(5.0, -10, 0.01)\nputs \"[#]\\nTime for Stormer Verlet integration is:\"\np time\nputs \"[#]\\nVelocity for Stormer Verlet integration is:\"\np vel\n\ntime, vel = velocity_verlet(5.0, -10, 0.01)\nputs \"[#]\\nTime for velocity Verlet integration is:\"\np time\nputs \"[#]\\nVelocity for velocity Verlet integration is:\"\np vel\n\npackage main\n\nimport \"fmt\"\n\nfunc verlet(pos, acc, dt float64) (time float64) {\n prevPos := pos\n time = 0\n\n for pos > 0 {\n time += dt\n nextPos := pos*2 - prevPos + acc*dt*dt\n prevPos, pos = pos, nextPos\n }\n\n return\n}\n\nfunc stormerVerlet(pos, acc, dt float64) (time, vel float64) {\n prevPos := pos\n time, vel = 0, 0\n\n for pos > 0 {\n time += dt\n vel += acc * dt\n nextPos := pos*2 - prevPos + acc*dt*dt\n prevPos, pos = pos, nextPos\n }\n\n return\n}\n\nfunc velocityVerlet(pos, acc, dt float64) (time, vel float64) {\n time, vel = 0, 0\n\n for pos > 0 {\n time += dt\n pos += vel*dt + .5*acc*dt*dt\n vel += acc * dt\n }\n\n return\n}\n\nfunc main() {\n time := verlet(5., -10., .01)\n fmt.Println(\"[#]\\nTime for Verlet integration is:\")\n fmt.Println(time)\n\n time, vel := stormerVerlet(5., -10., .01)\n fmt.Println(\"[#]\\nTime for Stormer Verlet integration is:\")\n fmt.Println(time)\n fmt.Println(\"[#]\\nVelocity for Stormer Verlet integration is:\")\n fmt.Println(vel)\n\n time, vel = velocityVerlet(5., -10., .01)\n fmt.Println(\"[#]\\nTime for velocity Verlet integration is:\")\n fmt.Println(time)\n fmt.Println(\"[#]\\nVelocity for velocity Verlet integration is:\")\n fmt.Println(vel)\n}\n\n.intel_syntax noprefix\n\n.section .rodata\n zero: .double 0.0\n two: .double 2.0\n half: .double 0.5\n verlet_fmt: .string \"[#]\\nTime for Verlet integration is:\\n%lf\\n\"\n stormer_fmt: .string \"[#]\\nTime for Stormer Verlet Integration is:\\n%lf\\n[#]\\nVelocity for Stormer Verlet Integration is:\\n%lf\\n\"\n velocity_fmt: .string \"[#]\\nTime for Velocity Verlet Integration is:\\n%lf\\n[#]\\nVelocity for Velocity Verlet Integration is:\\n%lf\\n\"\n pos: .double 5.0\n acc: .double -10.0\n dt: .double 0.01\n\n.section .text\n .global main\n .extern printf\n\n# xmm0 - pos\n# xmm1 - acc\n# xmm2 - dt\n# RET xmm0 - time\nverlet:\n pxor xmm7, xmm7 # Holds 0 for comparisons\n pxor xmm3, xmm3 # Holds time value\n comisd xmm0, xmm7 # Check if pos is greater then 0.0\n jbe verlet_return\n movsd xmm6, xmm1 # xmm6 = acc * dt * dt\n mulsd xmm6, xmm2\n mulsd xmm6, xmm2\n movsd xmm5, xmm0 # Holds previous position\nverlet_loop:\n addsd xmm3, xmm2 # Adding dt to time\n movsd xmm4, xmm0 # Hold old value of posistion\n addsd xmm0, xmm0 # Calculating new position\n subsd xmm0, xmm5\n addsd xmm0, xmm6\n movsd xmm5, xmm4\n comisd xmm0, xmm7 # Check if position is greater then 0.0\n ja verlet_loop\nverlet_return:\n movsd xmm0, xmm3 # Saving time value\n ret\n\n# xmm0 - pos\n# xmm1 - acc\n# xmm2 - dt\n# RET xmm0 - time\n# RET xmm1 - velocity\nstormer_verlet:\n pxor xmm7, xmm7 # Holds 0 for comparisons\n pxor xmm3, xmm3 # Holds time value\n comisd xmm0, xmm7 # Check if pos is greater then 0.0\n jbe stormer_verlet_return\n movsd xmm6, xmm1 # xmm6 = acc * dt * dt\n mulsd xmm6, xmm2\n mulsd xmm6, xmm2\n movsd xmm5, xmm0 # Holds previous position\nstormer_verlet_loop:\n addsd xmm3, xmm2 # Adding dt to time\n movsd xmm4, xmm0 # Hold old value of posistion\n addsd xmm0, xmm0 # Calculating new position\n subsd xmm0, xmm5\n addsd xmm0, xmm6\n movsd xmm5, xmm4\n comisd xmm0, xmm7 # Check if position is greater then 0.0\n ja stormer_verlet_loop\nstormer_verlet_return:\n movsd xmm0, xmm3 # Saving time and velocity\n mulsd xmm3, xmm1\n movsd xmm1, xmm3\n ret\n\n# xmm0 - pos\n# xmm1 - acc\n# xmm2 - dt\n# RET xmm0 - time\n# RET xmm1 - velocity\nvelocity_verlet:\n pxor xmm7, xmm7 # Holds 0 for comparisons\n pxor xmm3, xmm3 # Holds the velocity value\n pxor xmm4, xmm4 # Holds the time value\n comisd xmm0, xmm7 # Check if pos is greater then 0.0\n jbe velocity_verlet_return\n movsd xmm5, half # xmm5 = 0.5 * dt * dt * acc\n mulsd xmm5, xmm2\n mulsd xmm5, xmm2\n mulsd xmm5, xmm1\nvelocity_verlet_loop:\n movsd xmm6, xmm3 # Move velocity into register\n mulsd xmm6, xmm2 # Calculate new position\n addsd xmm6, xmm5\n addsd xmm0, xmm6\n addsd xmm4, xmm2 # Incrementing time\n movsd xmm3, xmm4 # Updating velocity\n mulsd xmm3, xmm1\n comisd xmm0, xmm7\n ja velocity_verlet_loop\nvelocity_verlet_return:\n movsd xmm0, xmm4 # Saving time and velocity\n movsd xmm1, xmm3\n ret\n\nmain:\n push rbp\n movsd xmm0, pos # Calling verlet\n movsd xmm1, acc\n movsd xmm2, dt\n call verlet\n mov rdi, OFFSET verlet_fmt # Print output\n mov rax, 1\n call printf\n movsd xmm0, pos # Calling stormer_verlet\n movsd xmm1, acc\n movsd xmm2, dt\n call stormer_verlet\n mov rdi, OFFSET stormer_fmt # Print output\n mov rax, 1\n call printf\n movsd xmm0, pos # Calling velocity_verlet\n movsd xmm1, acc\n movsd xmm2, dt\n call velocity_verlet\n mov rdi, OFFSET velocity_fmt # Print output\n mov rax, 1\n call printf\n pop rbp\n xor rax, rax # Set exit code to 0\n ret\n\ndata class VerletValues(val time: Double, val vel: Double)\n\nfun verlet(_pos: Double, acc: Double, dt: Double): Double {\n var pos = _pos // Since function parameter are val and can't be modified\n var prevPos = pos\n var time = 0.0\n\n while (pos > 0) {\n time += dt\n val nextPos = pos * 2 - prevPos + acc * dt * dt\n prevPos = pos\n pos = nextPos\n }\n return time\n}\n\nfun stormerVerlet(_pos: Double, acc: Double, dt: Double): VerletValues {\n var pos = _pos\n var prevPos = pos\n var time = 0.0\n var vel = 0.0\n while (pos > 0) {\n time += dt\n val nextPos = pos * 2 - prevPos + acc * dt * dt\n prevPos = pos\n pos = nextPos\n vel += acc * dt\n }\n return VerletValues(time, vel)\n}\n\nfun velocityVerlet(_pos: Double, acc: Double, dt: Double): VerletValues {\n var pos = _pos\n var time = 0.0\n var vel = 0.0\n while (pos > 0) {\n time += dt\n pos += vel * dt + 0.5 * acc * dt * dt\n vel += acc * dt\n }\n return VerletValues(time, vel)\n}\n\nfun main(args: Array) {\n val verletTime = verlet(5.0, -10.0, 0.01)\n println(\"[#]\\nTime for Verlet integration is:\")\n println(\"$verletTime\")\n\n val stormerVerlet = stormerVerlet(5.0, -10.0, 0.01)\n println(\"[#]\\nTime for Stormer Verlet integration is:\")\n println(\"${stormerVerlet.time}\")\n println(\"[#]\\nVelocity for Stormer Verlet integration is:\")\n println(\"${stormerVerlet.vel}\")\n\n val velocityVerlet = velocityVerlet(5.0, -10.0, 0.01)\n println(\"[#]\\nTime for Velocity Verlet integration is:\")\n println(\"${velocityVerlet.time}\")\n println(\"[#]\\nVelocity for Velocity Verlet integration is:\")\n println(\"${velocityVerlet.vel}\")\n}\n\nfunc verlet(pos_in, acc, dt: float): float =\n var\n pos: float = pos_in\n prevPos: float = pos\n time: float = 0.0\n tempPos: float\n\n while pos > 0.0:\n time += dt\n tempPos = pos\n pos = pos * 2 - prevPos + acc * dt * dt\n prevPos = tempPos\n\n time\n\nfunc stormerVerlet(pos_in, acc, dt: float): (float, float) =\n var\n pos: float = pos_in\n prevPos: float = pos\n time: float = 0.0\n vel: float = 0.0\n tempPos: float\n\n while pos > 0.0:\n time += dt\n tempPos = pos\n pos = pos * 2 - prevPos + acc * dt * dt\n prevPos = tempPos\n\n vel += acc * dt\n\n (time, vel)\n\nfunc velocityVerlet(pos_in, acc, dt: float): (float, float) =\n var\n pos: float = pos_in\n time: float = 0.0\n vel: float = 0.0\n\n while pos > 0.0:\n time += dt\n pos += vel * dt + 0.5 * acc * dt * dt\n vel += acc * dt\n\n (time, vel)\n\nwhen isMainModule:\n let timeV = verlet(5.0, -10.0, 0.01)\n echo \"[#]\\nTime for Verlet integration is:\"\n echo timeV\n\n let (timeSV, velSV) = stormerVerlet(5.0, -10.0, 0.01)\n echo \"[#]\\nTime for Stormer Verlet integration is:\"\n echo timeSV\n echo \"[#]\\nVelocity for Stormer Verlet integration is:\"\n echo velSV\n\n let (timeVV, velVV) = velocityVerlet(5.0, -10.0, 0.01)\n echo \"[#]\\nTime for velocity Verlet integration is:\"\n echo timeVV\n echo \"[#]\\nVelocity for velocity Verlet integration is:\"\n echo velVV\n\n;;;; Verlet integration implementation in Common Lisp\n\n(defun verlet (pos acc dt)\n \"Integrates Newton's equation for motion while pos > 0 using Verlet integration.\"\n (loop\n with prev-pos = pos\n for time = 0 then (incf time dt)\n while (> pos 0)\n ;; The starting speed is assumed to be zero.\n do (psetf\n pos (+ (* pos 2) (- prev-pos) (* acc dt dt))\n prev-pos pos)\n finally (return time)))\n\n(defun stormer-verlet (pos acc dt)\n \"Integrates Newton's equation for motion while pos > 0 using the Stormer-Verlet method.\"\n (loop\n with prev-pos = pos\n for time = 0 then (incf time dt)\n for vel = 0 then (incf vel (* acc dt))\n while (> pos 0)\n ;; Variables are changed simultaneously by 'psetf', so there's no need for a temporary variable.\n do (psetf\n pos (+ (* pos 2) (- prev-pos) (* acc dt dt))\n prev-pos pos)\n finally (return (list time vel))))\n\n(defun velocity-verlet (pos acc dt)\n \"Integrates Newton's equation for motion while pos > 0 using the velocity in calculations.\"\n (loop\n for time = 0 then (incf time dt)\n for vel = 0 then (incf vel (* acc dt))\n for p = pos then (incf p (+ (* vel dt) (* 0.5 acc dt dt)))\n while (> p 0)\n finally (return (list time vel))))\n\n(format T \"[#]~%Time for Verlet integration:~%\")\n(format T \"~d~%\" (verlet 5 -10 0.01))\n\n(defvar stormer-verlet-result (stormer-verlet 5 -10 0.01))\n(format T \"[#]~%Time for Stormer Verlet integration is:~%\")\n(format T \"~d~%\" (first stormer-verlet-result))\n(format T \"[#]~%Velocity for Stormer Verlet integration is:~%\")\n(format T \"~d~%\" (second stormer-verlet-result))\n\n(defvar velocity-verlet-result (velocity-verlet 5 -10 0.01))\n(format T \"[#]~%Time for velocity Verlet integration is:~%\")\n(format T \"~d~%\" (first velocity-verlet-result))\n(format T \"[#]~%Velocity for velocity Verlet integration is:~%\")\n(format T \"~d~%\" (second velocity-verlet-result))\n\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/split-operator_method/split-operator_method.html":{"url":"contents/split-operator_method/split-operator_method.html","title":"Split-Operator Method","keywords":"","body":"The Split-Operator Method\nThe Split-Operator Method (also called the Split-Step Method), was actually the primary method I used to solve the Schrödinger equation during my PhD.\nIt is one of the simplest and fastest methods for this purpose and is widely used throughout modern quantum research in the area, in particular when dealing with the Non-linear Schrödinger Equation (NLSE):\n\ni \\hbar \\frac{\\partial \\Psi(\\mathbf{r},t)}{\\partial t} = \\left[-\\frac{\\hbar^2}{2m}\\nabla^2 + V(\\mathbf{r}) + g|\\Psi(\\mathbf{r},t)|^2 \\right] \\Psi(\\mathbf{r},t),\n\nwhich follows from the notation provided in the quantum systems chapter: \\Psi(\\mathbf{r},t) is a quantum wave-function with spatial (\\mathbf{r}) and time (t) dependence, \\nabla^2 is a Laplacian, and V(\\mathbf{r}) is a potential of some sort (like \\omega x^2 or something).\nIn this case, we also add an interaction term g next to a nonlinear |\\Psi(\\mathbf{r},t)|^2 term.\nThis is the system I studied for most of my PhD (granted, we played a few tricks with parallelization and such, so it was slightly more complicated).\nAt its heart, the split-op method is nothing more than a pseudo-spectral differential equation solver... That is to say, it solves the Schrödinger equation with FFTs.\nIn fact, there is a large class of spectral and pseudo-spectral methods used to solve a number of different physical systems, and we'll definitely be covering those in the future.\nAs mentioned in the quantum systems section, we can represent a quantum wavefunction in momentum space, which is parameterized with the wavevector k.\nIn the Hamiltonian shown above, we can split our system into position space components, \\hat{H}_r = \\left[V(\\mathbf{r}) + g|\\Psi(\\mathbf{r},t)|^2 \\right] \\Psi(\\mathbf{r},t), and momentum space components, \\hat{H}_k = \\left[-\\frac{\\hbar^2}{2m}\\nabla^2 \\right]\\Psi(\\mathbf{r},t).\nI'll be honest, I didn't know what notation to use for \\hat H_r because p is used to describe momentum.\nI settled on r for real space, but that is somewhat notationally ambiguous.\nIn addition, k will indicate momentum space because it is a sum of all wavevectors, typically notated as k.\nBad notation aside, let's continue.\nIf we assume a somewhat general solution to our quantum system:\n\n\\Psi(\\mathbf{r},t + dt) = \\left[e^{-\\frac{i\\hat{H}dt}{\\hbar}}\\right]\\Psi(\\mathbf{r},t) = \\left[e^{-\\frac{i(\\hat{H}_r + \\hat{H}_k)dt}{\\hbar}}\\right]\\Psi(\\mathbf{r},t)\n\nand assume we are simulating our system by a series of small timesteps (dt), we can perform similar splitting by using the Baker-Campbell-Housdorff formula:\n\n\\Psi(\\mathbf{r},t+dt) = \\left[e^{-\\frac{i\\hat{H}_rdt}{\\hbar}}e^{-\\frac{i\\hat{H}_kdt}{\\hbar}}e^{-\\frac{[i\\hat{H}_r, i\\hat{H}_k]dt^2}{2}}\\right]\\Psi(\\mathbf{r},t)\n\nThis accrues a small amount of error (dt^2) related to the commutation of the real and momentum-space components of the Hamiltonian.\nThis is a relatively large error and that's not okay.\nIn order to change the dt^2 error to dt^3, we can split the system by performing a half-step in position space before doing a full-step in momentum space, through a process called Strang Splitting like so:\n\n\\Psi(\\mathbf{r},t+dt) = \\left[e^{-\\frac{i\\hat{H}_rdt}{2\\hbar}}e^{-\\frac{i\\hat{H}_kdt}{\\hbar}}e^{-\\frac{i\\hat{H}_rdt}{2\\hbar}} \\right]\\Psi(\\mathbf{r},t) + \\mathcal{O}(dt^3)\n\nWe can then address each part of this solution in chunks, first in position space, then in momentum space, then in position space again by using Fourier Transforms.\nWhich looks something like this:\n\n\\Psi(\\mathcal{r}, t+dt) = \\left[\\hat{U}_r\\left(\\frac{dt}{2}\\right)\\mathcal{F}^{-1}\\left[\\hat{U}_k(dt) \\mathcal{F} \\left[\\hat{U}_r\\left(\\frac{dt}{2}\\right) \\Psi(\\mathbf{r},t) \\right] \\right] \\right] + \\mathcal{O}(dt^3)\n\nwhere \\hat{U}_r = e^{-\\frac{i\\hat{H}_rdt}{\\hbar}}, \\hat{U}_k = e^{-\\frac{i\\hat{H}_kdt}{\\hbar}}, and \\mathcal{F} and \\mathcal{F}^{-1} indicate forward and inverse Fourier Transforms.\nHere's a flowchart of what we are looking for every timestep:\n\n \n\n\n\nFor the most part, that's it:\n\nMultiply the wavefunction in real space with the real-space operator.\nFlip to momentum space with a Fourier transform.\nMultiply the momentum-space wavefunction by the momentum-space operator.\nFlip to position space with an inverse Fourier transform.\nRepeat 1-4 until satisfied.\n\nIf we guess that our initial wavefunction is Gaussian-like and is slightly offset from the center or the trap, this should allow us to see our wavefunction \"sloshing\" back and forth in our trap, like so:\n\n \n\n\nAs a small concession, using this method enforces periodic boundary conditions, where the wavefunction will simply slide from one side of your simulation box to the other, but that's fine for most cases.\nIn fact, for many cases (such as large-scale turbulence models) it's ideal.\nThat said, there is more to the story.\nAs we mentioned in the quantum systems section, many simulations of quantum systems desire to find the ground state of our system.\nThe split-operator method can be used for that too!\nIf we run this simulation in imaginary time, by simply setting \\tau = it and stepping through \\tau instead of t, we will no longer see an \"real-world\" example of how the atoms should behave, but will instead see an exponential decay of higher-energy states.\nIf we run the simulation for long enough with a small enough timestep, all higher energy states will vanish.\nThis means that we can find the ground state of our system by running the simulation in imaginary time, which is an incredibly useful feature!\nIf we run the same simulation as above in imaginary time, we should see our wavefunction smoothly move to the center of our trap (the lowest energy position), like so:\n\n \n\n\n\nThe Algorithm\nLuckily, the code in this case is pretty straightforward.\nAs a note before starting, we will be using normalized units in this simulation where \\hbar = c = 1.\nThese units are often called natural units.\nMany of you (cough experimentalists cough) will probably think that these units are completely unphysical, and they are; however, they allow us to output fractions and whole numbers.\nFor example, if we are trying to find the energy of the ground state of atoms in a simple harmonic oscillator, we know it should be \\frac{1}{2}\\hbar \\omega, where \\omega is the coefficient in front of the x^2 term known as the frequency of the trap.\nIf we were to calculate the energy in real units, our simulation would output 5.272859 \\times 10^{-35}, which is hard to interpret.\nBy instead using natural units, we get precisely \\frac{1}{2} and we know that those are in units of \\hbar\\omega.\nThere is no doubt that it makes the simulation easier to understand (albeit a little misleading in the end).\nRegardless, we first need to set all the initial parameters, including the initial grids in real and momentum space:\nstruct Param\n xmax::Float64\n res::Int64\n dt::Float64\n timesteps::Int64\n dx::Float64\n x::Vector{Float64}\n dk::Float64\n k::Vector{Float64}\n im_time::Bool\n\n Param() = new(10.0, 512, 0.05, 1000, 2 * 10.0/512,\n Vector{Float64}(-10.0 + 10.0/512 : 20.0/512 : 10.0),\n pi / 10.0,\n Vector{Float64}(vcat(0:512/2 - 1, -512/2 : -1) * pi/10.0),\n false)\n Param(xmax::Float64, res::Int64, dt::Float64, timesteps::Int64,\n im_val::Bool) = new(\n xmax, res, dt, timesteps,\n 2*xmax/res, Vector{Float64}(-xmax+xmax/res:2*xmax/res:xmax),\n pi/xmax, Vector{Float64}(vcat(0:res/2-1, -res/2:-1)*pi/(xmax)),\n im_val\n )\nend\n\nstruct params {\n double xmax;\n unsigned int res;\n double dt;\n unsigned int timesteps;\n double dx;\n double *x;\n double dk;\n double *k;\n bool im_time;\n};\n\nvoid init_params(struct params *par, double xmax, unsigned int res, double dt,\n unsigned int timesteps, bool im) {\n\n par->xmax = xmax;\n par->res = res;\n par->dt = dt;\n par->timesteps = timesteps;\n par->dx = 2.0 * xmax / res;\n par->x = malloc(sizeof(double) * res);\n par->dk = M_PI / xmax;\n par->k = malloc(sizeof(double) * res);\n par->im_time = im;\n\n for (size_t i = 0; i x[i] = xmax / res - xmax + (double)i * (2.0 * xmax / res);\n if (i k[i] = (double)i * M_PI / xmax;\n } else {\n par->k[i] = ((double)i - res) * M_PI / xmax;\n }\n }\n}\n\nusing complex = std::complex;\nusing vector_real = std::vector;\nusing vector_complex = std::vector;\n\nstruct Params {\n Params(double _xmax, unsigned int _res, double _dt, unsigned int _timesteps, bool im) {\n xmax = _xmax;\n res = _res;\n dt = _dt;\n timesteps = _timesteps;\n dx = 2.0 * xmax / res;\n x.reserve(res);\n dk = M_PI / xmax;\n k.reserve(res);\n im_time = im;\n\n for (size_t i = 0; i (i) * (2.0 * xmax / res));\n if (i (i) * M_PI / xmax);\n } else {\n k.push_back((static_cast(i) - res) * M_PI / xmax);\n }\n }\n }\n\n double xmax;\n unsigned int res;\n double dt;\n unsigned int timesteps;\n double dx;\n vector_real x;\n double dk;\n vector_real k;\n bool im_time;\n};\n\nclass Param:\n \"\"\"Container for holding all simulation parameters.\"\"\"\n def __init__(self,\n xmax: float,\n res: int,\n dt: float,\n timesteps: int,\n im_time: bool) -> None:\n\n self.xmax = xmax\n self.res = res\n self.dt = dt\n self.timesteps = timesteps\n self.im_time = im_time\n\n self.dx = 2 * xmax / res\n self.x = np.arange(-xmax + xmax / res, xmax, self.dx)\n self.dk = pi / xmax\n self.k = np.concatenate((np.arange(0, res / 2),\n np.arange(-res / 2, 0))) * self.dk\n\ndata Parameters = Parameters\n { xmax :: Double\n , res :: Int\n , dt :: Double\n , timesteps :: Int\n , dx :: Double\n , x :: Vector\n , dk :: Double\n , ks :: Vector\n , imTime :: Bool\n }\n\ndefaultParameters :: Parameters\ndefaultParameters = makeParameters 10 512 0.01 1000 True\n\nmakeParameters :: Double -> Int -> Double -> Int -> Bool -> Parameters\nmakeParameters xmax res dt timesteps imTime =\n let fi = fromIntegral\n rng = (0, res - 1)\n ks = [0 .. div res 2 - 1] ++ [-div res 2 .. -1]\n in Parameters\n xmax\n res\n dt\n timesteps\n (2 * xmax / fi res)\n (listArray rng $\n map (\\n -> xmax * (-1 + 2 * fi n / fi res) :+ 0) [1 .. res])\n (pi / xmax)\n (listArray rng $ map ((:+ 0) . (pi / xmax *) . fi) ks)\n imTime\n\n xmax: f64,\n res: usize,\n dt: f64,\n timesteps: usize,\n dx: f64,\n x: Vec,\n dk: f64,\n k: Vec,\n im_time: bool,\n}\n\nimpl Parameters {\n pub fn new(xmax: f64, res: usize, dt: f64, timesteps: usize, im_time: bool) -> Parameters {\n let dx = 2.0_f64 * xmax / (res as f64);\n let mut x: Vec = Vec::with_capacity(res);\n let dk = PI / xmax;\n let mut k: Vec = Vec::with_capacity(res);\n for i in 0..res {\n x.push(xmax / (res as f64) - xmax + (i as f64) * dx);\n match i {\n i if (i k.push((i as f64) * PI / xmax),\n _ => k.push(((i as f64) - (res as f64)) * PI / xmax),\n }\n }\n Parameters {\n xmax,\n res,\n dt,\n timesteps,\n im_time,\n dx,\n x,\n dk,\n k,\n }\n }\n}\n\n\n\nAs a note, when we generate our grid in momentum space k, we need to split the grid into two lines, one that is going from 0 to -kmax and is then discontinuous and goes from kmax to 0.\nThis is simply because the FFT will naturally assume that the 0 in our grid is at the left side of the simulation, so we shift k-space to match this expectation.\nAlso, for this code we will be using notation to what we used above: opr.R will be the real space operators and opr.K will be the momentum space operators.\nThere is another Boolean value here called im_time, which is for imaginary time evolution.\nAfterwards, we turn them into operators:\nmutable struct Operators\n V::Vector{Complex{Float64}}\n R::Vector{Complex{Float64}}\n K::Vector{Complex{Float64}}\n wfc::Vector{Complex{Float64}}\n\n Operators(res) = new(zeros(res),\n zeros(res),\n zeros(res),\n zeros(res))\nend\n\n# Function to initialize the wfc and potential\nfunction init(par::Param, voffset::Float64, wfcoffset::Float64)\n opr = Operators(length(par.x))\n opr.V = 0.5 * (par.x .- voffset).^2\n opr.wfc = exp.(-(par.x .- wfcoffset).^2/2)\n if (par.im_time)\n opr.K = exp.(-0.5*par.k.^2*par.dt)\n opr.R = exp.(-0.5*opr.V*par.dt)\n else\n opr.K = exp.(-im*0.5*par.k.^2*par.dt)\n opr.R = exp.(-im*0.5*opr.V*par.dt)\n end\n\n return opr\nend\n\nstruct operators {\n size_t size;\n double complex *v;\n double complex *pe;\n double complex *ke;\n double complex *wfc;\n};\n\nvoid init_operators(struct operators *opr, struct params par, double voffset,\n double wfcoffset) {\n\n opr->size = par.res;\n opr->v = malloc(sizeof(double complex) * par.res);\n opr->pe = malloc(sizeof(double complex) * par.res);\n opr->ke = malloc(sizeof(double complex) * par.res);\n opr->wfc = malloc(sizeof(double complex) * par.res);\n\n for (size_t i = 0; i v[i] = 0.5 * cpow(par.x[i] - voffset, 2);\n opr->wfc[i] = cexp(-cpow(par.x[i] - wfcoffset, 2) / 2.0);\n\n if (par.im_time) {\n opr->ke[i] = cexp(-0.5 * par.dt * cpow(par.k[i], 2));\n opr->pe[i] = cexp(-0.5 * par.dt * opr->v[i]);\n } else {\n opr->ke[i] = cexp(-0.5 * par.dt * cpow(par.k[i], 2) * I);\n opr->pe[i] = cexp(-0.5 * par.dt * opr->v[i] * I);\n }\n }\n}\n\nstruct Operators {\npublic:\n Operators(Params &par, double voffset,\n double wfcoffset) {\n size = par.res;\n v.reserve(size);\n pe.reserve(size);\n ke.reserve(size);\n wfc.reserve(size);\n\n for (size_t i = 0; i \nclass Operators:\n \"\"\"Container for holding operators and wavefunction coefficients.\"\"\"\n def __init__(self, res: int) -> None:\n\n self.V = np.empty(res, dtype=complex)\n self.R = np.empty(res, dtype=complex)\n self.K = np.empty(res, dtype=complex)\n self.wfc = np.empty(res, dtype=complex)\n\n\ndef init(par: Param, voffset: float, wfcoffset: float) -> Operators:\n \"\"\"Initialize the wavefunction coefficients and the potential.\"\"\"\n opr = Operators(len(par.x))\n opr.V = 0.5 * (par.x - voffset) ** 2\n opr.wfc = np.exp(-((par.x - wfcoffset) ** 2) / 2, dtype=complex)\n if par.im_time:\n opr.K = np.exp(-0.5 * (par.k ** 2) * par.dt)\n opr.R = np.exp(-0.5 * opr.V * par.dt)\n else:\n opr.K = np.exp(-0.5 * (par.k ** 2) * par.dt * 1j)\n opr.R = np.exp(-0.5 * opr.V * par.dt * 1j)\n return opr\n\ndata Operators = Operators\n { v :: Vector\n , rStep :: Vector\n , kStep :: Vector\n , wfc :: Vector\n }\n\nmakeOperators :: Parameters -> Complex Double -> Complex Double -> Operators\nmakeOperators param v0 wfc0 =\n let rng = (0, res param - 1)\n time\n | imTime param = dt param :+ 0\n | otherwise = 0 :+ dt param\n v = liftArray (\\x -> 0.5 * (x - v0) ^ 2) (x param)\n rStep = liftArray (\\x -> exp (-0.5 * time * x)) v\n kStep = liftArray (\\k -> exp (-0.5 * time * k ^ 2)) (ks param)\n wfc = liftArray (\\x -> exp (-(x - wfc0) ^ 2 / 2)) (x param)\n in Operators v rStep kStep (normalize (dx param) wfc)\n\n v: Vec>,\n pe: Vec>,\n ke: Vec>,\n wfc: Vec>,\n}\n\nimpl Operators {\n pub fn new(par: &Parameters, v_offset: f64, wfc_offset: f64) -> Operators {\n let mut v: Vec> = Vec::with_capacity(par.res);\n let mut pe: Vec> = Vec::with_capacity(par.res);\n let mut ke: Vec> = Vec::with_capacity(par.res);\n let mut wfc: Vec> = Vec::with_capacity(par.res);\n\n for i in 0..par.res {\n v.push(Complex::new(\n 0.5_f64 * (par.x[i] - v_offset).powi(2),\n 0.0_f64,\n ));\n wfc.push(Complex::new(\n (-((par.x[i] - wfc_offset).powi(2)) / 2.0_f64).exp(),\n 0.0_f64,\n ));\n if par.im_time {\n ke.push(Complex::new(\n (-0.5_f64 * par.dt * par.k[i].powi(2)).exp(),\n 0.0_f64,\n ));\n pe.push(Complex::new((-0.5_f64 * par.dt * v[i].re).exp(), 0.0_f64));\n } else {\n ke.push(Complex::new(\n 0.0_f64,\n (-0.5_f64 * par.dt * par.k[i].powi(2)).exp(),\n ));\n pe.push(Complex::new(0.0_f64, (-0.5_f64 * par.dt * v[i].re).exp()));\n }\n }\n Operators { v, pe, ke, wfc }\n }\n}\n\n\n\nHere, we use a standard harmonic potential for the atoms to sit in and a Gaussian distribution for an initial guess for the probability distribution.\nIf we give either the trap or the atoms a slight offset (so the Gaussian distribution of atoms does not quite rest at the bottom of the x^2 potential, we can see the atoms moving back and forth in the potential as we move the simulation forward in time.\nThis means that we can easily see the dynamics of our quantum system!\nIf we run the simulation in imaginary time, we will see the Gaussian distribution of atoms move towards the center of the potential, which is the location with the lowest energy.\nBoth of these have been shown in the figures above.\nThe final step is to do the iteration, itself.\nfunction split_op!(par::Param, opr::Operators)\n\n for i = 1:par.timesteps\n # Half-step in real space\n opr.wfc = opr.wfc .* opr.R\n\n # fft to momentum space\n opr.wfc = fft(opr.wfc)\n\n # Full step in momentum space\n opr.wfc = opr.wfc .* opr.K\n\n # ifft back\n opr.wfc = ifft(opr.wfc)\n\n # final half-step in real space\n opr.wfc = opr.wfc .* opr.R\n\n # density for plotting and potential\n density = abs2.(opr.wfc)\n\n # renormalizing for imaginary time\n if (par.im_time)\n renorm_factor = sum(density) * par.dx\n\n for j = 1:length(opr.wfc)\n opr.wfc[j] /= sqrt(renorm_factor)\n end\n end\n\n # Outputting data to file. Plotting can also be done in a similar way\n # This is set to output exactly 100 files, no matter how many timesteps\n if ((i-1) % div(par.timesteps, 100) == 0)\n outfile = open(\"output\" * string(lpad(string(i-1), 5, string(0)))\n * \".dat\",\"w\")\n\n # Outputting for gnuplot. Any plotter will do.\n for j = 1:length(density)\n write(outfile, string(par.x[j]) * \"\\t\"\n * string(density[j]) * \"\\t\"\n * string(real(opr.V[j])) * \"\\n\")\n end\n\n close(outfile)\n println(\"Outputting step: \", i)\n end\n end\nend\n\nvoid split_op(struct params par, struct operators opr) {\n double density[opr.size];\n\n for (size_t i = 0; i \nvoid split_op(Params &par, Operators &opr) {\n auto density = std::vector(opr.size, 0);\n\n for (size_t i = 0; i \ndef split_op(par: Param, opr: Operators) -> None:\n\n for i in range(par.timesteps):\n\n # Half-step in real space\n opr.wfc *= opr.R\n\n # FFT to momentum space\n opr.wfc = np.fft.fft(opr.wfc)\n\n # Full step in momentum space\n opr.wfc *= opr.K\n\n # iFFT back\n opr.wfc = np.fft.ifft(opr.wfc)\n\n # Final half-step in real space\n opr.wfc *= opr.R\n\n # Density for plotting and potential\n density = np.abs(opr.wfc) ** 2\n\n # Renormalizing for imaginary time\n if par.im_time:\n renorm_factor = sum(density) * par.dx\n opr.wfc /= sqrt(renorm_factor)\n\n # Outputting data to file. Plotting can also be done in a\n # similar way. This is set to output exactly 100 files, no\n # matter how many timesteps were specified.\n if i % (par.timesteps // 100) == 0:\n filename = \"output{}.dat\".format(str(i).rjust(5, str(0)))\n with open(filename, \"w\") as outfile:\n # Outputting for gnuplot. Any plotter will do.\n for j in range(len(density)):\n template = \"{}\\t{}\\t{}\\n\".format\n line = template(par.x[j], density[j].real, opr.V[j].real)\n outfile.write(line)\n print(\"Outputting step: \", i + 1)\n\nevolve :: Parameters -> Operators -> [Operators]\nevolve param op@(Operators _ rStep kStep _) = iterate splitop op\n where\n splitop op = op {wfc = wfc' op}\n wfc' = norm . (rStep .*) . idft . (kStep .*) . dft . (rStep .*) . wfc\n norm = if imTime param then normalize (dx param) else id\n\n let mut density: Vec;\n\n for i in 0..par.timesteps {\n for j in 0..par.res {\n opr.wfc[j] *= opr.pe[j];\n }\n\n fft(&mut opr.wfc, false);\n\n for j in 0..par.res {\n opr.wfc[j] *= opr.ke[j];\n }\n\n fft(&mut opr.wfc, true);\n\n for j in 0..par.res {\n opr.wfc[j] *= opr.pe[j];\n }\n\n density = opr.wfc.iter().map(|x| x.norm().powi(2)).collect();\n\n if par.im_time {\n let sum = density.iter().sum::() * par.dx;\n\n for j in 0..par.res {\n opr.wfc[j] /= sum.sqrt();\n }\n }\n\n // Writing data into a file in the format of:\n // index, density, real potential.\n let path_name = format!(\"output{}.dat\", i);\n let path = Path::new(&path_name);\n let display = path.display();\n\n let mut file = match File::create(&path) {\n Err(why) => panic!(\"Couldn't create {}: {}\", display, why),\n Ok(good) => good,\n };\n\n for j in 0..par.res {\n if let Err(why) = writeln!(file, \"{}\\t{}\\t{}\", j, density[j], opr.v[j].re) {\n panic!(\"Couldn't write to {}: {}\", display, why)\n }\n if let Err(why) = file.flush() {\n panic!(\"Couldn't flush {}: {}\", display, why)\n }\n }\n }\n}\n\n\n\nAnd that's it.\nThere is something a bit odd about the simulation in imaginary time, though.\nBasically, in imaginary time, we see an exponential decay of all the higher energy states, which means we are technically losing a large amount of our wavefunction density every timestep!\nTo solve this issue, we renormalize by enforcing that \\int_{-\\infty}^{+\\infty}\\Psi^\\ast\\Psi dx = 1.\nAs you can see from the code, this involves summing the density, multiplying that sum by dx, and then dividing each element in the wavefunction by the sqrt() of that value.\nThe Split-Operator method is one of the most commonly used quantum simulation algorithms because of how straightforward it is to code and how quickly you can start really digging into the physics of the simulation results!\nVideo Explanation\nHere is a video describing the split-operator method:\n\n\n\n\nExample Code\nThis example code is a simulation of a Gaussian distribution of atoms slightly offset in a harmonic trap in imaginary time.\nSo long as the code is written appropriately, this means that the atoms should move towards the center of the trap and the energy should decay to \\frac{1}{2}\\hbar\\omega, which will be simply \\frac{1}{2} in this simulation.\nChecking to make sure your code can output the correct energy for a harmonic trap is a good test to make sure it is all working under-the-hood before simulating systems with more complicated Hamiltonians.\n#------------split_op.jl-------------------------------------------------------#\n#\n# Plotting: to plot individual timesteps, use gnuplot like so:\n# p \"output00000.dat\" u 1:2 w l\n# rep \"output00000.dat\" u 1:3 w l\n#\n#------------------------------------------------------------------------------#\n\nusing FFTW\n\nstruct Param\n xmax::Float64\n res::Int64\n dt::Float64\n timesteps::Int64\n dx::Float64\n x::Vector{Float64}\n dk::Float64\n k::Vector{Float64}\n im_time::Bool\n\n Param() = new(10.0, 512, 0.05, 1000, 2 * 10.0/512,\n Vector{Float64}(-10.0 + 10.0/512 : 20.0/512 : 10.0),\n pi / 10.0,\n Vector{Float64}(vcat(0:512/2 - 1, -512/2 : -1) * pi/10.0),\n false)\n Param(xmax::Float64, res::Int64, dt::Float64, timesteps::Int64,\n im_val::Bool) = new(\n xmax, res, dt, timesteps,\n 2*xmax/res, Vector{Float64}(-xmax+xmax/res:2*xmax/res:xmax),\n pi/xmax, Vector{Float64}(vcat(0:res/2-1, -res/2:-1)*pi/(xmax)),\n im_val\n )\nend\n\nmutable struct Operators\n V::Vector{Complex{Float64}}\n R::Vector{Complex{Float64}}\n K::Vector{Complex{Float64}}\n wfc::Vector{Complex{Float64}}\n\n Operators(res) = new(zeros(res),\n zeros(res),\n zeros(res),\n zeros(res))\nend\n\n# Function to initialize the wfc and potential\nfunction init(par::Param, voffset::Float64, wfcoffset::Float64)\n opr = Operators(length(par.x))\n opr.V = 0.5 * (par.x .- voffset).^2\n opr.wfc = exp.(-(par.x .- wfcoffset).^2/2)\n if (par.im_time)\n opr.K = exp.(-0.5*par.k.^2*par.dt)\n opr.R = exp.(-0.5*opr.V*par.dt)\n else\n opr.K = exp.(-im*0.5*par.k.^2*par.dt)\n opr.R = exp.(-im*0.5*opr.V*par.dt)\n end\n\n return opr\nend\n\n# Function for the split-operator loop\nfunction split_op!(par::Param, opr::Operators)\n\n for i = 1:par.timesteps\n # Half-step in real space\n opr.wfc = opr.wfc .* opr.R\n\n # fft to momentum space\n opr.wfc = fft(opr.wfc)\n\n # Full step in momentum space\n opr.wfc = opr.wfc .* opr.K\n\n # ifft back\n opr.wfc = ifft(opr.wfc)\n\n # final half-step in real space\n opr.wfc = opr.wfc .* opr.R\n\n # density for plotting and potential\n density = abs2.(opr.wfc)\n\n # renormalizing for imaginary time\n if (par.im_time)\n renorm_factor = sum(density) * par.dx\n\n for j = 1:length(opr.wfc)\n opr.wfc[j] /= sqrt(renorm_factor)\n end\n end\n\n # Outputting data to file. Plotting can also be done in a similar way\n # This is set to output exactly 100 files, no matter how many timesteps\n if ((i-1) % div(par.timesteps, 100) == 0)\n outfile = open(\"output\" * string(lpad(string(i-1), 5, string(0)))\n * \".dat\",\"w\")\n\n # Outputting for gnuplot. Any plotter will do.\n for j = 1:length(density)\n write(outfile, string(par.x[j]) * \"\\t\"\n * string(density[j]) * \"\\t\"\n * string(real(opr.V[j])) * \"\\n\")\n end\n\n close(outfile)\n println(\"Outputting step: \", i)\n end\n end\nend\n\n# We are calculating the energy to check \nfunction calculate_energy(par, opr)\n # Creating real, momentum, and conjugate wavefunctions\n wfc_r = opr.wfc\n wfc_k = fft(wfc_r)\n wfc_c = conj(wfc_r)\n\n # Finding the momentum and real-space energy terms\n energy_k = 0.5*wfc_c.*ifft((par.k.^2) .* wfc_k)\n energy_r = wfc_c.*opr.V .* wfc_r\n\n # Integrating over all space\n energy_final = 0\n for i = 1:length(energy_k)\n energy_final += real(energy_k[i] + energy_r[i])\n end\n\n return energy_final*par.dx\nend\n\n# main function\nfunction main()\n par = Param(5.0, 256, 0.05, 100, true)\n\n # Starting wavefunction slightly offset so we can see it change\n opr = init(par, 0.0, -1.00)\n split_op!(par, opr)\n\n energy = calculate_energy(par, opr)\n println(\"Energy is: \", energy)\nend\n\nmain()\n\n#include \n#include \n#include \n#include \n#include \n#include \n\n// Using fftw3 library.\n#include \n\nstruct params {\n double xmax;\n unsigned int res;\n double dt;\n unsigned int timesteps;\n double dx;\n double *x;\n double dk;\n double *k;\n bool im_time;\n};\n\nstruct operators {\n size_t size;\n double complex *v;\n double complex *pe;\n double complex *ke;\n double complex *wfc;\n};\n\nvoid fft(double complex *x, size_t n, bool inverse) {\n double complex y[n];\n memset(y, 0, sizeof(y));\n fftw_plan p;\n\n if (inverse) {\n p = fftw_plan_dft_1d((int)n, (fftw_complex*)x, (fftw_complex*)y,\n FFTW_BACKWARD, FFTW_ESTIMATE);\n } else {\n p = fftw_plan_dft_1d((int)n, (fftw_complex*)x, (fftw_complex*)y,\n FFTW_FORWARD, FFTW_ESTIMATE);\n }\n\n fftw_execute(p);\n fftw_destroy_plan(p);\n\n for (size_t i = 0; i xmax = xmax;\n par->res = res;\n par->dt = dt;\n par->timesteps = timesteps;\n par->dx = 2.0 * xmax / res;\n par->x = malloc(sizeof(double) * res);\n par->dk = M_PI / xmax;\n par->k = malloc(sizeof(double) * res);\n par->im_time = im;\n\n for (size_t i = 0; i x[i] = xmax / res - xmax + (double)i * (2.0 * xmax / res);\n if (i k[i] = (double)i * M_PI / xmax;\n } else {\n par->k[i] = ((double)i - res) * M_PI / xmax;\n }\n }\n}\n\nvoid init_operators(struct operators *opr, struct params par, double voffset,\n double wfcoffset) {\n\n opr->size = par.res;\n opr->v = malloc(sizeof(double complex) * par.res);\n opr->pe = malloc(sizeof(double complex) * par.res);\n opr->ke = malloc(sizeof(double complex) * par.res);\n opr->wfc = malloc(sizeof(double complex) * par.res);\n\n for (size_t i = 0; i v[i] = 0.5 * cpow(par.x[i] - voffset, 2);\n opr->wfc[i] = cexp(-cpow(par.x[i] - wfcoffset, 2) / 2.0);\n\n if (par.im_time) {\n opr->ke[i] = cexp(-0.5 * par.dt * cpow(par.k[i], 2));\n opr->pe[i] = cexp(-0.5 * par.dt * opr->v[i]);\n } else {\n opr->ke[i] = cexp(-0.5 * par.dt * cpow(par.k[i], 2) * I);\n opr->pe[i] = cexp(-0.5 * par.dt * opr->v[i] * I);\n }\n }\n}\n\nvoid split_op(struct params par, struct operators opr) {\n double density[opr.size];\n\n for (size_t i = 0; i \n#include \n#include \n#include \n#include \n#include \n\n// Using fftw3 library.\n#include \n\n#ifndef M_PI\n#define M_PI 3.14159265358979323846\n#endif\n\nusing complex = std::complex;\nusing vector_real = std::vector;\nusing vector_complex = std::vector;\n\nstruct Params {\n Params(double _xmax, unsigned int _res, double _dt, unsigned int _timesteps, bool im) {\n xmax = _xmax;\n res = _res;\n dt = _dt;\n timesteps = _timesteps;\n dx = 2.0 * xmax / res;\n x.reserve(res);\n dk = M_PI / xmax;\n k.reserve(res);\n im_time = im;\n\n for (size_t i = 0; i (i) * (2.0 * xmax / res));\n if (i (i) * M_PI / xmax);\n } else {\n k.push_back((static_cast(i) - res) * M_PI / xmax);\n }\n }\n }\n\n double xmax;\n unsigned int res;\n double dt;\n unsigned int timesteps;\n double dx;\n vector_real x;\n double dk;\n vector_real k;\n bool im_time;\n};\n\nstruct Operators {\npublic:\n Operators(Params &par, double voffset,\n double wfcoffset) {\n size = par.res;\n v.reserve(size);\n pe.reserve(size);\n ke.reserve(size);\n wfc.reserve(size);\n\n for (size_t i = 0; i > y(x.size(), std::complex(0.0, 0.0));\n fftw_plan p;\n\n fftw_complex *in = reinterpret_cast(x.data());\n fftw_complex *out = reinterpret_cast(y.data());\n p = fftw_plan_dft_1d(static_cast(x.size()), in, out,\n (inverse ? FFTW_BACKWARD : FFTW_FORWARD), FFTW_ESTIMATE);\n\n fftw_execute(p);\n fftw_destroy_plan(p);\n\n for (size_t i = 0; i (x.size()));\n }\n}\n\nvoid split_op(Params &par, Operators &opr) {\n auto density = std::vector(opr.size, 0);\n\n for (size_t i = 0; i \nfrom math import pi\nfrom math import sqrt\n\nimport numpy as np\n\n\nclass Param:\n \"\"\"Container for holding all simulation parameters.\"\"\"\n def __init__(self,\n xmax: float,\n res: int,\n dt: float,\n timesteps: int,\n im_time: bool) -> None:\n\n self.xmax = xmax\n self.res = res\n self.dt = dt\n self.timesteps = timesteps\n self.im_time = im_time\n\n self.dx = 2 * xmax / res\n self.x = np.arange(-xmax + xmax / res, xmax, self.dx)\n self.dk = pi / xmax\n self.k = np.concatenate((np.arange(0, res / 2),\n np.arange(-res / 2, 0))) * self.dk\n\n\nclass Operators:\n \"\"\"Container for holding operators and wavefunction coefficients.\"\"\"\n def __init__(self, res: int) -> None:\n\n self.V = np.empty(res, dtype=complex)\n self.R = np.empty(res, dtype=complex)\n self.K = np.empty(res, dtype=complex)\n self.wfc = np.empty(res, dtype=complex)\n\n\ndef init(par: Param, voffset: float, wfcoffset: float) -> Operators:\n \"\"\"Initialize the wavefunction coefficients and the potential.\"\"\"\n opr = Operators(len(par.x))\n opr.V = 0.5 * (par.x - voffset) ** 2\n opr.wfc = np.exp(-((par.x - wfcoffset) ** 2) / 2, dtype=complex)\n if par.im_time:\n opr.K = np.exp(-0.5 * (par.k ** 2) * par.dt)\n opr.R = np.exp(-0.5 * opr.V * par.dt)\n else:\n opr.K = np.exp(-0.5 * (par.k ** 2) * par.dt * 1j)\n opr.R = np.exp(-0.5 * opr.V * par.dt * 1j)\n return opr\n\n\ndef split_op(par: Param, opr: Operators) -> None:\n\n for i in range(par.timesteps):\n\n # Half-step in real space\n opr.wfc *= opr.R\n\n # FFT to momentum space\n opr.wfc = np.fft.fft(opr.wfc)\n\n # Full step in momentum space\n opr.wfc *= opr.K\n\n # iFFT back\n opr.wfc = np.fft.ifft(opr.wfc)\n\n # Final half-step in real space\n opr.wfc *= opr.R\n\n # Density for plotting and potential\n density = np.abs(opr.wfc) ** 2\n\n # Renormalizing for imaginary time\n if par.im_time:\n renorm_factor = sum(density) * par.dx\n opr.wfc /= sqrt(renorm_factor)\n\n # Outputting data to file. Plotting can also be done in a\n # similar way. This is set to output exactly 100 files, no\n # matter how many timesteps were specified.\n if i % (par.timesteps // 100) == 0:\n filename = \"output{}.dat\".format(str(i).rjust(5, str(0)))\n with open(filename, \"w\") as outfile:\n # Outputting for gnuplot. Any plotter will do.\n for j in range(len(density)):\n template = \"{}\\t{}\\t{}\\n\".format\n line = template(par.x[j], density[j].real, opr.V[j].real)\n outfile.write(line)\n print(\"Outputting step: \", i + 1)\n\n\ndef calculate_energy(par: Param, opr: Operators) -> float:\n \"\"\"Calculate the energy .\"\"\"\n # Creating real, momentum, and conjugate wavefunctions.\n wfc_r = opr.wfc\n wfc_k = np.fft.fft(wfc_r)\n wfc_c = np.conj(wfc_r)\n\n # Finding the momentum and real-space energy terms\n energy_k = 0.5 * wfc_c * np.fft.ifft((par.k ** 2) * wfc_k)\n energy_r = wfc_c * opr.V * wfc_r\n\n # Integrating over all space\n energy_final = sum(energy_k + energy_r).real\n\n return energy_final * par.dx\n\n\ndef main() -> None:\n par = Param(5.0, 256, 0.05, 100, True)\n\n # Starting wavefunction slightly offset so we can see it change\n opr = init(par, 0.0, -1.00)\n split_op(par, opr)\n\n energy = calculate_energy(par, opr)\n print(\"Energy is: \", energy)\n\n\nif __name__ == \"__main__\":\n main()\n\nimport Data.Array.CArray\nimport Data.Complex\nimport Data.List (intercalate, transpose)\nimport Math.FFT (dft, idft)\n\ntype Vector = CArray Int (Complex Double)\n\n(.*), (.+) :: Vector -> Vector -> Vector\na .* b = liftArray2 (*) a b\na .+ b = liftArray2 (+) a b\n\nnormalize :: Double -> Vector -> Vector\nnormalize dx v =\n let factor = 1 / sqrt dx / norm2 v :+ 0\n in liftArray (factor *) v\n\ndata Parameters = Parameters\n { xmax :: Double\n , res :: Int\n , dt :: Double\n , timesteps :: Int\n , dx :: Double\n , x :: Vector\n , dk :: Double\n , ks :: Vector\n , imTime :: Bool\n }\n\ndefaultParameters :: Parameters\ndefaultParameters = makeParameters 10 512 0.01 1000 True\n\nmakeParameters :: Double -> Int -> Double -> Int -> Bool -> Parameters\nmakeParameters xmax res dt timesteps imTime =\n let fi = fromIntegral\n rng = (0, res - 1)\n ks = [0 .. div res 2 - 1] ++ [-div res 2 .. -1]\n in Parameters\n xmax\n res\n dt\n timesteps\n (2 * xmax / fi res)\n (listArray rng $\n map (\\n -> xmax * (-1 + 2 * fi n / fi res) :+ 0) [1 .. res])\n (pi / xmax)\n (listArray rng $ map ((:+ 0) . (pi / xmax *) . fi) ks)\n imTime\n\ndata Operators = Operators\n { v :: Vector\n , rStep :: Vector\n , kStep :: Vector\n , wfc :: Vector\n }\n\nmakeOperators :: Parameters -> Complex Double -> Complex Double -> Operators\nmakeOperators param v0 wfc0 =\n let rng = (0, res param - 1)\n time\n | imTime param = dt param :+ 0\n | otherwise = 0 :+ dt param\n v = liftArray (\\x -> 0.5 * (x - v0) ^ 2) (x param)\n rStep = liftArray (\\x -> exp (-0.5 * time * x)) v\n kStep = liftArray (\\k -> exp (-0.5 * time * k ^ 2)) (ks param)\n wfc = liftArray (\\x -> exp (-(x - wfc0) ^ 2 / 2)) (x param)\n in Operators v rStep kStep (normalize (dx param) wfc)\n\nevolve :: Parameters -> Operators -> [Operators]\nevolve param op@(Operators _ rStep kStep _) = iterate splitop op\n where\n splitop op = op {wfc = wfc' op}\n wfc' = norm . (rStep .*) . idft . (kStep .*) . dft . (rStep .*) . wfc\n norm = if imTime param then normalize (dx param) else id\n\ncalculateEnergy :: Parameters -> Operators -> Double\ncalculateEnergy param ops = (* dx param) . sum . map realPart $ elems totalE\n where\n totalE = potentialE .+ kineticE\n potentialE = wfcConj .* v ops .* wfc ops\n kineticOp = liftArray ((/ 2) . (^ 2)) (ks param)\n kineticE = wfcConj .* idft (kineticOp .* dft (wfc ops))\n wfcConj = liftArray conjugate $ wfc ops\n\n-- Use gnuplot to make an animated GIF using ../gnuplot/plot_output.plt\n-- $ gnuplot -e \"folder='../haskell'\" plot_output.plt\nprintEvolution :: Parameters -> [Operators] -> IO ()\nprintEvolution param =\n mapM_ (export . (format )) . zip [0 ..] . take 100 . skip\n where\n skip (x:xs) = x : skip (drop (div (timesteps param) 100 - 1) xs)\n format (Operators v _ _ wfc) =\n let density = liftArray ((^ 2) . abs) wfc\n values = map (map (show . realPart) . elems) [x param, density, v]\n in intercalate \"\\n\" $ map (intercalate \"\\t\") $ transpose values\n export (i, f) = writeFile (\"output\" ++ pad (show i) ++ \".dat\") f\n pad n = replicate (5 - length n) '0' ++ n\n\nmain :: IO ()\nmain = do\n let p = defaultParameters\n o = makeOperators p 0 4\n evol = evolve p o\n print $ calculateEnergy p (evol !! timesteps p)\n printEvolution p evol\n\nextern crate rustfft;\n\nuse rustfft::num_complex::Complex;\nuse rustfft::FFTplanner;\nuse std::f64::consts::PI;\nuse std::fs::File;\nuse std::io::Write;\nuse std::path::Path;\n\n// This implementation is based on the C and C++ implementations.\n\n#[derive(Clone)]\nstruct Parameters {\n xmax: f64,\n res: usize,\n dt: f64,\n timesteps: usize,\n dx: f64,\n x: Vec,\n dk: f64,\n k: Vec,\n im_time: bool,\n}\n\nimpl Parameters {\n pub fn new(xmax: f64, res: usize, dt: f64, timesteps: usize, im_time: bool) -> Parameters {\n let dx = 2.0_f64 * xmax / (res as f64);\n let mut x: Vec = Vec::with_capacity(res);\n let dk = PI / xmax;\n let mut k: Vec = Vec::with_capacity(res);\n for i in 0..res {\n x.push(xmax / (res as f64) - xmax + (i as f64) * dx);\n match i {\n i if (i k.push((i as f64) * PI / xmax),\n _ => k.push(((i as f64) - (res as f64)) * PI / xmax),\n }\n }\n Parameters {\n xmax,\n res,\n dt,\n timesteps,\n im_time,\n dx,\n x,\n dk,\n k,\n }\n }\n}\n\nstruct Operators {\n v: Vec>,\n pe: Vec>,\n ke: Vec>,\n wfc: Vec>,\n}\n\nimpl Operators {\n pub fn new(par: &Parameters, v_offset: f64, wfc_offset: f64) -> Operators {\n let mut v: Vec> = Vec::with_capacity(par.res);\n let mut pe: Vec> = Vec::with_capacity(par.res);\n let mut ke: Vec> = Vec::with_capacity(par.res);\n let mut wfc: Vec> = Vec::with_capacity(par.res);\n\n for i in 0..par.res {\n v.push(Complex::new(\n 0.5_f64 * (par.x[i] - v_offset).powi(2),\n 0.0_f64,\n ));\n wfc.push(Complex::new(\n (-((par.x[i] - wfc_offset).powi(2)) / 2.0_f64).exp(),\n 0.0_f64,\n ));\n if par.im_time {\n ke.push(Complex::new(\n (-0.5_f64 * par.dt * par.k[i].powi(2)).exp(),\n 0.0_f64,\n ));\n pe.push(Complex::new((-0.5_f64 * par.dt * v[i].re).exp(), 0.0_f64));\n } else {\n ke.push(Complex::new(\n 0.0_f64,\n (-0.5_f64 * par.dt * par.k[i].powi(2)).exp(),\n ));\n pe.push(Complex::new(0.0_f64, (-0.5_f64 * par.dt * v[i].re).exp()));\n }\n }\n Operators { v, pe, ke, wfc }\n }\n}\n\nfn fft(x: &mut Vec>, inverse: bool) {\n let mut y = vec![Complex::new(0.0_f64, 0.0_f64); x.len()];\n let mut p = FFTplanner::new(inverse);\n let fft = p.plan_fft(x.len());\n fft.process(x.as_mut_slice(), y.as_mut_slice());\n\n for i in 0..x.len() {\n x[i] = y[i] / (x.len() as f64).sqrt();\n }\n}\n\nfn split_op(par: &Parameters, opr: &mut Operators) {\n let mut density: Vec;\n\n for i in 0..par.timesteps {\n for j in 0..par.res {\n opr.wfc[j] *= opr.pe[j];\n }\n\n fft(&mut opr.wfc, false);\n\n for j in 0..par.res {\n opr.wfc[j] *= opr.ke[j];\n }\n\n fft(&mut opr.wfc, true);\n\n for j in 0..par.res {\n opr.wfc[j] *= opr.pe[j];\n }\n\n density = opr.wfc.iter().map(|x| x.norm().powi(2)).collect();\n\n if par.im_time {\n let sum = density.iter().sum::() * par.dx;\n\n for j in 0..par.res {\n opr.wfc[j] /= sum.sqrt();\n }\n }\n\n // Writing data into a file in the format of:\n // index, density, real potential.\n let path_name = format!(\"output{}.dat\", i);\n let path = Path::new(&path_name);\n let display = path.display();\n\n let mut file = match File::create(&path) {\n Err(why) => panic!(\"Couldn't create {}: {}\", display, why),\n Ok(good) => good,\n };\n\n for j in 0..par.res {\n if let Err(why) = writeln!(file, \"{}\\t{}\\t{}\", j, density[j], opr.v[j].re) {\n panic!(\"Couldn't write to {}: {}\", display, why)\n }\n if let Err(why) = file.flush() {\n panic!(\"Couldn't flush {}: {}\", display, why)\n }\n }\n }\n}\n\nfn calculate_energy(par: &Parameters, opr: &Operators) -> f64 {\n let wfc_r = opr.wfc.clone();\n let mut wfc_k = opr.wfc.clone();\n let mut wfc_c = vec![Complex::new(0.0_f64, 0.0_f64); par.res];\n\n fft(&mut wfc_k, false);\n\n for i in 0..par.res {\n wfc_c[i] = wfc_r[i].conj();\n }\n\n let mut energy_k = vec![Complex::new(0.0_f64, 0.0_f64); par.res];\n let mut energy_r = vec![Complex::new(0.0_f64, 0.0_f64); par.res];\n\n for i in 0..par.res {\n energy_k[i] = wfc_k[i] * Complex::new(par.k[i], 0.0_f64).powi(2);\n }\n\n fft(&mut energy_k, true);\n\n for i in 0..par.res {\n energy_k[i] *= wfc_c[i].scale(0.5_f64);\n energy_r[i] = wfc_c[i] * opr.v[i] * wfc_r[i];\n }\n\n let energy_final = energy_k\n .into_iter()\n .zip(energy_r.into_iter())\n .fold(0.0_f64, |acc, x| acc + (x.0 + x.1).re);\n\n energy_final * par.dx\n}\n\nfn main() {\n let par = Parameters::new(5.0, 256, 0.05, 100, true);\n let mut opr = Operators::new(&par, 0.0, -1.0);\n\n split_op(&par, &mut opr);\n\n println!(\"The energy is {}\", calculate_energy(&par, &opr));\n}\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"split_op_method\" was created by Julian Schacher and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe animation \"realsplitop\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe animation \"imaginarysplitop\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/domain_coloring/domain_coloring.html":{"url":"contents/domain_coloring/domain_coloring.html","title":"Domain Coloring","keywords":"","body":"Domain coloring\nDomain coloring is a much more complicated plotting technique than those outlined in the plotting chapter and is used to plot complex functions where both the input and output have imaginary and real components.\nFor the code in this chapter, we will focus on languages that are easily able to plot two-dimensional images or heat maps, instead of languages meant for number-crunching.\nThat is to say that this chapter will certainly have a code implementation in gnuplot, but it will not likely have an implementation in C, Fortran, or Java because these languages do not have plotting capabilities in-built.\nTo start, imagine the following function: f(z) = z^2.\nIn this case, we could create a plot that looks like this:\n\n \n\n\nThis indicates that for various input values along z, we have different function outputs from f(z).\nFor this function, z\\in\\mathbb{R} is purely in real space and because of this, the output is also in real space.\nNow let's imagine another function with complex input (z \\in \\mathbb{C}), but a purely real output (f(z) \\in \\mathbb{R}):\n\nf(z) = |z|\n\nIn this case, this can be plotted as a two-dimensional dataset like so:\n\n \n\n\nHere, the x-axis and y-axis represent the imaginary and real components of the input variable, respectively.\nThe color bar represents the output of f(z).\nAt this point, we can start to see the problem.\nIf the output of f(z) also requires plotting of real and imaginary components, then we would need four dimensions to appropriately represent the full function space, one axis for the real component and another for the imaginary component of both the input (z) and the output of f(z)!\nUnfortunately, feeble human minds are incapable of understanding four spatial dimensions without projecting onto lower dimensionality, so we need to improvise.\nWe do this by assuming the complex output can be represented in the following form:\n\nz = re^{i \\theta} = r(\\cos(\\theta) + i\\sin(\\theta))\n\nwhere, r is a complex magnitude and \\theta is a complex phase.\nThis is the formula for a circle in the complex plane and we can easily find r and \\theta like so:\n\n\\begin{align}\n r &= \\sqrt{\\text{Re}(z)^2 + \\text{Im}(z)^2} \\\\ \n \\theta &= \\text{atan}\\left(\\frac{\\text{Im}(z)}{\\text{Re}(z)}\\right)\n\\end{align}\n\nOnce we have our complex function output in this form, we then color the output domain according to a color space with at least 2 independent dimensions, like RGB (Red, Green, Blue), or HSV (Hue, Saturation, Value) [1].\nThe choice of color space is completely dependent on what the users feel is most visually intuitive.\nIn any case, one dimension of the color system will be used to represent the complex magnitude and another dimension of the color system will be used to represent the complex phase of the output.\nThe xy grid will be representing the real and imaginary inputs to these functions.\nThat is to say, we plug every value in the 2D complex plane into the function and then color each pixel based on the function output.\nAs an example, let's look at the simplest function we can f(z) = z, but in this case z \\in \\mathbb{C}.\nIf we use an RGB color scheme, where red represents \\theta and blue represents r, we can generate the following image:\n\n \n\n\nAs a note here, there is a clear phase discontinuity along the horizontal axis, which is a consequence of the fact that\nthe complex phase wraps around the origin, ranging from 0 (clear) to 2\\pi (red).\nIn addition, the edges of the plot are blue because the function's magnitude increases linearly as we move from the origin.\nIf we instead look at the function f(z) = z^2, we can generate a similar plot:\n\n \n\n\nHere, it is clear that the complex phase wraps around the origin twice, creating two separate phase discontinuities on top of each other.\nThis indicates a 4\\pi phase winding.\nFor some purposes, such as vortex tracking for inviscid fluids, this visualization is ideal, because a vortex is located precisely at the center of the phase discontinuity [2] [3].\nFor other purposes, the discontinuity is visually distracting, and for this reason, many people use an HSV scheme for plotting complex functions [4] [5] [6].\nSo here is the same function \\left(f(z)=z^2\\right), but using hue to represent the complex phase and saturation to represent the magnitude:\n\n \n\n\nIn this plot, the Value for HSV was always set to 1.\nWhen looking at the edges of the plot, the hue changes rapidly, but each color is mirrored on the opposite edge.\nThis indicates the 4\\pi phase winding we saw in the RGB plot.\nAlso, because the complex magnitude increases as we move further from the center of the plot, the saturation also increases.\nThus the center of the plot is completely washed out!\nWe need to fix this in subsequent plots to make them more representative of the actual data.\nOne easy way to show the increasing complex magnitude without sacrificing phase information is by using contours.\nEssentially, at ever integer value of the magnitude, we want to draw some kind of line.\nThere are a number of ways to generate these lines, and one simple way is by using an alternative shading function like so:\n\ng(r) = r-\\lfloor r \\rfloor.\n\nThis will create the following image:\n\n \n\n\nThis function will essentially create a smooth gradient, but because of the floor operation \\left(\\lfloor \\cdot \\rfloor \\right), the saturation will go from 0 to 1 between each integer value of the magnitude.\nHere, it is clear that the magnitude is increasing as z^2 from the origin; however, because the saturation is fluctuating so much, it is difficult to see the phase pattern next to each contour.\nThis can be fixed simply by adding an offset to the shading function such that,\n\ng(r) = \\frac{1}{2} + \\frac{1}{2}\\left(r-\\lfloor r \\rfloor \\right).\n\nWhich will produce the following image:\n\n \n\n\nThis means that the saturation will fluctuate from \\frac12 to 1 instead of from 0 to 1, which makes it way easier to see phase information next to contours.\nAgain, there are a lot of different ways to play with these equations, so feel free to use whatever function you want!\nAs long as some sort of rounding operation is used to establish some form of integer value for the magnitude, it should be possible to create contours of various types.\nAt this point, changing the saturation shows changes in the complex magnitude, and changing the hue shows changes in the complex phase.\nUnfortunately, neither the magnitude nor the phase directly show what is happening in real or imaginary space with the output.\nTo show this, we might want to draw grid lines that color our pixels black whenever the imaginary or real components of the output function are integer values.\nFor example, let's go back to a simpler function f(z) = z.\nIf we draw lines on this plot, corresponding to integer values in the output, we get a simple grid\n\n \n\n\nLike before, the choice of which function to use in order to create the grid lines is somewhat arbitrary.\nIt is important to choose a function that sharply drops to 0 or peaks at 1 for all integer values, and then we simply plug values of f(z) into this function.\nFor the purposes of this chapter, we chose the following function\n\nh(z) = |\\sin(\\pi\\times\\text{Re}(f(z)))^t|\\times|\\sin(\\pi\\times\\text{Im}(f(z)))^t|,\n\nwhere t is some threshold value, and was set to be 0.1 in our plot.\nA plot of h(z) for f(z) = z where z\\in\\mathbb{R} is shown below:\n\n \n\n\nSo, putting it all together and returning to the function of f(z) = z^2, we find the following image.\n\n \n\n\nHere, the diagonal lines through the center represent integer values along the imaginary axis for f(z) and the vertical and horizontal lines represent integer values of the real axis for f(z).\nAn easy way to determine which lines correspond to which integer values is by plugging in certain values for z into f(z).\nFor example, there is a black line at z = 1 + 1i where f(z) = 2i, this means that all values along that contour correspond to values that are constrained to having an imaginary component of precisely 2.\nOverall, there are plenty of interesting ways to plot complex functions and make really compelling and beautiful images!\nWe will be using domain coloring in other contexts throughout this text when describing methods that heavily use complex space.\nVideo Explanation\nHere is a video describing domain coloring:\n\n\n\n\nExample Code\nHere is the full script to generate a domain colored output of f(z)=z^2.\n# setting output to file of size 800 x 800\nset terminal pngcairo size 1000, 1000 \nset output 'domain.png'\n\n# sets title for full plot\nset title 'f(z)=z^2'\n\n# removes legend\nunset key\n\n# projects image onto 2D plane\nset view map\n\n# sets aspect ratio of plot to be square \nset size square\n\n# sets x and y range and labels\nset xrange[-2:2]\nset yrange[-2:2]\n\nset xlabel \"Re(z)\"\nset ylabel \"Im(z)\"\n\n# scaling the x, y, and colorbar tics to zero so they are not seen in the plot\nset xtics border scale 0,0\nset ytics border scale 0,0\nset cbtics border scale 0,0\n\n# sets tics in color bar at 0 and 2pi\nset cbtics (\"0\" -3.14159, '2pi' 3.14159)\n\nset cblabel \"Phase Angle\" \nset cbrange [ -3.14159 : 3.14159 ]\n\n# use hsv for colorbar and set palette to use full hsv space\nset palette model HSV\nset palette defined ( 0 0 1 1, 1 1 1 1 )\n\n# setting isosamples for output grid and samples for input grid\nset isosamples 2000, 2000\nset samples 2000, 2000\n\n# setting functions necessary for domain coloring\n# setting threshold for gridlines. Smaller threshold will make smaller lines\nthresh = 0.1\nf(z) = z**2\n\n# atan2 returns a range from -pi to pi, so we need to add pi, but this offsets\n# the value by 180 degrees, so we also imput (-y, -x) for another 180 degrees\n# to invert rotation\nangle(x,y) = (pi + atan2(-y,-x)) / (2*pi)\n\n# complex magnitude\nr(x,y) = sqrt(x*x + y*y)\n\n# complex phase and magnitude\ntheta(x,y) = atan2(y,x)\nz(x,y) = r(x,y)*exp(theta(x,y)*sqrt(-1))\n\n# imaginary and real output functions\nimaginary_f(z) = imag(f(z))\nreal_f(z) = real(f(z))\n\n# magnitude contours\nmagnitude_shading(x,y) = 0.5 + 0.5*(abs(f(z(x,y)))-floor(abs(f(z(x,y)))))\n\n# gridlines\ngridlines(x,y) = (abs(sin(real_f(z(x,y))*pi)**thresh) \\\n * abs(sin(imaginary_f(z(x,y))*pi))**thresh)\n\n# overall coloring function\ncolor(x,y) = hsv2rgb(angle(real_f(z(x,y)), imaginary_f(z(x,y))), \\\n magnitude_shading(x,y), \\\n gridlines(x,y))\n\nsave_encoding = \"utf8\"\n\n# Last datafile plotted: \"++\"\n# In this case, it means, \"plot the data file created with the\n# samples and isosamples\"\nsplot '++' using 1:2:(color($1,$2)) with pm3d lc rgb variable nocontour\n\n\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport matplotlib.colors\nfrom matplotlib.cm import ScalarMappable\n\n\ndef f(z):\n return z**2\n\n\ndef magnitude_shading(f_val):\n f_val_abs = np.abs(f_val)\n return 0.5 + 0.5 * (f_val_abs - np.floor(f_val_abs))\n\n\ndef gridlines(f_val, threshold):\n return (np.abs(np.sin(np.pi * np.real(f_val))) ** threshold\n * np.abs(np.sin(np.pi * np.imag(f_val))) ** threshold)\n\n\ndef color(f_val, threshold):\n hue = (np.pi - np.angle(f_val)) / (2.0 * np.pi)\n saturation = magnitude_shading(f_val)\n value = gridlines(f_val, threshold)\n\n # Currently we have a tuple of 2D-arrays (hue, saturation, value).\n # This makes it a 2D-array of tuples, which the conversion function requires.\n hsv = np.moveaxis((hue, saturation, value), 0, -1)\n return matplotlib.colors.hsv_to_rgb(hsv)\n\n\nif __name__ == \"__main__\":\n # Create a new figure containing a single plot\n fig, axes = plt.subplots(1, 1)\n\n # Set the title for the plot\n axes.set_title(\"$f(x)=z^2$\")\n\n # Create color bar\n cbar = fig.colorbar(\n ScalarMappable(matplotlib.colors.Normalize(0.0, 2.0 * np.pi), \"hsv\"),\n ax=axes,\n label=\"Phase Angle\")\n\n # Set x and y labels\n axes.set_xlabel(\"$Re(z)$\")\n axes.set_ylabel(\"$Im(z)$\")\n\n # Set color bar tick locations and labels\n cbar.set_ticks([0.0, np.pi, 2.0 * np.pi])\n cbar.set_ticklabels([\"$0.0$\", \"$\\pi$\", \"$2\\pi$\"])\n\n # Hide x and y ticks\n for tick in axes.get_xticklines():\n tick.set_visible(False)\n\n for tick in axes.get_yticklines():\n tick.set_visible(False)\n\n # Create a 500x500 input grid\n coords = np.linspace(-2.0, 2.0, 500)\n z_real, z_imag = np.meshgrid(coords, coords)\n z = z_real + 1j * z_imag\n\n # Calculate function values\n f_val = f(z)\n\n # Map function values to colors\n colors = color(f_val, 0.1)\n\n # Plot the colors\n # extent=(-2.0, 2.0, -2.0, 2.0) sets the x and y ranges\n # origin=\"lower\" places index (0,0) of the color array in the lower-left corner\n # aspect=\"equal\" ensures that the plot is square\n axes.imshow(\n colors,\n extent=(-2.0, 2.0, -2.0, 2.0),\n origin=\"lower\",\n aspect=\"equal\")\n\n # Save output\n fig.savefig(\"domain.png\")\n\n\n\nBibliography\n1.Wikipedia: HSL and HSV, 2020.2.Schloss, James, Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units, 2019.3.Pethick, Christopher J and Smith, Henrik, Bose--Einstein condensation in dilute gases, Cambridge university press, 2008.4.Wegert, Elias, Visual complex functions: an introduction with phase portraits, Springer Science \\& Business Media, 2012.5.Poelke, Konstantin and Polthier, Konrad, Domain Coloring of Complex Functions.6.Lundmark, Hans, Visualizing complex analytic functions using domain coloring, 2004.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"z2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"absz\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"rgb1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"rgb2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"hsv1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"hsv2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"hsv3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"hsv4\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"shade\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"hsv5\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nThe following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/barnsley/barnsley.html":{"url":"contents/barnsley/barnsley.html","title":"The Barnsley Fern","keywords":"","body":"The Barnsley Fern\nAt the end of the chapter on Iterated Function Systems, we introduced two separate attractors: the Sierpinski triangle, and a uniform two-dimensional square, shown below with their corresponding Hutchinson operator.\n\n\n\nHutchinson Operator\nAttractor\n\n\n\n\n\\begin{align} f_1(P) &= \\frac{P+A}{2} \\\\ f_2(P) &= \\frac{P+B}{2} \\\\ f_3(P) &= \\frac{P+C}{2} \\end{align}\n\n\n\n\\begin{align} f_1(P) &= \\frac{P+A}{2} \\\\ f_2(P) &= \\frac{P+B}{2} \\\\ f_3(P) &= \\frac{P+C}{2} \\\\ f_4(P) &= \\frac{P+D}{2} \\end{align}\n\n\n\n\nAs a reminder, the Hutchinson operator is a set of functions that act on a point in space, P, and return another another point at a new location.\nThese functions are meant to be used over and over again in some fashion, and as you continually iterate through them, some shape will eventually be drawn.\nThis shape is known as an attractor, and the entire system is called an iterated function system due to the iterative nature of drawing the attractor.\nIn these cases, each function will move the point to be halfway between its original position and the position of A, B, C, and D for f_1, f_2, f_3, and f_4, respectively.\nEven though f_1, f_2, and f_3 are the same for both attractors, the addition of f_4 drastically changes the final result!\nIt is surprising that two seemingly identical sets of functions can look so different in the end, and this leads us to a somewhat challenging question: given a set of functions, is there any way to predict what the attractor will be without iterating through the functions?\nIn general, the answer is no.\nYou must sample the function set in some fashion to get find the resulting attractor.\nThis feels somewhat unsettling to me.\nAfter all, each individual function is simple, so why is the result so difficult to predict?\nIn this chapter, I hope to provide a slightly more satisfying answer by introducing another iterated function system with beautiful attractor, known as the Barnsley fern [1]:\n\n\n\nHutchinson Operator\nAttractor\n\n\n\n\n\\begin{align} f_1(P) &= \\begin{bmatrix} 0 &0 \\\\ 0 &0.16 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix} \\\\ f_2(P) &= \\begin{bmatrix} 0.85 &0.04 \\\\ -0.04 &0.85 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 1.6 \\end{bmatrix} \\\\ f_3(P) &= \\begin{bmatrix} 0.2 &-0.26 \\\\ 0.23 &0.22 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 1.6 \\end{bmatrix} \\\\ f_4(P) &= \\begin{bmatrix} -0.15 &0.28 \\\\ 0.26 &0.24 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 0.44 \\end{bmatrix} \\end{align}\n\n\n\n\nAt first glance, this set of functions looks like an incomprehensible mess of magic numbers to create a specific result, and in a sense, that is precisely correct.\nThat said, we will go through each function and explain how it works, while also providing a simple chaos game implementation in code.\nBy the end of this chapter, we do not hope to provide a general strategy for understanding all iterated function systems, but we hope to at least make this one set of functions a bit more understandable.\nIndividual affine transforms\nThe first thing to note about the Barnsley set of functions is that each one is an affine transformation.\nThough it is not a hard rule, most iterated function systems use affine transforms, so this notation is common.\nIn fact, the Sierpinski operators can also be written in an affine form:\n\n\n\nNon-affine\nAffine\n\n\n\n\n\\begin{align} f_1(P) &= \\frac{P+A}{2} \\\\ f_2(P) &= \\frac{P+B}{2} \\\\ f_3(P) &= \\frac{P+C}{2} \\end{align}\n\\begin{align} f_1(P) &= \\begin{bmatrix} 0.5 &0 \\\\ 0 &0.5 \\end{bmatrix}P + \\frac{A}{2} \\\\ f_2(P) &= \\begin{bmatrix} 0.5 &0 \\\\ 0 &0.5 \\end{bmatrix}P + \\frac{B}{2} \\\\ f_3(P) &= \\begin{bmatrix} 0.5 &0 \\\\ 0 &0.5 \\end{bmatrix}P + \\frac{C}{2} \\end{align}\n\n\n\nThe affine variant performs the same operation by scaling the x and y component of P by 0.5 and then adding half of either A, B, or C for f_1, f_2, or f_3, respectively.\nEach of these transforms involves some linear component (scaling or shearing) with an additional translation.\nAs an important side-note: in both the Barnsley and Sierpinski function systems, the coefficients of the transformation matrix are all less than 1.\nThis property is known as contractivity, and an iterated function system can only have an attractor if the system is contractive.\nUpon reflection, this makes sense.\nIf the matrix elements were greater than 1, the point could tend towards infinity after successive iterations of the function.\nNow let's hop into disecting the Barnsley fern by seeing how each transform affects a random distribution of points:\n\n\n\nFunction\nOperation\n\n\n\n\nf_1(P) = \\begin{bmatrix} 0 &0 \\\\ 0 &0.16 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix} This operation moves every point to a single line.\n Your browser does not support the video tag. \n\n\nf_2(P) = \\begin{bmatrix} 0.85 &0.04 \\\\ -0.04 &0.85 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 1.6 \\end{bmatrix} This operation moves every point up and to the right.\n Your browser does not support the video tag. \n\n\nf_3(P) = \\begin{bmatrix} 0.2 &-0.26 \\\\ 0.23 &0.22 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 1.6 \\end{bmatrix} This operation rotates every point to the left.\n Your browser does not support the video tag. \n\n\nf_4(P) = \\begin{bmatrix} -0.15 &0.28 \\\\ 0.26 &0.24 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 0.44 \\end{bmatrix} This operation flips every point and rotates to the right.\n Your browser does not support the video tag. \n\n\n\nAt this stage, it might be clear what is going on, but it's not exactly obvious.\nEssentially, each operation corresponds to another part of the fern:\n\nf_1 creates the stem.\nf_2 creates successively smaller ferns moving up and to the right.\nf_3 creates the leaves on the right.\nf_4 creates the leaves on the left.\n\nThe easiest way to make sense of this is to show the operations on the Barnsley fern, itself, instead of a random distribution of points.\n\n\n\nFunction\nOperation\n\n\n\n\nf_1(P) = \\begin{bmatrix} 0 &0 \\\\ 0 &0.16 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix}\n Your browser does not support the video tag. \n\n\nf_2(P) = \\begin{bmatrix} 0.85 &0.04 \\\\ -0.04 &0.85 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 1.6 \\end{bmatrix}\n Your browser does not support the video tag. \n\n\nf_3(P) = \\begin{bmatrix} 0.2 &-0.26 \\\\ 0.23 &0.22 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 1.6 \\end{bmatrix}\n Your browser does not support the video tag. \n\n\nf_4(P) = \\begin{bmatrix} -0.15 &0.28 \\\\ 0.26 &0.24 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 0.44 \\end{bmatrix}\n Your browser does not support the video tag. \n\n\n\nHere, the self-similar nature of the fern becomes apparent.\nEach operation is effectively moving a point on one part of the fern to a point on another part of the fern.\nIn the final construction, it is clear that fewer points are necessary on some parts than others.\nThe stem, for example, does not need many points at all.\nMeanwhile, the bulk of the fern seems to be generated by f_2, so we probably want the majority of the points to choose that function when iterating through he set.\nTo account for this, each function is also given a probability of being chosen:\n\n\n\nFunction\nProbability\n\n\n\n\nf_1(P) = \\begin{bmatrix} 0 &0 \\\\ 0 &0.16 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix}\n0.01\n\n\nf_2(P) = \\begin{bmatrix} 0.85 &0.04 \\\\ -0.04 &0.85 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 1.6 \\end{bmatrix}\n0.85\n\n\nf_3(P) = \\begin{bmatrix} 0.2 &-0.26 \\\\ 0.23 &0.22 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 1.6 \\end{bmatrix}\n0.07\n\n\nf_4(P) = \\begin{bmatrix} -0.15 &0.28 \\\\ 0.26 &0.24 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 0.44 \\end{bmatrix}\n0.07\n\n\n\nPlaying around a bit...\nOne big advantage of using affine transformations to construct an attractor is that mathematicians and programmers can leverage their knowledge of how these transformations work to also modify the resulting image.\nHere are a few examples of ferns that can be generated by modifying constituent functions:\n\n\n\nFunction\nOperation\n\n\n\n\nf_1(P) = \\begin{bmatrix} \\tau &0 \\\\ 0 &0.16 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix} where -0.5 Turning stems to leaves\n Your browser does not support the video tag. \n\n\nf_2(P) = \\begin{bmatrix} 0.85 & \\tau \\\\ -0.04 &0.85 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 1.6 \\end{bmatrix} where -0.01 Changing fern tilt\n Your browser does not support the video tag. \n\n\nf_3(P) = \\begin{bmatrix} 0.2 &-0.26 \\\\ 0.23 &0.22 \\end{bmatrix}P + \\begin{bmatrix} \\tau \\\\ 1.6 \\end{bmatrix} where -0.5 Plucking left leaves\n Your browser does not support the video tag. \n\n\nf_4(P) = \\begin{bmatrix} -0.15 &0.28 \\\\ 0.26 &0.24 \\end{bmatrix}P + \\begin{bmatrix} \\tau \\\\ 0.44 \\end{bmatrix} where -0.5 Plucking right leaves\n Your browser does not support the video tag. \n\n\n\nAs an important note: the idea of modifying a resulting image by twiddling the knobs of an affine transform is the heart of many interesting methods, including fractal image compression where a low resolution version of an image is stored along with a reconstructing function set to generate high-quality images on-the-fly [2][3].\nIf this seems mystifying, don't worry!\nWe'll definitely come back to this soon, I just wanted to briefly mention it now so it's on everyone's mind as we move forward.\nVideo Explanation\nHere is a video describing the Barnsley fern:\n\n\n\n\nExample Code\nSimilar to the chapter on iterated function systems, the example code here will show a chaos game for the construction of an attractor;\nhowever, in this case the attractor will be the Barnsley fern instead of the Sierpinski triangle.\nThe biggest differences between the two code implementations is that the Barnsley implementation must take into account the varying probabilities for choosing each function path and that we will be choosing an initial point that is on the attractor this time (namely (0,0)).\nusing DelimitedFiles\n\n# This is a function that reads in the Hutchinson operator and corresponding\n# probabilities and outputs a randomly selected transform\n# This works by choosing a random number and then iterating through all \n# probabilities until it finds an appropriate bin\nfunction select_array(hutchinson_op, probabilities)\n\n # random number to be binned\n rnd = rand()\n\n # This checks to see if a random number is in a bin, if not, that \n # probability is subtracted from the random number and we check the\n # next bin in the list\n for i = 1:length(probabilities)\n if (rnd \nuse rand::prelude::*;\n#[derive(Clone, Copy)]\nstruct Point2 {\n x: f64,\n y: f64,\n}\n\n#[derive(Clone, Copy)]\nstruct Point3 {\n x: f64,\n y: f64,\n z: f64,\n}\n\nimpl Point3 {\n fn new(x: f64, y: f64, z: f64) -> Self {\n Self { x, y, z }\n }\n\n fn matrix_mul(self, rhs: Vec) -> Self {\n let x = rhs[0].x * self.x + rhs[0].y * self.y + rhs[0].z * self.z;\n let y = rhs[1].x * self.x + rhs[1].y * self.y + rhs[1].z * self.z;\n let z = rhs[2].x * self.x + rhs[2].y * self.y + rhs[2].z * self.z;\n Self::new(x, y, z)\n }\n}\n\nfn select_array(hutchinson_op: &[Vec], probabilities: &[f64]) -> Vec {\n let mut rng = rand::thread_rng();\n let mut rnd = rng.gen::();\n\n for (i, probability) in probabilities.iter().enumerate() {\n if rnd ],\n probabilities: &[f64],\n) -> Vec {\n let mut point = Point3 {\n x: initial_location.x,\n y: initial_location.y,\n z: 1.0,\n };\n (0..iters)\n .into_iter()\n .map(|_| {\n let old_point = point;\n let operation = select_array(hutchinson_op, probabilities);\n point = point.matrix_mul(operation);\n Point2 {\n x: old_point.x,\n y: old_point.y,\n }\n })\n .collect()\n}\n\nfn main() {\n let barnsley_hutchinson = vec![\n vec![\n Point3::new(0.0, 0.0, 0.0),\n Point3::new(0.0, 0.16, 0.0),\n Point3::new(0.0, 0.0, 1.0),\n ],\n vec![\n Point3::new(0.85, 0.04, 0.0),\n Point3::new(-0.04, 0.85, 1.60),\n Point3::new(0.0, 0.0, 1.0),\n ],\n vec![\n Point3::new(0.20, -0.26, 0.0),\n Point3::new(0.23, 0.22, 1.60),\n Point3::new(0.0, 0.0, 1.0),\n ],\n vec![\n Point3::new(-0.15, 0.28, 0.0),\n Point3::new(0.26, 0.24, 0.44),\n Point3::new(0.0, 0.0, 1.0),\n ],\n ];\n\n let barnsley_probabilities = vec![0.01, 0.85, 0.07, 0.07];\n\n let mut out = String::new();\n\n for point in chaos_game(\n 10_000,\n Point2 { x: 0.0, y: 0.0 },\n &barnsley_hutchinson,\n &barnsley_probabilities,\n ) {\n out += format!(\"{}\\t{}\\n\", point.x, point.y).as_str();\n }\n\n std::fs::write(\"./out.dat\", out).unwrap();\n}\n\n// The code bellow uses C++-17 features, compile it with C++-17 flags, e.g.:\n// clang++ -Wall -Wextra -Wshadow -Wnon-virtual-dtor -Wold-style-cast -Wcast-align -Wunused -Woverloaded-virtual -Wpedantic -Wconversion -Wsign-conversion -Wnull-dereference -Wdouble-promotion -Wformat=2 -gdwarf-3 -D_GLIBCXX_DEBUG -std=c++17 -O3 -c ./barnsley.cpp barnsley\n\n#include \n#include \n#include \n#include \n\nusing Vec2 = std::array;\nusing Vec3 = std::array;\nusing Row = std::array;\nusing Op = std::array;\n\nconstexpr auto OpN = 4U;\n\ntemplate \nauto operator+(std::array x, std::array y) {\n for (auto i = 0U; i \nauto operator*(double k, std::array v) {\n for (auto i = 0U; i \nauto operator*(std::array v, double k) {\n return k * v;\n}\n\nauto operator*(const Op& x, const Vec3& y) {\n auto ret = Vec3{};\n for (auto i = 0U; i (0.0, 1.0)(rng());\n}\n\n// This is a function that reads in the Hutchinson operator and\n// corresponding\n// probabilities and outputs a randomly selected transform\n// This works by choosing a random number and then iterating through all\n// probabilities until it finds an appropriate bin\nauto select_array(\n const std::array& hutchinson_op,\n const std::array& probabilities) {\n\n // random number to be binned\n auto rnd = drand();\n\n // This checks to see if a random number is in a bin, if not, that\n // probability is subtracted from the random number and we check the\n // next bin in the list\n for (auto i = 0U; i (\"check if probabilities adding up to 1\"));\n return hutchinson_op[0];\n}\n\n// This is a general function to simulate a chaos game\n// n is the number of iterations\n// initial_location is the the starting point of the chaos game\n// hutchinson_op is the set of functions to iterate through\n// probabilities is the set of probabilities corresponding to the likelihood\n// of choosing their corresponding function in hutchinson_op\nauto chaos_game(\n size_t n,\n Vec2 initial_location,\n const std::array& hutchinson_op,\n const std::array& probabilities) {\n\n // Initializing the output array and the initial point\n auto output_points = std::vector{};\n\n // extending point to 3D for affine transform\n auto point = Vec3{initial_location[0], initial_location[1], 1};\n\n for (auto i = 0U; i \n#include \n#include \n\nstruct matrix {\n double xx, xy, xz,\n yx, yy, yz,\n zx, zy, zz;\n};\n\nstruct point2d {\n double x, y;\n};\n\nstruct point3d {\n double x, y, z;\n};\n\nstruct point3d matmul(struct matrix mat, struct point3d point)\n{\n struct point3d out = {\n mat.xx * point.x + mat.xy * point.y + mat.xz * point.z,\n mat.yx * point.x + mat.yy * point.y + mat.yz * point.z,\n mat.zx * point.x + mat.zy * point.y + mat.zz * point.z\n };\n return out;\n}\n\n// This function reads in the Hutchinson operator and corresponding\n// probabilities and returns a randomly selected transform\n// This works by choosing a random number and then iterating through all\n// probabilities until it finds an appropriate bin\nstruct matrix select_array(struct matrix *hutchinson_op, double *probabilities,\n size_t num_op)\n{\n // random number to be binned\n double rnd = (double)rand() / RAND_MAX;\n\n // This checks to see if a random number is in a bin, if not, that\n // probability is subtracted from the random number and we check the next\n // bin in the list\n for (size_t i = 0; i \nimport java.io.FileWriter;\nimport java.io.IOException;\nimport java.util.Random;\n\npublic class Barnsley {\n\n private static class Point {\n public double x, y, z;\n\n public Point(double x, double y, double z) {\n this.x = x;\n this.y = y;\n this.z = z;\n }\n\n public Point(double[] coordinates) {\n this.x = coordinates[0];\n this.y = coordinates[1];\n this.z = coordinates[2];\n }\n\n public Point matrixMultiplication(double[][] matrix) {\n double[] results = new double[3];\n for (int i = 0; i \nfrom random import choices\nimport numpy as np\n\ndata Point(x=0, y=0):\n def __rmatmul__(self, mat: np.array):\n point_array = np.array([self.x, self.y, 1])\n x, y, *_ = tuple(*(mat @ point_array))\n return Point(x, y)\n\n\ndef chaos_game(initial_location is Point, hutchinson_op, probabilities):\n point = initial_location\n while True:\n yield (point := choices(hutchinson_op, probabilities) @ point)\n\nbarnsley_hutchinson = [\n np.array([\n [0., 0., 0.],\n [0., 0.16, 0.],\n [0., 0., 1.],\n ]),\n np.array([\n [0.85, 0.04, 0.],\n [-0.04, 0.85, 1.6],\n [0., 0., 1.],\n ]),\n np.array([\n [0.2, -0.26, 0.],\n [0.23, 0.22, 1.6],\n [0., 0., 1.],\n ]),\n np.array([\n [-0.15, 0.28, 0.],\n [0.26, 0.24, 0.44],\n [0., 0., 1.],\n ]),\n]\n\nbarnsley_probabilities = [0.01, 0.85, 0.07, 0.07]\n\nif __name__ == '__main__':\n output_gen = chaos_game(Point(0, 0), barnsley_hutchinson, barnsley_probabilities)\n output_points = np.array([*output_gen$[:10000]])\n np.savetxt(\"out.dat\", output_points)\n\nimport Data.Array (Array, bounds, elems, listArray, (!))\nimport Data.List (intercalate)\nimport System.Random\n\ndata Point = Point Double Double\n\nchaosGame :: RandomGen g => g -> Int -> Array Int (Double, (Point -> Point)) -> [Point]\nchaosGame g n hutchinson = take n points\n where\n (x, g') = random g\n (y, g'') = random g'\n\n cumulProbabilities = scanl1 (+) $ map fst $ elems hutchinson\n to_choice x = length $ takeWhile (x >) cumulProbabilities\n\n picks = map to_choice $ randomRs (0, 1) g''\n step = fmap snd hutchinson\n\n points = Point x y : zipWith (step !) picks points\n\naffine :: (Double, Double, Double, Double) -> (Double, Double) -> Point -> Point\naffine (xx, xy, yx, yy) (a, b) (Point x y) = Point (a + xx * x + xy * y) (b + yx * x + yy * y)\n\nshowPoint :: Point -> String\nshowPoint (Point x y) = show x ++ \"\\t\" ++ show y\n\nmain :: IO ()\nmain = do\n g \n\n\nBibliography\n1.Barnsley, Michael F, Fractals everywhere, Academic press, 2014.2.Wikipedia: Fractal Compression, 2019.3.Saupe, Dietmar and Hamzaoui, Raouf, A review of the fractal image compression literature, ACM, 1994.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"IFS triangle 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"IFS square 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Simple Barnsley fern\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine random transform 0\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine random transform 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine random transform 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine random transform 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine fern transform 0\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine fern transform 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine fern transform 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine fern transform 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Fern twiddle 0\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Fern twiddle 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Fern twiddle 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Fern twiddle 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n"},"contents/box_muller/box_muller.html":{"url":"contents/box_muller/box_muller.html","title":"Box Muller Transform","keywords":"","body":"The Box—Muller Transform\nThe Box—Muller transform holds a special place in my heart as it was the first method I ever had to implement for my own research.\nThe purpose of this transformation is simple.\nIt takes a uniform (probably random) distribution and turns it into a Gaussian one.\n\n \n\n\nThat's it.\nIt was originally developed by George Box (yes, Box is his last name) and Mervin Muller in 1958 and is one of the most common methods to create a random, Gaussian distribution of points [1].\nIt's particularly useful when initializing a set of particles for a physical, N-body simulation.\nThis chapter will be divided into a few subsections:\n\nHow to initialize the Box—Muller transform\nHow to use the Box—Muller transform in Cartesian coordinates [2].\nHow to use the Box—Muller transform in Polar Coordinates, also called the Marsaglia transform [3].\n\nOf course, there will be full code examples at the bottom.\nSo, let's get to it!\nHow to initialize the Box—Muller transform\nThe main thing to mention here is that the Box—Muller transform requires some form of uniform distribution as its input.\nOne obvious way to initialize a random distribution of points is to start with a grid, like so:\n\nfunction create_grid(n, endpoints)\n\n grid_extents = endpoints[2] - endpoints[1]\n\n # number of points along any given axis\n # For 2D, we take the sqrt(n) and then round up\n axis_num = ceil(Int, sqrt(n))\n\n # we are now rounding n up to the nearest square if it was not already one\n if sqrt(n) != axis_num\n n = axis_num^2\n end \n\n # Distance between each point\n dx = grid_extents / (axis_num)\n\n # Initializing the array, particles along the column, dimensions along rows\n a = zeros(n, 2)\n\n # This loops over the relevant dimensions\n for i = 1:axis_num\n for j = 1:axis_num\n a[(i - 1) * axis_num + j, :] .=\n [(i - 0.5) * dx + endpoints[1],\n (j - 0.5) * dx + endpoints[1]]\n end\n end\n\n return a\n\n\n\nThis will create the following set of points for n=100:\n\n \n\n\nTo be honest, there are a bunch of ways to generate this exact same distribution.\nHere, we simply walked backwards half of the grid size, determined the step size, and then placed a particle at each step.\nNote that there is an inherent limitation with this method in that it only works for a square numbers.\nBecause of this, we decided to round n up to the nearest square to make a nice grid.\nIt's not the cleanest implementation, but the grid will mainly be used for debugging anyway, so it's OK to be a little messy here.\nThe real star of the show is the uniform random distribution, which can be generated like this:\n\nfunction create_rand_dist(n, endpoints)\n grid_extents = endpoints[2] - endpoints[1]\n return(rand(n,2) * grid_extents .+ endpoints[1])\n\n\n\nThis will create the following set of points for n=100:\n\n \n\n\nOK, but how do we know this is uniform?\nGood question!\nThe easiest way is to plot a histogram of a super large number of points.\nIf the random distribution is uniform, then all the bins should be roughly the same value.\nThe more points we have, the smaller the percent difference between the bins will be.\nHere is a set of images generated by rand() for n=100, 1,000, and 10,000 all in one dimension:\n\n\n\n100\n1,000\n10,000\n\n\n\n\n\n\n\n\n\n\nIt is clear that the 10,000 case looks the most uniform.\nNote that for two dimensions, the same logic applies, but we need to create separate histograms for the x and y coordinates.\nOnce this test is complete, we can be fairly sure that the function we are using to generate the initial distribution is uniform and ready for the next step of the process: actually using the Box—Muller transform!\nHow to use the Box—Muller transform in Cartesian coordinates\nThe two dimensional Cartesian version of the Box—Muller transform starts with two random input values (u_1 and u_2), both of which come from their own uniform distributions that are between 0 and 1.\nIt then creates two output points (z_1 and z_2).\nFor this, u_1 is used to create a Gaussian distribution along some radial value r, and u_2 is used to spin that around a circle with some angular component \\theta, such that \n\n\\begin{align}\nr &= \\sqrt{-2\\ln(u_1)} \\\\\n\\theta &= 2\\pi u_2.\n\\end{align}\n\nLooking at these equations, \\theta seems to make a decent amount of sense.\nAfter all, angles typically vary from 0 \\rightarrow 2\\pi, and our input distribution varies from 0 \\rightarrow 1, so we can get some value between 0 and 2\\pi by multiplying 2\\pi by one of our input values.\nSo what about r?\nWell, remember that if we want u to be in a Gaussian form, then we might say something like, u = e^{-\\frac{r^2}{2}}, so if we solve this for r, we get r=\\sqrt{-2\\ln(u)}.\nFrom these values, we can calculate our new x,y points as,\n\n\\begin{align}\nx &= r\\cos(\\theta) \\\\\ny &= r\\sin(\\theta).\n\\end{align}\n\nFinally, in order to specify the size and shape of the generated Gaussian distribution, we can use the standard deviation, \\sigma, and the mean, \\mu, like so:\n\n\\begin{align}\nz_1 &= x\\sigma + \\mu \\\\\nz_2 &= y\\sigma + \\mu.\n\\end{align}\n\nIn general, this can be written in code like so:\n# Box--Muller transform\nfunction cartesian_box_muller(input_pts, sigma, mu)\n r = sqrt(-2 * log(input_pts[1]))\n theta = 2 * pi * input_pts[2]\n\n return [sigma * r * cos(theta) + mu[1],\n sigma * r * sin(theta) + mu[2]]\n\nend\n\n\n\nWhich produces the following output\n\n \n \n\n\nNote that we have written the code to work on a single set of input values, but it could also be written to read in the entire distribution of points all at once.\nAs this particular technique is usually implemented in parallel, it's up to you to decided which is the fastest for your own individual use-case.\nAt this stage, we have a good idea of how the transform works, but some people shy away from the Cartesian method in practice and instead opt for the polar form, which will be discussed next!\nHow to use the Box—Muller transform in polar coordinates\nThe Cartesian form of the Box—Muller transform is relatively intuitive.\nThe polar method is essentially the same, but without the costly \\sin and \\cos operations.\nIn this case, we use the input values to create an initial radial point (to be scaled later):\n\nr_0 = \\sqrt{u_1^2 + u_2^2}.\n\nThis means that we are essentially trying to transform our set of u values into a new input value r_0.\nTo do this, we need to start with a uniformly distributed circle, so we must reject any values for u_1 and u_2 where r is either 0 or \\gt 1.\nThis also means that the initial distributions of u_1 and u_2 must range from -1 \\rightarrow +1.\nFrom here, we can use basic trigonometric identities to redefine the \\sin and \\cos to be\n\n\\begin{align}\n\\cos(\\theta) &= u_1/\\sqrt{r_0} \\\\\n\\sin(\\theta) &= u_2/\\sqrt{r_0}.\n\\end{align}\n\nThis changes the output equations to be\n\n\\begin{align}\nx &= r\\cos(\\theta) = \\sqrt{-2\\ln(r_0)}\\left(\\frac{u_1}{\\sqrt{r_0}}\\right) = u_1 \\sqrt{\\frac{-2\\ln(r_0)}{r_0}} \\\\\ny &= r\\sin(\\theta) = \\sqrt{-2\\ln(r_0)}\\left(\\frac{u_2}{\\sqrt{r_0}}\\right) = u_2 \\sqrt{\\frac{-2\\ln(r_0)}{r_0}}.\n\\end{align}\n\nAgain, the final values are:\n\n\\begin{align}\nz_1 &= \\sigma x + \\mu \\\\\nz_2 &= \\sigma y + \\mu.\n\\end{align}\n\nIn code, it might look like this:\n# Box--Muller transform\nfunction polar_box_muller(input_pts, sigma, mu)\n r_0 = input_pts[1]^2 + input_pts[2]^2\n\n # this method is only valid for points within the unit circle\n if r_0 == 0 || r_0 > 1\n return [NaN, NaN]\n end\n\n return [sigma * input_pts[1] * sqrt(-2 * log(r_0) / r_0) + mu[1],\n sigma * input_pts[2] * sqrt(-2 * log(r_0) / r_0) + mu[2]]\n\n\n\nThis will produce the following output:\n\n \n \n\n\nAgain, this is ultimately the same as the Cartesian method, except that it:\n\nRejects points in the initial distribution that are outside of the unit circle (also called rejection sampling)\nAvoids costly \\sin and \\cos operations\n\nPoint 2 means that the polar method should be way faster than the Cartesian one, but rejection sampling is somewhat interesting in it's own right, which we have discussed in a separate chapter\nExample Code\nThe example code here is straightforward: we start with a uniform distribution of points (both on a grid and a uniform random distribution) and then we preform the Box—Muller transform to see how far off it is from the Gaussian we expect.\nusing DelimitedFiles, LinearAlgebra\nusing Test\n\nfunction create_grid(n, endpoints)\n\n grid_extents = endpoints[2] - endpoints[1]\n\n # number of points along any given axis\n # For 2D, we take the sqrt(n) and then round up\n axis_num = ceil(Int, sqrt(n))\n\n # we are now rounding n up to the nearest square if it was not already one\n if sqrt(n) != axis_num\n n = axis_num^2\n end \n\n # Distance between each point\n dx = grid_extents / (axis_num)\n\n # Initializing the array, particles along the column, dimensions along rows\n a = zeros(n, 2)\n\n # This loops over the relevant dimensions\n for i = 1:axis_num\n for j = 1:axis_num\n a[(i - 1) * axis_num + j, :] .=\n [(i - 0.5) * dx + endpoints[1],\n (j - 0.5) * dx + endpoints[1]]\n end\n end\n\n return a\nend\n\nfunction create_rand_dist(n, endpoints)\n grid_extents = endpoints[2] - endpoints[1]\n return(rand(n,2) * grid_extents .+ endpoints[1]) \nend\n\n# This function reads in a pair of input points and performs the Cartesian\n# Box--Muller transform\nfunction cartesian_box_muller(input_pts, sigma, mu)\n r = sqrt(-2 * log(input_pts[1]))\n theta = 2 * pi * input_pts[2]\n\n return [sigma * r * cos(theta) + mu[1],\n sigma * r * sin(theta) + mu[2]]\n\nend\n\n# This function reads in a pair of input points and performs the Cartesian\n# Box--Muller transform\nfunction polar_box_muller(input_pts, sigma, mu)\n r_0 = input_pts[1]^2 + input_pts[2]^2\n\n # this method is only valid for points within the unit circle\n if r_0 == 0 || r_0 > 1\n return [NaN, NaN]\n end\n\n return [sigma * input_pts[1] * sqrt(-2 * log(r_0) / r_0) + mu[1],\n sigma * input_pts[2] * sqrt(-2 * log(r_0) / r_0) + mu[2]]\n\nend\n\nfunction is_gaussian(input_pts; bounds = [-1 1; -1 1], dx = 0.1,\n sigma = 1, mu = [0,0], threshold = 0.1)\n histogram = zeros(ceil(Int,(bounds[1,2]-bounds[1,1])/dx),\n ceil(Int,(bounds[2,2]-bounds[2,1])/dx))\n\n for i = 1:size(input_pts)[1]\n input_x = input_pts[i, 1]\n input_y = input_pts[i, 2]\n if !(isnan(input_x) || isnan(input_y))\n\n bin = CartesianIndex(ceil(Int, (input_x - bounds[1,1]) / dx),\n ceil(Int, (input_y - bounds[2,1]) / dx))\n\n if bin[1] 0 &&\n bin[2] 0\n histogram[bin] += 1\n end\n end\n end\n\n n = sum(histogram)\n normalize!(histogram)\n\n rms = 0\n for i = 1:size(histogram)[1]\n x = bounds[1,1] + i*dx\n for j = 1:size(histogram)[2]\n y = bounds[2,1] + j*dx\n gaussian_value = exp(-(((x+mu[1])^2)/(2*sigma^2) +\n ((y+mu[2])^2)/(2*sigma^2)))\n rms += (gaussian_value - histogram[i,j])^2\n end\n end\n\n return sqrt(rms/n) \n\n\nBibliography\n1.Box, George EP, A note on the generation of random normal deviates, 1958.2.Wikipedia: Box-Muller Transform, 2022.3.Wikipedia: Marsaglia Transform, 2022.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"IFS triangle 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"IFS square 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Simple Barnsley fern\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine random transform 0\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine random transform 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine random transform 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine random transform 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine fern transform 0\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine fern transform 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine fern transform 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine fern transform 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Fern twiddle 0\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Fern twiddle 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Fern twiddle 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Fern twiddle 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n"},"contents/computus/computus.html":{"url":"contents/computus/computus.html","title":"Computus","keywords":"","body":"The Easter Algorithm (Computus)\nThough the word Computus can technically describe any sort of computation [1] or else a set of medieval tables for calculating various astrological events [2], it is also one of the most common historical names for the calculation of the Christian holiday of Easter every year.\nNominally, Easter happens the Sunday after the first full moon after the spring equinox (roughly March 21st).\nThis particular full moon is known by a number of names, such as the Pink (Strawberry) Moon, Hunter's Moon, or the Snow Moon, along with several others.\nThe most common name for it is the paschal full moon, which translates to \"Passover\" in Greek and signifies an important Jewish festival.\nFor the first few centuries, the date of Easter each year was dictated by the Pope; however, after the church grew, it was no longer straightforward to communicate this date to all of Christendom.\nAs such, the church did what it could to algorithmically generate tables for clergy to determine the date of Easter each year.\nTo this day, the calculation of Easter still poses a problem, with western and eastern (orthodox) churches celebrating on different dates approximately 50% of the time.\nI'll be honest, there is a lot of good, Christian drama surrounding the calculation of this event and it's remarkably interesting to read about [3].\nSuffice it to say that the date of Easter bamboozled many historical scholars, with at least one algorithm appearing in the early archives of the now famous scientific journal of Nature [4].\nThe calculation was so complicated that even Frederick Gauss had to try his hand at it (and failed before being corrected by one of his students).\nEssentially, the date of Easter depends on both the lunar and solar cycles\nThe date of the paschal full moon, for example, is static in the lunar calendar, but it is not in the solar calendar.\nIn this way, computus is the act of mapping a lunar cycle onto the Gregorian (solar) calendar everyone knows and loves.\nBecause many different calendar systems have existed throughout history, there was a natural question as to which calendar system would be used to calculate the precise date of Easter.\nThe western churches chose the Gregorian calendar and the eastern churches chosethe Julian one, and this is one reason why western and eastern churches sometimes celebrate on different dates.\nThat said, the Gregorian calendar more accurately represents the true date of the paschal full moon, so the western church's approach ended up being more precise.\nThough there are many methods to calculate Easter, for now, we will focus only on Gauss's algorithm; however, we mayl certainly come back (in subsequent years) to incorporate other Easter algorithms if there is demand.\nThese algorithms are some of my favorite gems in the history of algorithm design because of all the drama surrounding the calculation of something that seems trivial!\nAfter all, how hard could it be to calculate Easter?\nGauss's Easter algorithm history\nGauss is known for a lot of things: Gaussian elimination, the Cooley-Tukey method before Cooley or Tukey even existed, Gauss's Law for electromagnetism, etc.\nOne thing he is not particularly well known for is an algorithm he devised in 1800, which was later corrected by his student Peter Paul Tittle in 1816.\nIn fact, there were a series of publications from Gauss in this era all relating to the precise date of Easter.\nThe legend goes that Gauss actually did not know his real birthday in the Gregorian calendar and used this same algorithm to determine it.\nApparently, his mother only told him that he was born on a Wednesday 8 days before Ascension Day in 1777, which corresponds to April 30th [3].\nHonestly, Gauss's Easter algorithm was the 19th century equivalent of undocumented code.\nI could imagine Gauss grumpily \"patching\" his method when users complained that it did not work on dates past 4200 or even certain dates within his own era!\nWhen some of his compatriots (such as Johann Lambert and Jean Joseph Delambre) expressed their concern over the method's performance, Gauss replied by saying,\n\nThe investigation by which the formula [...] is found is based on higher arithmetic, for which I presumably cannot refer to any publication.\n\nWhich was the 19th century equivalent of saying, \"you are too dumb to understand my genius.\"\nI have definitely met a few fledgling programmers who feel the same, but none of them were anywhere near as prolific as Gauss.\nOne of the most important fans of Gauss's work was Servois, who created a calendar based on Gauss's 1800 publication, shown below:\n\nThis calendar shows the date the paschal full moon, indicating that Easter will be the following Sunday [5].\nIn this table, a value greater than 22 indicates the full moon will be on the presented number (date) in March and a value less than 22 indicates the full moon will be on that date in April.\nThe y-axis of this table indicates the decade and the x-axis indicates the precise year.\nAdmittedly, the notation is a bit funky, but it was 1813.\nTimes were different then.\nThe task for this chapter will be to explain (to the best of my abilities) how one would go about using Gauss's Easter algorithm to calculate the date of Easter for any given year (within the limitations of the algorithm).\nBackground\nBecause Easter is the Sunday following the paschal full moon, which is the first full moon of spring, Gauss's algorithm is tasked at finding a way to map the lunar calendar to the Gregorian (solar) calendar.\nFor this reason, before discussing the algorithm, itself, we must first introduce both calendar systems.\nThe Gregorian (solar) calendar has been created to mark Earth's full revolution around the Sun, which is approximately 365.2425 days.\nUnfortunately, days are based on the Earth's rotation about its axis, not its revolution around the Sun, so the number of days in a year is not an integer number (such as 365).\nThis discrepancy has actually lead to a large number of calendar systems, including one invented by Gauss, himself [6].\nBefore the Gregorian calendar, there was another correction made from an old Roman calendar to set the days in a year to be 365.25 days.\nThis was called the Julian calendar.\nFrom there, the Julian calendar was further corrected to the Gregorian calendar with 365.2425 days.\nThough there is only a small change necessary to use Gauss's Easter algorithm for the Julian calendar, this will not be covered here; however, if you want to see this, we can add it in upon request.\nTo account for the non-integer nature of the Gregorian year, a leap day is celebrated on February 29th every 4 years, with exception of when the year is a multiple of 100, where no leap-day is observed; if the year is divisible by 400, however, a leap day is still observed.\nThis means that every 400 years, there are 97 leap days.\nThis is why a leap day was celebrated in 2020 and 2000, but was not in 1900.\nIf at this point, you feel like your favorite calendar system is held together by duct tape and string, you would be right.\nIn addition to the solar year, Gauss's Easter algorithm also needs to keep the lunar year into account.\nA lunar month corresponds to the time it takes the Moon to complete one full revolution around the Earth.\nIn most cases, this is approximately 27.5 days [7].\nThat said, space is complicated and the Moon is not the only revolving body.\nLunar phases are related to the time it takes for the Moon to return to its location in relation to the line connecting the Sun and Earth, as shown below:\n\nThis is called the synodic month and will be the approximation used for this chapter.\nBelow, we also show a snapshot of this simulation after 6 synodic months:\n\nHere, we show an outline of the Earth and Moon in an arbitrary initial position, each with an angle of -\\frac{\\pi}{4} from the horizontal axis.\nIn addition, we show the location of the Moon and Earth again after 6 synodic months and additional outlines for each intermediate synodic month.\nRed lines are drawn from the center of the sun to the moon to indicate the positioning of the moon in relation to the sun and earth.\nIn all positions, the Moon is hidden behind the Earth, creating the full moon phase.\nIn this way, the synodic month is the time between two consecutive phases, which is slightly longer than the time it takes to revolve around the Earth and return to the same angle (here \\frac{\\pi}{4}).\nEach synodic month is approximately 29.5 days, so a synodic year of 12 lunar months is 354 days, which is 11 days shorter than the normal 365 days in a Gregorian year.\nThe following is a pictorial representation of offset between a solar and lunar year:\n\nHere, we see the Sun at the center, with the Earth and Moon starting the year at an angle of -\\frac{\\pi}{4} from the horizontal axis.\nThe initial location of the Earth and Moon are shown as an outline with the letter \"A\" at their center.\nAfter a full synodic lunar year (12 lunar months), another outline of the Earth and Moon are shown at position B, and after a full Gregorian year, they are shown in position C.\nAn arc is then drawn showing the difference of 11 days between the Earth's position after a synodic year, and another arc is drawn to show the difference between the Moon's position after a full Gregorian year.\nBecause the synodic month and the solar year are not synchronized, the phase of the Moon will be different on the same day of the Gregorian year.\nThat said, the lunar and solar calendars will re-synchronize roughly every 19 years.\nFor example, if there is a new moon on January 1st, 2020, there will not be a new moon on January 1st, 2021; however, there will be a new moon on January 1st, 2039.\nThis 19-year cycle where the Moon and Sun are waiting to re-synchronize is known as the Metonic cycle and has been studied for centuries.\nThis cycle allows us to somewhat easily transition between solar and lunar calendars.\nIf we imagine any Gregorian date (let's say January 1st again for clarity), the moon could be in one of 19 different phases, as shown below:\n\nHere, we show each possible phase of the moon as an outline, but the actual phase as a grey circle.\nEssentially, by knowing what year we are on in the Metonic cycle, we can single out which phase of the moon we will see on any given date.\nThis is powerful and will allow us to find the next full moon by looking ahead a few days.\nAs a final note, there is a small offset in the Metonic cycle of 1 hour and 45 minutes every 19 years, so in 2500 years, it will be 8 days off, but that's a problem for people in 2500.\nFor now, we should be able to start discussing the algorithm, itself.\nThe algorithm\nAs alluded to in Gauss's quote above, the Easter algorithm is closer to a set of formulas than a method used to compute anything on a modern computer.\nThis is partially because of bad software engineering by Gauss and partially because computers did not really exist at that point.\nConsidering this method was literally called Computus, there probably was not much to compute at all at the time.\nNowadays, you could more easily find the date of Easter with loops and conditions, but this is the Arcane Algorithm Archive, and this is definitely an arcane algorithm, so let's go!\nFor this section, we will be following similar notation to Gauss's original 1800 work, which is a bit terse and hard to follow; however, each term is significantly meaningful.\nIf you are reading this and think you have a better way to present anything, please let us know (with an issue or pull request on github) and we can correct the text!\nThis method can be split into 2 parts:\n\nCalculating the days from March 21st to the next full moon\nCalculating the days from the full moon to the next Sunday\n\nIn the following sections, we will discuss both individually.\nCalculating the date of the next full moon\nTo start, we will be calculating d, which is the number of days until the next full moon from March 21st (the first day of spring according to the pope).\nTo calculate this, we need to first calculate a number of auxiliary variables, starting with the current year's location on the Metonic calendar,\n\na = \\text{year}~\\%~19,\n\nwhere \\% is the modulo operator and 19 is the length of the Metonic calendar in years.\nFrom here, we also need to calculate an offset to a, and for this we need the century index,\n\nk = \\left\\lfloor\\frac{\\text{year}}{100}\\right\\rfloor,\n\nwhere \\lfloor\\cdot\\rfloor is the flooring operation of rounding the value down to the nearest integer.\nWith this, we can calculate the shift in the Metonic cycle to be,\n\np = \\left\\lfloor\\frac{13+8k}{25}\\right\\rfloor.\n\nThis expression represents the fact that the Metonic cycle will be 8 days off every 2500 years and adds an additional offset of 13 to ensure the Metonic cycle aligns with empirical observation.\nAt this point, we know what year we are at on the Metonic calendar and have calculated an offset accordingly; however, we have yet to take into account leap years.\nAs stated above, there are 97 leap days every 400 years, and the calculation of p above requires correction for the 3 leap days missed.\nIf one adds 25 leap days per century and subtracts k, they will find 96 leap days every 400 years instead, which is a close approximation, but off by one.\nThis accounts for the fact that leap days are not celebrated on years that are multiples of 100.\nThere is, however, an exception made for years that are multiples of 400, which is why Gauss calculated an additional variable,\n\nq = \\left\\lfloor\\frac{k}{4}\\right\\rfloor.\n\nThis means that 100-k-q will provide the appropriate number of leap days every 400 years.\nAfter this is found, we then calculate a sum of all offsets within a lunar month.\n\nM = (15-p+k-q)~\\%~30\n\nwhere 15 is an offset indicating that the full moon on year 0 is 15 days from March 21st, p is the number of days we are off from the Metonic cycle, and k-q are non-observed leap days.\nThe values of p, k, and q all provide century offsets, which means that the value of M will provide the correct starting point for each century.\nThe \\%30 (modulo 30 arithmetic) constricts our calculation to be within a single synodic lunar month of approximately 30 days.\nWith all this information, we can finally calculate the number of days from March 21st until the first full moon, as\n\nd = (19a+M)~\\%~30\n\nAgain, the \\%~30 operation makes sense here because there is no way the next full moon could occur over 30 days (a synodic lunar month) from March 21st.\nAt first glance, this is simply a calculation of a (where we are on the Metonic cycle) with some offset, M.\nThis is true, but there is an additional multiplicative factor of 19.\nOne might be tempted to wave this away by saying, \"19 is the number of years in the Metonic cycle, so this makes sense!\"\nThe truth is that that 19 is a bit more complicated.\nThis calculation is a calculation of days, not years.\nEvery 12 lunar months is roughly 354 days, which is 11 days shorter than 365.\nThis means that every year in the Metonic cycle, the lunar phase will be 11 days behind.\nIt just so happens that -11~\\%~30 = 19.\nThus, 19a is a combination of this 11 day offset and the fact that we are using modulo 30 arithmetic.\nAfter 19 years, the lunar calendar will be a full 365 days off in the solar calendar, but again, we only care about day offsets in this calculation.\nNo one really keeps track of lunar years, just solar ones.\nRegardless, we now have d, the number of days until the next full moon.\nInterestingly, this is all the information necessary to replicate Servois's table above.\nFrom here, we simply need to create a two-dimensional array with the decade on the y axis and year on the x axis and set within it the value of (21+d)~\\%~31, where the 21 represents the 21st of March, and the \\%~31 comes from the fact that there are 31 days in March.\nFor example, if we were to do this computation for the years from 2000 to 2099, we would find the following table:\n\nWhich shows that the date of the paschal full moon for 2020 is April 9th.\nNow we can move on to finding the precise date of Easter, which should be the following Sunday\nCalculating the next Sunday\nThis calculation will take a few variables from the previous section, namely k-q (the number of non-observed leap days), and d (the number of days since March 21st to the next full moon).\nFor the last calculation, we synchronized the number of days in a lunar month with the Gregorian (solar) calendar.\nFor this computation, we do similar operations, but for the weekly calendar of 7 days, this value will be stored in e.\nThe first step is calculating the correct offset each century based on the fact that Jan 1st, in year 1 was a Friday and then accounting for all the non-observed leap days (k-q),\n\nN = (4+k-q)~\\%~7.\n\nFrom here, things get a little tricky.\nThere are 52 weeks in a year, but 52\\times7=364, meaning we are essentially one day off every year, with exception of leap years where we are two days off.\nAs an example, look at the following table\n\n\n\nJanuary 1st\nDay of the week\nSpecial considerations\n\n\n\n\n2017\nSunday\nNone\n\n\n2018\nMonday\nNone\n\n\n2019\nTuesday\nNone\n\n\n2020\nWednesday\nLeap Year\n\n\n2021\nFriday\nNone\n\n\n\nSimply put, every year we should subtract one day of the week, but on leap years, we should subtract 2.\nTo keep tabs on this, we need two separate counts,\n\nb = \\text{year}~\\%~4,\n\nand\n\nc = \\text{year}~\\%~7,\n\nwhere b keeps track of leap years, and c simply increments by 1 every year.\nThrough a bit of mathematical magic, we can find the expression 2b+4c, which will be -1 in modulo 7 arithmetic for every year, except leap years where it will be -2.\nWith all these terms put together, we can finally calculate the offset from the full moon to Easter Sunday as\n\ne = (2b+4c+6d+N)~\\%~7.\n\nHere, all terms are described as above and the multiplicative factor of 6 to d will provide an offset to Sunday without correcting for leap days.\nWrapping up\nAt this point, we can calculate the days from March 21st to Easter Sunday to be d+e.\nIn particular\n\n\\text{Easter} = \\left\\{\n \\begin{align}\n d+e+22\\text{ March}& \\qquad \\text{if } 22+d+e\\leq31 \\\\\n d+e-9\\text{ April}& \\qquad \\text{if } 22+d+e>31 \\\\\n \\end{align}\n\\right.\n\nRemember that March 22nd would be the first possible day to celebrate Easter because March 21st would be the first possible full moon of spring.\nAll said, there are a few exceptions that are somewhat tricky to understand, namely:\n\ne = \\left\\{\n \\begin{align}\n &e \\\\\n &-1, \\qquad \\text{if } d=29 \\text{ and } e=6 \\text{ or } d=28, e=6, \\text{ and } a>10\n \\end{align}\n\\right.\n\nThese conditionals are placed on the output of d and correspond to when Easter falls on April 26th (if d = 29) or April 25th (if d = 28).\nIn both of these cases, we are setting e=-1, which has the effect of removing a week from the date of Easter.\nFor example, an Easter that would be celebrated on the 26th would instead be celebrated on the 19th.\nMany say that these conditionals are placed on the output for historical reasons, but between you and me, I feel there is a more mathematical reason that I do not fully understand.\nAfter all, why is the correction for d=28 only placed on the Easter date output on the second half of the Metonic cycle (if a > 10)?\nIf you think you might have a better idea as to why these dates are corrected as such, please let us know!\nAs mentioned, this particular algorithm does not make use of any standard computational techniques.\nThere are no loops, conditionals, stacks, or queues.\nHowever, there can be no doubt that Gauss was a master of his craft.\nThe sheer complexity of this calculation both baffles and astounds me -- especially because this was done hundreds of years before computational thinking became common-place.\nSure, this can be done straightforwardly with a calculator, but it is no doubt an algorithm worth discussing and celebrating for its ingenuity at the time of creation.\nVideo Explanation\nHere is a video describing key elements of Gauss's Easter Algorithm:\n\n\n\n\nExample Code\nUnlike many other chapters in the Algorithm Archive, this particular method can be described almost entirely by mathematical expressions.\nAs such, it should be relatively straightforward to implement in a number of different languages, and I heartily encourage you to do so!\nFor now, we have the code outputting a tuple of d and e, so users can use this to calculate either the date of Easter or Servois's table, depending on their use-case; however, please modify the code however you wish!\nfunction computus(year; servois=false)\n\n # Year's position on the 19 year metonic cycle\n a = mod(year, 19)\n\n # Century index\n k = fld(year, 100)\n\n # Shift of metonic cycle, add a day offset every 300 years\n p = fld(13 + 8 * k, 25)\n\n # Correction for non-observed leap days\n q = fld(k, 4)\n\n # Correction to starting point of calculation each century\n M = mod(15 - p + k - q, 30)\n\n # Number of days from March 21st until the full moon\n d = mod(19 * a + M, 30)\n\n # Returning if user wants value for Servois' table\n if servois\n return string(mod(21 + d,31))\n end\n\n # Finding the next Sunday\n # Century-based offset in weekly calculation\n N = mod(4 + k - q, 7)\n\n # Correction for leap days\n b = mod(year, 4)\n c = mod(year, 7)\n\n # Days from d to next Sunday\n e = mod(2 * b + 4 * c + 6 * d + N, 7)\n\n # Historical corrections for April 26 and 25\n if (d == 29 && e == 6) || (d == 28 && e == 6 && a > 10)\n e = -1\n end\n\n # Determination of the correct month for Easter\n if(22 + d + e > 31)\n return \"April \" * string(d + e - 9)\n else\n return \"March \" * string(22 + d + e)\n end\nend\n\n# Here, we will output the date of the Paschal full moon\n# (using Servois notation), and Easter for 2020-2030\n\na = collect(2020:2030)\nservois_numbers = computus.(a; servois=true)\neaster_dates = computus.(a)\n\nprintln(\"The following are the dates of the Paschal full moon (using Servois \" *\n \"notation) and the date of Easter for 2020-2030 AD:\")\nprintln(\"Year\\tServois number\\tEaster\")\nfor i = 1:length(a)\n println(\"$(a[i])\\t$(servois_numbers[i])\\t\\t$(easter_dates[i])\")\nend\n\ndata Mode = Servois | Easter\n\ncomputus :: Mode -> Int -> String\ncomputus mode year =\n case mode of\n Servois ->\n -- Value for Servois' table\n show $ (21 + d) `mod` 31\n Easter ->\n -- Determination of the correct month for Easter\n if 22 + d + f > 31\n then \"April \" ++ show (d + f - 9)\n else \"March \" ++ show (22 + d + f)\n where\n a, b, c, d, e, f, k, m, n, p, q :: Int\n -- Year's position on the 19 year metonic cycle\n a = year `mod` 19\n -- Century index\n k = year `div` 100\n -- Shift of metonic cycle, add a day offset every 300 years\n p = (13 + 8 * k) `div` 25\n -- Correction for non-observed leap days\n q = k `div` 4\n -- Correction to starting point of calculation each century\n m = (15 - p + k - q) `mod` 30\n -- Number of days from March 21st until the full moon\n d = (19 * a + m) `mod` 30\n -- Finding the next Sunday\n -- Century-based offset in weekly calculation\n n = (4 + k - q) `mod` 7\n -- Correction for leap days\n b = year `mod` 4\n c = year `mod` 7\n -- Days from d to next Sunday\n e = (2 * b + 4 * c + 6 * d + n) `mod` 7\n -- Historical corrections for April 26 and 25\n f =\n if (d == 29 && e == 6) || (d == 28 && e == 6 && a > 10)\n then -1\n else e\n\n-- Here, we will output the date of the Paschal full moon\n-- (using Servois notation), and Easter for 2020-2030\nmain :: IO ()\nmain = do\n let years :: [Int]\n years = [2020 .. 2030]\n servoisNumbers, easterDates :: [String]\n servoisNumbers = map (computus Servois) years\n easterDates = map (computus Easter) years\n putStrLn \"The following are the dates of the Paschal full moon (using Servois notation) and the date of Easter for 2020-2030 AD:\"\n putStrLn \"Year\\tServois number\\tEaster\"\n let conc :: Int -> String -> String -> String\n conc y s e = show y ++ \"\\t\" ++ s ++ \"\\t\\t\" ++ e\n mapM_ putStrLn $ zipWith3 conc years servoisNumbers easterDates\n\ndef computus(year, servois=False):\n # Year's position on the 19-year metonic cycle\n a = year % 19\n\n # Century index\n k = year // 100\n\n # Shift of metonic cycle, add a day offset every 300 years\n p = (13 + 8 * k) // 25\n\n # Correction for non-observed leap days\n q = k // 4\n\n # Correction to starting point of calculation each century\n M = (15 - p + k - q) % 30\n\n # Number of days from March 21st until the full moon\n d = (19 * a + M) % 30\n\n # Returning if user wants value for Servois' table\n if servois:\n return str((21 + d) % 31)\n\n # Finding the next Sunday\n # Century-based offset in weekly calculation\n N = (4 + k - q) % 7\n\n # Correction for leap days\n b = year % 4\n c = year % 7\n\n # Days from d to next Sunday\n e = (2 * b + 4 * c + 6 * d + N) % 7\n\n # Historical corrections for April 26 and 25\n if (d == 29 and e == 6) or (d == 28 and e == 6 and a > 10):\n e = -1\n\n # Determination of the correct month for Easter\n if 22 + d + e > 31:\n return \"April \" + str(d + e - 9)\n else:\n return \"March \" + str(22 + d + e)\n\n\n# Here, we will output the date of the Paschal full moon\n# (using Servois notation), and Easter for 2020-2030\n\nprint(\n \"The following are the dates of the Paschal full moon (using Servois\",\n \"notation) and the date of Easter for 2020-2030 AD:\",\n)\nprint(\"Year\\tServois number\\tEaster\")\nfor year in range(2020, 2031):\n print(f\"{year}\\t{computus(year, servois=True)}\\t\\t{computus(year)}\")\n\ndef computus(year, servois = false)\n # Year's position on the 19 year metonic cycle\n a = year % 19\n\n # Century index\n k = year // 100\n\n # Shift of metonic cycle, add a day offset every 300 years\n p = (13 + 8 * k) // 25\n\n # Correction for non-observed leap days\n q = k // 4\n\n # Correction to starting point of calculation each century\n m = (15 - p + k - q) % 30\n\n # Number of days from March 21st until the full moon\n d = (19 * a + m) % 30\n\n # Returning if user wants value for Servois' table\n if servois\n return ((21 + d) % 31).to_s\n end\n\n # Finding the next Sunday\n # Century-based offset in weekly calculation\n n = (4 + k - q) % 7\n\n # Correction for leap days\n b = year % 4\n c = year % 7\n\n # Days from d to next Sunday\n e = (2 * b + 4 * c + 6 * d + n) % 7\n\n # Historical corrections for April 26 and 25\n if (d == 29 && e == 6) || (d == 28 && e == 6 && a > 10)\n e = -1\n end\n\n # Determination of the correct month for Easter\n if (22 + d + e > 31)\n return \"April \" + (d + e - 9).to_s\n else\n return \"March \" + (22 + d + e).to_s\n end\nend\n\n# Here, we will output the date of the Paschal full moon\n# (using Servois notation), and Easter for 2020-2030\ndef main\n a = (2020..2030).to_a\n servois_numbers = a.map { |y| computus(y, servois = true) }\n easter_dates = a.map { |y| computus(y) }\n\n puts \"The following are the dates of the Paschal full moon (using Servois \" +\n \"notation) and the date of Easter for 2020-2030 AD:\"\n puts \"Year\\tServois number\\tEaster\"\n a.each_index { |i|\n puts \"#{a[i]}\\t#{servois_numbers[i]}\\t\\t#{easter_dates[i]}\"\n }\nend\n\nmain\n\nfn computus(year: usize, servois: bool) -> String {\n // Year's position on the 19 year metonic cycle\n let a = year % 19;\n\n // Century index\n let k = year / 100; // NOTE: dividing integers always truncates the result\n\n // Shift of metonic cycle, add a day offset every 300 years\n let p = (13 + 8 * k) / 25;\n\n // Correction for non-observed leap days\n let q = k / 4;\n\n // Correction to starting point of calculation each century\n let m = (15 - p + k - q) % 30;\n\n // Number of days from March 21st until the full moon\n let d = (19 * a + m) % 30;\n\n if servois {\n return ((21 + d) % 31).to_string();\n }\n\n // Finding the next Sunday\n // Century-based offset in weekly calculation\n let n = (4 + k - q) % 7;\n\n // Correction for leap days\n let b = year % 4;\n let c = year % 7;\n\n // Days from d to next Sunday\n let temp_e = ((2 * b + 4 * c + 6 * d + n) % 7) as isize;\n\n // Historical corrections for April 26 and 25\n let e = if (d == 29 && temp_e == 6) || (d == 28 && temp_e == 6 && a > 10) {\n -1\n } else {\n temp_e\n };\n\n // Determination of the correct month for Easter\n if (22 + d) as isize + e > 31 {\n format!(\"April {}\", d as isize + e - 9)\n } else {\n format!(\"March {}\", 22 + d as isize + e)\n }\n}\n\nfn main() {\n // Here, we will output the date of the Paschal full moon\n // (using Servois notation), and Easter for 2020-2030\n\n let years = 2020..=2030;\n\n println!(\n \"The following are the dates of the Paschal full moon (using \\\n Servois notation) and the date of Easter for 2020-2030 AD:\"\n );\n println!(\"Year\\tServois number\\tEaster\");\n years.for_each(|year| {\n println!(\n \"{}\\t{:\nfunction Calculate-Computus([int]$Year, [switch]$Servois) {\n\n # Year's position on the 19 year metonic cycle\n $a = $Year % 19\n\n # Century index\n $k = [Math]::Floor($Year / 100)\n\n # Shift of metonic cycle, add a day offset every 300 years\n $p = [Math]::Floor((13 + 8 * $k) / 25)\n\n # Correction for non-observed leap days\n $q = [Math]::Floor($k / 4)\n\n # Correction to starting point of calculation each century\n $M = (15 - $p + $k - $q) % 30\n\n # Number of days from March 21st until the full moon\n $d = (19 * $a + $M) % 30\n\n # Returning if user wants value for Servois' table\n if($Servois) {\n return ((21 + $d) % 31).ToString()\n }\n\n # Finding the next Sunday\n # Century-based offset in weekly calculation\n $N = (4 + $k - $q) % 7\n\n # Correction for leap days\n $b = $Year % 4\n $c = $Year % 7\n\n # Days from d to next Sunday\n $e = (2 * $b + 4 * $c + 6 * $d + $N) % 7\n\n # Historical corrections for April 26 and 25\n if(($d -eq 29 -and $e -eq 6) -or ($d -eq 28 -and $e -eq 6 -and $a -gt 10)) {\n $e = -1\n }\n\n # Determination of the correct month for Easter\n if(22 + $d + $e -gt 31) {\n return \"April \" + ($d + $e - 9)\n }\n else {\n return \"March \" + (22 + $d + $e)\n }\n}\n\n\n# Here, we will output the date of the Paschal full moon\n# (using Servois notation), and Easter for 2020-2030\n\nWrite-Host \"The following are the dates of the Paschal full moon (using Servois\",\n \"notation) and the date of Easter for 2020-2030 AD:\"\nWrite-Host \"Year`tServois number`tEaster\"\nforeach($year in 2020..2030) {\n Write-Host \"$year`t$(Calculate-Computus $year -Servois)`t`t$(Calculate-Computus $year)\"\n}\n\n#include \n\nchar *computus(int year, int servois, char *out, size_t out_size) {\n // Year's position on the 19 year metonic cycle\n int a = year % 19;\n\n // Century index\n int k = year / 100;\n\n //Shift of metonic cycle, add a day offset every 300 years\n int p = (13 + 8 * k) / 25;\n\n // Correction for non-observed leap days\n int q = k / 4;\n\n // Correction to starting point of calculation each century\n int M = (15 - p + k - q) % 30;\n\n // Number of days from March 21st until the full moon\n int d = (19 * a + M) % 30;\n\n // Returning if user wants value for Servois' table\n if (servois) {\n snprintf(out, out_size, \"%d\",(21 + d) % 31);\n return out;\n }\n\n // Finding the next Sunday\n // Century-based offset in weekly calculation\n int N = (4 + k - q) % 7;\n\n // Correction for leap days\n int b = year % 4;\n int c = year % 7;\n\n // Days from d to next Sunday\n int e = (2 * b + 4 * c + 6 * d + N) % 7;\n\n // Historical corrections for April 26 and 25\n if ((d == 29 && e == 6) || (d == 28 && e == 6 && a > 10)) {\n e = -1;\n }\n\n if ((22 + d + e) > 31) {\n snprintf(out, out_size, \"April %d\", d + e - 9);\n } else {\n snprintf(out, out_size, \"March %d\", 22 + d + e);\n }\n\n return out;\n}\n\nint main() {\n char tmp1[9], tmp2[9];\n\n printf(\"The following are the dates of the Paschal full moon (using \"\n \"Servois notation) and the date of Easter for 2020-2030 AD:\\n\");\n\n printf(\"Year\\tServois number\\tEaster\\n\");\n\n for (int year = 2020; year \n#include \n#include \n\nstd::string computus(int year, bool servois = false) {\n // Year's position on the 19 year metonic cycle\n int a = year % 19;\n\n // Century index\n int k = year / 100;\n\n // Shift of metonic cycle, add a day offset every 300 years\n int p = (13 + 8 * k) / 25;\n\n // Correction for non-observed leap days\n int q = k / 4;\n\n // Correction to starting point of calculation each century\n int M = (15 - p + k - q) % 30;\n\n // Number of days from March 21st until the full moon\n int d = (19 * a + M) % 30;\n\n // Returning if user wants value for Servois' table\n if (servois) {\n return std::to_string((21 + d) % 31);\n }\n\n // Finding the next Sunday\n // Century-based offset in weekly calculation\n int N = (4 + k - q) % 7;\n\n // Correction for leap days\n int b = year % 4;\n int c = year % 7;\n\n // Days from d to next Sunday\n int e = (2 * b + 4 * c + 6 * d + N) % 7;\n\n // Historical corrections for April 26 and 25\n if ((d == 29 && e == 6) || (d == 28 && e == 6 && a > 10)) {\n e = -1;\n }\n\n // Determination of the correct month for Easter\n return 22 + d + e > 31 ? \"April \" + std::to_string(d + e - 9)\n : \"March \" + std::to_string(22 + d + e);\n}\n\n// Here, we will output the date of the Paschal full moon (using Servois\n// notation), and Easter for 2020-2030\nint main() {\n std::cout \n;;;; Gauss's Easter algorithm implementation\n\n(defun computus (year &optional (servois nil))\n \"Calculates the day of Easter for a given year and optionally its Servois number\"\n (let*\n ((a (mod year 19)) ; year's position on the 19 year metonic cycle\n (k (floor year 100)) ; century index\n (p (floor (+ 13 (* 8 k)) 25)) ; shift of metonic cycle, add a day offset every 300 years\n (q (floor k 4)) ; correction for non-observed leap days\n (m (mod (+ 15 (- p) k (- q)) 30)) ; correction to starting point of calculation each century\n (d (mod (+ (* 19 a) m) 30)) ; number of days from March 21st until the full moon\n (n (mod (+ 4 k (- q)) 7)) ; century-based offset in weekly calculation\n (b (mod year 4)) ; correction for leap days\n (c (mod year 7)) ; also a correction for leap days\n ;; days from d to next Sunday\n (e (mod (+ (* 2 b) (* 4 c) (* 6 d) n) 7)))\n ;; historical corrections for April 26 and 25\n (when (or (and (eql d 29) (eql e 6)) (and (eql d 28) (eql e 6) (> a 10)))\n (setf e -1))\n (values\n ;; determination of the correct month for Easter\n (if (> (+ 22 d e) 31)\n (format nil \"April ~a\" (+ d e -9))\n (format nil \"March ~a\" (+ 22 d e)))\n ;; optionally return a value for the Servois' table\n (if servois (mod (+ 21 d) 31)))))\n\n(format t \"~{~a~%~}\"\n '(\"The following are the dates of the Paschal full moon (using Servois\"\n \"notation) and the date of Easter for 2020-2030 AD:~%\"\n \"Year Servois number Easter\"))\n(loop for year from 2020 to 2030 do\n (multiple-value-bind (easter servois) (computus year t)\n (format t \"~8a~18a~a~%\" year servois easter)))\n\nimport strformat\n\nfunc computus(year: int, servois: bool = false): string =\n let\n # Year's position on the 19 year metonic cycle\n a = year mod 19\n # Century index\n k = year div 100\n # Shift of metonic cycle, add a day offset every 300 years\n p = (13 + 8 * k) div 25\n # Correction for non-observed leap days\n q = k div 4\n # Correction to starting point of calculation each century\n m = (15 - p + k - q) mod 30\n # Number of days from March 21st until the full moon\n d = (19 * a + m) mod 30\n # Returning of user wants value for Servois' table\n if servois:\n return $((21 + d) mod 31)\n let\n # Find the next Sunday\n # Century-based offset in weekly calculation\n n = (4 + k - q) mod 7\n # Correction for leap days\n b = year mod 4\n c = year mod 7\n # Days from d to next Sunday\n temp_e = (2 * b + 4 * c + 6 * d + n) mod 7\n # Historical corrections for April 26 and 25\n e = if (d == 29 and temp_e == 6) or (d == 28 and temp_e == 6 and a > 10):\n -1\n else:\n temp_e\n # Determination of the correct month for Easter\n if (22 + d + e) > 31:\n result = \"April {d + e - 9}\".fmt\n else:\n result = \"March {22 + d + e}\".fmt\n\nwhen isMainModule:\n echo \"The following are the dates of the Paschal full moon (using Servois \"\n echo \"notation) and the date of Easter for 2020-2030 AD:\"\n echo \"Year Servois number Easter\"\n for year in 2020..2030:\n echo \"{year} {computus(year, true):14} {computus(year, false):6}\".fmt\n\nobject GaussEaster {\n def computus(year : Int, servois: Boolean = false): String = {\n\n // Year's position on the 19 year metonic cycle\n val a = year % 19\n\n // Century index\n val k = (year / 100).toInt\n\n // Shift of metonic cycle, add a day offset every 300 years\n val p = ((13 + 8 * k) / 25).toInt\n\n // Correction for non-observed leap days\n val q = (k / 4).toInt\n\n // Correction to starting point of calculation each century\n val M = (15 - p + k - q) % 30\n\n // Number of days from March 21st until the full moon\n val d = (19 * a + M) % 30\n\n // Returning if user wants value for Servois' table\n if (servois) \n return s\"${(21 + d) % 31}\"\n\n // Finding the next Sunday\n // Century-based offset in weekly calculation\n val N = (4 + k - q) % 7\n\n // Correction for leap days\n val b = year % 4\n val c = year % 7\n\n // Days from d to next Sunday\n var e = (2 * b + 4 * c + 6 * d + N) % 7\n\n // Historical corrections for April 26 and 25\n if ((d == 29 && e == 6) || (d == 28 && e == 6 && a > 10)) {\n e = -1\n }\n\n // Determination of the correct month for Easter\n if (22 + d + e > 31) \n s\"April ${d + e - 9}\"\n else \n s\"March ${22 + d + e}\"\n }\n\n def main(args: Array[String]): Unit = {\n println(\"The following are the dates of the Paschal full moon (using \" + \n \"Servois notation) and the date of Easter for 2020-2030 AD:\\n\" +\n \"Year\\tServois number\\tEaster\\n\")\n\n for( year \nString computus(int year, {bool servois = false}) {\n // Year's position in metonic cycle\n final a = year % 19;\n\n // Century index\n final k = (year / 100).floor();\n\n // Shift of metonic cycle, add a day offset every 300 years\n final p = ((13 + 8 * k) / 25).floor();\n\n // Correction for non-observed leap days\n final q = (k / 4).floor();\n\n // Correction to starting point of calculation each century\n final M = (15 - p + k - q) % 30;\n\n // Number of days from March 21st until the full moon\n final d = (19 * a + M) % 30;\n\n // Returning if user wants value for Servois' table\n if (servois) {\n return ((21 + d) % 31).toString();\n }\n\n // Finding the next Sunday\n // Century-based offset in weekly calculation\n final N = (4 + k - q) % 7;\n\n // Correction for leap days\n final b = year % 4;\n final c = year % 7;\n\n // Days from d to next Sunday\n var e = (2 * b + 4 * c + 6 * d + N) % 7;\n\n // Historical corrections for April 26 and 25\n if (e == 6) {\n if (d == 29 || (d == 28 && a > 10)) {\n e = -1;\n }\n }\n\n // Determination of the correct month for Easter\n if (22 + d + e > 31) {\n return 'April ${d + e - 9}';\n } else {\n return 'March ${22 + d + e}';\n }\n}\n\nvoid main() {\n print(\"The following are the dates of the Paschal full moon (using Servois \" +\n \"notation) and the date of Easter for 2020-2030 AD:\");\n\n print(\"Year\\tServois number\\tEaster\");\n\n for (var year = 2020; year \n/**\n * In this code, the modulus operator is used.\n * However, this operator in javascript/typescript doesn't support negative numbers.\n * So, where there may be negative numbers, the function mod is used.\n * This function gives the modulo of any relative number a\n */\n\n/**\n * @param {number} a\n * @param {number} b\n * @returns {number}\n */\nfunction mod(a, b) {\n if (a 10)) {\n e = -1;\n }\n }\n\n // Determination of the correct month for Easter\n if (22 + d + e > 31) {\n return `April ${d + e - 9}`;\n } else {\n return `March ${22 + d + e}`;\n }\n}\n\nconsole.log(\n \"The following are the dates of the Paschal full moon (using Servois \" +\n \"notation) and the date of Easter for 2020-2030 AD:\"\n);\n\nconst values = [];\n\nfor (let year = 2020; year \n/**\n * In this code, the modulus operator is used.\n * However, this operator in javascript/typescript doesn't support negative numbers.\n * So, where there may be negative numbers, the function mod is used.\n * This function gives the modulo of any relative number a\n */\n\nfunction mod(a: number, b: number): number {\n if (a 10)) {\n e = -1;\n }\n }\n\n // Determination of the correct month for Easter\n if (22 + d + e > 31) {\n return `April ${d + e - 9}`;\n } else {\n return `March ${22 + d + e}`;\n }\n}\n\nconsole.log(\n \"The following are the dates of the Paschal full moon (using Servois \" +\n \"notation) and the date of Easter for 2020-2030 AD:\"\n);\n\n// Type of a line in the output table\ninterface IOutputLine {\n \"servois number\": number;\n easter: string;\n}\n\nconst values: IOutputLine[] = [];\n\nfor (let year = 2020; year \n\n\n\nBibliography\n1.Venerabilis, Beda and others, Bede, the Reckoning of Time, Liverpool University Press, 1999.2.Dictionary.com definition of computus, 2020.3.Bien, Reinhold, Gauss and beyond: The making of Easter algorithms, Springer, 2004.4.unknown, To find Easter: a new York correspondent sends us the following, 1876.5.Servois, M, 84 Calendrier, Annales de Mathématiques pures et appliquées.6.Standish, EM, The astronomical unit now, Cambridge University Press, 2004.7.Wikipedia: Lunar Month, 2020.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"Servois 1800 Colored Table\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Relative Orbits\" was created by Xadisten and was provided during a discussion on Twitch. It is licensed under the Creative Commons Attribution 4.0 International License.\nThe image \"Synodic Half Year\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Metonic shadows\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Full Year Orbit\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Servois 2000 Colored Table\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n"},"contents/gaussian_elimination/gaussian_elimination.html":{"url":"contents/gaussian_elimination/gaussian_elimination.html","title":"Gaussian Elimination","keywords":"","body":"Gaussian Elimination\nLet's say we have a system of equations,\n\n\\begin{align}\n2x + 3y + 4z &= 6 \\\\\nx + 2y + 3z &= 4 \\\\\n3x - 4y &= 10\n\\end{align}\n\nand we want to solve for x, y, and z.\nWell, one way to do this is with Gaussian Elimination, which you may have encountered before in a math class or two.\nThe first step is to transform the system of equations into a matrix by using the coefficients in front of each variable, where each row corresponds to another equation and each column corresponds to an independent variable like x, y, or z.\nFor the previous system of equations, this might look like this:\n\n\\left[\n\\begin{array}{ccc}\n2 & 3 & 4\\\\\n1 & 2 & 3\\\\\n3 & -4 & 0\n\\end{array}\n\\right]\n\\left[\n\\begin{array}{c}\nx \\\\\ny \\\\\nz\n\\end{array}\n\\right]\n=\n\\left[\n\\begin{array}{c}\n6 \\\\\n4 \\\\\n10\n\\end{array}\n\\right]\n\nOr more simply:\n\n\\left[\n\\begin{array}{ccc|c}\n2 & 3 & 4 & 6 \\\\\n1 & 2 & 3 & 4 \\\\\n3 & -4 & 0 & 10\n\\end{array}\n\\right]\n\nAt first, translating the set of equations into a matrix like this doesn't seem to help with anything, so let's think of this in another way.\nRow Echelon Form\nInstead of the complicated mess of equations shown above, imagine if the system looked like this:\n\n\\begin{align}\n2x + 3y + 4z &= 6 \\\\\ny + 2z &= 2 \\\\\n11z &= 18\n\\end{align}\n\nThen we could just solve for z and plug that value in to the top two equations to solve for x and y through a process known as back-substitution.\nIn matrix form, this set of equations would look like this:\n\n\\left[\n\\begin{array}{ccc|c}\n2 & 3 & 4 & 6 \\\\\n0 & 1 & 2 & 2 \\\\\n0 & 0 & 11 & 18\n\\end{array}\n\\right]\n\nThis matrix form has a particular name: Row Echelon Form.\nBasically, any matrix can be considered in row echelon form if the leading coefficient or pivot (the first non-zero element in every row when reading from left to right) is right of the pivot of the row above it.\nThis creates a matrix that sometimes resembles an upper-triangular matrix; however, that doesn't mean that all row-echelon matrices are upper-triangular.\nFor example, all of the following matrices are in row echelon form:\n\n\\left[\n\\begin{array}{ccc|c}\n2 & 3 & 4 & 6 \\\\\n0 & 1 & 2 & 2 \\\\\n0 & 0 & 11 & 18\n\\end{array}\n\\right]\n\\;,\\;\n\\left[\n\\begin{array}{ccc|c}\n5 & 4 & 0 & 10 \\\\\n0 & 0 & 5 & 7 \\\\\n0 & 0 & 0 & 1\n\\end{array}\n\\right]\n\\;,\\;\n\\left[\n\\begin{array}{ccccc}\n1 & -3 & 4 & 1 & 6 \\\\\n0 & 3 & 3 & 5 & 0 \\\\\n0 & 0 & 0 & 2 & 0\n\\end{array}\n\\right]\n\\;,\\;\n\\left[\n\\begin{array}{cc}\n1 & 2 \\\\\n2 & 0 \\\\\n0 & 0\n\\end{array}\n\\right]\n\nThe first two of these have the right dimensions to find a solution to a system of equations; however, the last two matrices are respectively under- and over-constrained, meaning they do not provide an appropriate solution to a system of equations.\nThat said, this doesn't mean that every matrix in the correct form can be solved either.\nFor example, if you translate the second matrix into a system of equations again, the last row translates into 0x+0y+0z=1, which is a contradiction.\nThis is due to the fact that the matrix is singular, and there are no solutions to this particular system.\nNevertheless, all of these matrices are in row echelon form.\nReduced Row Echelon Form\nRow echelon form is nice, but wouldn't it be even better if our system of equations looked simply like this:\n\n\\begin{align}\nx &= \\frac{18}{11} \\\\\ny &= \\frac{-14}{11} \\\\\nz &= \\frac{18}{11}\n\\end{align}\n\nThen we would know exactly what x, y, and z are without any fuss! In matrix form, it looks like this:\n\n\\left[\n\\begin{array}{ccc|c}\n1 & 0 & 0 & \\frac{18}{11} \\\\\n0 & 1 & 0 & \\frac{-14}{11} \\\\\n0 & 0 & 1 & \\frac{18}{11}\n\\end{array}\n\\right]\n\nThis introduces yet another matrix configuration: Reduced Row Echelon Form.\nA matrix is in reduced row echelon form if it satisfies the following conditions:\n\nIt is in row echelon form.\nEvery pivot is 1 and is the only nonzero entry in its column.\n\nAll the following examples are in the reduced row echelon form:\n\n\\left[\n\\begin{array}{ccc|c}\n1 & 0 & 0 & 8 \\\\\n0 & 1 & 0 & -3 \\\\\n0 & 0 & 1 & 9\n\\end{array}\n\\right]\n\\;,\\;\n\\left[\n\\begin{array}{ccc|c}\n1 & 4 & 0 & 9 \\\\\n0 & 0 & 1 & 7 \\\\\n0 & 0 & 0 & 1\n\\end{array}\n\\right]\n\\;,\\;\n\\left[\n\\begin{array}{cc}\n0 & 0 \\\\\n0 & 0 \\\\\n0 & 0\n\\end{array}\n\\right]\n\nAgain, only the first of these (the one that looks like an identity matrix) is desirable in the context of solving a system of equations, but transforming any matrix in this form gives us an immediate and definitive answer at the question: can I solve my system of equations?\nBeyond solving a system of equations, reshaping a matrix in this form makes it very easy to deduce other properties of the matrix, such as its rank — the maximum number of linearly independent columns.\nIn reduced row echelon form, the rank is simply the number of pivots.\nFor now, I hope the motivation is clear: we want to convert a matrix into row echelon and then reduced row echelon form to make large systems of equations trivial to solve, so we need some method to do that.\nIn general, the term Gaussian Elimination refers to the process of transforming a matrix into row echelon form, and the process of transforming a row echelon matrix into reduced row echelon form is called Gauss-Jordan Elimination.\nThat said, the notation here is sometimes inconsistent.\nSeveral authors use the term Gaussian Elimination to include Gauss-Jordan elimination as well.\nIn addition, the process of Gauss-Jordan elimination is sometimes called Back-substitution, which is also confusing because the term can also be used to mean solving a system of equations from row echelon form, without simplifying to reduced row echelon form.\nFor this reason, we will be using the following definitions in this chapter:\n\nGaussian Elimination: The process of transforming a matrix into row echelon form\nGauss-Jordan Elimination: The process of transforming a row echelon matrix into reduced row echelon form\nBack-substitution: The process of directly solving a row echelon matrix, without transforming into reduced row echelon form\n\nThe Analytical Method\nGaussian elimination is inherently analytical and can be done by hand for small systems of equations; however, for large systems, this (of course) become tedious and we will need to find an appropriate numerical solution.\nFor this reason, I have split this section into two parts. One will cover the analytical framework, and the other will cover an algorithm you can write in your favorite programming language.\nIn the end, reducing large systems of equations boils down to a game you play on a seemingly random matrix with 3 possible moves. You can:\n\nSwap any two rows.\nMultiply any row by a non-zero scale value.\nAdd any row to a multiple of any other row.\n\nThat's it.\nBefore continuing, I suggest you try to recreate the row echelon matrix we made above.\nThat is, do the following:\n\n\\left[\n\\begin{array}{ccc|c}\n2 & 3 & 4 & 6 \\\\\n1 & 2 & 3 & 4 \\\\\n3 & -4 & 0 & 10\n\\end{array}\n\\right]\n\\quad \\rightarrow \\quad\n\\left[\n\\begin{array}{ccc|c}\n2 & 3 & 4 & 6 \\\\\n0 & 1 & 2 & 2 \\\\\n0 & 0 & 11 & 18\n\\end{array}\n\\right]\n\nThere are plenty of different strategies you could use to do this, and no one strategy is better than the rest.\nOne method is to subtract a multiple of the top row from subsequent rows below it such that all values beneath the pivot value are zero.\nThis process might be easier if you swap some rows around first and can be performed for each pivot.\nAfter you get a row echelon matrix, the next step is to find the reduced row echelon form. In other words, we do the following:\n\n\\left[\n\\begin{array}{ccc|c}\n2 & 3 & 4 & 6 \\\\\n0 & 1 & 2 & 2 \\\\\n0 & 0 & 11 & 18\n\\end{array}\n\\right]\n\\quad \\rightarrow \\quad\n\\left[\n\\begin{array}{ccc|c}\n1 & 0 & 0 & \\frac{18}{11} \\\\\n0 & 1 & 0 & \\frac{-14}{11} \\\\\n0 & 0 & 1 & \\frac{18}{11}\n\\end{array}\n\\right]\n\nHere, the idea is similar to above and the same rules apply.\nIn this case, we might start from the right-most column and subtracts upwards instead of downwards.\nThe Computational Method\nThe analytical method for Gaussian Elimination may seem straightforward, but the computational method does not obviously follow from the \"game\" we were playing before.\nUltimately, the computational method boils down to two separate steps and has a complexity of \\mathcal{O}(n^3).\nAs a note, this process iterates through all the rows in the provided matrix.\nWhen we say \"current row\" (curr_row), we mean the specific row iteration number we are on at that time, and as before, the \"pivot\" corresponds to the first non-zero element in that row.\nStep 1\nFor each element in the pivot column under the current row, find the highest value and switch the row with the highest value with the current row.\nThe pivot is then considered to be the first element in the highest swapped row.\nFor example, in this case the highest value is 3:\n\n\\left[\n\\begin{array}{ccc|c}\n2 & 3 & 4 & 6 \\\\\n1 & 2 & 3 & 4 \\\\\n\\mathbf{3} & -4 & 0 & 10\n\\end{array}\n\\right]\n\nAfter finding this value, we simply switch the row with the 3 to the current row:\n\n\\left[\n\\begin{array}{ccc|c}\n\\mathbf{2} & \\mathbf{3} & \\mathbf{4} & \\mathbf{6} \\\\\n1 & 2 & 3 & 4 \\\\\n\\mathbf{3} & \\mathbf{-4} & \\mathbf{0} & \\mathbf{10}\n\\end{array}\n\\right]\n\\rightarrow\n\\left[\n\\begin{array}{ccc|c}\n\\mathbf{3} & \\mathbf{-4} & \\mathbf{0} & \\mathbf{10} \\\\\n1 & 2 & 3 & 4 \\\\\n\\mathbf{2} & \\mathbf{3} & \\mathbf{4} & \\mathbf{6}\n\\end{array}\n\\right]\n\nIn this case, the new pivot is 3.\nIn code, this process might look like this:\n# finding the maximum element for each column\nmax_index = argmax(abs.(A[row:end,col])) + row-1\n\n# Check to make sure matrix is good!\nif (A[max_index, col] == 0)\n println(\"matrix is singular!\")\n continue\nend\n\n# swap row with highest value for that column to the top\ntemp_vector = A[max_index, :]\nA[max_index, :] = A[row, :]\nA[row, :] = temp_vector\n\n// finding the maximum element\nfor (int i = row + 1; i Math.abs(a[pivot][col])) {\n pivot = i;\n }\n}\n\nif (a[pivot][col] == 0) {\n System.err.println(\"The matrix is singular\");\n continue;\n}\n\nif (row != pivot) {\n // Swap the row with the highest valued element\n // with the current row\n swapRow(a, col, pivot);\n}\n\nvoid swap_rows(double *a, const size_t i, const size_t pivot,\n const size_t cols) {\n\n for (size_t j = 0; j \nsize_t pivot = row;\n\nfor (size_t i = row + 1; i fabs(a[pivot * cols + col])) {\n pivot = i;\n }\n}\n\nif (a[pivot * cols + col] == 0) {\n printf(\"The matrix is singular.\\n\");\n continue;\n}\n\nif (col != pivot) {\n swap_rows(a, col, pivot, cols);\n}\n\n std::size_t pivot = i;\n\nfor (std::size_t j = i + 1; j fabs(eqns[pivot][i])) pivot = j;\n}\n\nif (eqns[pivot][i] == 0.0)\n continue; // But continuing to simplify the matrix as much as possible\n\nif (i != pivot) // Swapping the rows if new row with higher maxVals is found\n std::swap(eqns[pivot], eqns[i]); // C++ swap function\n\nswapRows :: Int -> Int -> Matrix a -> Matrix a\nswapRows r1 r2 m\n | r1 == r2 = m\n | otherwise =\n m //\n concat [[((r2, c), m ! (r1, c)), ((r1, c), m ! (r2, c))] | c \n(target, pivot) =\n maximumBy (compare `on` abs . snd) [(k, m ! (k, c)) | k \nlet pivot = row;\nfor (let i = row + 1; i Math.abs(a[pivot][col])) {\n pivot = i;\n }\n}\n\nif (a[pivot][col] === 0) {\n console.log(\"The matrix is singular.\");\n continue;\n}\n\nif (col !== pivot) {\n const t = a[col];\n a[col] = a[pivot];\n a[pivot] = t;\n}\n\n// 1. find highest value in column below row to be pivot\np, highest := r, 0.\nfor i, row := range a[r:] {\n if abs := math.Abs(row[c]); abs > highest {\n p = r + i\n highest = abs\n }\n}\nhighest = a[p][c] // correct sign\n\nif highest == 0. {\n if !singular {\n singular = true\n fmt.Println(\"This matrix is singular.\")\n }\n continue\n}\n\ntemp = A[pivot_row, :].copy()\nA[pivot_row, :] = A[max_i, :]\nA[max_i, :] = temp\n\n# Skip on singular matrix, not actually a pivot\nif A[pivot_row, pivot_col] == 0:\n continue\n\n // find the maximum element for this column\n let mut max_row = k;\n let mut max_value = a[(k, k)].abs();\n for row in (k + 1)..a.rows {\n if max_value \n\n\nAs a note, if the highest value is 0, the matrix is singular and the system has no single solution.\nThis makes sense because if the highest value in a column is 0, the entire column must be 0, thus there can be no unique solution when we read the matrix as a set of equations.\nThat said, Gaussian elimination is more general and allows us to continue, even if the matrix is not necessarily solvable as a set of equations.\nFeel free to exit after finding a 0 if your end-goal is to solve a system of equations.\nStep 2\nFor the row beneath the current pivot row and within the pivot column, find a fraction that corresponds to the ratio of the value in that column to the pivot, itself.\nAfter this, subtract the current pivot row multiplied by the fraction from each corresponding row element.\nThis process essentially subtracts an optimal multiple of the current row from each row underneath (similar to Step 3 from the above game).\nIdeally, this should always create a 0 under the current row's pivot value.\nFor example, in this matrix, the next row is 1 and the pivot value is 3, so the fraction is \\frac{1}{3}.\n\n\\rightarrow\n\\left[\n\\begin{array}{ccc|c}\n3 & -4 & 0 & 10 \\\\\n\\mathbf{1} & 2 & 3 & 4 \\\\\n2 & 3 & 4 & 6\n\\end{array}\n\\right] \\\\\n\\begin{align}\n f &= A(\\text{curr_row}, \\text{pivot}_{\\text{col}}) / A(\\text{pivot}_{\\text{row}}, \\text{pivot}_{\\text{col}}) \\\\\n &= \\frac{1}{3}\n\\end{align}\n\nAfter finding the fraction, we simply subtract \\text{current_row} - \\frac{1}{3}\\times \\text{pivot_row}, like so:\n\n\\left[\n\\begin{array}{ccc|c}\n3 & -4 & 0 & 10 \\\\\n\\mathbf{1} & \\mathbf{2} & \\mathbf{3} & \\mathbf{4} \\\\\n2 & 3 & 4 & 6\n\\end{array}\n\\right]\n\\rightarrow\n\\left[\n\\begin{array}{ccc|c}\n3 & -4 & 0 & 10 \\\\\n0 & \\mathbf{\\frac{10}{3}} & \\mathbf{3} & \\mathbf{\\frac{2}{3}}\n\\\\\n2 & 3 & 4 & 6\n\\end{array}\n\\right]\n\nAfter this, repeat the process for all other rows.\nHere is what it might look like in code:\n# Loop for all remaining rows\nfor i = (row+1):rows\n\n # finding fraction\n fraction = A[i,col]/A[row,col]\n\n # loop through all columns for that row\n for j = (col+1):cols\n\n # re-evaluate each element\n A[i,j] -= A[row,j]*fraction\n\n end\n\nfor (int i = row + 1; i \nfor (size_t i = row + 1; i \nfor (std::size_t j = i + 1; j \nsubRows ::\n Fractional a\n => (Int, Int) -- pivot location\n -> (Int, Int) -- rows to cover\n -> (Int, Int) -- columns to cover\n -> Matrix a\n -> Matrix a\nsubRows (r, c) (r1, rn) (c1, cn) m =\n accum\n (-)\n m\n [ ((i, j), m ! (i, c) * m ! (r, j) / m ! (r, c))\n | i \n| otherwise = go (r + 1, c + 1) $ subRows (r, c) (r + 1, rn) (c, cn) m'\n\nfor (let i = row + 1; i \nfor _, row := range a[r+1:] {\n // 3. find fraction from pivot value\n frac := row[c] / highest\n\n // 4. subtract row to set rest of column to zero\n for j := range row {\n row[j] -= frac * a[r][j]\n }\n\n // 5. ensure col goes to zero (no float rounding)\n row[c] = 0.\n}\n\n# Zero out elements below pivot\nfor r in range(pivot_row + 1, A.shape[0]):\n # Get fraction\n frac = -A[r, pivot_col] / A[pivot_row, pivot_col]\n # Add rows\n A[r, :] += frac * A[pivot_row, :]\n\n// Loop over all remaining rows\nfor i in k + 1..a.rows {\n // find the fraction\n let fraction = a[(i, k)] / a[(k, k)];\n\n // Loop through all columns for that row\n for j in (k + 1)..a.cols {\n // re-evaluate each element\n a[(i, j)] -= a[(k, j)] * fraction;\n }\n\n // set lower elements to 0\n a[(i, k)] = 0.0;\n}\n\n\n\nAll together\nWhen we put everything together, it looks like this:\nfunction gaussian_elimination!(A::Array{Float64,2})\n\n rows = size(A,1)\n cols = size(A,2)\n\n # Row index\n row = 1\n\n # Main loop going through all columns\n for col = 1:(cols-1)\n\n # finding the maximum element for each column\n max_index = argmax(abs.(A[row:end,col])) + row-1\n\n # Check to make sure matrix is good!\n if (A[max_index, col] == 0)\n println(\"matrix is singular!\")\n continue\n end\n\n # swap row with highest value for that column to the top\n temp_vector = A[max_index, :]\n A[max_index, :] = A[row, :]\n A[row, :] = temp_vector\n\n # Loop for all remaining rows\n for i = (row+1):rows\n\n # finding fraction\n fraction = A[i,col]/A[row,col]\n\n # loop through all columns for that row\n for j = (col+1):cols\n\n # re-evaluate each element\n A[i,j] -= A[row,j]*fraction\n\n end\n\n # Set lower elements to 0\n A[i,col] = 0\n end\n row += 1\n end\nend\n\nvoid gaussian_elimination(double *a, const size_t rows, const size_t cols) {\n size_t row = 0;\n\n for (size_t col = 0; col fabs(a[pivot * cols + col])) {\n pivot = i;\n }\n }\n\n if (a[pivot * cols + col] == 0) {\n printf(\"The matrix is singular.\\n\");\n continue;\n }\n\n if (col != pivot) {\n swap_rows(a, col, pivot, cols);\n }\n\n for (size_t i = row + 1; i \nvoid gaussianElimination(std::vector > &eqns) {\n // 'eqns' is the matrix, 'rows' is no. of vars\n std::size_t rows = eqns.size(), cols = eqns[0].size();\n\n for (std::size_t i = 0; i fabs(eqns[pivot][i])) pivot = j;\n }\n\n if (eqns[pivot][i] == 0.0)\n continue; // But continuing to simplify the matrix as much as possible\n\n if (i != pivot) // Swapping the rows if new row with higher maxVals is found\n std::swap(eqns[pivot], eqns[i]); // C++ swap function\n\n for (std::size_t j = i + 1; j \nswapRows :: Int -> Int -> Matrix a -> Matrix a\nswapRows r1 r2 m\n | r1 == r2 = m\n | otherwise =\n m //\n concat [[((r2, c), m ! (r1, c)), ((r1, c), m ! (r2, c))] | c (Int, Int) -- pivot location\n -> (Int, Int) -- rows to cover\n -> (Int, Int) -- columns to cover\n -> Matrix a\n -> Matrix a\nsubRows (r, c) (r1, rn) (c1, cn) m =\n accum\n (-)\n m\n [ ((i, j), m ! (i, c) * m ! (r, j) / m ! (r, c))\n | i Matrix a -> Matrix a\ngaussianElimination mat = go (r1, c1) mat\n\ndef gaussian_elimination(A):\n\n pivot_row = 0\n\n # Go by column\n for pivot_col in range(min(A.shape[0], A.shape[1])):\n\n # Swap row with highest element in col\n max_i = np.argmax(abs(A[pivot_row:, pivot_col])) + pivot_row\n\n temp = A[pivot_row, :].copy()\n A[pivot_row, :] = A[max_i, :]\n A[max_i, :] = temp\n\n # Skip on singular matrix, not actually a pivot\n if A[pivot_row, pivot_col] == 0:\n continue\n\n # Zero out elements below pivot\n for r in range(pivot_row + 1, A.shape[0]):\n # Get fraction\n frac = -A[r, pivot_col] / A[pivot_row, pivot_col]\n # Add rows\n A[r, :] += frac * A[pivot_row, :]\n\n pivot_row += 1\n\nstatic void gaussianElimination(double[][] a) {\n int row = 0;\n\n int rows = a.length;\n int cols = a[0].length;\n\n for (int col = 0; col Math.abs(a[pivot][col])) {\n pivot = i;\n }\n }\n\n if (a[pivot][col] == 0) {\n System.err.println(\"The matrix is singular\");\n continue;\n }\n\n if (row != pivot) {\n // Swap the row with the highest valued element\n // with the current row\n swapRow(a, col, pivot);\n }\n\n for (int i = row + 1; i \nfunction gaussianElimination(a) {\n const rows = a.length\n const cols = a[0].length\n let row = 0;\n for (let col = 0; col Math.abs(a[pivot][col])) {\n pivot = i;\n }\n }\n\n if (a[pivot][col] === 0) {\n console.log(\"The matrix is singular.\");\n continue;\n }\n\n if (col !== pivot) {\n const t = a[col];\n a[col] = a[pivot];\n a[pivot] = t;\n }\n\n for (let i = row + 1; i \nfunc gaussianElimination(a [][]float64) {\n singular := false\n rows := len(a)\n cols := len(a[0])\n\n for c, r := 0, 0; c highest {\n p = r + i\n highest = abs\n }\n }\n highest = a[p][c] // correct sign\n\n if highest == 0. {\n if !singular {\n singular = true\n fmt.Println(\"This matrix is singular.\")\n }\n continue\n }\n\n // 2. swap pivot with current row\n if p != r {\n a[r], a[p] = a[p], a[r]\n }\n\n for _, row := range a[r+1:] {\n // 3. find fraction from pivot value\n frac := row[c] / highest\n\n // 4. subtract row to set rest of column to zero\n for j := range row {\n row[j] -= frac * a[r][j]\n }\n\n // 5. ensure col goes to zero (no float rounding)\n row[c] = 0.\n }\n\n r++\n }\n}\n\nfn gaussian_elimination(a: &mut Matrix) {\n for k in 0..min(a.cols, a.rows) {\n // find the maximum element for this column\n let mut max_row = k;\n let mut max_value = a[(k, k)].abs();\n for row in (k + 1)..a.rows {\n if max_value \n\n\nTo be clear: if the matrix is found to be singular during this process, the system of equations is either over- or under-determined and no general solution exists.\nFor this reason, many implementations of this method will stop the moment the matrix is found to have no unique solutions.\nIn this implementation, we allowed for the more general case and opted to simply output when the matrix is singular instead.\nIf you intend to solve a system of equations, then it makes sense to stop the method the moment you know there is no unique solution, so some small modification of this code might be necessary!\nSo what do we do from here?\nWell, we continue reducing the matrix; however, there are two ways to do this:\n\nReduce the matrix further into reduced row echelon form with Gauss-Jordan elimination\nSolve the system directly with back-substitution if the matrix allows for such solutions\n\nLet's start with Gauss-Jordan Elimination and then back-substitution\nGauss-Jordan Elimination\nGauss-Jordan Elimination is precisely what we said above; however, in this case, we often work from the bottom-up instead of the top-down.\nWe basically need to find the pivot of every row and set that value to 1 by dividing the entire row by the pivot value.\nAfterwards, we subtract upwards until all values above the pivot are 0 before moving on to the next column from right to left (instead of left to right, like before).\nHere it is in code:\nfunction gauss_jordan_elimination!(A::Array{Float64,2})\n\n rows = size(A,1)\n cols = size(A,2)\n\n\n # After this, we know what row to start on (r-1)\n # to go back through the matrix\n row = 1\n for col = 1:cols-1\n if (A[row, col] != 0)\n\n # divide row by pivot and leaving pivot as 1\n for i = cols:-1:col\n A[row,i] /= A[row,col]\n end\n\n # subtract value from above row and set values above pivot to 0\n for i = 1:row-1\n for j = cols:-1:col\n A[i,j] -= A[i,col]*A[row,j]\n end\n end\n row += 1\n end\n end\nend\n\nvoid gauss_jordan(double *a, const size_t cols) {\n size_t row = 0;\n\n for (size_t col = 0; col col - 1; --i) {\n a[row * cols + i] /= a[row * cols + col];\n }\n\n for (size_t i = 0; i col - 1; --j) {\n a[i * cols + j] -= a[i * cols + col] * a[row * cols + j];\n }\n }\n\n row++;\n }\n }\n}\n\nvoid gaussJordan(std::vector > &eqns) {\n // 'eqns' is the (Row-echelon) matrix, 'rows' is no. of vars\n std::size_t rows = eqns.size();\n\n for (std::size_t i = rows - 1; i \n((r1, c1), (rn, cn)) = bounds mat\ngo (r, c) m\n | c == cn = m\n | pivot == 0 = go (r, c + 1) m\n | otherwise = go (r + 1, c + 1) $ subRows (r, c) (r + 1, rn) (c, cn) m'\n where\n (target, pivot) =\n maximumBy (compare `on` abs . snd) [(k, m ! (k, c)) | k \n# Assumes A is already row echelon form\ndef gauss_jordan_elimination(A):\n\n col = 0\n\n # Scan for pivots\n for row in range(A.shape[0]):\n while col = A.shape[1]:\n continue\n\n # Set each pivot to one via row scaling\n A[row, :] /= A[row, col]\n\n # Zero out elements above pivot\n for r in range(row):\n A[r, :] -= A[r, col] * A[row, :]\n\nstatic void gaussJordan(double[][] a) {\n int row = 0;\n\n int cols = a[0].length;\n\n for (int col = 0; col col - 1; i--) {\n // divide row by pivot so the pivot is set to 1\n a[row][i] /= a[row][col];\n }\n\n // subtract the value form above row and set values above pivot to 0\n for (int i = 0; i col - 1; j--) {\n a[i][j] -= a[i][col] * a[row][j];\n }\n }\n row++;\n }\n }\n}\n\nfunction gaussJordan(a) {\n const cols = a[0].length;\n let row = 0;\n\n for (let col = 0; col col - 1; --i) {\n a[row][i] /= a[row][col];\n }\n\n for (let i = 0; i col - 1; --j) {\n a[i][j] -= a[i][col] * a[row][j];\n }\n }\n\n ++row;\n }\n }\n}\n\nfunc gaussJordan(a [][]float64) {\n for r := len(a) - 1; r >= 0; r-- {\n // Find pivot col\n p := -1\n for c, cell := range a[r] {\n if cell != 0. {\n p = c\n break\n }\n }\n if p \nfn gauss_jordan(a: &mut Matrix) {\n let mut row = 0;\n for k in 0..(a.cols - 1) {\n if a[(row, k)] != 0.0 {\n for i in (k..a.cols).rev() {\n a[(row, i)] /= a[(row, k)];\n }\n\n for i in 0..row {\n for j in (k..a.cols).rev() {\n a[(i, j)] -= a[(i, k)] * a[(row, j)];\n }\n }\n\n row += 1;\n }\n }\n}\n\n\n\nAs a note: Gauss-Jordan elimination can also be used to find the inverse of a matrix by following the same procedure to generate a reduced row echelon matrix, but with an identity matrix on the other side instead of the right-hand side of each equation.\nThis process is straightforward but will not be covered here, simply because there are much faster numerical methods to find an inverse matrix; however, if you would like to see this, let me know and I can add it in for completeness.\nBack-substitution\nThe idea of back-substitution is straightforward: we create a matrix of solutions and iteratively solve for each variable by plugging in all variables before it.\nFor example, if our matrix looks like this:\n\n\\left[\n\\begin{array}{ccc|c}\n2 & 3 & 4 & 6 \\\\\n0 & 1 & 2 & 2 \\\\\n0 & 0 & 11 & 18\n\\end{array}\n\\right]\n\nWe can quickly solve 11z = 18 for z, and then use that to solve y + 2z = 2 for y by plugging in for z.\nAfter that, we simply need to solve 2x + 3y + 4z = 6 for x in a similar fashion.\nIn code, this involves keeping a rolling sum of all the values we substitute, subtracting that sum from the solution column and then dividing by the coefficient variable.\nIn code, it looks like this:\nfunction back_substitution(A::Array{Float64,2})\n\n rows = size(A,1)\n cols = size(A,2)\n\n # Creating the solution Vector\n soln = zeros(rows)\n\n for i = rows:-1:1\n sum = 0.0\n for j = rows:-1:i\n sum += soln[j]*A[i,j]\n end\n soln[i] = (A[i, cols] - sum) / A[i, i]\n end\n\n return soln\nend\n\nvoid back_substitution(const double *a, double *x, const int rows,\n const int cols) {\n\n for (int i = rows - 1; i >= 0; --i) {\n double sum = 0.0;\n\n for (int j = cols - 2; j > i; --j) {\n sum += x[j] * a[i * cols + j];\n }\n\n x[i] = (a[i * cols + cols - 1] - sum) / a[i * cols + i];\n }\n}\n\nstd::vector backSubs(const std::vector > &eqns) {\n // 'eqns' is matrix, 'rows' is no. of variables\n std::size_t rows = eqns.size();\n\n std::vector ans(rows);\n for (std::size_t i = rows - 1; i (0);\n }\n return ans;\n}\n\nfn back_substitution(a: &Matrix) -> Vec {\n let mut soln = vec![0.0; a.rows];\n\n soln[a.rows - 1] = a[(a.rows - 1, a.cols - 1)] / a[(a.rows - 1, a.cols - 2)];\n\n for i in (0..a.rows - 1).rev() {\n let mut sum = 0.0;\n for j in (i..a.rows).rev() {\n sum += soln[j] * a[(i, j)];\n }\n soln[i] = (a[(i, a.cols - 1)] - sum) / a[(i, i)];\n }\n\n soln\n}\n\ngaussJordan :: (Fractional a, Eq a) => Matrix a -> Matrix a\ngaussJordan mat = go (r1, c1) mat\n where\n ((r1, c1), (rn, cn)) = bounds mat\n go (r, c) m\n | c == cn = m\n\n# Assumes A has a unique solution and A in row echelon form\ndef back_substitution(A):\n\n sol = np.zeros(A.shape[0]).T\n\n # Go by pivots along diagonal\n for pivot_i in range(A.shape[0] - 1, -1, -1):\n s = 0\n for col in range(pivot_i + 1, A.shape[1] - 1):\n s += A[pivot_i, col] * sol[col]\n sol[pivot_i] = (A[pivot_i, A.shape[1] - 1] - s) / A[pivot_i, pivot_i]\n\n return sol\n\nstatic double[] backSubstitution(double[][] a) {\n int rows = a.length;\n int cols = a[0].length;\n\n double[] solution = new double[rows];\n\n for (int i = rows - 1; i >= 0; i--) {\n double sum = 0;\n\n for (int j = cols - 2; j > i; j--) {\n sum += solution[j] * a[i][j];\n }\n solution[i] = (a[i][cols - 1] - sum) / a[i][i];\n }\n return solution;\n}\n\nfunction backSubstitution(a) {\n const rows = a.length;\n const cols = a[0].length;\n const sol = [];\n\n for (let i = rows - 1; i >= 0; --i) {\n\n let sum = 0;\n for (let j = cols - 2; j > i; --j) {\n sum += sol[j] * a[i][j];\n }\n\n sol[i] = (a[i][cols - 1] - sum) / a[i][i];\n }\n return sol;\n}\n\nfunc backSubstitution(a [][]float64) []float64 {\n rows := len(a)\n cols := len(a[0])\n x := make([]float64, rows)\n for r := rows - 1; r >= 0; r-- {\n sum := 0.\n\n for c := cols - 2; c > r; c-- {\n sum += x[c] * a[r][c]\n }\n\n x[r] = (a[r][cols-1] - sum) / a[r][r]\n }\n return x\n}\n\n\n\nVisual Representation\nWe have thus far used Gaussian elimination as a method to solve a system of equations; however, there is often a much easier way to find a similar solution simply by plotting each row in our matrix.\nFor the case of 2 equations and 2 unknowns, we would plot the two lines corresponding to each equation and the (x, y) location of their point of intersection would be the solution for x and y.\nSimilarly, for the case of 3 equations and 3 unknowns, we would plot 3 planes and the (x, y, z) location of their point of intersection would be the solution for x, y, and z.\nWhat, then, is the point of Gaussian elimination if we can simply plot our set of equations to find a solution?\nWell, this analogy breaks down quickly when we start moving beyond 3D, so it is obvious we need some method to deal with higher-dimensional systems.\nThat said, it is particularly interesting to see what happens as we plot our matrix during Gaussian elimination for the 3D case.\n\n\n \nYour browser does not support the video tag.\n\n\n\nAs we can see in the above visualization, the planes wobble about in 3D until they reach row echelon form, where one plane is parallel to the x and y axes.\nAt this point, it's trivial to find the z-coordinate for the solution because it's simply the z intercept of the parallel plane.\nFrom there, the matrices become even easier to interpret as they move to the reduced row echelon form.\nIn this form, the solution is simply the x, y, and z intercepts of the appropriate planes.\nThis visualization might have been obvious for some readers, but I found it particularly enlightening at first.\nBy performing Gaussian elimination, we are manipulating our planes such that they can be interpreted at a glance -- which is precisely the same thing we are doing with the matrix interpretation!\nConclusions\nAnd with that, we have two possible ways to reduce our system of equations and find a solution.\nIf we are sure our matrix is not singular and that a solution exists, it's fastest to use back-substitution to find our solution.\nIf no solution exists or we are trying to find a reduced row echelon matrix, then Gauss-Jordan elimination is best.\nAs we said at the start, the notation for Gaussian Elimination is rather ambiguous in the literature, so we are hoping that the definitions provided here are clear and consistent enough to cover all the bases.\nAs for what's next... Well, we are in for a treat!\nThe above algorithm clearly has 3 for loops and has a complexity of \\sim O(n^3), which is abysmal!\nIf we can reduce the matrix to a specifically tridiagonal matrix, we can actually solve the system in \\sim O(n)!\nHow? Well, we can use an algorithm known as the Tri-Diagonal Matrix Algorithm (TDMA) also known as the Thomas Algorithm.\nThere are also plenty of other solvers that do similar things that we will get to in due time.\nVideo Explanation\nHere's a video describing Gaussian elimination:\n\n\n\n\nExample Code\nfunction gaussian_elimination!(A::Array{Float64,2})\n\n rows = size(A,1)\n cols = size(A,2)\n\n # Row index\n row = 1\n\n # Main loop going through all columns\n for col = 1:(cols-1)\n\n # finding the maximum element for each column\n max_index = argmax(abs.(A[row:end,col])) + row-1\n\n # Check to make sure matrix is good!\n if (A[max_index, col] == 0)\n println(\"matrix is singular!\")\n continue\n end\n\n # swap row with highest value for that column to the top\n temp_vector = A[max_index, :]\n A[max_index, :] = A[row, :]\n A[row, :] = temp_vector\n\n # Loop for all remaining rows\n for i = (row+1):rows\n\n # finding fraction\n fraction = A[i,col]/A[row,col]\n\n # loop through all columns for that row\n for j = (col+1):cols\n\n # re-evaluate each element\n A[i,j] -= A[row,j]*fraction\n\n end\n\n # Set lower elements to 0\n A[i,col] = 0\n end\n row += 1\n end\nend\n\nfunction back_substitution(A::Array{Float64,2})\n\n rows = size(A,1)\n cols = size(A,2)\n\n # Creating the solution Vector\n soln = zeros(rows)\n\n for i = rows:-1:1\n sum = 0.0\n for j = rows:-1:i\n sum += soln[j]*A[i,j]\n end\n soln[i] = (A[i, cols] - sum) / A[i, i]\n end\n\n return soln\nend\n\n\nfunction gauss_jordan_elimination!(A::Array{Float64,2})\n\n rows = size(A,1)\n cols = size(A,2)\n\n\n # After this, we know what row to start on (r-1)\n # to go back through the matrix\n row = 1\n for col = 1:cols-1\n if (A[row, col] != 0)\n\n # divide row by pivot and leaving pivot as 1\n for i = cols:-1:col\n A[row,i] /= A[row,col]\n end\n\n # subtract value from above row and set values above pivot to 0\n for i = 1:row-1\n for j = cols:-1:col\n A[i,j] -= A[i,col]*A[row,j]\n end\n end\n row += 1\n end\n end\nend\n\nfunction main()\n A = [2. 3 4 6;\n 1 2 3 4;\n 3 -4 0 10]\n\n gaussian_elimination!(A)\n println(A)\n\n gauss_jordan_elimination!(A)\n println(A)\n\n soln = back_substitution(A)\n println(soln)\n\nend\n\nmain()\n\n#include \n#include \n#include \n\nvoid swap_rows(double *a, const size_t i, const size_t pivot,\n const size_t cols) {\n\n for (size_t j = 0; j fabs(a[pivot * cols + col])) {\n pivot = i;\n }\n }\n\n if (a[pivot * cols + col] == 0) {\n printf(\"The matrix is singular.\\n\");\n continue;\n }\n\n if (col != pivot) {\n swap_rows(a, col, pivot, cols);\n }\n\n for (size_t i = row + 1; i = 0; --i) {\n double sum = 0.0;\n\n for (int j = cols - 2; j > i; --j) {\n sum += x[j] * a[i * cols + j];\n }\n\n x[i] = (a[i * cols + cols - 1] - sum) / a[i * cols + i];\n }\n}\n\nvoid gauss_jordan(double *a, const size_t cols) {\n size_t row = 0;\n\n for (size_t col = 0; col col - 1; --i) {\n a[row * cols + i] /= a[row * cols + col];\n }\n\n for (size_t i = 0; i col - 1; --j) {\n a[i * cols + j] -= a[i * cols + col] * a[row * cols + j];\n }\n }\n\n row++;\n }\n }\n}\n\nint main() {\n double a[3][4] = {{3.0, 2.0, -4.0, 3.0},\n {2.0, 3.0, 3.0, 15.0},\n {5.0, -3.0, 1.0, 14.0}};\n\n gaussian_elimination((double *)a, 3, 4);\n\n printf(\"Gaussian elimination:\\n\");\n for (size_t i = 0; i \n#include \n#include \n#include \n#include \n#include \n\n\nvoid gaussianElimination(std::vector > &eqns) {\n // 'eqns' is the matrix, 'rows' is no. of vars\n std::size_t rows = eqns.size(), cols = eqns[0].size();\n\n for (std::size_t i = 0; i fabs(eqns[pivot][i])) pivot = j;\n }\n\n if (eqns[pivot][i] == 0.0)\n continue; // But continuing to simplify the matrix as much as possible\n\n if (i != pivot) // Swapping the rows if new row with higher maxVals is found\n std::swap(eqns[pivot], eqns[i]); // C++ swap function\n\n for (std::size_t j = i + 1; j > &eqns) {\n // 'eqns' is the (Row-echelon) matrix, 'rows' is no. of vars\n std::size_t rows = eqns.size();\n\n for (std::size_t i = rows - 1; i backSubs(const std::vector > &eqns) {\n // 'eqns' is matrix, 'rows' is no. of variables\n std::size_t rows = eqns.size();\n\n std::vector ans(rows);\n for (std::size_t i = rows - 1; i (0);\n }\n return ans;\n}\n\n\nvoid printMatrix(const std::vector > &matrix) {\n for (std::size_t row = 0; row > equations{\n {2, 3, 4, 6},\n {1, 2, 3, 4},\n {3, -4, 0, 10}};\n\n std::cout ans = backSubs(equations);\n std::cout \n// submitted by jess 3jane\n\nuse std::cmp::min;\nuse std::ops::{Index, IndexMut};\n\npub struct Matrix {\n rows: usize,\n cols: usize,\n data: Vec,\n}\n\nimpl Matrix {\n fn new(rows: usize, cols: usize, data: &[f64]) -> Matrix {\n Matrix {\n rows,\n cols,\n data: data.to_vec(),\n }\n }\n\n fn swap_rows(&mut self, a: usize, b: usize) {\n for col in 0..self.cols {\n self.data.swap(a * self.cols + col, b * self.cols + col);\n }\n }\n}\n\nimpl Index for Matrix {\n type Output = f64;\n fn index(&self, (row, col): (usize, usize)) -> &f64 {\n &self.data[row * self.cols + col]\n }\n}\n\nimpl IndexMut for Matrix {\n fn index_mut(&mut self, (row, col): (usize, usize)) -> &mut f64 {\n &mut self.data[row * self.cols + col]\n }\n}\n\nfn gaussian_elimination(a: &mut Matrix) {\n for k in 0..min(a.cols, a.rows) {\n // find the maximum element for this column\n let mut max_row = k;\n let mut max_value = a[(k, k)].abs();\n for row in (k + 1)..a.rows {\n if max_value Vec {\n let mut soln = vec![0.0; a.rows];\n\n soln[a.rows - 1] = a[(a.rows - 1, a.cols - 1)] / a[(a.rows - 1, a.cols - 2)];\n\n for i in (0..a.rows - 1).rev() {\n let mut sum = 0.0;\n for j in (i..a.rows).rev() {\n sum += soln[j] * a[(i, j)];\n }\n soln[i] = (a[(i, a.cols - 1)] - sum) / a[(i, i)];\n }\n\n soln\n}\n\nfn main() {\n // The example matrix from the text\n let mut a = Matrix::new(\n 3,\n 4,\n &vec![2.0, 3.0, 4.0, 6.0, 1.0, 2.0, 3.0, 4.0, 3.0, -4.0, 0.0, 10.0],\n );\n\n gaussian_elimination(&mut a);\n gauss_jordan(&mut a);\n let soln = back_substitution(&a);\n println!(\"Solution: {:?}\", soln);\n}\n\nimport Data.Array\nimport Data.Function (on)\nimport Data.List (intercalate, maximumBy)\nimport Data.Ratio\n\ntype Matrix a = Array (Int, Int) a\n\ntype Vector a = Array Int a\n\nswapRows :: Int -> Int -> Matrix a -> Matrix a\nswapRows r1 r2 m\n | r1 == r2 = m\n | otherwise =\n m //\n concat [[((r2, c), m ! (r1, c)), ((r1, c), m ! (r2, c))] | c (Int, Int) -- pivot location\n -> (Int, Int) -- rows to cover\n -> (Int, Int) -- columns to cover\n -> Matrix a\n -> Matrix a\nsubRows (r, c) (r1, rn) (c1, cn) m =\n accum\n (-)\n m\n [ ((i, j), m ! (i, c) * m ! (r, j) / m ! (r, c))\n | i Matrix a -> Matrix a\ngaussianElimination mat = go (r1, c1) mat\n where\n ((r1, c1), (rn, cn)) = bounds mat\n go (r, c) m\n | c == cn = m\n | pivot == 0 = go (r, c + 1) m\n | otherwise = go (r + 1, c + 1) $ subRows (r, c) (r + 1, rn) (c, cn) m'\n where\n (target, pivot) =\n maximumBy (compare `on` abs . snd) [(k, m ! (k, c)) | k Matrix a -> Matrix a\ngaussJordan mat = go (r1, c1) mat\n where\n ((r1, c1), (rn, cn)) = bounds mat\n go (r, c) m\n | c == cn = m\n | m ! (r, c) == 0 = go (r, c + 1) m\n | otherwise = go (r + 1, c + 1) $ subRows (r, c) (r1, r - 1) (c, cn) m'\n where\n m' = accum (/) m [((r, j), m ! (r, c)) | j Matrix a -> Vector a\nbackSubstitution m = sol\n where\n ((r1, _), (rn, cn)) = bounds m\n sol =\n listArray (r1, rn) [(m ! (r, cn) - sum' r) / m ! (r, r) | r Matrix a -> String\nprintM m =\n let ((r1, c1), (rn, cn)) = bounds m\n in unlines\n [ intercalate \"\\t\" [show $ m ! (r, c) | c Vector a -> String\nprintV = unlines . map show . elems\n\nmain :: IO ()\nmain = do\n let mat = [2, 3, 4, 6, 1, 2, 3, 4, 3, -4, 0, 10] :: [Ratio Int]\n m = listArray ((1, 1), (3, 4)) mat\n putStrLn \"Original Matrix:\"\n putStrLn $ printM m\n putStrLn \"Echelon form\"\n putStrLn $ printM $ gaussianElimination m\n putStrLn \"Reduced echelon form\"\n putStrLn $ printM $ gaussJordan $ gaussianElimination m\n putStrLn \"Solution from back substitution\"\n putStrLn $ printV $ backSubstitution $ gaussianElimination m\n\nimport numpy as np\n\ndef gaussian_elimination(A):\n\n pivot_row = 0\n\n # Go by column\n for pivot_col in range(min(A.shape[0], A.shape[1])):\n\n # Swap row with highest element in col\n max_i = np.argmax(abs(A[pivot_row:, pivot_col])) + pivot_row\n\n temp = A[pivot_row, :].copy()\n A[pivot_row, :] = A[max_i, :]\n A[max_i, :] = temp\n\n # Skip on singular matrix, not actually a pivot\n if A[pivot_row, pivot_col] == 0:\n continue\n\n # Zero out elements below pivot\n for r in range(pivot_row + 1, A.shape[0]):\n # Get fraction\n frac = -A[r, pivot_col] / A[pivot_row, pivot_col]\n # Add rows\n A[r, :] += frac * A[pivot_row, :]\n\n pivot_row += 1\n\n\n# Assumes A is already row echelon form\ndef gauss_jordan_elimination(A):\n\n col = 0\n\n # Scan for pivots\n for row in range(A.shape[0]):\n while col = A.shape[1]:\n continue\n\n # Set each pivot to one via row scaling\n A[row, :] /= A[row, col]\n\n # Zero out elements above pivot\n for r in range(row):\n A[r, :] -= A[r, col] * A[row, :]\n\n\n# Assumes A has a unique solution and A in row echelon form\ndef back_substitution(A):\n\n sol = np.zeros(A.shape[0]).T\n\n # Go by pivots along diagonal\n for pivot_i in range(A.shape[0] - 1, -1, -1):\n s = 0\n for col in range(pivot_i + 1, A.shape[1] - 1):\n s += A[pivot_i, col] * sol[col]\n sol[pivot_i] = (A[pivot_i, A.shape[1] - 1] - s) / A[pivot_i, pivot_i]\n\n return sol\n\n\ndef main():\n A = np.array([[2, 3, 4, 6],\n [1, 2, 3, 4,],\n [3, -4, 0, 10]], dtype=float)\n\n print(\"Original\")\n print(A, \"\\n\")\n\n gaussian_elimination(A)\n print(\"Gaussian elimination\")\n print(A, \"\\n\")\n\n print(\"Back subsitution\")\n print(back_substitution(A), \"\\n\")\n\n gauss_jordan_elimination(A)\n print(\"Gauss-Jordan\")\n print(A, \"\\n\")\n\n\nif __name__ == \"__main__\":\n main()\n\nimport java.util.Arrays;\n\npublic class GaussianElimination {\n\n static void gaussianElimination(double[][] a) {\n int row = 0;\n\n int rows = a.length;\n int cols = a[0].length;\n\n for (int col = 0; col Math.abs(a[pivot][col])) {\n pivot = i;\n }\n }\n\n if (a[pivot][col] == 0) {\n System.err.println(\"The matrix is singular\");\n continue;\n }\n\n if (row != pivot) {\n // Swap the row with the highest valued element\n // with the current row\n swapRow(a, col, pivot);\n }\n\n for (int i = row + 1; i col - 1; i--) {\n // divide row by pivot so the pivot is set to 1\n a[row][i] /= a[row][col];\n }\n\n // subtract the value form above row and set values above pivot to 0\n for (int i = 0; i col - 1; j--) {\n a[i][j] -= a[i][col] * a[row][j];\n }\n }\n row++;\n }\n }\n }\n\n static double[] backSubstitution(double[][] a) {\n int rows = a.length;\n int cols = a[0].length;\n\n double[] solution = new double[rows];\n\n for (int i = rows - 1; i >= 0; i--) {\n double sum = 0;\n\n for (int j = cols - 2; j > i; j--) {\n sum += solution[j] * a[i][j];\n }\n solution[i] = (a[i][cols - 1] - sum) / a[i][i];\n }\n return solution;\n }\n\n static void swapRow(double[][] a, int rowA, int rowB) {\n double[] temp = a[rowA];\n a[rowA] = a[rowB];\n a[rowB] = temp;\n }\n\n public static void main(String[] args) {\n double[][] a = {\n { 3, 2, -4, 3 },\n { 2, 3, 3, 15 },\n { 5, -3, 1, 14 }\n };\n\n gaussianElimination(a);\n System.out.println(\"Gaussian elimination:\");\n Arrays.stream(a).forEach(x -> System.out.println(Arrays.toString(x)));\n\n gaussJordan(a);\n System.out.println(\"\\nGauss-Jordan:\");\n Arrays.stream(a).forEach(x -> System.out.println(Arrays.toString(x)));\n\n System.out.println(\"\\nSolutions:\");\n System.out.println(Arrays.toString(backSubstitution(a)));\n }\n}\n\nfunction gaussianElimination(a) {\n const rows = a.length\n const cols = a[0].length\n let row = 0;\n for (let col = 0; col Math.abs(a[pivot][col])) {\n pivot = i;\n }\n }\n\n if (a[pivot][col] === 0) {\n console.log(\"The matrix is singular.\");\n continue;\n }\n\n if (col !== pivot) {\n const t = a[col];\n a[col] = a[pivot];\n a[pivot] = t;\n }\n\n for (let i = row + 1; i = 0; --i) {\n\n let sum = 0;\n for (let j = cols - 2; j > i; --j) {\n sum += sol[j] * a[i][j];\n }\n\n sol[i] = (a[i][cols - 1] - sum) / a[i][i];\n }\n return sol;\n}\n\nfunction gaussJordan(a) {\n const cols = a[0].length;\n let row = 0;\n\n for (let col = 0; col col - 1; --i) {\n a[row][i] /= a[row][col];\n }\n\n for (let i = 0; i col - 1; --j) {\n a[i][j] -= a[i][col] * a[row][j];\n }\n }\n\n ++row;\n }\n }\n}\n\nfunction printMatrixRow(row) {\n const text = row\n .map(v => (v \n// Package demonstrates Gaussian Elimination\npackage main\n\nimport (\n \"fmt\"\n \"math\"\n)\n\nfunc gaussianElimination(a [][]float64) {\n singular := false\n rows := len(a)\n cols := len(a[0])\n\n for c, r := 0, 0; c highest {\n p = r + i\n highest = abs\n }\n }\n highest = a[p][c] // correct sign\n\n if highest == 0. {\n if !singular {\n singular = true\n fmt.Println(\"This matrix is singular.\")\n }\n continue\n }\n\n // 2. swap pivot with current row\n if p != r {\n a[r], a[p] = a[p], a[r]\n }\n\n for _, row := range a[r+1:] {\n // 3. find fraction from pivot value\n frac := row[c] / highest\n\n // 4. subtract row to set rest of column to zero\n for j := range row {\n row[j] -= frac * a[r][j]\n }\n\n // 5. ensure col goes to zero (no float rounding)\n row[c] = 0.\n }\n\n r++\n }\n}\n\nfunc gaussJordan(a [][]float64) {\n for r := len(a) - 1; r >= 0; r-- {\n // Find pivot col\n p := -1\n for c, cell := range a[r] {\n if cell != 0. {\n p = c\n break\n }\n }\n if p = 0; r-- {\n sum := 0.\n\n for c := cols - 2; c > r; c-- {\n sum += x[c] * a[r][c]\n }\n\n x[r] = (a[r][cols-1] - sum) / a[r][r]\n }\n return x\n}\n\nfunc printMatrixRow(row []float64) {\n fmt.Print(\"[\")\n for _, cell := range row {\n fmt.Printf(\"%9.4f \", cell)\n }\n fmt.Println(\"]\")\n}\n\nfunc printMatrix(a [][]float64) {\n for _, row := range a {\n printMatrixRow(row)\n }\n fmt.Println()\n}\n\nfunc main() {\n a := [][]float64{\n {2, 3, 4, 6},\n {1, 2, 3, 4},\n {3, -4, 0, 10},\n }\n fmt.Println(\"Original Matrix:\")\n printMatrix(a)\n\n fmt.Println(\"Gaussian elimination:\")\n gaussianElimination(a)\n printMatrix(a)\n\n gaussJordan(a)\n fmt.Println(\"Gauss-Jordan:\")\n printMatrix(a)\n\n fmt.Println(\"Solutions are:\")\n x := backSubstitution(a)\n printMatrixRow(x)\n}\n\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe animation \"GEvis\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/quantum_systems/quantum_systems.html":{"url":"contents/quantum_systems/quantum_systems.html","title":"Quantum Systems","keywords":"","body":"Quantum Systems\nAs I am sure you have heard, the quantum world is weird.\nAs you deal with progressively smaller and smaller systems, at some point, it becomes less accurate to describe objects as particles.\nInstead, it is better to describe objects as probability densities.\nThese densities are easiest to understand in terms of wavefunctions, which are complex functions characterizing a quantum system's behavior.\nAgain, this is pretty common knowledge; however, there is a distinct lack of readable literature on how to simulate quantum systems, even though there are numerous methods for exactly that!\nThis section will deal with the computation of quantum states with classical machines.\nNow, I know what you are thinking, \"Wait. Why are we simulating quantum systems on classical computers? Why not simulate it with some sort of experiment or with quantum computers?\"\nWell, here's where the notation gets really sticky.\nThere is a clear difference between quantum computers and quantum simulators.\nA quantum computer is the quantum analog to a classical computer, replacing bits with qubits by using quantum information theory.\nQuantum computers are usually thought of as a way to use quantum mechanics to eventually solve real-world problems with new quantum algorithms.\nBoth Grover's and Shor's algorithms are good examples of cases where quantum computation could greatly change the landscape of modern computation as we know it!\nQuantum simulators on the other hand are quantum systems used to better understand quantum mechanics.\nThese will often come in the form of experimental quantum systems that express quantum behavior and allow us to better understand other areas of quantum systems.\nIn other words, quantum simulators are general techniques to study quantum systems on quantum hardware; however, quantum computers are quantum hardware used for the explicit purpose of quantum computation with qubits.\nBecause supercomputers are not great at performing quantum computations, certain quantum simulators exist as a building block for quantum computation.\nA universal quantum simulator is often called a quantum computer for this reason.\nThe truth is that quantum simulators are hard to make in laboratories, so simulating quantum systems on classical hardware is as good as we can do in most cases.\nThis section is devoted to all the different methods currently used to solve complex quantum systems, so let's start with the Schrödinger Equation, which has many different formulations.\nHere is the easiest one to explain:\n\ni \\hbar \\frac{\\partial \\Psi(\\mathbf{r},t)}{\\partial t} = \\left[-\\frac{\\hbar^2}{2m} \\nabla^2 + V(\\mathbf{r},t) \\right] \\Psi(\\mathbf{r},t)\n\nWhere \\Psi(\\mathbf{r},t) is a quantum wavefunction, V(\\mathbf{r},t) is a trapping potential, \\nabla^2 is a Laplacian, \\mathbf{r} is some sort of spatial component, and t is time.\nThere is a lot to take in here; however, it's ultimately just some time derivative on the left-hand side and a spatial derivative (with some extra steps) on the right-hand side.\nIn this way, it isn't too different from the diffusion (heat) equation:\n\n\\frac{\\partial\\phi(\\mathbf{r},t)}{\\partial t} = D \\nabla^2 \\phi(\\mathbf{r},t)\n\nwhere D is some positive definite matrix and \\phi(\\mathbf{r},t) is the density (or temperature) of the system.\nIn fact, this is why one of the most common types of quantum simulation is sometimes called diffusion Monte Carlo.\nThere really isn't that much of a difference between the two systems in terms of how they are simulated on classical hardware... but we are getting ahead of ourselves.\nFor now, let's talk about how quantum mechanics differs from classical mechanics and how we can use this to our advantage.\nProbability Density\nQuantum mechanics works fundamentally differently than classical mechanics in physics.\nThe wavefunction can be thought of as a set of all possible states for an object to be in, where there is some probability for the particle to be found in each state.\nThis means that it is not possible to say that a particle is at a particular location, and instead we often say that it could be at any location with probability, as shown in the probability density:\n\nP(\\mathbf{r}, t) = |\\Psi(\\mathbf{r},t)|^2 = \\Psi(\\mathbf{r},t)^{*}\\Psi(\\mathbf{r},t)\n\nHere, there are 2 things to note:\n\nThe absolute value squared of a complex parameter \\Psi(\\mathbf{r},t) is a dot product (inner product) between a complex function and it's Hermitian conjugate. This means the value will always be real, while the wavefunction, itself, might not be.\nAs you have probably heard, once a wavefunction is observed it collapses onto a single state. This can be simply interpreted as absolute knowledge of the particle's location. A probability density doesn't make sense if we know where the particle is!\n\nNow, to be clear: the probabilities must all sum to 1, or (more formally):\n\n\\int_{-\\infty}^{+\\infty}|\\Psi(\\mathbf{r},t)|^2 d\\mathbf{r} = 1\n\nThis simply means that the probability of finding our quantum particle somewhere in real space is 1.\nIn other words, our particle must exist somewhere in the known universe.\nAs another note: Just like position space can be parameterized by a position vector \\textbf{x}, wavefunctions can also be parameterized by a wave vector \\textbf{k} in frequency space.\nAny wavevector \\textbf{k} has the same units as reciprocal space and is thus analogous to angular frequency \\omega.\nOften times, the wavevector space is called momentum space, which makes sense when considering the de Broglie formula:\n\np = \\frac{h}{\\lambda} = \\frac{2 \\pi h}{2 \\pi \\lambda} = \\hbar k\n\nwhere h is Planck's constant and \\lambda is the wavelength.\nThis means that we can ultimately move between position and momentum space by using Fourier Transforms, which is incredibly useful in a number of cases!\nEven though the relation between position and momentum space is an essential cornerstone of understanding modern quantum mechanics, it is difficult to understand at a fundamental level.\nPosition space and momentum space are related by a Fourier transform; however, the rather hand-wavey argument above might not have been convincing enough and it does not offer any intuitive description of why the Fourier transform comes into this discussion at all.\nThe easiest way to understand this might be to look at the Heisenberg uncertainty principle, which is a fundamental relation between position and momentum space.\nHeisenberg Uncertainty Principle\nSimply put, the Heisenberg uncertainty principle states that we cannot definitely know both the position and momentum of a quantum particle.\nIn particular, it says:\n\n\\sigma_x \\sigma_p \\geq \\frac{\\hbar}{2}\n\nwhere \\hbar is Planck's constant and \\sigma_q = \\sqrt{\\frac{1}{N}\\sum_{i=1}^{N}(q_i-\\mu)^2}.\nIn this case, \\sigma is the standard deviation, \\mu is the statistical mean of your distribution, N is the number of points sampled, q_i is the value for each point i, and q stands for r or p.\nUltimately, this means that if we have a higher precision in position space, we will have a lower precision in momentum space.\nThe converse is also true: a higher precision in momentum space will lead to a lower precision in position space.\nThis makes the most sense if we imagine having a Gaussian-like probability density (|\\Psi(x)|^2) in position space, which will provide a Gaussian-like density when in momentum space.\nHere, we see that if we have a broader distribution in one space, we must have a thinner distribution in the opposite space, as shown here:\n\n \n\n\n\nBecause the density can be interpreted as \"the probability of finding a quantum particle at any provided location in position (x_i) or momentum (k_i) space, the interpretation is clear: the more we understand about a particle's position, the less we understand about it's momentum.\nThis is a powerful statement and should be given some thought.\nTo me, the most interesting part of this description is not the physical interpretation, but the fact that this act of transforming between larger and smaller Gaussians is precisely what Fourier transforms do!\nThis further strengthens our argument from before.\nPosition and momentum space are related by the Fourier transform!\nThis is the heart of several algorithms for simulating quantum systems, including the Split-operator method.\nAt least for me, I found this description to be intuitive, but not complete.\nThere is still something missing from the picture that should be described in more depth, and to do that, we need to dive deeper into the heart of quantum mechanics and into Hamiltonians.\nHamiltonian\nHere is the Schrödinger equation again:\n\ni \\hbar \\frac{\\partial \\Psi(\\mathbf{r},t)}{\\partial t} = \\left[-\\frac{\\hbar^2}{2m} \\nabla^2 + V(\\mathbf{r},t) \\right] \\Psi(\\mathbf{r},t)\n\nWe described it in the initial section of this chapter.\nFor the most part, when we are trying to solve this equation the left-hand side does not change.\nIt's always i \\hbar \\frac{\\partial \\Psi(\\mathbf{r},t)}{\\partial t}.\nOn the other hand, the right-hand side can change a lot depending on the situation.\nThat is to say that we can easily simplify the Schrödinger equation by using a mathematical formalism known as the Hamiltonian.\nTo be clear, Hamiltonian mechanics is not a quantum-specific idea.\nIt's everywhere in statistical physics and is often taught in classical physics courses as an analogue to another notational form known as Lagrangian mechanics.\nFor simplicity, we will restrict our discussion here to interpreting Hamiltonians physically.\nWe can basically say that the Hamiltonian is a measure of the energy of our quantum system.\nMore specifically, we can say that the Hamiltonian is a set of energy operators that act on our wavefunction.\nIn the case of a 1D particle in a harmonic trap, we might use the following definitions:\n\n\\begin{align}\n\\hat H &= \\hat T + \\hat V \\\\\n\\hat T &= \\frac{p^2}{2m} \\\\\n\\hat V &= \\frac{1}{2}\\omega x^2\n\\end{align}\n\nwhere p = -i\\hbar \\nabla is the momentum operator and \\omega is the trapping frequency indicating how confined our quantum system will be.\nIn this case, \\hat T is an operator that works on our wavefunction in momentum space, while \\hat V acts in position space.\nBoth of these are operators.\nThat is to say that they operate on our quantum system by transforming it in some way.\nUltimately, this means that the operators are not meant to be interpreted on their own without acting on some other object, in this case, the wavefunction \\Psi(x).\nIn the end, we can update our Schrödinger equation to be\n\ni \\hbar \\frac{\\partial \\Psi(\\mathbf{r},t)}{\\partial t} = \\hat H \\Psi(\\mathbf{r},t)\n\nWhich is a lot cleaner and more general.\nNow, the Schrödinger equation can solve any quantum system so long as it can be written in terms of Hamiltonian mechanics!\nWhen looking at the operators, it is clear that the \\hat V operator is in position space.\nWe can clearly see that it operates as a function of x.\nThat said, it is not immediately obvious why the \\hat T is in momentum space.\nThis is not an easy question to answer, but it is definitely important and will be covered in more depth when we discuss spectral methods.\nFor now, we will blanketly say\n\n\\frac{\\partial f}{\\partial x} = \\mathcal{F}^{-1}\\left( 2\\pi i k \\mathcal{F}\\left( f \\right)\\right)\n\nIn other words, we can derive a function by performing a Fourier transform on the function, multiplying by some momentum-space grid, and then inverse-transforming it back.\nBecause this operation inherently involves a transform into momentum space before transformation, it is a momentum-space operator.\nThis is the most intuitive reasoning I can find; however, I am sure there are more intuitive explanations of why the derivatives are always momentum-space operations.\nThis section will be updated further when we discuss spectral methods, but if you have better descriptions, please let me know!\nBra Ket Notation\nUnfortunately, the interpretation of quantum simulation is rather tricky and is sometimes easier to understand with slightly different notation.\nThis notation is called braket notation, where a ket looks like this:\n\n\\lvert A \\rangle\n\nand basically describes A as a column vector.\nThe bra represents the Hermitian conjugate of the ket and looks like this:\n\n\\langle B \\rvert\n\nThe ket is often represented as a row vector for B.\nBecause of this, \\langle B \\rvert A \\rangle represents the inner product of the two vectors and \\lvert A \\rangle \\langle B \\rvert represents the outer product.\nNow, to this point, the braket notation does not have any particularly quantum-like features; however, it becomes useful when describing actual quantum phenomenon.\nFor example, if we want to indicate the probability of a wavefunction \\psi collapsing onto state \\phi, we might write: \\langle \\phi \\rvert \\psi \\rangle, which is precisely the same as the probability density defined above.\nNow that we have a basic understanding of the notation, we should go through several other important quantum mechanical ideas and properties.\nEigenstates\nAs mentioned, the wavefunction \\Psi(x) is complex and has both real and imaginary parts; however, there are certain states that are exclusively real.\nThese states are eigenstates of the system, and are often described as the constituent states that make up all other possible wavefunctions.\nIn other words,\n\n\\lvert \\Psi(x)\\rangle = \\sum_i c_i \\lvert \\Psi_i \\rangle\n\nWhere c_i is some constant describing how much of a given eigenstate i is in the full wavefunction.\nAs you might expect, all of the c_i's should sum to 1.\nEnergy Calculations\nWhen it comes to quantum systems, there is no quantity more important than energy.\nBasically, every eigenstate of the system has a different energy associated with it, and you can find this energy with a simple calculation:\n\nE = \\langle \\Psi \\lvert \\hat H \\lvert \\Psi \\rangle\n\nWhich can be done rather trivially in code by finding the conjugate of the wavefunction and multiplying it with another wavefunction after operation in position and momentum space.\nThis ultimately looks like this:\n# We are calculating the energy to check \nfunction calculate_energy(par, opr)\n # Creating real, momentum, and conjugate wavefunctions\n wfc_r = opr.wfc\n wfc_k = fft(wfc_r)\n wfc_c = conj(wfc_r)\n\n # Finding the momentum and real-space energy terms\n energy_k = 0.5*wfc_c.*ifft((par.k.^2) .* wfc_k)\n energy_r = wfc_c.*opr.V .* wfc_r\n\n # Integrating over all space\n energy_final = 0\n for i = 1:length(energy_k)\n energy_final += real(energy_k[i] + energy_r[i])\n end\n\n return energy_final*par.dx\nend\n\ncalculateEnergy :: Parameters -> Operators -> Double\ncalculateEnergy param ops = (* dx param) . sum . map realPart $ elems totalE\n where\n totalE = potentialE .+ kineticE\n potentialE = wfcConj .* v ops .* wfc ops\n kineticOp = liftArray ((/ 2) . (^ 2)) (ks param)\n kineticE = wfcConj .* idft (kineticOp .* dft (wfc ops))\n wfcConj = liftArray conjugate $ wfc ops\n\ndouble calculate_energy(struct params par, struct operators opr) {\n double complex wfc_r[opr.size];\n double complex wfc_k[opr.size];\n double complex wfc_c[opr.size];\n memcpy(wfc_r, opr.wfc, sizeof(wfc_r));\n\n memcpy(wfc_k, opr.wfc, sizeof(wfc_k));\n fft(wfc_k, opr.size, false);\n\n for (size_t i = 0; i \ndouble calculate_energy(Params &par, Operators &opr) {\n vector_complex wfc_r(opr.wfc);\n vector_complex wfc_k(opr.wfc);\n vector_complex wfc_c(opr.size);\n fft(wfc_k, false);\n\n for (size_t i = 0; i \ndef calculate_energy(par: Param, opr: Operators) -> float:\n \"\"\"Calculate the energy .\"\"\"\n # Creating real, momentum, and conjugate wavefunctions.\n wfc_r = opr.wfc\n wfc_k = np.fft.fft(wfc_r)\n wfc_c = np.conj(wfc_r)\n\n # Finding the momentum and real-space energy terms\n energy_k = 0.5 * wfc_c * np.fft.ifft((par.k ** 2) * wfc_k)\n energy_r = wfc_c * opr.V * wfc_r\n\n # Integrating over all space\n energy_final = sum(energy_k + energy_r).real\n\n return energy_final * par.dx\n\n\n\nThis calculation will be used in many different simulations of quantum systems to check our results.\nIn the end, many quantum simulations are focused on the ground state, which is the lowest energy state (\\Psi_0); however, sometimes higher energy states are desired.\nThe Future\nAs we proceed to add new algorithms to simulate quantum systems, I will add more and more notation to this section; however, there are already huge textbooks out there related to understanding and studying quantum systems.\nWe don't want to re-invent the wheel here.\nInstead, we want to focus on an area that is often not considered with too much detail: algorithms and methods researchers use to ascertain new knowledge about quantum mechanics, like the split-operator method, DMRG, quantum Monte Carlo, exact diagonalization, and many more.\nQuantum mechanics is one of those areas of physics that really does push the boundary of human knowledge in a number of different areas and computing is one of those areas.\nIn fact, quantum information theory is currently set to be the next innovation to radically change the landscape of modern computation as we know it!\nOf course, because of the large-scale effects that this will likely have on the industry, it deserved it's own section.\nAs always, if there is something that you feel is missing from this section, please feel free to contact me or create an issue on GitHub and we'll get to it as soon as we can!\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe animation \"FTgaussian\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/affine_transformations/affine_transformations.html":{"url":"contents/affine_transformations/affine_transformations.html","title":"Affine Transformations","keywords":"","body":"Affine Transformations\nAffine transformations are a class of mathematical operations that encompass rotation, scaling, translation, shearing, and several similar transformations that are regularly used for various applications in mathematics and computer graphics.\nTo start, we will draw a distinct (yet thin) line between affine and linear transformations before discussing the augmented matrix formalism typically used in practice.\nA quick intro to affine (and linear) transforms\nLet us start with a provided point, (x,y), on a two-dimensional plane.\nIf we treat this point as a 1 \\times 2 vector, we can transform it into another 1 \\times 2 vector by multiplying it with a 2 \\times 2 transformation matrix.\nSimilarly, a three-dimensional point could be seen as a 1\\times 3 vector and would need a 3 \\times 3 transformation matrix.\nThese types of operations are known as linear transformations and are often notated as,\n\n\\mathbf{v} = \\mathbf{A}\\mathbf{v}_0.\n\nHere, \\mathbf{A} is an n\\times n transformation matrix, where n is the length of the input and output vectors, \\mathbf{v_0} and \\mathbf{v}, respectively.\nThough these transformations are powerful, all of them are centered about the origin.\nAffine transformations extend linear transformations beyond this limitation and allow us to also translate our initial vector locations such that\n\n\\textbf{v} = \\mathbf{A}\\mathbf{v}_0 + \\ell.\n\nHere, \\ell is an n\\times 1 translation vector.\nTo understand the power of these transformations, it is important to see them in practice:\n\n\n\nDescription\nTransform\n\n\n\n\nScaling along x\n Your browser does not support the video tag. \n\n\nScaling along y\n Your browser does not support the video tag. \n\n\nShearing along x\n Your browser does not support the video tag. \n\n\nShearing along y\n Your browser does not support the video tag. \n\n\nTranslation along x\n Your browser does not support the video tag. \n\n\nTranslation along y\n Your browser does not support the video tag. \n\n\n\nFor all of these visualizations, we show a set of 4 points that are assigned to the vertices of a square.\nInitially, \\mathbf{A} is set to be the identity matrix and \\ell = [0,0], such that there is no transformation or translation to the input vectors.\nFrom there, each element of \\mathbf{A} and \\ell are modified individually and the resulting transformation can be seen on the left.\nThe amount by which each element has been modified is shown numerically in the matrix representation and also as small dials underneath.\nThe hope is that these visualizations show that each element within \\mathbf{A} and \\ell are simply dials that can be manipulated to perform a specified transformation on the set of input vectors.\nOf course, it is entirely possible to move more than one dial at a time, which is why it is worth diving into an example that everyone loves: rotation.\nRotation: a special side-note\nI will be honest, when I initially learned how to perform rotation with a linear transformation, I did not really understand how it worked.\nFor this reason, I think it is important to delve a bit deeper into this topic, hopefully providing an intuitive explanation for those who are new (and potentially those who already use the rotation matrix regularly, but do not fully understand it).\nIf someone were to take the set of dials shown above and mix them to create a rotational effect, they might start by shearing in one direction along x and then another direction along y which will create a \"pseudo-rotation\" effect.\nThis is definitely a step in the right direction, but if the shearing components are modified while the other components remain 1, the points will also move further away from the origin.\nFor this reason, an additional scaling along x and y is necessary.\nThis is shown in the following animation:\n\n\n \nYour browser does not support the video tag.\n\n\n\nHere, we see that (at least for angles less than \\pi/2), rotation is simply a matter of shearing in opposite directions and scaling accordingly.\nNow the only question is, \"How do we know the amount we need to shear and scale?\"\nWell, the answer is not particularly surprising.\nIf we want to rotate our points, we probably are already imagining this rotation along a circle with some angle \\theta.\nWe know that the identity matrix should correspond to a non-rotated object with \\theta = 0.\nFor this reason, we know that two elements should start at 1 (note: \\cos(0) = 1) and the other two should start at 0 (note: \\sin(0) = 0).\nWe also know that the shearing should happen in opposite directions, so we might guess that the rotation matrix would be:\n\n\\mathbf{A}_{\\text{rot}} = \\begin{bmatrix}\n\\cos(\\theta) & -\\sin(\\theta) \\\\\n\\sin(\\theta) & \\cos(\\theta) \\\\\n\\end{bmatrix}\n\nIn this case, the amount we want to shear should start at 0 when \\theta = 0 and then go to \\pm 1 when \\theta = \\pm \\pi/2.\nMeanwhile, the scale factor should start at 1 when \\theta = 0 and go to 0 when \\theta = \\pi/2.\nThis seems right, but it is worth dwelling on this a bit more.\nIf the scale factor is 0 at \\pi/2, surely this means that all points on the square are also at 0, right?\nAfter all, anything scaled by 0 should be 0!\nWell, not exactly.\nIn this case,\n\n\\mathbf{A} = \\begin{bmatrix}\n1 & 0 \\\\\n0 & 1 \\\\\n\\end{bmatrix}\n\\rightarrow\n\\begin{bmatrix}\n0 & -1 \\\\\n1 & 0 \\\\\n\\end{bmatrix}\n\nThis means that even though the scaling components are 0, the shear components are \\pm 1.\nThis might still be a little confusing so let us multiply the vector [1,2] with both of these matrices:\n\n\\begin{align}\n\\begin{bmatrix}\n1 & 0 \\\\\n0 & 1 \\\\\n\\end{bmatrix}\n\\begin{bmatrix}\n1 \\\\\n2 \\\\\n\\end{bmatrix}\n&=\n\\begin{bmatrix}\n1 \\\\\n2 \\\\\n\\end{bmatrix},\\\\\n\n\n\\begin{bmatrix}\n0 & -1 \\\\\n1 & 0 \\\\\n\\end{bmatrix}\n\\begin{bmatrix}\n1 \\\\\n2 \\\\\n\\end{bmatrix}\n&=\n\\begin{bmatrix}\n-2 \\\\ \n1 \\\\\n\\end{bmatrix}.\n\n\\end{align}\n\nHere, we see that when multiplying by the identity matrix, the vector remains the same, but when multiplying by the second matrix, the x and y components flip.\nEssentially, all of the vector magnitude moved into the \"shear\" component, while none of it remains in the \"scale\" component.\nMy point is that even though it is useful to think of two of our dials as scale factors along x and y, it does not necessarily paint the whole picture and it is important to consider how these different components work together.\nBefore continuing to show what the \\mathbf{A}_{\\text{rot}} matrix does when applied to a square, it is worth considering two somewhat related matrices where the identity matrix is modified with only the \\sin(\\theta) or \\cos(\\theta) components.\n\n\n\nDescription\nTransform\n\n\n\n\nJust sines\n Your browser does not support the video tag. \n\n\nJust cosines\n Your browser does not support the video tag. \n\n\n\nHere, we see two completely different behaviors:\n\nIn the sine-only case, we see that as \\theta wraps around from 0 \\rightarrow 2\\pi, the square seems to grow and rotate like expected, but at \\pi/2, it somewhat abruptly decides to move in the other direction.\nIn cosine-only case, we see the square flip around entirely at \\pi/2.\n\nBefore watching the next video, it is important to think for a little bit about how these two different interactions will work together in practice.\nWhen you are ready, go ahead and click the play button:\n\n\n \nYour browser does not support the video tag.\n\n\n\nAt least for me, it took some thinking to figure out why the two animations above create rotation when put together.\nWhen thinking about it, it makes sense that at \\pi/2, the sine component will start to encourage the square to slowly oscillate back towards the original position, but will be tugged in the opposite direction by the cosine component that has turned negative at the same time.\nThis \"coincidence\" is what creates a rotational effect.\nOverall, the rotation matrix is a fun and interesting application to linear transformations that really helped me understand how the entire class of operations can be used to create more complicated movements.\nGuarantees of affine transformations\nAt this stage, we have discussed what affine transforms are from a functional perspective; however, (as always) there is a lot more to discuss.\nThis particular chapter is meant to provide an intuitive feel for the transformations for those who might need to use them for whatever application they need, so I am hesitant to dive too deeply into more rigorous definitions; however, it is important to talk about certain properties of affine transforms that make them suitable for a wide variety of applications.\nNamely, affine transformations preserve the following:\n\ncollinearity between points. This means that any points that are on the same line before an affine transform must be on that same line after the transformation. The line can still change in slope or position.\nparallelism between lines. Any lines parallel before the transform must also be parallel after.\nratios of the lengths of parallel line segments. This means if you have two different line segments, one of which is parameterized by p_1 and p_2, while the other is parameterized by p_3 and p_4, then \\frac{\\vec{p_1 p_2}}{\\vec{p_3 p_4}} must be the same before and after transformation.\nconvexity of any transformed shape. If a shape does not have any concave component (a point that points in towards its center), then it cannot have a concave component after the transformation.\nbarycenters of the collection of points. The barycenter is the collective center of mass of the system, like the balancing point for a plate. Essentially, there is an equal amount of \"stuff\" on either side of the barycenter. This location must remain at the same location relative to each point after transformation.\n\nAgain, there is a lot more we could talk about, but I feel we will leave more rigorous discussions for later if we need them for subsequent algorithms.\nInstead, I believe it is useful to move on to a relatively common implementation of affine transformations: the augmented matrix formalism.\nAugmented matrix implementation\nAs stated before, affine transformations are basically a mix of a transformation matrix and translation.\nFor two-dimensional input vectors, the augmented matrix formalism combines both of these into a large 3 \\times 3 transformation matrix.\nIf you are like me, this might be a bit confusing.\nAfter all, if the two-dimensional vector is described by a 1 \\times 2 array, then how do you do a matrix multiplication with a 3 \\times 3 array?\nTo be honest, the answer feels like a bit of a hack: we simply append a 1 to the end of the input, output, and translation vectors, such that:\n\n\\begin{bmatrix}\n\\mathbf{v} \\\\\n1 \\\\\n\\end{bmatrix}\n=\n\\left[\\begin{array}{@{}ccc|c@{}}\n & \\mathbf{A} & & \\ell \\\\\n0 & \\cdots & 0 & 1 \\\\\n\\end{array}\\right]\n\\begin{bmatrix}\n\\mathbf{v}_0 \\\\\n1\n\\end{bmatrix}\n\nSo, using \n\n\\begin{align}\n\\mathbf{v}_0 &= \\begin{bmatrix}\n1 \\\\ \n2 \\\\\n\\end{bmatrix} \\\\\n\\mathbf{A} &= \\begin{bmatrix}\n0 & -1 \\\\\n1 & 0 \\\\\n\\end{bmatrix} \\\\\n\\ell &= \\begin{bmatrix}\n0 \\\\ \n0 \\\\\n\\end{bmatrix}\n\\end{align},\n\nwe would perform the following computation:\n\n\\begin{bmatrix}\n\\mathbf{v} \\\\\n1 \\\\\n\\end{bmatrix}\n=\n\\left[\\begin{array}{@{}cc|c@{}}\n0 & -1 & 0 \\\\\n1 & 0 & 0 \\\\\n0 & 0 & 1 \\\\\n\\end{array}\\right]\n\\begin{bmatrix}\n1 \\\\\n2 \\\\\n1\n\\end{bmatrix}\n\nDoing this, we find that \\mathbf{v} = [-2,1], just as we found in the previous example.\nOk, now we need to talk about why this works.\nAppending the 1 to the end of the two-dimensional vectors essentially turn them into three-dimensional vectors, with the z dimension simply set to be 1.\nThe easiest way to visualize this is by thinking of the top plane on a larger cube, so here are the same vector operations as before on that cube:\n\n\n\nDescription\nTransform\n\n\n\n\nScaling along x\n Your browser does not support the video tag. \n\n\nScaling along y\n Your browser does not support the video tag. \n\n\nShearing along x\n Your browser does not support the video tag. \n\n\nShearing along y\n Your browser does not support the video tag. \n\n\nTranslation along x\n Your browser does not support the video tag. \n\n\nTranslation along y\n Your browser does not support the video tag. \n\n\n\nThe shear and scaling operations seem about the same as before; however, the translation operations are now clearly a shear along the entire cube!\nThe only reason this acts as translation for two dimensions is because we only care about the slice through the cube at z=1.\nNow, the reason I always feel this implementation is a bit hacky is because there is a little magic that everyone keeps quiet about: the last row in the matrix.\nWith all of the operations shown above, it was simply set to [0,0,1] and never touched again...\nBut that is terribly unsatisfying!\nWhat would happen if we actually moved those dials and modified the bottom row?\nWell...\n\n\n\nDescription\nTransform\n\n\n\n\nShearing along z and x\n Your browser does not support the video tag. \n\n\nShearing along z and y\n Your browser does not support the video tag. \n\n\nScaling along z\n Your browser does not support the video tag. \n\n\n\nIn this case, the first two components are shearing along z and x and z and y, while the last component is a scale along z.\nIf someone was taking a picture from above, none of these transformations would be visible.\nBecause we are hyper-focused on the top-down view for affine transformations, none of these operations are technically affine; however, they are still linear, and it is still nice to show all possible linear transforms for the cube as well.\nFinally, let us go back to the rotation example:\n\n\n \nYour browser does not support the video tag.\n\n\n\nHere, we see that we can embed just about any affine transformation into three dimensional space and still see the same results as in the two dimensional case.\nI think that is a nice note to end on: affine transformations are linear transformations in an n+1 dimensional space.\nVideo Explanation\nHere is a video describing affine transformations:\n\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe video \"A11 square\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A22 square\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A12 square\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A21 square\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A13 square\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A23 square\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Semi Rotate\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Sines\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Cosines\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Rotate Square\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A11 cube\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A22 cube\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A12 cube\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A21 cube\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A13 cube\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A23 cube\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A31 cube\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A32 cube\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A33 cube\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Rotation cube\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n"},"contents/approximate_counting/approximate_counting.html":{"url":"contents/approximate_counting/approximate_counting.html","title":"Approximate Counting Algorithm","keywords":"","body":"The Approximate Counting Algorithm\nThis might seem like a straightforward question, but how high can you count on your fingers?\nThis depends on how many fingers you have, but in general the answer has to be 10, right?\nWell, not exactly, it can actually go much, much higher with a few simple abstractions.\nThe first strategy is to think of your fingers as binary registers, like so [1]:\n\n \n\n\nIf your fingers are out, they count as a 1 for that register.\nIf they are not, they count as a 0.\nThis means that after you have decided on the appropriate finger configuration, you have created a bitstring that can be read from left to right, where each number represents a power of 2.\nFor this example, we would have a bitstring of 1110010101, which reads to 917:\n\n1 \\cdot 2^9 + 1 \\cdot 2^8 + 1 \\cdot 2^7 + 0 \\cdot 2^6 + 0 \\cdot 2^5 + 1 \\cdot 2^4 + 0 \\cdot 2^3 + 1 \\cdot 2^2 + 0 \\cdot 2^1 + 1 \\cdot 2^0\n\n\n=\n\n\n512 + 256 + 128 + 16 + 4 + 1 = 917\n\nBecause you have 10 fingers and each one represents a power of 2, you can count up to a maximum of 2^{10}-1 or 1023, which is about 100 times higher than simple finger counting!\nFor those who might be wondering why you can count to 2^{10}-1 instead of 2^{10} exactly, remember that each finger represents a power of 2.\nThe right thumb counts as 2^0 = 1 and the left thumb is 2^9 = 512.\nWith all fingers out, we have counted to \\sum_{n=0}^9 2^n = 1023 = 2^{10}-1.\nSo what if we wanted to go beyond 1023?\nWell, we could start counting with our fingers as trits where 0 is closed, 1 is half-up, and 2 is fully up.\nThere are actually a huge variety of different ways we could move our hands about to count in odd ways, but we are interested in a more concrete problem: how high can we count with only 10 bits?\nThis is almost exactly the problem that Morris encountered in Bell Labs around 1977 [2].\nThere, he was given an 8-bit register and asked to count much higher than 2^8 - 1= 255.\nHis solution was to invent a new method known as the approximate counting algorithm.\nWith this method, he could count to about 130,000 with a relatively low error (standard deviation, \\sigma \\approx 17,000).\nUsing 10 registers (fingers), he could count to about 1.1\\times 10^{16} with similar parameters, which is undoubtedly impressive!\nThe approximate counting algorithm is an early predecessor to streaming algorithms where information must be roughly processed in real-time.\nAs we dive into those methods later, this chapter will certainly be updated.\nFor now, we will not be showing any proofs (though those might come later as well), but a rigorous mathematical description of this method can be found in a follow-up paper by Philippe Flajolet [3].\nIn addition, there are several blogs and resources online that cover the method to varying degrees of accessibility [4] [5].\nHere, we hope to provide a basic understanding of the method, along with code implementations for anyone who might want to try something similar in the future.\nA Simple Example\nIf we need to count more than 255 items with 8 bits, there is one somewhat simple strategy: count every other item.\nThis means that we will increment our counter with 2, 4, 6, 8... items, effectively doubling the number of items we can count to 511!\n(Note: that \"!\" is out of excitement and is not a factorial.)\nSimilarly, if we need to count above 511, we can increment our counter every 3 or 4 items; however, the obvious drawback to this method is that if we only count every other item, there is no way to represent odd numbers.\nSimilarly, if we count every 3rd or 4th item, we would miss out on any numbers that are not multiples of our increment number.\nThe most important thing to take away from this line of reasoning is that counting can be done somewhat approximately by splitting the process into two distinct actions: incrementing the counter and storing the count, itself.\nFor example, every time a sheep walks by, you could lift a finger.\nIn this case, the act of seeing a sheep is a trigger for incrementing your counter, which is stored on your hand.\nAs mentioned, you could also lift a finger every time 2 or 3 sheep go by to count higher on your hand.\nIn code, bits are obviously preferred to hands for long-term storage.\nTaking this example a bit further, imagine counting 1,000,000 sheep.\nIf we wanted to save all of them on 8 bits (maximum size of 255), we could increment our counter every \\sim 4000 sheep.\nBy counting in this way, we would first need to count around 4000 sheep before incrementing the main counter by 1.\nAfter all the sheep have gone by, we would have counted up to 250 on our counter, and also counted up to 4000 on a separate counter 250 times.\nThis has a few important consequences:\n\nIf the final number of sheep is not a multiple of 4000, then we will have an error associated with the total count of up to 4000 (0.4%).\nThere is no way to determine the final number of sheep if it is not a multiple of 4000.\nWe now need some way to count up to 4000 before incrementing the main counter.\nThis means we need a second counter!\n\nIn a sense, 4000 would be a type of \"counting resolution\" for our system.\nOverall, a 0.4% error is not bad, but it is possible to ensure that the approximate count is more accurate (but potentially less precise) by using randomness to our advantage.\nThat is to say, instead of incrementing out counter every 4000th sheep, we could instead give each item a 1/4000 = 0.025\\% chance of incrementing our main counter.\nThis averages out to be roughly 1 count every 4000 sheep, but the expectation value of a large number of counting experiments should be the correct number.\nThis means that even though we need to count all the sheep multiple times to get the right expectation value, we no longer need to keep a separate counter for the counting resolution of 4000.\nBecause multiple counting trials are necessary to ensure the correct result, each counting experiment will have some associated error (sometimes much higher than 0.4%).\nTo quantify this error, let's actually perform multiple the experiment, as shown below:\n\n \n\n\nIn this image, we have counted 1,000,000 sheep (items) 10,000 different times.\nIn each run, we have given each item a 0.025% chance to flip our primary counter and have given each increment in our primary counter a weight of 4000 items.\nWe have plotted 10 of the 10,000 runs (chosen at random), and each upward tick of the lines represents one of the items winning a game of chance and adding 1 to the primary counter and thus adding 4000 to the approximate count.\nWe have also shaded the maximum and minimum approximate count for each true count of the 10,000 trials in gray, thereby highlighting the range of possible outputs.\nOn top of the plot, we have shown the distribution of all 10,000 runs for the approximate count at 10,000, 500,000, and 1,000,000 items.\nThere's a lot to unpack here, so let's start with the upward trending lines.\nHere, it seems like the approximate counts are roughly following the line of y=x (dotted black line), which would indicate simple counting (without any randomness or approximation).\nThis makes sense because in a perfect world, the approximate count would always be exactly equal to the true number of items being counted.\nUnfortunately, none of the lines shown here exactly follow y=x.\nIn fact, it would be impossible for any of the approximations to do so because we are always increasing the approximation in steps of 4000 while the true count increments by 1 with each new item.\nThat said, the average of all these counts together is a really good approximation for the true number of items.\nThis is where the 3 additional plots come in:\n\n \n\n\nEach of these is a histogram of the approximate count for all 10,000 runs at 10,000 (left), 500,000 (middle), and 1,000,000 (left) items.\nAll three (especially the approximation for 1,000,000) look Gaussian, and the peak of the Gaussian seems to be the correct count.\nIn fact, the expectation value for our approximate counting scheme will always be correct.\nIn practice, this means that we can approximate any count on a small number of bits by doing a large number of counting trials and averaging their results.\nThere is still a little catch that becomes more evident as we look at the approximation for 10,000 items.\nIn this case, even though the expectation value for the Gaussian distribution looks correct, it's kinda hard to tell exactly because there are only 8 (or so) possible values for each individual experiment.\nEssentially, we are trying to count to 10,000 in steps of 4,000.\nClearly the closest we can get on any individual run is either 8,000 or 12,000, as these are multiples of 4,000.\nSimply put: we cannot resolve 10,000 items with this method!\nDoes this mean that this counting method is less useful for a small number of items?\nIn a sense, yes.\nHere is a table for the true count, approximate count, and percent error for 10,000, 500,000, and 1,000,000 for the case where we do 10,000 counting experiments:\n\n\n\nTrue Count\nApproximate Count\nPercent Error\n\n\n\n\n10,000\n9,958.0\n0.42\n\n\n500,000\n499,813.2\n0.037\n\n\n1,000,000\n999,466.0\n0.053\n\n\n\nHere, it seems that the percent error is 10 times higher when we count 10,000 items; however,\nwith these numbers, I could imagine some people reading this are thinking that we are splitting hairs.\nA 0.42% error is still really good, right?\nRight.\nIt's definitely not bad, but this was with 10,000 counting experiments.\nHere a new table where we only did 10:\n\n\n\nTrue Count\nApproximate Count\nPercent Error\n\n\n\n\n10,000\n8,000.0\n20.0\n\n\n500,000\n483,200.0\n3.36\n\n\n1,000,000\n961,600.0\n3.84\n\n\n\nThis time, there is a 20% error when counting to 10,000.\nThat's unacceptably high!\nTo solve this problem, we need to find some way to for the value of each increment on the actual counter to be more meaningful for lower counts.\nThis is precisely the job for a logarithm, which is what we will be looking at in the next section.\nFor now, it's important to look at another anomaly: why are the percent errors for the 500,000 and 1,000,000 cases so close?\nI gotta be honest, I don't know the correct answer here, but I would guess that it has something to do with the fact that both 500,000 and 1,000,000 are multiples of 4000 so our counting scheme can resolve both of them with roughly equal precision.\nOn top of that, both values are significantly higher than 4,000 so the counting resolution does not have as significant of an impact on the measured count.\nSimply put, 4000 is a big step size when counting to 10,000, but a smaller one when counting to 500,000 or 1,000,000.\nAs an important note, each approximate count shown in the tables above was the expectation value for a Gaussian probability distribution of different counting experiments all providing a guess at what the count could be.\nBecause we are no longer counting with integer increments but instead with probability distributions, we now need to quantify our error with the tools of probability, namely standard deviations.\nIn the next section, we will tackle both issues brought up here:\n\nIn order to better approximate different scales of counting, it makes sense to use a logarithmic scale.\nBecause we are counting by using the expectation value of a Gaussian probability distribution from a set of counting experiments, it makes sense to quantify error with the tools we learned from probability and statistics.\n\nSo I guess we should hop to it!\nAdding a logarithm\nAt this stage, I feel it's important to use terminology that more closely matches Morris's original paper [2], so we will begin to talk about events, which are a general abstraction to the previous item / sheep analogy.\nWe will also introduce three different values:\n\nn: the number of events that have occurred.\nv: the number we have stored in our bitstring.\nn_v: the approximate number of events that have occurred.\n\nIt's important to stop here and think about what's actually going on.\nWe have a certain number of events (n) that have occurred and have stored that number on a binary register as v.\nTraditionally, the number stored on the binary register would be exactly equal to the number of events, but because we do not have enough space on the register, we end up settling for an approximation of the number of events, n_v.\nThis is precisely what we did in the previous example, where v = \\frac{n}{4000} and n_v = 4000*v.\nAs mentioned, using a constant scaling value (4000) for our approximate counting scheme means that the approximation is not ideal for a smaller number of events.\nFor this reason, it might be more appropriate to create a new method of storing the number of events by using a logarithmic scale, such that\n\nv = \\log_2(1+n),\n\nwhich would mean that the approximate count would be\n\nn_v = 2^v-1.\n\nIn this case, we are adding 1 to the argument of the logarithm for v because \\log_2(1) = 0 and we start counting at 1; therefore, we need some way to represent the value of 0.\nAlso, for this we can use any base logarithm (like e), but because we are dealing with bits, it makes sense to use base 2.\nWe'll talk about different bases next.\nTo be clear, here is a table of several values that could be stored in a bitstring along with their corresponding approximate counts:\n\n\n\nv(n)\nn_v\n\n\n\n\n00000000 = 0\n0\n\n\n00000001 = 1\n1\n\n\n00000010 = 2\n3\n\n\n00000100 = 4\n15\n\n\n00010000 = 16\n65535\n\n\n01000000 = 64\n1.85 \\times 10^{19}\n\n\n10000000 = 128\n3.40 \\times 10^{38}\n\n\n11111111 = 255\n5.79 \\times 10^{76}\n\n\n\nThis means that we can hold from 0 to 2^{255} - 1 \\approx 5.79 \\times 10^{76} with 8 bits using this new method.\nSo let's now think about what happens every time a new event occurs.\nTo do this, Morris calculated a new value:\n\n\\Delta = \\frac{1}{n_{v+1} - n_{v}}\n\nwhere n_{v+1} is the approximate count for the next possible value v stored in the register.\nIn this case, \\Delta will always be between 0 and 1, so we can consider it to be the probability of whether we should increment our stored count or not.\nFor example, if we have a stored value of 2 (v=2), then\n\n\\Delta = \\frac{1}{n_3 - n_2} = \\frac{1}{(2^3-1)-(2^2-1)} \\approx \\frac{1}{7-3} \\approx 0.25.\n\nThis indicates that there will be a 25% chance to increment v from 2 to 3.\nIn practice, this means that we need to create another random variable r and set our counter such that\n\n\\begin{align}\n\\text{if } & r \\Delta, \\qquad v = v.\n\\end{align}\n\nAgain, \\Delta is essentially the probability that we will increment our counter with each object, and as we count higher, the probability decreases exponentially.\n\n \n\n\nNote: the y-axis to this figure is in logscale, which is why it looks like a straight line.\nBefore leaving this section, it's important to note that the highest anyone can count with this method in base 2 using an 8-bit register is 5.79 \\times 10^{76}.\nThat's great!\nWay, way better than 255, but we can still go higher with a different base of logarithm.\nFor example, if we use e as our base, we can get up to e^{255}-1 = 5.56 \\times 10^{110}.\nIn addition, by choosing smaller bases, we can also find a more accurate approximate count for lower values.\nIn practice, we want to select a base that allows us to count to a value of the same order (or one order higher) than the number of events we are expected to have.\nIn the next section, we will consider how to generalize this logarithmic method to take arbitrary bases into account.\nA slightly more general logarithm\nLet's start by considering the differences between base 2 and base e.\nFor base e,\n\n\\begin{align}\nn_v &= e^v - 1 \\\\\nv &= \\log_e(1+n).\n\\end{align}\n\nIf we were to update our count and wanted to keep the value in the counter as accurate as possible, then the new value in the register with every new event would be\n\nv = \\log_e(1+e^v).\n\nThis is generally not an integer value, but v must be an integer value (unless we want to try and store floating-point values (which we definitely don't have space for)), so what do we do in this situation?\nWell, let's look at the very first event where we need to increment our count from 0 to 1.\nWith base e, there would only be a 58% chance of counting the first event (\\Delta = \\frac{1}{1.72-0} = 0.58), and if the event is counted, the value in the register would be \\approx 1.71 \\neq 1.\nAgain, the expectation value for a bunch of trials is correct, but we did not have this issue with base 2, because\n\nv = \\frac{\\log_e(n+1)}{\\log_e(2)} = 1\n\nwhen n=1.\nAs a reminder, the above formula is a way to convert any logarithm from a given base (in this case e) to another base (in this case 2).\nGoing one step further, we need to chose a specific base to a logarithm that will at least ensure that the first count is correct, and for this reason, Morris studied a specific solution:\n\n\\begin{align}\n v &= \\frac{\\log(1+n/a)}{\\log(1+1/a)}. \\\\\n n_v &= a\\left(\\left(1+\\frac{1}{a}\\right)^v-1\\right).\n\\end{align}\n\nHere, a is an effective tuning parameter and sets the maximum count allowed by the bitstring and the expected error.\nThe expression 1+1/a acts as a base for the logarithm and exponents and ensures that the first count of n=1 will also set the value v=1.\nAs an example, if the bitstring can be a maximum of 255 (for 8 bits) and we arbitrarily set\na=30, then the highest possible count with this approach will be \\approx 130,000, which was the number reported in Morris's paper.\nIf we perform a few counting experiments, we find that this formula more closely tracks smaller numbers than before (when we were not using the logarithm):\n\n \n\n\nNow, let's pause for a second and look back at the case where our counting resolution was a constant 4000:\n\n \n\n\nIt would seem that for higher counts, the previous method (with a constant counting resolution) is actually better!\nRemember that in the case of a constant counting resolution, the step size is really small for higher counts, so we get a higher resolution probability distribution for when we count 500,000 and 1,000,000 items.\nWith the logarithmic scale, this is not the case, as the counting resolution now changes with the count, itself.\nThis is also why all three probability distributions for the logarithmic scaling have a similar distance between each bar.\nIn fact, it is probably worthwhile to look at each case more specifically:\n\n\n\nConstant Counting Resolution\nLogarithmic Counting Resolution\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nIn the case where we count only to 10,000, we see a moderate increase in the resolution of the probability distribution, but in the 500,000 and 1,000,000 cases, we do not.\nIt's also important to notice that the logarithmic plots are a bit skewed to the left and are only Gaussian on logarithmic scales along x.\nOn the one hand, the logarithmic plots are nice in that they have the same relative error for all scales, but on the other hand, the error is relatively high.\nHow do we fix this?\nWell, by modifying the base of the logarithm with the variable a:\n\n \n\n\nHere, we show the differences in n_v for 25 \\leq a \\leq 35 when v=255.\nIt is important to twiddle a based on what the maximum count is expected for\n each experiment.\nAs an important note, the expected error estimate (variance) for each count will\n be\n\n\\sigma(n,a)^2 = \\frac{n(n-1)}{2a}.\n\nFinally, before ending the paper, Morris mentioned that it is possible to pre-compute all values \\Delta_j = (a/(a+1))^j for all j \\in [1,N] where N is the largest value possible integer with that bitstring (as an example, 255 for 8 bits).\nThis was probably more useful in 1978 than it is now, but it's still nice to keep in mind if you find yourself working on a machine with compute constrictions.\nVideo Explanation\nHere is a video describing the Approximate Counting Algorithm:\n\n\n\n\nExample Code\nFor this example, we have returned to the question asked above: how high can someone count on their fingers using the approximate counting algorithm?\nWe know from the formula that with a=30 and 10 bits, we should be able to count to 1.1\\times 10^{16}, but what happens when we perform the actual experiment?\nAs we do not have any objects to count, we will instead simulate the counting with a while loop that keeps going until out bitstring is 1023 (2^{10}).\nusing Test \n\n# This function takes \n# - v: value in register\n# - a: a scaling value for the logarithm based on Morris's paper\n# It returns n(v,a), the approximate count\nfunction n(v, a)\n a*((1+1/a)^v-1) \nend\n\n# This function takes\n# - v: value in register\n# - a: a scaling value for the logarithm based on Morris's paper\n# It returns a new value for v\nfunction increment(v, a)\n # delta is the probability of incrementing our counter\n delta = 1/(n(v+1, a)-n(v, a))\n\n if rand() \n#include \n#include \n#include \n#include \n#include \n\n// This function returns a pseudo-random number between 0 and 1\ndouble drand()\n{\n return (double)rand() / RAND_MAX;\n}\n\n// This function takes\n// - v: value in register\n// - a: a scaling value for the logarithm based on Morris's paper\n// It returns the approximate count\ndouble n(double v, double a)\n{\n return a * (pow(1 + 1 / a, v) - 1);\n}\n\n// This function takes\n// - v: value in register\n// - a: a scaling value for the logarithm based on Morris's paper\n// It returns a new value for v\ndouble increment(double v, double a)\n{\n // delta is the probability of incrementing our counter\n double delta = 1 / (n(v + 1, a) - n(v, a));\n\n if (drand() \n#include \n#include \n#include \n#include \n\n// Returns a pseudo-random number generator\nstd::default_random_engine& rng() {\n // Initialize static pseudo-random engine with non-deterministic random seed\n static std::default_random_engine randEngine(std::random_device{}());\n return randEngine;\n}\n\n// Returns a random double in [0, 1)\ndouble drand() {\n return std::uniform_real_distribution(0.0, 1.0)(rng());\n}\n\n// This function takes\n// - v: value in register\n// - a: a scaling value for the logarithm based on Morris's paper\n// It returns n(v,a), the approximate count\nauto n(double v, double a) { return a * (pow((1 + 1 / a), v) - 1); }\n\n// This function takes\n// - v: value in register\n// - a: a scaling value for the logarithm based on Morris's paper\n// It returns a new value for v\nauto increment(int v, double a) {\n // delta is the probability of incrementing our counter\n const auto delta = 1 / (n(v + 1, a) - n(v, a));\n return (drand() \nfrom random import random\n\n# This function takes\n# - v: value in register\n# - a: a scaling value for the logarithm based on Morris's paper\n# It returns n(v,a), the approximate_count\ndef n(v, a):\n return a*((1 + 1/a)**v - 1)\n\n# This function takes\n# - v: value in register\n# - a: a scaling value for the logarithm based on Morris's paper\n# It returns a new value for v\ndef increment(v, a):\n delta = 1/(n(v + 1, a) - n(v, a))\n if random() \n// This function takes\n// - v: value in register\n// - a: a scaling value for the logarithm based on Morris's paper\n// It returns n(v,a), the approximate count\nfn n(v: f64, a: f64) -> f64 {\n a * ((1_f64 + 1_f64 / a).powf(v) - 1_f64)\n}\n\n\n// This function takes\n// - v: value in register\n// - a: a scaling value for the logarithm based on Morris's paper\n// It returns a new value for v\nfn increment(v: f64, a: f64) -> f64 {\n // delta is the probability of incrementing our counter\n let delta = 1_f64 / (n(v + 1_f64, a) - n(v, a));\n\n if rand::random::() f64 {\n let mut v = 0_f64;\n\n for _ in 0..n_items {\n v = increment(v, a);\n }\n\n v\n}\n\n// This function takes\n// - n_trials: the number of counting trials\n// - n_items: the number of items to count to\n// - a: a scaling value for the logarithm based on Morris's paper\n// - threshold: the maximum percent error allowed\n// It returns a \"passed\" / \"failed\" test value\nfn test_approximate_count(n_trials: usize, n_items: usize, a: f64, threshold: f64) {\n let avg = std::iter::from_fn(|| Some(approximate_count(n_items, a)))\n .take(n_trials)\n .sum::() / n_trials as f64;\n\n let n_items_float = n_items as f64;\n\n if ((avg - n_items_float) / n_items_float) \nimport java.lang.Math;\nimport java.util.stream.DoubleStream;\n\npublic class ApproximateCounting {\n\n /*\n * This function taks\n * - v: value in register\n * - a: a scaling value for the logarithm based on Morris's paper\n * It returns the approximate count\n */\n static double n(double v, double a) {\n return a * (Math.pow(1 + 1 / a, v) - 1);\n }\n\n\n /*\n * This function takes\n * - v: value in register\n * - a: a scaling value for the logarithm based on Morris's paper\n * It returns the new value for v\n */\n static double increment(double v, double a) {\n double delta = 1 / (n(v + 1, a) - n(v, a));\n\n if (Math.random() approximateCount(nItems, a))\n .limit(nTrials)\n .average()\n .getAsDouble();\n\n if (Math.abs((avg - nItems) / nItems) \n\n\nBibliography\n1.Sanderson, G, How to count to 1000 on two hands, 2015.2.Morris, R, Counting large numbers of events in small registers, ACM New York, NY, USA, 1978.3.Flajolet, P, Approximate counting: a detailed analysis, Springer, 1985.4.Bhayani, A, Morris's Algorithm for Approximate Counting, 2020.5.Gundersen, G, Approximate Counting with Morris's Algorithm, 2019.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"Finger Counting\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Approximate trials\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Histograms\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Delta v v\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Approximate trials Logarithm\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Histograms 10,000\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Histograms exp 10,000\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Histograms 500,000\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Histograms exp 500,000\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Histograms 1,000,000\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Histograms exp 1,000,000\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"A from 25 to 35\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n"},"contents/metropolis/metropolis.html":{"url":"contents/metropolis/metropolis.html","title":"Metropolis","keywords":"","body":"The Metropolis Algorithm\nThe Monte Carlo Integration method uses random numbers to approximate the area of pretty much any shape we choose. \nThe Metropolis algorithm [1] is a slightly more advanced Monte Carlo method which uses random numbers to approximate a probability distribution:\n\nP(\\mathbf{x}) = \\frac{f(\\mathbf{x})}{\\displaystyle\\int_D f(\\mathbf{x})d\\mathbf{x}},\n\nwhere D is the domain of P(\\mathbf{x}), i.e., all possible values of the \\mathbf{x} for which P(\\mathbf{x}) is defined.\nf(\\mathbf{x}) is a function that is proportional to P(x), such as a statistical frequency distribution which counts the number of occurrences of each \\mathbf{x}.\nThe integral in the denominator is the normalization factor which ensures that the sum of all probabilities is unity, i.e.,\n\n\\int_D P(\\mathbf{x}) d\\mathbf{x} = 1.\n\nA one-dimensional example is the normal distribution, or Gaussian distribution, given by\n\nP(x) = \\frac{e^{-x^2}}{\\displaystyle\\int_{-\\infty}^{\\infty} e^{-x^2} dx} = \\frac{1}{\\sqrt{\\pi}} e^{-x^2}.\n\nIn practice, it's often easy for us to know f(x), but the integral in the denominator can be quite difficult to calculate, even numerically. \nThis is especially true when the coordinates (\\mathbf{x}) are multidimensional, and f(\\mathbf{x}) is an expensive calculation, as we shall see in the examples below.\nAn example application\nOne example of a complicated probability function arises when considering a physical system of N particles. \nThese could be atoms, molecules, or even star systems! \nFor such systems, we can usually describe the potential energy [2] of the system as a function of the coordinates of all particles, \\mathbf{x},\n\nE(\\mathbf{x}) = E(x_1, y_1, z_1, x_2, y_2, z_2, ... ,x_N, y_N, z_N),\n\nwhere x_i, y_i, z_i are the spatial coordinates of particle i. \nSo altogether there are 3N coordinates – making E(\\mathbf{x}) a 3N dimensional function, which can be a computationally intensive calculation on it's own. But it doesn't end there!\nThe physicist Ludwig Boltzmann [3] discovered that when such a system is in equilibrium at some temperature T, you can describe the probability density of the system for any set of coordinates \\mathbf{x} using, [4] \n\nP(\\mathbf{x}) = \\frac{\\displaystyle \\exp\\left[{\\displaystyle\\frac{-E(\\mathbf{x})}{T} } \\right]} {Q},\n\nwhere the numerator is called the Boltzmann factor, and Q is the normalization constant,\n\nQ = \\int_D \\exp\\left[{\\displaystyle\\frac{-E(\\mathbf{x})}{T} } \\right] d\\mathbf{x}.\n\nWe can see now that the probability density function is a difficult calculation, particularly because of Q. \nAlmost always, no analytical solution exists to the integral in Q, and the numerical integration is unfeasible. \nTo see that Q is unfeasible to calculate, imagine there are just 10 particles which all exist in a 1D world, restricted to a line segment.\n\n 1D particles\">\n\n\nLet's assume that the particles interact, meaning that the position of one particle affects that of another. \nThis could be the case, for example, if all the particles were charged, and so they would be repelling or attracting each other. \nThis means that the energy E(\\mathbf{x}) = E(x_1,...,x_{10}) of the system is a 10D function, and it would not be possible to simplify it any further due to the interactions. \nThus, the Boltzmann factor, \\exp\\left[-E(\\mathbf{x})/T\\right], is also a 10D function. To calculate Q, we would have to integrate the Boltzmann factor 10 times, one for each coordinate,\n\nQ = \\int_{x_1} \\dots \\int_{x_{10}} \\exp\\left[\\frac{-E(x_1,\\dots x_{10})}{T}\\right]\\ dx_1\\dots dx_{10}.\n\nIn most cases, there is no known analytical expression for the above integral, so it has to be done numerically.\nTo do so, imagine that we divide the 1D line segment into only 50 different intervals, allowing each particle to take on 50 different positions. \nThis is equivalent to dividing the length of a football field into intervals of about 2 meters – not a resolution you'd wanna watch a game in! \nEven with such poor resolution, the number of different combinations of positions is 10^{50} – a colossal number indeed. \nTo see how large this number is, imagine that a single computation of E(\\mathbf{x}) took only 1 nanosecond on a single processor, which is much faster than most energy calculations for physical systems in practice.\n With that speed, it would require 10^{41} seconds on a single processor to calculate Q – which means that even with all the processors in the world running in parallel (there could be billions or trillions of them), calculating Q would still take longer than the age of the universe – by many orders of magnitude!\nWhat's really powerful about the Metropolis approach is that you don't need to know the probability function itself.\nInstead, you just need a function which is proportional to it. \nWhat this means for the Boltzmann distribution is that you only need to know the term,\n\nf(\\mathbf{x}) = \\exp\\left[{\\displaystyle\\frac{-E(\\mathbf{x})}{T} } \\right].\n\nThe Metropolis algorithm can bypass the calculation of Q altogether and use f(x) to generate a distribution of x which follows the probability density P(x). \nIn other words, it can sample values of x in such away that the probability of sampling x will follow the actual distribution P(x). \nThus, if Metropolis was used to sample from x, the number of occurrences of x would be proportional to P(x).\nNumerical normalization can then be done by using the total number of samples instead of performing an integration. \nThis fact dramatically reduces the number of calculations needed to approximate the probability distribution.\nFinally, the Metropolis algorithm can be modified or implemented in other methods, and forms the basis of many advanced sampling algorithms. \nThe most popular is probably the Metropolis-Hastings algorithm [5] which is fundamentally the same. \nSome other algorithms that use this method are Metropolis-adjusted Langevin algorithm [6], and Hamiltonian Monte Carlo [7], to name a few. \nThey are often used for physical systems that follow a Boltzmann distribution.\nA Random Walk in One Dimension\nIn the rest of this chapter, we will look at 1D examples to understand the Metropolis algorithm. \nAlthough the algorithm is not particularly efficient in just one dimension, it is much easier to understand in one dimension than in multiple dimensions. \nThe Metropolis algorithm is very similar to a random walk, so let's first see how we can get a distribution from a random walk.\n\n\n \nYour browser does not support the video tag.\n\n\n\nThe dot in the figure above is a \"walker\", whose initial position is x=0. \nThe step size, g, is a random number in the interval (-1, 1). \nTo get the next position of the walker, we simply generate g and add it to the current position. \nTo get a distribution of x from this walk, we can divide the domain into discrete locations or \"bins\" and count how often the walker visits each bin. \nEach time it visits a bin, the frequency for that bin goes up by one. \nOver many iterations, we get a frequency distribution of x. \nA Random Walk With an Acceptance Criterion\nThe Metropolis algorithm works in a similar way to the random walk, but differs crucially in one way – after choosing a random step for the walker, a decision is made about whether to accept or reject the step based on the function f(x). \nTo understand how this works, let's call x_t the position before the step, and x' the position after it. \nWe then define the probability of accepting the step to be\n\nA = \\min \\left(\\frac{f(x')}{f(x_t)}, 1\\right).\n\nThe \\min function above implies that A=1 if f(x') \\gt f(x_t), which means that the move will always be accepted if it is toward a higher probability position. \nOtherwise, it will be accepted with a probability of f(x') / f(x_t). \nIf we create a histogram of this walk for some arbitrary target function P(x), we can see from the figure below that the frequency starts to look very much like it after many iterations! \n\n\n \nYour browser does not support the video tag.\n\n\n\nAlthough convergence occurs eventually, not all parts of the distribution achieve convergence quickly. \nNote from the animation above, that the walker very quickly replicates the distribution of the two peaks on the left, but takes quite a while to even reach the third peak to the right. \nThis is because there is a long low probability region between the third peak and second peak that acts as a \"barrier.\" \nThis may not necessarily be a bad thing – sometimes one might want to estimate how long something takes to transition from one state to another, and often these peaks represent such 'states'. \nSo averaging over many metropolis runs may give some estimate of these transition times. \nIf global sampling is the goal, the process of exploration could be sped up by choosing larger step sizes for the walker, for example by choosing step size g from an interval like (-3,3) instead of (-1,1). \nThe Algorithm for a One Dimensional Example\nNow let's dive into the actual algorithm with some example code!\nThe Initial Setup\nLet our target distribution be\n\nP(x) = \\frac{f(x)}{\\int_{-10}^{10} f(x)},\n\nwhere f(x) is the same function we have shown above and is given by\n\nf(x) = 10e^{-4(x+4)^2} + 3e^{-0.2(x+1)^2} + e^{-2(x-5)^2}.\n\nThe code for defining this function is given below.\ndef f(x, normalize=False):\n '''\n Function proportional to target distribution, a sum of Gaussians.\n For testing, set normalize to True, to get target distribution exactly.\n '''\n # Gaussian heights, width parameters, and mean positions respectively:\n a = np.array([10., 3., 1.]).reshape(3, 1)\n b = np.array([ 4., 0.2, 2.]).reshape(3, 1)\n xs = np.array([-4., -1., 5.]).reshape(3, 1)\n\n if normalize:\n norm = (np.sqrt(np.pi) * (a / np.sqrt(b))).sum()\n a /= norm\n\n return (a * np.exp(-b * (x - xs)**2)).sum(axis=0)\n\n\n\nSince this is an easy function to integrate, and hence get our target distribution P(x) directly, we can use it to verify the Metropolis algorithm. \nThe plot of P(x) in the figure below shows three different peaks of varying width and height, with some overlap as well.\n\n Plot of P(x)\" style=\"width:80%\">\n\n\nNext, we define our walker's symmetric step generating function. \nAs in the random walk example, we will use a random real number between -1 and +1 as the step size. \ndef g():\n '''Random step vector.'''\n return np.random.uniform(-1,1)\n\n\n\nHowever, g can be any function symmetric about 0 for the above algorithm to work. \nFor example, it can be a number chosen randomly from a discrete list, such as [ -3, -1, -1, +1, +1, +3]. \nIt can also be a number chosen from a symmetric continuous distribution, like the Gaussian, e^{-x^2}. \nIn higher dimensions, the function should be spherically symmetric, such as a multidimensional Gaussian function, e^{-(x^2 +y^2 + ...)}. \nWhatever function you choose, there are at least a couple of things to note:\n\nIf the function g is discrete, you will only sample discrete values. \nFor example, if g returns only -1 or +1, and nothing in between, you will sample only integer steps away from the initial x_0. \nThe average step size really matters! \nA small step-size means the walker will carefully sample nearby regions more, but will walk more slowly, so might not be good at exploring far and wide. \nOn the other hand, a walker with a large step size may not sample nearby regions accurately – and actually has a higher chance of being rejected if the walker is already in a high probability region, since the acceptance ratio is more drastic for large steps. \nThe effect of step-size on the walker's efficiency is far from obvious! \n\nThe question of how to choose an optimal g is a research area on its own, and depends largely on what the goal of the sampling is.\nSome techniques even use an \"adaptive\" method where g is \"trained\" on-the-fly using a learning algorithm! \nSome of these methods and others are discussed in Ref. [8] and Ref. [9]. \nIn a lot of cases, people just use trial and error, as the algorithm is not too difficult to implement.\nAfter choosing g, we are almost ready to iterate. \nWe just need to choose the domain of x, and an initial point for x_0 (x_t at t = 0) chosen randomly from the domain of x.\nxmin, xmax = -10, 10\nx0 = np.random.uniform(xmin, xmax)\n\n\n\nHow to Iterate\n\nGenerate new proposed position x' = x_t + g.\nCalculate the acceptance probability, \n\nA = \\min\\left(1, \\frac{f(x')}{f(x_t)}\\right).\n\nAccept proposal, x' with probability A. If your programming language doesn't have a built-in method for this,\nGenerate a random number u between 0 and 1.\nIf u \\leq A , then accept move, and set new position, x_{t+1} = x' .\nOtherwise, reject move, and set new position to current position, x_{t+1} = x_t .\n\n\nIncrement t \\rightarrow t + 1 and repeat from step 1.\n\nThe code for steps 1 to 3 is:\ndef metropolis_iterate(x0, num_steps):\n '''Iterate metropolis algorithm for num_steps using iniital position x_0'''\n\n for n in range(num_steps):\n if n == 0:\n x = x0\n else:\n x = metropolis_step(x)\n yield x\n\n\n\nThe following plot shows the result of running the algorithm for different numbers of iterations (N), with the same initial position. \nThe histograms are normalized so that they integrate to 1. \nWe can see the convergence toward P(x) as we increase N.\n\n multiple histograms\" style=\"width:80%\">\n\n\n\nExample Code\nThe following code puts everything together, and runs the Metropolis algorithm for a number of steps given by num_steps. \nAll the positions visited by the algorithm are then written to a file, which can be later read and fed into a histogram or other density calculating scheme. \nThe code also incorporates a few tests of the algorithm using the test_metropolis_iterate method. \nThis test will create a normalized density histogram from the generated data, and compare it to P(x) using the Root Mean Square Deviations metric [10].\nimport numpy as np\n\n\ndef f(x, normalize=False):\n '''\n Function proportional to target distribution, a sum of Gaussians.\n For testing, set normalize to True, to get target distribution exactly.\n '''\n # Gaussian heights, width parameters, and mean positions respectively:\n a = np.array([10., 3., 1.]).reshape(3, 1)\n b = np.array([ 4., 0.2, 2.]).reshape(3, 1)\n xs = np.array([-4., -1., 5.]).reshape(3, 1)\n\n if normalize:\n norm = (np.sqrt(np.pi) * (a / np.sqrt(b))).sum()\n a /= norm\n\n return (a * np.exp(-b * (x - xs)**2)).sum(axis=0)\n\ndef g():\n '''Random step vector.'''\n return np.random.uniform(-1,1)\n\ndef metropolis_step(x, f=f, g=g):\n '''Perform one full iteration and return new position.'''\n\n x_proposed = x + g()\n a = min(1, (f(x_proposed) / f(x)).item())\n\n x_new = np.random.choice([x_proposed, x], p=[a, 1-a])\n\n return x_new\n\ndef metropolis_iterate(x0, num_steps):\n '''Iterate metropolis algorithm for num_steps using iniital position x_0'''\n\n for n in range(num_steps):\n if n == 0:\n x = x0\n else:\n x = metropolis_step(x)\n yield x\n\n\ndef test_metropolis_iterate(num_steps, xmin, xmax, x0):\n '''\n Calculate error in normalized density histogram of data \n generated by metropolis_iterate() by using \n normalized-root-mean-square-deviation metric. \n '''\n\n bin_width = 0.25\n bins = np.arange(xmin, xmax + bin_width/2, bin_width)\n centers = np.arange(xmin + bin_width/2, xmax, bin_width)\n\n true_values = f(centers, normalize=True)\n mean_value = np.mean(true_values - min(true_values))\n\n x_dat = list(metropolis_iterate(x0, num_steps))\n heights, _ = np.histogram(x_dat, bins=bins, density=True)\n\n nmsd = np.average((heights - true_values)**2 / mean_value)\n nrmsd = np.sqrt(nmsd)\n\n return nrmsd\n\n\n\nif __name__ == \"__main__\":\n xmin, xmax = -10, 10\n x0 = np.random.uniform(xmin, xmax)\n\n num_steps = 50_000\n\n x_dat = list(metropolis_iterate(x0, 50_000))\n\n # Write data to file\n output_string = \"\\n\".join(str(x) for x in x_dat)\n\n with open(\"output.dat\", \"w\") as out:\n out.write(output_string)\n out.write(\"\\n\")\n\n\n # Testing\n print(f\"Testing with x0 = {x0:5.2f}\")\n print(f\"{'num_steps':>10s} {'NRMSD':10s}\")\n for num_steps in (500, 5_000, 50_000):\n nrmsd = test_metropolis_iterate(num_steps, xmin, xmax, x0)\n print(f\"{num_steps:10d} {nrmsd:5.1%}\")\n\n\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nBibliography\n1.Metropolis,Nicholas et al., Equation of State Calculations by Fast Computing Machines, 1953.2.Wikipedia: Potential Energy, 2021.3.Wikipedia: Ludwig Boltzmann, 2021.4.Wikipedia: Boltzmann distribution, 2021.5.Hastings, W. K., Monte Carlo sampling methods using Markov chains and their applications, 1970.6.Wikipedia: Metropolis-adjusted Langevin Algorithm, 2021.7.Wikipedia: Hamiltonian Monte Carlo, 2021.8.Rosenthal, Jeffrey S and others, Optimal proposal distributions and adaptive MCMC, Chapman & Hall/CRC Boca Raton, FL, 2011.9.Gareth O. Roberts and Jeffrey S. Rosenthal, Optimal scaling for various Metropolis-Hastings algorithms, Institute of Mathematical Statistics, 2001.10.Wikipedia: Root Mean Square Deviation, 2021.\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nImages/Graphics\n\nThe animation \"Animated Random Walk\" was created by K. Shudipto Amin and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nThe animation \"Animated Metropolis\" was created by K. Shudipto Amin and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nThe image \"Plot of P(x)\" was created by K. Shudipto Amin and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nThe image \"Multiple Histograms\" was created by K. Shudipto Amin and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n\nText\nThe text of this chapter was written by K. Shudipto Amin and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/probability_distributions/distributions.html":{"url":"contents/probability_distributions/distributions.html","title":"Probability Distributions","keywords":"","body":"What's a probability distribution?\nProbability distributions are mathematical functions that give the probabilities of a range or set of outcomes. \nThese outcomes can be the result of an experiment or procedure, such as tossing a coin or rolling dice. \nThey can also be the result of a physical measurement, such as measuring the temperature of an object, counting how many electrons are spin up, etc.\nBroadly speaking, we can classify probability distributions into two categories - discrete probability distributions and continuous probability distributions.\nDiscrete Probability Distributions\nIt's intuitive for us to understand what a discrete probability distribution is. \nFor example, we understand the outcomes of a coin toss very well, and also that of a dice roll. \nFor a single coin toss, we know that the probability of getting heads (H) is half, or P(H) = \\frac{1}{2}. \nSimilarly, the probability of getting tails (T) is P(T) = \\frac{1}{2}. \nFormally, we can write the probability distribution for such a coin toss as,\n\nP(n) = \\begin{matrix}\n \\displaystyle \\frac 1 2 &;& n \\in \\left\\{H,T\\right\\}. \n \\end{matrix}\n\nHere, n denotes the outcome, and we used the \"set notation\", n \\in\\left\\{H,T\\right\\}, which means \"n belongs to a set containing H and T\". \nFrom the above equation, we can also assume that any other outcome for n (such as landing on an edge) is incredibly unlikely, impossible, or simply \"not allowed\" (for example, just toss again if it does land on its edge!).\nFor a probability distribution, it's important to take note of the set of possibilities, or the domain of the distribution. \nHere, \\left\\{H,T\\right\\} is the domain of P(n), telling us that n can only be either H or T.\nIf we use a different system, the outcome n could mean other things.\nFor example, it could be a number like the outcome of a die roll which has the probability distribution,\n\nP(n) = \\begin{matrix}\n \\displaystyle\\frac 1 6 &;& n \\in [\\![1,6]\\!] \n \\end{matrix}.\n\nThis is saying that the probability of n being a whole number between 1 and 6 is 1/6, and we assume that the probability of getting any other n is 0. \nThis is a discrete probability function because n is an integer, and thus only takes discrete values. \nBoth of the above examples are rather boring, because the value of P(n) is the same for all n. \nAn example of a discrete probability function where the probability actually depends on n, is when n is the sum of numbers on a roll of two dice. \nIn this case, P(n) is different for each n as some possibilities like n=2 can happen in only one possible way (by getting a 1 on both dice), whereas n=4 can happen in 3 ways (1 and 3; or 2 and 2; or 3 and 1). \nThe example of rolling two dice is a great case study for how we can construct a probability distribution, since the probability varies and it is not immediately obvious how it varies. \nSo let's go ahead and construct it! \nLet's first define the domain of our target P(n). \nWe know that the lowest sum of two dice is 2 (a 1 on both dice), so n \\geq 2 for sure. Similarly, the maximum is the sum of two sixes, or 12, so n \\leq 12 also. \nSo now we know the domain of possibilities, i.e., n \\in [\\![2,12]\\!]. \nNext, we take a very common approach - for each outcome n, we count up the number of different ways it can occur. \nLet's call this number the frequency of n, f(n). \nWe already mentioned that there is only one way to get n=2, by getting a pair of 1s. \nBy our definition of the function f, this means that f(2)=1. \nFor n=3, we see that there are two possible ways of getting this outcome: the first die shows a 1 and the second a 2, or the first die shows a 2 and the second a 1. \nThus, f(3)=2. \nIf you continue doing this for all n, you may see a pattern (homework for the reader!). \nOnce you have all the f(n), we can visualize it by plotting f(n) vs n, as shown below.\n\n Die Roll\" style=\"width:80%\"/>\n\n\nWe can see from the plot that the most common outcome for the sum of two dice is a n=7, and the further away from n=7 you get, the less likely the outcome. \nGood to know, for a prospective gambler!\nNormalization\nThe f(n) plotted above is technically NOT the probability P(n) – because we know that the sum of all probabilities should be 1, which clearly isn't the case for f(n). \nBut we can get the probability by dividing f(n) by the total number of possibilities, N. \nFor two dice, that is N = 6 \\times 6 = 36, but we could also express it as the sum of all frequencies,\n\nN = \\sum_n f(n),\n\nwhich would also equal to 36 in this case. \nSo, by dividing f(n) by \\sum_n f(n) we get our target probability distribution, P(n). \nThis process is called normalization and is crucial for determining almost any probability distribution. \nSo in general, if we have the function f(n), we can get the probability as\n\nP(n) = \\frac{f(n)}{\\displaystyle\\sum_{n} f(n)}.\n\nNote that f(n) does not necessarily have to be the frequency of n – it could be any function which is proportional to P(n), and the above definition of P(n) would still hold. \nIt's easy to check that the sum is now equal to 1, since\n\n\\sum_n P(n) = \\frac{\\displaystyle\\sum_{n}f(n)}{\\displaystyle\\sum_{n} f(n)} = 1.\n\nOnce we have the probability function P(n), we can calculate all sorts of probabilites. \nFor example, let's say we want to find the probability that n will be between two integers a and b, inclusively (also including a and b). \nFor brevity, we will use the notation \\mathbb{P}(a \\leq n \\leq b) to denote this probability. \nAnd to calculate it, we simply have to sum up all the probabilities for each value of n in that range, i.e.,\n\n\\mathbb{P}(a \\leq n \\leq b) = \\sum_{n=a}^{b} P(n).\n\nProbability Density Functions\nWhat if instead of a discrete variable n, we had a continuous variable x, like temperature or weight? \nIn that case, it doesn't make sense to ask what the probability is of x being exactly a particular number – there are infinite possible real numbers, after all, so the probability of x being exactly any one of them is essentially zero! \nBut it does make sense to ask what the probability is that x will be between a certain range of values. \nFor example, one might say that there is 50\\% chance that the temperature tomorrow at noon will be between 5 and 15, or 5\\% chance that it will be between 16 and 16.5. \nBut how do we put all that information, for every possible range, in a single function? \nThe answer is to use a probability density function. \n What does that mean? \nWell, suppose x is a continous quantity, and we have a probability density function, P(x) which looks like\n\n probability density\" style=\"width:100%\"/>\n\n\nNow, if we are interested in the probability of the range of values that lie between x_0 and x_0 + dx, all we have to do is calculate the area of the green sliver above. \nThis is the defining feature of a probability density function: \n the probability of a range of values is the area of the region under the probability density curve which is within that range. \nSo if dx is infinitesimally small, then the area of the green sliver becomes P(x)dx, and hence,\n\n\\mathbb{P}(x_0 \\leq x \\leq x_0 + dx) = P(x)dx.\n\nSo strictly speaking, P(x) itself is NOT a probability, but rather the probability is the quantity P(x)dx, or any area under the curve. \nThat is why we call P(x) the probability density at x, while the actual probability is only defined for ranges of x. \nThus, to obtain the probability of x lying within a range, we simply integrate P(x) between that range, i.e.,\n\n\\mathbb{P}(a \\leq x \\leq b ) = \\int_a^b P(x)dx.\n\nThis is analagous to finding the probability of a range of discrete values from the previous section:\n\n\\mathbb{P}(a \\leq n \\leq b) = \\sum_{n=a}^{b} P(n).\n\nThe fact that all probabilities must sum to 1 translates to\n\n\\int_D P(x)dx = 1.\n\nwhere D denotes the domain of P(x), i.e., the entire range of possible values of x for which P(x) is defined.\nNormalization of a Density Function\nJust like in the discrete case, we often first calculate some density or frequency function f(x), which is NOT P(x), but proportional to it. \nWe can get the probability density function by normalizing it in a similar way, except that we integrate instead of sum:\n\nP(\\mathbf{x}) = \\frac{f(\\mathbf{x})}{\\int_D f(\\mathbf{x})d\\mathbf{x}}.\n\nFor example, consider the following Gaussian function (popularly used in normal distributions), \n\nf(x) = e^{-x^2},\n\nwhich is defined for all real numbers x. \nWe first integrate it (or do a quick google search, as it is rather tricky) to get\n\nN = \\int_{-\\infty}^{\\infty} e^{-x^2} dx = \\sqrt{\\pi}.\n\nNow we have a Gaussian probability distribution,\n\nP(x) = \\frac{1}{N} e^{-x^2} = \\frac{1}{\\sqrt{\\pi}} e^{-x^2}.\n\nIn general, normalization can allow us to create a probability distribution out of almost any function f(\\mathbf{x}). \nThere are really only two rules that f(\\mathbf{x}) must satisfy to be a candidate for a probability density distribution:\n\nThe integral of f(\\mathbf{x}) over any subset of D (denoted by S) has to be non-negative (it can be zero):\n\n\\int_{S}f(\\mathbf{x})d\\mathbf{x} \\geq 0.\n \nThe following integral must be finite:\n\n\\int_{D} f(\\mathbf{x})d\\mathbf{x}.\n \n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nImages/Graphics\n\nThe image \"Frequency distribution of a double die roll\" was created by K. Shudipto Amin and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nThe image \"Probability Density\" was created by K. Shudipto Amin and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n\nText\nThe text of this chapter was written by K. Shudipto Amin and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"}}} \ No newline at end of file +{"index":{"version":"0.5.12","fields":[{"name":"title","boost":10},{"name":"keywords","boost":15},{"name":"body","boost":1}],"ref":"url","documentStore":{"store":{"./":["(found","(leiosos):","(potentially)","/","4.0","adventur","algorithm","allow","ambiti","anyth","arcan","archiv","archive.org/","archivists/algorithm","associ","attribut","available.","becom","book","chang","channel","chapter","chapter.","code","collabor","common","commun","community.","content","contribut","contribute,","cover","creat","creativ","differ","discord","effort","else,","end","enjoy","entry.","essenti","exampl","favorit","feel","few","find","focu","fortunately,","free","fun","future!","future.","github","go","goal","graphic","great","grow","guid","hand","help","here","hopefulli","hopefully,","https://discord.gg/pr2e9s6","https://github.com/algorithm","https://www.algorithm","https://www.twitch.tv/leioslab","https://www.youtube.com/user/leioso","implement","import","incred","individu","instead","instruct","intern","jame","know","language,","languages.","learn","licens","license.md).","links:","little,","livestream:","lot","materi","mean","mit","necessary.","need","never","note","noth","obvious","onlin","out","pleas","practic","probabl","process","programm","project","projects.","pull","purpose.","read","regard","repository:","request.","resourc","said,","schloss.","see","server:","sharealik","site:","size,","someth","specifi","specified,","state","still","submit","text","thank","there'","there,","top","tri","twitch","ui","under","unfortunately,","us","veri","via","want","we'll","website:","wiki","work","written","wrong","youtub"],"contents/introduction/introduction.html":["\"languag","\"textbook\"","(#560),","(and","(found","(or","/","4.0","5","5:00am","abil","addition,","advanc","adventur","age,","agnostic.\"","ago,","ahem","algorithm","algorithm;","algorithms.","all,","along","anyon","appendix.","arcan","archiv","around","arxiv,","attribut","author","author.","avail","away","back","background","basic","be,","becom","befor","before.","begin","between","big)","bit","blissfulli","blog","book","book,","book.","both","brows","bulk","call","can.","case","challeng","chanc","chapter","chapter:","chip","choic","class.","classic","clear,","code","collect","combin","comment","common","commun","community,","complet","comprehens","comput","concerns,","conglomer","content","cool","counter","creat","creativ","day,","deeper","degre","delv","develop","differently,","discoveri","doubt","each","echo","effort","end","end,","enjoy","enjoy.","entir","era","everyone'","everything,","exampl","example,","example.","excit","express","extens","fact,","fantast","favorit","feel","few","fill","final","find","fingertips,","first","flexibl","focus","follow","forward.","found","free","freeli","fun","fun.","gener","genuin","github","graphic","great","greatest","guess","guid","hard","harsh","heavili","hero","hesit","high","hobbi","hobbies:","honest","hope","hour","however,","human","idea","ignor","implement","improv","inclined,","incred","initi","interest","intern","introduc","introduct","intuitive,","is)","it!","it'","jame","journey.","jr.","keep","know.","knowledg","lab","lack","languag","latest","learn","learning!","learning.","lecture.","lectures,","left?","licens","license.","license.md).","line","littl","live","livecod","look","lose","lot.","love","main","manag","mani","master","material;","mathematics.","matter","mayb","mean","meaning","mention","mentioned,","mind,","mine.","mit","modern","modifi","more","morsel","motiv","move","much","myself","natur","nearli","never","nice","none","note","notebook","noth","now","now,","now.","nowaday","offer","on","one,","online,","outsid","overwhelm","pages.","paper","part,","pass","past","peopl","perfectli","person","phd","physic","physics.","piec","place","pleas","please.","pleasur","point","poor","pore","possibl","post","posts,","power","prefer","problem","professor","program","programmers.","project","prospect!","provid","pseudocod","public.","pull","push","puzzl","quantum","question","quickly,","read","reader.","reality.","realli","really,","reason,","redefin","request","research","right","right.","rigor","schloss","school","scienc","science,","science.","scientist.","see","see,","seem","shame.","sharealik","show","signific","significantly,","slowli","small","solve;","someth","sometim","sorts.","sourc","spend","spent","stage","start","still","stori","storytel","straddl","stream","streaming.","studi","subject","submit","sum","suppos","sure,","systems;","tackl","teacher","tend","tests,","text","text,","text.","that'","that.","theme,","there'","there.","think","this,","those","though","through","throughout","throw","time","time.","train","twitch","two","type","unawar","under","understand","understood!","uniqu","up","us","version","villain","wait","want","way","ways,","well","well,","well.","what'","wish","without","work","work.","world","write","writing,","written","year","years,","you!","you,","younger,","youtube,"],"contents/how_to_contribute/how_to_contribute.html":["\"","%}","(#560),","(and","(found","(where","1","17","17,","4.0","80",">>","[import:1","abil","accept","add","addition,","algorithm","algorithm,","algorithms.","allow","anoth","anyon","api","api,","api.","archiv","archive!","archive.","archive:","around","ask","associ","attribut","basic","be","befor","between","book,","browser","build","c++,","capit","certain","chapter","chapter:","check","choice.","clean","cleanli","clutter,","code","code,","code/","codeblock","columns,","common","commun","community.","consid","consist","consult","contribut","contribute,","contributors.md","contributors.md.","contributors.md:","control,","cpp","creativ","current","currently,","depend","detail","details.","develop","differ","directori","directory.","discord","discussion,","display","each","echo","effort","end","endmethod","especi","etc.","exampl","example,","extens","faq","far.","feel","file","flip","follow","found","free","future.","git","gitbook","go","graphic","grows.","guid","guide,","guide.","guidelin","haskell,","have","help","here","however,","hs","https://discord.gg/pb976sy.","i'll","import","includ","initi","instal","intern","is).","jame","join","julia","keep","lang","lang:\"julia\"](code/julia/conv.jl)","lang=\"jl\"","languag","language'","language.","languages.","learn","level","licens","license.","license.md).","license.md;","licensing:","line","list","local","machine.","main","make","markdown","members.","method","mit","modifi","more","name","name\"","near","need","new","node","noncommerci","none","note","now,","npm","on","ongo","out","page","part","part,","pleas","plugin","project","provid","pull","readabl","readme.md","rememb","remov","request","requir","review","run","sampl","schemes,","schloss","seri","serv","server","server:","sharealik","snippet","so),","specif","standard","start","statement","style","style:","submission,","submissions;","submit","such,","support","sure","teach","text","thank","theme","this,","those","titl","together:","tri","troubl","trust","two","under","understand","understandable.","updat","updating!","url","us","user","variabl","version","video","view","visual","want","whatev","work","written","written.","yourself","{%"],"contents/code_reviews/code_reviewers.html":["@amara","@amaras,@peanutbutterwarrior","@leio","@ntindl","@ntindle,","@ntindle,@shadowmitia","@ntindle,@shadowmitia,@amaras,@peanutbutterwarrior","@shadowmitia","@shadowmitia,@peanutbutterwarrior","action","add","asm","bash","below:","c","c#","c++","change,","chapter","clojur","coconut","code","comfort","contain","crystal","d","dart","dev","docker","elm","emojicod","factor","featur","fortran","github","gnuplot","go","haskel","honkit","java","javascript","julia","kotlin","labview","languag","language,","lisp","list","lolcod","lua","matlab","nim","ocaml","php","piet","pleas","powershel","python","r","racket","review","rubi","rust","scala","scheme","scon","scratch","smalltask","swift","tabl","toolchain","typescript","v","viml","whitespac","x64","yourself"],"contents/data_structures/data_structures.html":["(#560),","(found","4.0","ad","algorithm","algorithms.","archive,","attribut","block","book","build","chapter","chapter:","code","common","creativ","data","exampl","follow","fundament","graphic","initi","intern","jame","licens","license.","license.md).","mit","modifi","more","none","pull","request","schloss","section.","sharealik","structur","structures,","text","thu","under","written"],"contents/stacks_and_queues/stacks_and_queues.html":["!=","\"__main__\":","\"call","\"michael","#!/usr/bin/env","#includ","&&","'dequeue'","'enqueue'","'front'","'pop'","'push'","'size'","'top'","(#560),","(count","(fifo),","(found","(front","(front_pointer.get()","(intermediat","(lifo),","(pop())","(push())","(rear","(top","(top())","(top_pointer.get()","*","*/","+","...","/*","/**","//","0","0)","0;","1)","1);","1;","1]","1];","2","4","4.0","5","6",":","=","==",">",">next",">next);",">next;",">value;","[]","[];","[value][next]","__author__","__init__(self)","__len__(self)","__name__","__str__(self)","`dequeue`","`enqueue`","`front`","`pop`","`push`","`size`","`top`","access","act","ad","add","address","algorithm","allow","args)","array","arraylist<>();","assert(count","attend","attent","attribut","auto","basic","between","biggest","book","book,","books,","bool","both","camp\"","chapter","chapter:","ciccotosto","class","code","coin","common","comput","console.log(numberqueue.dequeue());","console.log(numberqueue.front());","console.log(numberqueue.size());","console.log(numberstack.pop());","console.log(numberstack.size());","console.log(numberstack.top());","const","const&","contrast","count","count(0ull)","count:","count;","creativ","current","data","def","depend","dequeu","dequeue(&mut","dequeue()","dequeue():","dequeue();","dequeue(self)","detail","differ","element","element)","element);","element:","elements,","empti","empty()","end","enqueue(&mut","enqueue(const","enqueue(data:","enqueue(self,","enqueue(t","exactli","exampl","example,","examplequeue()","examplequeue();","examplestack()","examplestack();","final","first","fn","follow","front","front(&self)","front()","front():","front();","front(self)","front_point","front_pointer.reset();","front_pointer:","front_pointer;","frontel","function","gener","give","graphic","groceri","held","here","hold","i32queu","i32queue.dequeue().unwrap());","i32queue.enqueue(4);","i32queue.enqueue(5);","i32queue.enqueue(6);","i32queue.front().unwrap());","i32queue.size());","i32stack.pop().unwrap());","i32stack.push(4);","i32stack.push(5);","i32stack.push(6);","i32stack.size());","i32stack.top().unwrap());","i32stack:","imagin","impl","implement","import","in,","initi","instead","int","int:","int_queue.enqueue(4)","int_queue.enqueue(5)","int_queue.enqueue(9)","int_queue:","int_stack.push(4)","int_stack.push(5)","int_stack.push(9)","int_stack:","interfac","intern","intqueu","intqueue.dequeue();","intqueue.enqueue(4);","intqueue.enqueue(5);","intqueue.enqueue(9);","intqueue.front();","intqueue;","intstack","intstack.pop();","intstack.push(4);","intstack.push(5);","intstack.push(9);","intstack.top();","intstack;","iqueu","istack","it'","item:","jame","java.util.arraylist;","java.util.list;","keep","know","languag","last","left","len(self)","len(self.__list)","length","licens","license.","license.md).","life.","line","link","list","list()","list:","list;","list[t]","look","main()","main(string[]","mean","mit","modifi","multipl","mut","mutabl","my::queu","my::stack","namespac","new","new()","new_nod","new_node;","next:","next;","node","node(const","node)","nodes)","none","none:","notat","note","now","nullptr)","number","number;","numberqueu","numberqueue.enqueue(4);","numberqueue.enqueue(5);","numberqueue.enqueue(9);","numberstack","numberstack.push(4);","numberstack.push(5);","numberstack.push(9);","onc","onto","option","order","out","out.","ownership","part,","people.","person","point","pop","pop(&mut","pop()","pop():","pop();","pop(self)","present","print(int_queue.dequeue())","print(int_queue.front())","print(int_stack.pop())","print(int_stack.top())","print(len(int_queue))","print(len(int_stack))","println!(\"{:?}\",","privat","private:","public","public:","pull","push","push(&mut","push(const","push(data:","push(self,","push(t","put","python3","queue","queue\");","queue()","queue();","queue(generic[t]):","queue,","queue:","queue::new();","queue<>();","queue[int]","queues,","queuetest","queue{","readonli","real","rear_point","rear_pointer.reset();","rear_pointer:","rear_pointer;","receiv","recent","refer","remov","repres","request","return","right","same","schloss","science.","see","self","self)","self,","self.__list.append(element)","self.__list.pop()","self.__list.pop(0)","self.__list:","self.__list[","self.__list[0]","self.list.front()","self.list.last()","self.list.len()","self.list.pop()","self.list.pop_front()","self.list.push(item);","self.list.push_back(item);","sharealik","show","side","sift","simpl","simpli","singl","size","size(&self)","size()","size():","size();","size_t","someon","sourc","specif","stack","stack\");","stack()","stack();","stack(generic[t]):","stack.","stack:","stack::new();","stack<>();","stack[int]","stacks,","stacktest","static","std::collections::vecdeque;","std::cout","std::make_shared>(element);","std::make_unique>(element);","std::move(new_node);","std::move(top_point","std::move(top_pointer);","std::shared_ptr>","std::unique_ptr>","store","str(self.__list)","str:","struct","structur","structure.","system.out.println(intqueue.dequeue());","system.out.println(intqueue.front());","system.out.println(intqueue.size());","system.out.println(intstack.pop());","system.out.println(intstack.size());","system.out.println(intstack.top());","t","t&","t)","t):","t:","t;","take","templat","text","them.","this.list","this.list.add(element);","this.list.get(0);","this.list.get(this.size()","this.list.length;","this.list.pop();","this.list.push(data);","this.list.remove(0);","this.list.remove(this.size()","this.list.shift();","this.list.size();","this.list[0];","this.list[this.list.length","this.size();","though,","through","time.","to:","top","top(&self)","top()","top().","top():","top();","top(self)","top_point","top_pointer:","top_pointer;","topel","track","treat","two","type","typevar(\"t\")","typevar,","under","unfair","up.","us","useful","using.","usiz","v)","valu","value(v)","value;","vec","vec::new(),","vecdequ","vecdeque::new(),","veri","void","way","way.","whichev","within","without","written","{","}","};","~queue()","~stack()"],"contents/mathematical_background/mathematical_background.html":["(#560),","(found","4.0","add","algorithm","algorithms,","algorithms.","ask,","attempt","attribut","away","background","bioinformatics.","book","calculu","case","cases,","certain","chapter","chapter:","class","code","common","creativ","deeper","depend","differenti","doesn't","domain","equations.","exampl","except","follow","foundat","graphic","high","honestly,","however,","initi","intern","jame","knowledge,","learn","licens","license.","license.md).","littl","math.","mathemat","mathematics.","matter","method","mit","modifi","more","much","much.","need","new","none","notabl","part,","place","probabl","program","programmers,","provid","pull","quantum","relev","request","requir","rule","said,","schloss","school.","section","section.","sections.","see","sharealik","simul","sometim","specialty,","specif","text","those","tools,","under","understand","written"],"contents/tree_traversal/tree_traversal.html":["!=","!==","\"","\"\"\"a","\"\"\"creat","\"#{node.id}","\"#{temp.id}","\"%d","\")","\"),","\");","\",","\"[#]\\nqueue","\"[#]\\nrecurs","\"[#]\\nstack","\"[#]~%queue","\"[#]~%recurs","\"[#]~%stack","\"a","\"bfssimple\"","\"children","\"creat","\"data","\"depth","\"dfsinorder\"","\"dfspostorder\"","\"dfspreorder\"","\"fmt\"","\"invalid","\"levels\"","\"not","\"recurs","\"thi","\"tree\"","\"utility.h\"","\"~%\")","\"~a","#","#[derive(debug)]","#defin","#endif","#ifndef","#includ","#node","$","$child)","$child):","$child;","$children","$children;","$i","$id,","$id;","$node","$node;","$numofchildren):","$numofrows,","$stack","$stack[]","$temp","$thi","$tree","$tree):","%","%%","🆔","🆕","🆕🌲🆕","🆕🌲⭐️","🆕⏩⏩","🆕⏹⏫❗️","🌀","🌀tree❗️","🌌","🌌🐕","🌲","🍆","🍇","🍉","🍥","🍥tree❗️","🍨","🍨🍆","🍨🐚🌲🍆","🍬⏹","🍭","🍭🐽","🍭binary_tree❗️","🍭tree❗️","🏁","🏢","🏢tree❗️","🐇","🐔","🐕","🐨","🐻","🐽","💭","📗","🔁","🔂","🔐","🔘","🔡","🔡return❗❗️️","🔢","🔤🌀","🔤🍥","🔤🍭","🔤🏢","🔤🔤","🔤🥞","🔤the","🔤tree","🖍🆕","🖍children","🖍id","😀","🙅","🙌","🤜depth_count","🤜id","🤷‍♀️","🥞","🥞tree❗️","🦃","🧒","&n);","&n.children","&n.children[..]","&node)","&node{id:","&tmp","'","''","')","',","';","'[#]'","'__main__':","'children","'children'","'id'","'num","'num_child'","'num_rows'","'queue","'recurs","'stack","'thi","(!queue_empty(&q))","(!stack_empty(&stk))","(!tmp)","(!tree)","(#560),","($i","($numofrow","($temp","($tree","((node","())","(),","();","(0","(0..num_child)","(1","(2","(>","(auto","(bf","(bfs)","(case","(child","(children","(concatmap","(count($tre","(createtre","(current","(defstruct","(defun","(defvar","(depthcount","(df","(dfs)","(eql","(fail)\");","(first","(float)","(format","(found","(if","(int","(length","(length(n.children)","(list","(loop","(make","(n.children)","(n.children.size())","(n.children_size)","(nconc","(node","(node)","(node.children.size())","(null","(num","(num_row","(numrow","(output","(pop","(post","(print","(push","(q","(queue.count","(queue.length","(queue.size()","(queue_empty(q))","(row","(rowcount","(second","(setf","(show)","(size_t","(stack.count","(stack.length","(stack.size()","(stack_empty(stk))","(stk","(struct","(t","(temp","(top","(tree._children.count)","(tree.children.length)","(var","(when","*","**data;","**tmp","*=","*children;","*dequeue(struct","*element)","*node","*node)","*q)","*q,","*queue.front();","*ret","*stack.top();","*stack_pop(struct","*stk)","*stk,","*tmp;","+","++","++i)",".","...",".collect();",".equ",".extern",".global",".intel_syntax",".map(|_|",".rodata",".section",".string",".text","//","//system.out.println(\"us","//tree.dfsrecursiveinorderbinary();","//utility_h","0","0)","0,","0:","0;","0]","0}","0};","0❗️","0❗️❗️","1","1🤛","1)","1))","1);","1,","1...numchildren","10","10❗️❗️","12","128","12]","12]#","12],","15","16","16]","16]#","16],","1:","1:num_child","1;","1]","1❗️","1❗️❗️","2","2)","2))","2),","2);","2,","2.","20","24]","2:","2;","2❗️","3","3)","3))","3);","3,","32","36","3❗️","4","4.","4.0","4;","5.","64","7","8","8]","8],",":","::",":=",":child",":children",":data",";;",";;;;","=","==","=='__main__':","===","=>",">",">=",">back",">back;",">back]",">capac",">capacity)",">capacity;",">children",">children,",">children;",">children[]",">children[i]);",">data",">data);",">data,",">data[",">data[0]));",">data[0]);",">data[q",">data[stk",">front",">front)",">front,",">front];",">getchildren()",">getchildren()))",">getchildren()[0]);",">getchildren()[1]);",">getid()",">id",">id);",">id,",">id;",">top",">top++]",">top];","@(a,","@(k,v)","@children","@overrid","[","[$tree];","[&]","[...array(children).keys()].map(()","[]","[])","[]*node","[]*node{n}","[];","[a]","[l,","[l])","[left,","[left]","[node]","[node])","[node]?","[r12","[r12]","[r12],","[r13","[r13]","[r14","[r14]","[r14],","[rax","[rax]","[rax],","[rbx","[rbx],","[rdi","[rdi]","[stack","[t]","[tree","[tree];","[x]","\\n\"","]","].","];","^","^self.","_","_,","__construct(int","__init__(self):","__name__","_children","`children`","a,","a]","abov","above,","access","account","action","actual","add","addchild($child);","addchild(tre","addit","addition,","addlast:","address","alloc","allow","append(cur.children,","append(queue,","approach","args)","argu","around","array","array(node))","array.","array_pop($stack)))","array_shift($stack)))","arraylist","arraylist();","ask","assum","at:","attribut","auto","avoid","a{b};","b)","back","back,","balanc","base","befor","below.","bf","bfs(root);","bfs(tree)","bfs.","bfs:\"","bfs:\")","bfs:\");","bfs:'","bfs:\\n\");","bfs:~%\")","bfs_queue","bfs_queue(&root);","bfs_queue(n)","bfs_queue(n:","bfs_queue(n::node)","bfs_queue(nod","bfs_queue(node)","bfs_queue(node):","bfs_queue(root)","bfs_queue(root);","bfs_queue(struct","bfs_queue(tree)","bfs_queue:","bfs_queue_end_push","bfs_queue_end_push:","bfs_queue_loop","bfs_queue_loop:","bfs_queue_push_child","bfs_queue_push_child:","bfs_queue_return","bfs_queue_return:","bfsqueue()","bfsqueue(n","bfsqueue(node:","bigger","binari","binary!🔤","binary🔤❗️","binary_root","binary_tre","bit","bits),","bool","bottom","bottom.","bottom.\"","bottom.\"\"\"","branch","branch.","branches.","breadth","break;","btree","byte","c","calcul","call","calle","calloc((q","calloc(4,","can't","capac","capacity,","capacity;","capcaiti","care","case","case!","case,","cdq","cell_index","cell_index(keys(n),","cell_index(keys(parent),","cell_index(values(n),","cell_index(values(parent),","chapter","chapter:","cheatsheet","check","child","child'","child)","child))","child)))","child)))))","child.","children","children'","children)","children))","children)):","children,","children.","children:","children::vector{node}","children;","children_count","children_count❗️","children_count❗️❗️","children_s","children_size,","children_size;","childrencount)","childrencount);","children|value|children_s","children❗️","child};","child❗️","class","classvariablenames:","cleanup:","cmp","code","code,","collect","collect:","comment","common","compar","compareto(nod","compos","concatmap","console.log(\"[#]\\nqueu","console.log(\"[#]\\nrecurs","console.log(\"[#]\\nstack","console.log();","console.log(tree.id);","console.write(queue.peek().id","console.write(stack.peek().id","console.write(tree.id","console.writeline(\"[#]\\nqueu","console.writeline(\"[#]\\nrecurs","console.writeline(\"[#]\\nstack","console.writeline();","const","const&","constructed.","containers.map(k,v);","convent","copi","cr.","creat","create_btree()","create_btree();","create_tre","create_tree()","create_tree();","create_tree(2,","create_tree(3,","create_tree(3,2)","create_tree(int","create_tree(levels,","create_tree(node(),","create_tree(node,","create_tree(num_row","create_tree(num_row:","create_tree(num_row::int64,","create_tree(num_rows,","create_tree:","create_tree_children","create_tree_children:","create_tree_leaf","create_tree_leaf:","create_tree_return","create_tree_return:","createallchildren(nod","created.","createtre","createtree(2,","createtree(3,","createtree(numrow,","createtree(numrows:","createtree(row","createtree(rows,","creativ","crucial","cur","cur.children...)","cur.id","cur.id)","current","current.value);","current_nod","current_node.children:","data","data'","data);","data;","datastructures,","deep.\"","deep.\"\"\"","def","default:","depend","depth","depth_count","depthcount,","dequ","deque([node])","deque.new","dequeu","dequeue!(q)","dequeue:","dequeue_return","dequeue_return:","deriv","describ","destroy_tree(root);","destroy_tree(root_binary);","detail","df","dfs.","dfs:\"","dfs:\")","dfs:\");","dfs:'","dfs:\\n\");","dfs:~%\")","dfs_recurs","dfs_recursive(&root);","dfs_recursive(...)","dfs_recursive(child)","dfs_recursive(child);","dfs_recursive(n)","dfs_recursive(n:","dfs_recursive(n::node)","dfs_recursive(nod","dfs_recursive(node(value,","dfs_recursive(node)","dfs_recursive(node):","dfs_recursive(root)","dfs_recursive(root);","dfs_recursive(struct","dfs_recursive(tree)","dfs_recursive:","dfs_recursive_bt_return","dfs_recursive_bt_return:","dfs_recursive_bt_size0","dfs_recursive_bt_size0:","dfs_recursive_bt_size1","dfs_recursive_bt_size1:","dfs_recursive_bt_size2","dfs_recursive_bt_size2:","dfs_recursive_children","dfs_recursive_children:","dfs_recursive_inorder_btre","dfs_recursive_inorder_btree(&root_binary);","dfs_recursive_inorder_btree(binary_tree)","dfs_recursive_inorder_btree(children[0])","dfs_recursive_inorder_btree(children[1])","dfs_recursive_inorder_btree(children{1})","dfs_recursive_inorder_btree(children{2})","dfs_recursive_inorder_btree(left);","dfs_recursive_inorder_btree(n)","dfs_recursive_inorder_btree(n.children[0]);","dfs_recursive_inorder_btree(n.children[1])","dfs_recursive_inorder_btree(n.children[1]);","dfs_recursive_inorder_btree(n.children[2])","dfs_recursive_inorder_btree(n:","dfs_recursive_inorder_btree(n::node)","dfs_recursive_inorder_btree(nod","dfs_recursive_inorder_btree(node(value,","dfs_recursive_inorder_btree(node)","dfs_recursive_inorder_btree(node):","dfs_recursive_inorder_btree(node.children[0])","dfs_recursive_inorder_btree(node.children[1])","dfs_recursive_inorder_btree(right);","dfs_recursive_inorder_btree(root_binary)","dfs_recursive_inorder_btree(root_binary);","dfs_recursive_inorder_btree(rootb)","dfs_recursive_inorder_btree(struct","dfs_recursive_inorder_btree:","dfs_recursive_po_children","dfs_recursive_po_children:","dfs_recursive_po_return","dfs_recursive_po_return:","dfs_recursive_postord","dfs_recursive_postorder(&root);","dfs_recursive_postorder(child)","dfs_recursive_postorder(child);","dfs_recursive_postorder(n)","dfs_recursive_postorder(n:","dfs_recursive_postorder(n::node)","dfs_recursive_postorder(nod","dfs_recursive_postorder(node(value,","dfs_recursive_postorder(node)","dfs_recursive_postorder(node):","dfs_recursive_postorder(root)","dfs_recursive_postorder(root);","dfs_recursive_postorder(struct","dfs_recursive_postorder(tree)","dfs_recursive_postorder:","dfs_recursive_return","dfs_recursive_return:","dfs_stack","dfs_stack(&root);","dfs_stack(...)","dfs_stack(n)","dfs_stack(n:","dfs_stack(n::node)","dfs_stack(nod","dfs_stack(node)","dfs_stack(node):","dfs_stack(root)","dfs_stack(root);","dfs_stack(struct","dfs_stack(tree)","dfs_stack:","dfs_stack_end_push","dfs_stack_end_push:","dfs_stack_loop","dfs_stack_loop:","dfs_stack_push_child","dfs_stack_push_child:","dfs_stack_return","dfs_stack_return:","dfsinord","dfsinorder(root_binary);","dfsinorder(tree)","dfsinorder(tree.children[0]);","dfsinorder(tree.children[1]);","dfsinorderbinarytree.","dfsinorderbinarytree:","dfsiterative(root);","dfsiterative(tree)","dfspostord","dfspostorder(root);","dfspostorder(tree)","dfspreorder(root);","dfspreorder(tree)","dfsqueue(tre","dfsrecurs","dfsrecursive()","dfsrecursive(c);","dfsrecursive(child)","dfsrecursive(n","dfsrecursive(n);","dfsrecursive(nod","dfsrecursive(node:","dfsrecursive(this);","dfsrecursive(tre","dfsrecursive.","dfsrecursiveinorderbinari","dfsrecursiveinorderbinary()","dfsrecursiveinorderbinary()!\");","dfsrecursiveinorderbinary(nod","dfsrecursiveinorderbinary(node.children.get(0));","dfsrecursiveinorderbinary(node.children.get(1));","dfsrecursiveinorderbinary(node:","dfsrecursiveinorderbinary(this);","dfsrecursiveinorderbinary(this.root);","dfsrecursiveinorderbinary(tre","dfsrecursiveinorderbinary(tree._children[0]);","dfsrecursiveinorderbinary(tree._children[1]);","dfsrecursiveinorderbtree(n","dfsrecursiveinorderbtree(n.children[0])","dfsrecursiveinorderbtree(n.children[1])","dfsrecursivepostorder()","dfsrecursivepostorder(c);","dfsrecursivepostorder(child)","dfsrecursivepostorder(n","dfsrecursivepostorder(n);","dfsrecursivepostorder(nod","dfsrecursivepostorder(node:","dfsrecursivepostorder(this);","dfsrecursivepostorder(tre","dfsrecursivepostorder)].","dfsrecursivepostorder.","dfsstack","dfsstack()","dfsstack(n","dfsstack(node:","dfsstack(tre","dfsstack.","differ","discuss","do","does!","doesn't","down","dword","each","eax","eax,","echo","edi","edi,","edx","edx,","element","element.","element;","elements,","elif","else:","elseif","empti","empty,","end","end,","end='","enqueu","enqueue!(q,","enqueue(&q,","enqueue(struct","enqueue:","enqueue_append","enqueue_append:","equal","error","error🔤❗️","error(\"postord","error,","errors!","esi","esi,","exactli","exampl","example,","except","exception(\"not","exists!","explan","explicitli","few","fight","fill","first","first,","first.","flip(children)","fmt.printf(\"%d","fmt.println(\"thi","fmt_tree","fmt_tree:","fn","follow","foreach","forest","fprintf(\"not","fprintf('%u","fprintf('\\n')","fprintf('\\nbf","fprintf('\\ndf","free","free(q","free(q.data);","free(stk.data);","free,","free_queu","free_queue(q);","free_queue(struct","free_queue:","free_stack","free_stack(stk);","free_stack(struct","free_stack:","free_tre","free_tree:","free_tree_free_array","free_tree_free_array:","free_tree_free_kid","free_tree_free_kid:","free_tree_return","free_tree_return:","front","front,","func","function","function,","further","gener","generate_tree(2,","generate_tree(3,","generate_tree(int","get;","get_queu","get_queue(size_t","get_queue(sizeof(struct","get_queue:","get_stack","get_stack(size_t","get_stack(sizeof(struct","get_stack:","getchildren():","getid():","getter\"","getter.\"","given","given_id","go","goe","graphic","greatli","handl","here","hold","hous","however,","human","id","id)","id);","id,","id:","id::int64","id;","idea","ideal,","idiv","iftrue:","imag","images/graph","implement","implies:","import","in.","inbetween","incred","init","init(value:","initi","initialize(@id","initialized;","inord","instancevariablenames:","instead","instead,","int","int)","int,","int32,","integer.compare(this.id,","interact","interest","intern","invalidargumentexception('not","is.","i{1};","jame","java.util.arraylist;","java.util.linkedlist;","java.util.queue;","java.util.stack;","javascript,","je","jmp","jne","jsonserializ","jsonserialize():","jz","know","known","l","languag","last","last.","lea","lead","leaf","leav","left","len(children):","len(n.children)","len(node.children)","len(queue)","len(stack)","length(children)","level","levels:","licens","license.","license.md).","like:","line","linkedlist","linkedlist();","lisp","list","list();","long","look","loop","lot","made","main","main()","main():","main(string[]","main:","make","malloc","malloc(4","malloc,","mani","map","match","mathjax.hub.queue([\"typeset\",mathjax.hub]);","me,","memcpi","memcpy(tmp","memcpy(tmp,","memori","method","method:","miss","mit","mix","modifi","more","mov","move","multipl","mut","n","n'","n)","n.children","n.children)","n.children_s","n.id)","n.id);","n.value),","n.value);","name","namespac","natur","necessari","necessarili","need","new","new(node)","new(vector{node}(),","new.","new:","newchildren","newchildren.","newdata","newdata.","next_nod","next_nodes;","nil","nil)","node","node(0,","node(1,","node(10,","node(11,","node(12,","node(2,","node(3,","node(4,","node(5,","node(6,","node(7,","node(8,","node(9,","node(id::int64)","node(int","node(num_row)","node(num_rows,","node(rowcount);","node(value:","node)","node))","node)))","node))))","node));","node):","node*));","node*)dequeue(&q);","node*)malloc(num_children","node*)stack_pop(&stk);","node,","node.children!","node.children![0])","node.children![1])","node.children)","node.children.append(child)","node.children.each{","node.children.s","node.children:","node.children?.append(child)","node.children?.count","node.children[0]","node.children[1]","node.data","node.new(levels,","node1","node10","node11","node11,","node12","node12});","node2","node3","node3,","node3});","node4","node4});","node5","node5,","node6","node6});","node7","node7,","node8","node8});","node9","node9});","node:","node>>bf","node>>children","node>>children:","node>>data","node>>data:","node>>dfsinorderbinarytre","node>>dfsrecurs","node>>dfsrecursivepostord","node>>dfsstack","node[])","node_queu","node_stack","node_stack(end)","node_stack{end};","nodes,","nodes.","node{std::move(vec),","non","none","none:","noprefix","not_bt","not_bt:","note","note,","now,","null","null)","null;","num","num_child","num_child)","num_child))","num_child):","num_child);","num_child,","num_child:","num_child::int64)","num_children)","num_children;","num_childs)","num_childs.times{children.push","num_childs:","num_row","num_row,","num_row};","number","numchild","numchildren)","numchildren:","numrow","numrows,","object","offset","old","on","onc","order","order🔤❗️","order).\"","order.\"","other)","other,","other.id);","out","output","overrid","packag","package:","paramet","params:","parent","parent_cel","parent_cell{1};","perform","php_eol","php_eol;","place","point","point,","pointer","pop","pop!(s)","pop.","possibl","post","postord","postorder\\n')","pre","primarili","print","print!(\"thi","print!(\"{}","print(\"[#]\\nqueu","print(\"[#]\\nrecurs","print(\"[#]\\nstack","print(\"not","print('invalid","print()","print(current_node.value,","print(first(q).id,","print(n.id,","print(node.data)","print(node.data,","print(node.value,","print(temp.value,","print(top(s).id,","print(value,","print:","printf","printf(\"%d","printf(\"[#]\\nqueu","printf(\"[#]\\nrecurs","printf(\"[#]\\nstack","printf(\"\\n\");","printf(\"thi","printf,","println!(\"[#]\\nqueu","println!(\"[#]\\nrecurs","println!(\"[#]\\nstack","println!();","println(\"[#]\\nqueu","println(\"[#]\\nrecurs","println(\"[#]\\nstack","println(\"not","println()","privat","process.stdout.write(current.id","process.stdout.write(tree.id","program","program.c","project","properti","ptr","ptr[r12]","public","pull","push","push!(ret.children,","push!(s,","push:","put","putstrln","q","q)","q.back","q.capac","q.data","q.front","q;","queue","queue🔤❗️","queue();","queue)","queue))","queue)))","queue,","queue.add(c);","queue.add(this.root);","queue.append(child)","queue.count","queue.dequeue();","queue.empty?","queue.enqueue(c);","queue.enqueue(this);","queue.extend(¤t.children);","queue.extend(node.children)","queue.poll();","queue.pop();","queue.pop(0)","queue.pop_front()","queue.popleft()","queue.push","queue.push(&n);","queue.push(...current.children);","queue.push_back(n);","queue.remove(at:","queue.shift","queue.shift();","queue:","queue;","queue[0]","queue[1:]","queue\\n')","queue_array,","queue_back,","queue_cap,","queue_empty(struct","queue_front,","queue_res","queue_resize(q);","queue_resize(struct","queue_resize:","queue_size,","queues.\"","queue{node}()","queue❗️","qword","r","r10,","r11","r12","r12,","r12]","r12d","r12d,","r13","r13,","r13]","r13d","r13d,","r14","r14,","r14]","r14d","r14d,","r15","r15,","r15]","r15d,","r8,","r9,","r])","rang","range(num_child)))","range(num_child):","rax","rax,","rax:rdx","rax]","rbp,","rbx","rbx,","rcx,","rdi","rdi,","rdx","rdx,","reach","realloc","realloc(stk","recurs","recursion!","recursion,","recursive.","recursive\\n')","regist","relat","removefirst.","repeat","replic","request","resiz","rest","restrict","result","ret","ret;","return","return:","return;","reus","reversedo:","right.","right]","root","root)","root;","root_bin","root_binari","rootb","rootbinari","rootbinary)","row","rowcount","rowcount,","rows'","rows)","rows,","rows};","rsi","rsi,","rsi]","rsp","rsp,","run","s","said,","same","save","scheme","schloss","scratch","scratch:","search","search.","search.\"","see","seem","self.","self.children","self.data","self.valu","sense.","set;","setter\"","setter.\"","shape","sharealik","shift","shl","show","show:","shownod","shr","similar","simpl","simple,","simple:","simpli","singl","situation.","size","size)","size);","size;","size_t","sizeof(q","sizeof(stk","sizeof(struct","sizeof(tree)","snippet","so:","some(current)","someth","something...","spend","stack","stack🔤❗️","stack();","stack)","stack))","stack)))","stack))))","stack,","stack.\"","stack.\"\"\"","stack...)","stack.append(child)","stack.count","stack.empty?","stack.extend(¤t.children);","stack.extend(node.children)","stack.pop","stack.pop()","stack.pop();","stack.poplast()!","stack.push","stack.push(&n);","stack.push(...current.children);","stack.push(c);","stack.push(this);","stack.push(this.root);","stack:","stack;","stack[0]","stack[1:]","stack\\n')","stack_array,","stack_cap,","stack_empty(struct","stack_pop","stack_pop:","stack_pop_el","stack_pop_element:","stack_pop_return","stack_pop_return:","stack_push","stack_push(&stk,","stack_push(struct","stack_push:","stack_push_append","stack_push_append:","stack_size,","stack_top,","stack{node}()","stack❗️","start","static","static::dfsrecursive($child);","static::dfsrecursiveinorderbinary($tre","static::dfsrecursivepostorder($child);","std::collections::vecdeque;","std::cout","std::generate_n(std::back_inserter(vec),","std::queue","std::size_t;","std::stack","std::vector","step:","still","stk","stk)","stk.capac","stk.data","stk.top","stk;","store","straightforward","struct","structur","structure.","structures,","sub","subclass:","subtract","sure","surprisingly,","swap","switch","system","system.collections.generic;","system.err.println(\"not","system.out.print(node.id","system.out.print(queue.peek().id","system.out.print(stack.peek().id","system.out.println(\"[#]\\nqueu","system.out.println(\"[#]\\nrecurs","system.out.println(\"[#]\\nstack","system.out.println();","system;","t","take","taken","temp","temp)","temp))","temp)))))","temp._children)","temp.children","temp.children!","temp.children)","temp.children.each{","temp:","temp_children","temp❗️","terminator:\"","ternari","test","testtre","text","that,","therefor","this,","this.","this.children","this.createallchildren(this.root,","this.dfsrecursive(this.root);","this.dfsrecursivepostorder(this.root);","this.id","this.root","this:","thought","through","throw","thrown","time","tmp","tmp.children)","tmp;","top","top,","transcript","travers","traversal🔤️❗️","traversal,","traversal:","tree","tree!\"","tree!\")","tree!\");","tree!');","tree!';","tree\"","tree\")","tree'","tree')","tree($numofrows);","tree(2,","tree(3,","tree(int","tree)","tree,","tree.","tree.\"","tree.\"\"\"","tree.\"))))","tree.\\n\"","tree.\\n\");","tree._children)","tree.bfsqueue();","tree.c","tree.children.foreach(dfspostorder);","tree.children.foreach(dfspreorder);","tree.dfsrecursive();","tree.dfsrecursiveinorderbinary();","tree.dfsrecursivepostorder();","tree.dfsstack();","tree.java","tree:\"","tree:\")","tree:\");","tree:'","tree:\\n\");","tree:~%\")","tree\\n')","tree_children,","tree_num_children,","tree_siz","tree_size,","tree_traversal.c","tree_value,","trees\");","treetravers","treetraversal::dfsqueue($node);","treetraversal::dfsrecursive($node);","treetraversal::dfsrecursiveinorderbinary($node);","treetraversal::dfsrecursivepostorder($node);","treetraversal::dfsstack($node);","tri","ts","ts)","tuple(create_tree(num_row","twice,","two","type","types,","u64)","u64,","uncom","under","unless","until","unword","up","upper","us","used;","using,","utility.h","utility_h","v","valid","valu","value,","value.","value:","value;","value|children_s","var","vari","variabl","vec![],","vec![n];","vec,","vec;","vecdeque::new();","vector","vector,","vector.","veri","video","visit","void","want","warn","way","we'll","while(length(q)","while(length(s)","whiletrue:","with:","without","won't","work","work.","would'v","write","written","x","xmm0","xor","zero","{","{next_nodes{:},","{node1,","{node10,","{node2,","{node5,","{node6,","{node_stack{:}","{null,","{n};","{{}});","{};","|","|child|","}","});","}.","};","~isempty(child)","~isempty(children{1})","~isempty(node_queue)","~isempty(node_stack)","↩️","↪️","⏫","⏹","▶️","◀️🙌","✖️","❎","❗️","➕","➖","➡️","⭐️","️↪️"],"contents/euclidean_algorithm/euclidean_algorithm.html":["!","!=","!==","\"$1\")","\"$2\")","\"$a\"","\"%s\"","\"[#]\\nmodulu","\"[#]\\nsubtract","\"[#]`nmodulu","\"[#]`nsubtract","\"[#]~%modulu","\"[#]~%subtract","\"euclidean","\"euclidmod\"","\"euclidsub\"","\"find","\"fmt\"","\"~d~%\"","#","#!/usr/bin/env","#includ","#lang","$((128","$((64","$(128","$(64","$a","$a)","$a,","$a;","$b","$b)","$b):","$b,","$b;","$b];","$tmp","%","🍇","🍉","🏁","🏧","🏧a","🏧b","🐇","💭","🔡","🔢","🔼","🖍🆕var_a","🖍🆕var_b","🖍var_a","🖍var_b","😀","🙅","🙌","🚮","🤜128","🤜64","'(g0)')","',num2str(euclidmod(64","',num2str(euclidsub(128","'[#]'","'modulu","'subtract","(","(#560),","($a","($b","(%","(%)","((","((128","((64","((a","((b","((defin","((tmp","()","(*","(0,","(128","(64","(=","(>","(_,","(a","(a,","(ab","(ad)","(almost","(assert","(b","(chin123)","(cond","(defin","(defn","(defun","(display","(displayln","(dp","(end","(envis","(eql","(euclid","(euclid_mod","(euclid_mod*","(euclid_sub","(euclid_sub*","(format","(found","(gcd","(gcd)","(if","(inner","(jspp)","(like","(local","(loop","(math.abs(a),","(math/ab","(mod","(modulo","(negative?","(newline)","(on","(print","(recur","(return","(ubsan)","(x","(x,","(zero?","(zerop","(~",")","))","));","*","*)",".",".extern",".global",".intel_syntax",".rodata",".section",".string",".text","//","/=","0","0)","0,","0/1","0/1a","0:","0;","0aa","1","1.2","1/0","10","11aa","12","12🤛","12)","12))","12,","128","128*77)","12ab","12ba","13aab","13bba","13tba","14","1536","180","1800's.","1:","1aa","2","2ab","2ba","2dup","3","300","31","3aab","3bba","3tba","4.0","42","4288","48","5184","56","64","64*81)","67","67🤛","67)","67))","67,","71)","77","77🤛","77)","77))","77))\"","77)))","77)).","77));","77))]","77);","81","81🤛","81)","81))","81))\"","81)))","81))))","81)).","81));","81))]","81);","9856",":","::",":=",";",";;",";;;;","=","==","=>",">",">=","[","[$a","['[#]","[(>","[(eq?","[(or","[a","[els","[i","[lf][lf][lf]","[lf][lf][lf][lf]","[lf][space][lf][lf]","[lf][space][space][lf]","[lf][space][space][tab][lf]","[lf][space][space][tab][space][lf]","[lf][tab][space][tab][lf]","[lf][tab][tab][tab][space][lf]","[math]::abs($a)","[math]::abs($b)","[space][lf][space]","[space][lf][tab]","[space][space][space][lf]","[space][space][space][tab][lf]","[tab][lf][space][tab]","[tab][lf][tab][tab]","[tab][space][space][tab]","[tab][space][tab][tab]","[tab][tab][space]","[tab][tab][tab]","]","].","^a.","_","_)","_________________________________________________________________________","__name__==\"__main__\":","`b`","`mod`","a%b","a%b,b","a)","a)(ab","a)(negative?","a))","a)))))","a))]))","a,","a.","a.ab","a.abs();","a.absolutevalu","a:","a;","a=$(ab","a=abs(a);","a=b","a>b:","a]","aa","aab","ab","aba","abs($a);","abs($b);","abs()","abs(a","abs(a)","abs(a);","abs(a:a)","abs(a:b)","abs(b)","abs(b);","abs(in1)","abs(in2)","abs.","absolut","abz","addpattern","again","algorithm","algorithm,","algorithm.","algorithm:","amaz","ancient","appeal.","applic","args)","arguabl","array)","array[string]):","attribut","auto","b","b)","b)(euclid","b))","b))(euclid","b)))","b))))","b))]","b):","b);","b)]","b,","b,a","b.","b.ab","b.abs();","b.absolutevalu","b.zero?","b:","b::int64)","b;","b=$(ab","b=0","b=abs(b);","b]","ba","bab","back","base","bash","bat","bba","bc)","becom","befor","better","bi@","bigger","biggr","both","call","case","certain","chang","chapter","chapter:","check","check1","check1);","check2","check2);","check:","chinmaya","chk1","chk1);","chk2","chk2);","class","clockwise)","clockwise,","cmp","code","come","command","comments.","common","comput","conceptu","console.log('[#]\\nmodulu","console.log('[#]\\nsubtract","console.log(euclidmod(64","console.log(euclidsub(128","console.writeline(\"[#]\\nmodulu","console.writeline(\"[#]\\nsubtract","console.writeline(check);","console.writeline(check2);","contribut","cool.","cr.","creat","creativ","death","deeper","def","definit","definition)","describ","devic","diff","differ","difficult","diffrint","discuss","div","divid","divisor","divisor.","divsor","done","done.","down","dp","drop","dup","duplic","e","earthfail","echo","element","elif","else:","empty:","end","end.","endfunct","endif","endwhil","enter","equal","equal,","era","euclid","euclid%","euclid'","euclid($a,","euclid()","euclid)","euclid_mod","euclid_mod()","euclid_mod(0,","euclid_mod(128","euclid_mod(64","euclid_mod(a","euclid_mod(a,","euclid_mod(a:","euclid_mod(a::int64,","euclid_mod(b,","euclid_mod(in1,","euclid_mod(int","euclid_mod:","euclid_mod_fmt","euclid_mod_fmt:","euclid_rem(64","euclid_rem(mut","euclid_sub","euclid_sub()","euclid_sub(0,","euclid_sub(128","euclid_sub(64","euclid_sub(a","euclid_sub(a,","euclid_sub(a:","euclid_sub(a::int64,","euclid_sub(in1,","euclid_sub(int","euclid_sub(mut","euclid_sub(x","euclid_sub(x,","euclid_sub,","euclid_sub:","euclid_sub_fmt","euclid_sub_fmt:","euclidean","euclideanalgo","euclideanalgorithm","euclideanalgorithm();","euclideanalgorithm.c","euclideanalgorithm.euclidmod(64","euclideanalgorithm.euclidsub(128","euclidian","euclidmod","euclidmod(64*67,","euclidmod(a,","euclidmod(a,b)","euclidmod(a:","euclidmod(int","euclidmod:","euclidsub","euclidsub(128*12,","euclidsub(a,","euclidsub(a,b)","euclidsub(a:","euclidsub(int","euclidsub:","exampl","exist","exit","explan","fact","fals","few","fewer","fi","find","first","first,","fmt.println(\"[#]\\nmodulu","fmt.println(\"[#]\\nsubtract","fmt.println(check1)","fmt.println(check2)","fn","follow","found","fractions).","fun","func","function","fundament","gcd","gcd_minus(128","gcd_minus(a,","gcd_mod(64","gcd_mod(a,","go","goe","graph","graphic","greater","greatest","gt","hai","here","here'","here,","higher","histori","host","i))))))","i64","i64)","i64,","if_tru","if_true:","iffalse:","iftrue:","im","imag","images/graph","implement","implementation,","implementations,","implicit","import","in(number)","in2:","incredibly,","inform","initi","inner","input","input:","int","int)","int):","int,","integ","integer,","integer>>euclidmod:","integer>>euclidsub:","integers\"","integers.","intent(inout)","intern","io","is.","ismainmodule:","it'","itz","iz","j","j)","j)))))","jame","jle","jmp","jne","julian","known","kotlin.math.absolutevalu","kthxbye","l:a","l:b","l:c","label_0","label_0:","label_1","label_1:","label_2","label_2:","last","later.","leav","licens","license.","license.md).","line","lisp","list($b,","live","local","lolatomroflsinnlos,","look","loop","loop)","loop:","lower","mahesh","main","main()","main(args:","main(string[]","main:","make","mani","match","math.ab","math.abs(a)","math.abs(a);","math.abs(b)","math.abs(b))","math.abs(b);","mathemat","mathjax.hub.queue([\"typeset\",mathjax.hub]);","max","mazzuca","me,","method","method.","method:","millennia","millennia.","mit","mkay","mod","mod(a,b);","mod_check","mod_check:","mod_loop","mod_loop:","modern","modifi","modulo","modulo(a,b)","modulu","modulus.\"","mov","much","mut","namespac","ne","neg","new","nicol","non","none","noprefix","now,","num","num1","num2","num2,","number","numbers,","numbers.","o","object","offset","oic","oldb","oldb.","older","on","onc","oper","origin","otherwise,","out","out(number)","output","outta","over","p","packag","php_eol;","pointer","pop","posit","pretti","print","print(\"[#]\\nmodulu","print(\"[#]\\nsubtract","print('[#]\\nmodulu","print('[#]\\nsubtract","print(euclid_mod(64","print(euclid_sub(128","print(euclidmod(a:","print(euclidsub(a:","print_int","print_newlin","print_newline;","printf","printf(\"[#]\\nmodulu","printf(\"[#]\\nsubtract","printf('[#]'.php_eol.'modulu","printf('[#]'.php_eol.'subtract","printf.printf","printi","println!(\"[#]\\nmodulu","println!(\"[#]\\nsubtract","println(\"[#]\\nmodulu","println(\"[#]\\nsubtract","println(euclid_mod(64","println(euclid_sub(128","println(euclidmod(64","println(euclidsub(128","produkt","program","program.c","project","provid","public","pull","push","putstrln","quick","r","racket","rax","rax,","rdi","rdi,","rdx","rdx,","read","readabl","readi","rec","recurs","reduc","remaind","request","result","result:","result:\"","result:\")","result:\");","result:'","result:')","result:'),","result:'.php_eol.'%s',","result:\\n\"","result:\\n\",","result:\\n\";","result:\\n$(check1)\")","result:\\n$(check2)\")","result:\\n$result\"","result:\\n%d\\n\"","result:\\n%d\\n\",","result:\\n{}\",","result:`n$(mod","result:`n$(sub","result:~%\")","result=$(euclid_mod","result=$(euclid_sub","ret","ret=$1","retriev","return","revolutionary,","rid","right","rly,","rly?","roll","rot","rsi","rsi,","s:check_1","s:check_2","s:euclid_mod(64","s:euclid_mod(a,","s:euclid_sub(128","s:euclid_sub(a,","saem","said,","same","same)","same.","sar","schacher","schloss","scienc","scratch","secondnumb","see","self","set","sharealik","show","show:","simpl","simpli","smallr","snippet","someth","stack","start","state","static","stay","std.math;","std.stdio;","std::abs(a);","std::abs(b);","std::cout","std::exchange(b,","step","steps:","still","store","sub","sub(","sub*","submit","subtract","subtraction\"","subtraction:","such","support","sure","swap","system.out.println(\"[#]\\nmodulu","system.out.println(\"[#]\\nsubtract","system.out.println(euclidmod(64","system.out.println(euclidsub(128","system;","t","take","taken","tba","temp","temp:","temp;","test","text","that'","them.","think","this:","though,","throughout","time,","timeless","timestep.","tmp","tmp))","tmp;","today","today.","top)","top,","transcript","true;","truli","twice","two","u","uklidmod","uklidsup","under","unit","univers","until","up","us","val","valu","value)","var","var_a","var_b","version","versions.","video","visibl","void","wai,","way","weinstein","whatev","while(b","whilefalse:","without","works,","world","write","write(*,","write(*,'(a)')","writeln(\"[#]\\nmodulu","writeln(\"[#]\\nsubtract","written","x","x)","x))","xam4lor","xor","y","y)","y,","ya","yr","zero","zero?","{","|","|>","}","~=","↩️","↪️","≠","⏫","▶️","✖️","❎","❗️","❗️❗️","➖","➡️","⬅️","⬆️","️🔁","️🔼🐇⬆️","️⏫🐇⬆️"],"contents/matrix_methods/matrix_methods.html":["(#560),","(found","/","4.0","algorithms.","along!","applic","area","attribut","categories:","certainli","chapter","chapter:","code","common","creat","creativ","diagon","divid","don't","eigenvalu","engineering,","equat","everyth","exampl","fail","favorit","feel","fill","find","follow","form.","foundat","go","graphic","initi","intern","jame","larg","licens","license.","license.md).","list","lower","mani","manipul","mathemat","mathematical.","mathematics,","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matric","matrices.","matrix","method","mit","modifi","more","none","offend","on","out","part,","pull","reason,","request","requir","schloss","scienc","sharealik","solv","system","text","there,","though","tour","type","uncommon","under","upper","us","usabl","we'll","written"],"contents/computational_geometry/computational_geometry.html":["(#560),","(found","4.0","add","algorithm","archiv","area","arxiv.org","attribut","automat","bring","chapter","chapter:","code","come","common","comput","cover","creativ","definit","differ","dimension","evolves,","exampl","follow","foundat","future!","gener","geometri","geometry.","go","graphic","graphics.","initi","interest","intern","jame","joy","know","licens","license.","license.md).","mathematics,","mathjax.hub.queue([\"typeset\",mathjax.hub]);","mit","modifi","more","none","pore","pull","recommend","request","research,","schloss","section","sector","sense,","sharealik","spend","text","three","through","time","two","under","written"],"contents/gift_wrapping/gift_wrapping.html":["\"gift\",","(#560),","(found","4.0","accur","algorithm","algorithm;","allow","attribut","case","chapter","chapter:","classifi","code","code.","common","complic","convex","creativ","defin","dimens","dimensions,","distribut","entir","exampl","fair,","find","follow","gift","give","given","graphic","here","histori","hold","however,","hull","incred","initi","interior","intern","it'","jame","jarvi","lead","leap","licens","license.","license.md).","mani","march","mathjax.hub.queue([\"typeset\",mathjax.hub]);","methods.","mit","modifi","more","name","neat","none","on","point","points.","problem.","programm","pull","random","request","rich","said,","schloss","shape","sharealik","smallest","solv","speaking,","strictli","term","text","though,","three","two","under","wrap","written"],"contents/decision_problems/decision_problems.html":["(#560),","(candid","(found","4.0","algorithm","all;","appropri","assign","associ","attribut","bunch","certain","certainli","chang","chapter","chapter:","classifi","code","come","common","comput","cost","creativ","decis","design","each","everyth","exampl","example,","follow","future.","graphic","here:","honest","however,","hungarian","i'll","i'm","in,","inform","initi","input","intern","jame","job","licens","license.","license.md).","make","mathematics,","mathjax.hub.queue([\"typeset\",mathjax.hub]);","minim","mit","modifi","near","none","now,","output","outputs.","over","overall,","perform","place","positions)","problem","pull","put","read","relat","request","right!","schloss","section","sharealik","studi","sure","task","task.","text","under","up","whether","worth","written"],"contents/physics_solvers/physics_solvers.html":["(#560),","(found","4.0","algorithm","along","archiv","area","area.","attribut","benefit","biologi","certain","chapter","chapter:","chemistry.","code","common","comput","creat","creativ","differ","differenti","drawback","equat","equation,","exampl","example,","follow","future,","gener","graphic","heat","initi","integr","intern","it'","itself","jame","kinemat","lend","licens","license.","license.md).","mani","method","mit","modifi","more","none","note","particular","physic","place","pull","readili","request","research,","schloss","schrödinger","scientif","section,","sever","sharealik","solv","solver","solvers.","specif","such","system","systems.","text","throughout","under","uniqu","us","verlet","way","ways.","worth","written"],"contents/huffman_encoding/huffman_encoding.html":["!=","!input[start..].is_empty()","!node.right)","!t","\"","\"\"","\"\")","\"\"))","\"\",","\"\",:code","\"\";","\"\"}","\"(bibbiti","\"0\"","\"0\")","\"0\"),","\"0\",","\"0\":","\"1\"","\"1\")","\"1\")))))","\"1\"),","\"1\",","\"1\":","\"?\"))","\"\\\":","\"\\ndecoding...\")","\"\\t\"","\"b","\"b\"","\"bbbbbbbb\"","\"bibbiti","\"bibbity_bobbity\"","\"coding...\")","\"container/heap\"","\"decod","\"decoding:","\"encod","\"endod","\"fmt\"","\"huffman_tree\"","\"length:","\"make","\"origin","\"remov","\"take","\"test\"","\"the","#","#(+","#(appli","#(str","#[derive(debug)]","#freq","#includ","#messag","$","%","%1","%1))","%1)))]","%2)","%2))","%s\\n\"","%t\\n\",","&&","&builder,","&cb,","&codebook);","&count)|","&encoder](char","&heap","&mut","&result);","&self)","&self.codebook[&c]).join(\"\")","&str)","&str,","&tree,","'","''","''.join(decoded_message)","''.join(messag","'':","'(((node1","'0'","'0')","'0'),","'0',","'0';","'1')","'1',","'1';","'100'),","'1000'),","'1001'),","'101'),","'110'),","'1100'),","'1101'),","'111')]","'\\0';","'__main__':","'a')","'a',","'bibbity_bobbity'","'i']]]","'o'],","'y'],","(","(!heap","(!isa(current,","(!node.left","(!tree)","(#560),","('_',","('i',","('o',","('t',","('y',","(*cb)[node.char]","(*dst)[len","(*dst)[len]","(*input","(*input);","(*it)","(+)","(5","(;","(;;)","(a,","(appli","(assoc","(auto","(bit","(char)i;","(char,","(char?","(clojure.pprint/pprint","(clojure.set/map","(coder","(complement","(concat","(cond","(const","(counts[char]","(decod","(def","(default","(defn","(drop","(eq","(first","(float)","(fn","(found","(freq","(freq.empty())","(func","(get","(hash","(haskey(weights,","(heap","(heap.length","(i","(i,","(if","(inc","(index","(index)","(insert,","(int","(integer?","(interleav","(is_leaf(tree))","(it","(it',","(jspp),","(just","(key","(last","(leaf","(leav","(left","(length","(let","(list","(loop","(m","(map","(map.entri","(map[c]","(mayb","(merg","(n","(node","(node.isleaf)","(node.left","(node.left)","(node.leftchild","(node.right","(node.right)","(node.rightchild","(node2","(nodeprioritylist.count","(one:","(ord","(partial","(println","(priorityqueue.data.length","(priorityqueue.size()","(ptr)","(recur","(reduc","(remov","(repeat","(ret.size()","(right","(second","(set","(show","(show,","(size_t","(sometim","(sort","(split","(str","(string,","(t,","(t1:t2:ts)","(t2,","(tabl","(take","(target","(thi","(tree","(tree,","(tree.siz","(uncurri","(updat","(val","(var","(vec","(we","(zero:","({",")","*","*/","*=","*codebook","*codebook,","*dst","*huffman_tre","*input));","*input;","*lh","*lhs;","*map.entry(c).or_insert(0)","*n","*node","*node)","*node,","*nodeheap)","*rh","*rhs;","*self","*str","+","++","++=","++input)","++it)","++str)","+=",".","..","...this.data.slice(target)];",".code",".collect::>();",".equ",".extern",".flatmap(bit",".global",".groupby(identity)",".intel_syntax",".iter()",".map(|(&value,",".mapvalues(_.length)",".map{",".next_index",".rodata",".section",".select(n",".str",".string",".text",".tolist();","/","/*","//","0","0)","0))","0))))","0),","0,","01000010010111011110111000100101110.","01110011110110011010110000111101100","01110011111010110000100100111110101","0;","0x1","1","1)","1)),","1),","1);","1,","100","101","1024","1040","110","1110","1111","12","128","15","16","16]","16],","1:","1;","1]","1],","2","2)),","2),","2);","2.7+","20","24","255","256","2;","3","3))))","301","32","32]","32],","4","4*r12]","4*r8]","4*rax]","4*rdi]","4.0","40","4096","512","5128","6","6),","63","64","64,","7","7]","8","8*r13],","8*rax]","8*rcx]","8*rcx],","8*rdx]","8]",":","::",":=",":code",":code)",":els",":messag",":message))",";",";;",";add",";extract",";of",";remov",";to","=","==","===","=>",">",">\",",">>",">capac",">codes)",">codes[(unsign",">codes[0]);",">count",">count)",">count;",">data",">data);",">data,",">data[",">data[0],",">data[0];",">data[heap",">data[index]);",">data[index],",">data[left]",">data[parent_index]",">data[parent_index],",">data[right]",">data[target]);",">decoder.get();",">encoder;",">frequenc",">frequency),",">frequency;",">key);",">key,",">left",">left);",">left,",">length",">length)",">length++]",">length]);",">lhs.get(),",">lhs.get();",">next_index",">next_index++]",">next_index]",">rhs.get(),",">rhs.get();",">right",">right);",">right,",">right;",">second;",">str);",">str[builder",">value);",">value]","?","@test","@testset","[&freq](char","[&ret,","['b',","['t',","[('b',","[(a,","[(char,","[(int,","[(t1,","[...bitstring])","[...iterable].sort((a,","[...str].map(c","[...str];","[...this.data.slice(0,","[0]","[64","[[['_',","[[noreturn]]","[]","[](auto","[])","[]*node","[];","[]rune)","[a]","[bit","[bit]","[bit])","[c](auto","[charact","[code","[codebook]","[ecx","[it',","[it,","[left","[letter","[m","[middl","[new","[new_freq](auto","[r10","[r10]","[r10],","[r11","[r12","[r12]","[r13","[r14","[r14]","[r14],","[r8","[r8]","[r9","[r9]","[r9],","[rax","[rax],","[rcx","[rcx]","[rdi","[rdx","[rdx]","[rdx],","[rsi","[rsp","[rsp],","[s","[st]","[t]","[top](it","[tree","[tree]","[tree_left,","\\\"\"","_","_)","_,","_.weight))","__name__","__repr__","__str__","__str__(self):","_}","a)","a),","a)]","a,","a.weight","a[2]","accept","accord","achiev","actual","ad","add","add(nod","addition,","addpattern","address","advanc","again","al","al,","algorithm","align","alloc","allow","alphabet,","alreadi","alway","amount","anoth","anything.","anyway","appar","appear","append","append(*n,","append(code,","append(code[:len(code)","appli","appropriate.","args)","argument","arithmet","arr","arr[#arr","array","array[string]):","assign","at.","attribut","auto","auto&","b","b)","b.weight),","b[2]","back","backward","backwards,","base","becom","befor","begin","begin(freq),","between","bibbity_bobb","bibbity_bobbity:","bigger","biggest","binari","bisect","bisect(tre","bit","bitmask","bits),","bits,","bits.","bits.push_back(b);","bits;","bitstr","bitstr_len,","bitstr_len]","bitstr_siz","bitstr_size,","bitstring)","bitstring);","bitstring,","bitstring.","bitstring::string)","bitstring;","bitstring_build","bitstring_builder*","block","bobbity\"","bobbity\")","bobbity\");","bobbity\",","bobbity\";","bobbity)\")","bobbity)\";","book\");","bool","both","bottom","box,","box::new(left),","box::new(right),","branch","branch(left,","branch(left:","branch(node1,","branch(node_ptr","branch)","branch))","branch);","branch.","branch.freq","branch.left","branch.right","branch:","branch}","break;","build","build_codebook(empty(),","build_codebook(leaf(char,","build_codebook(left,","build_codebook(node(left,","build_codebook(right,","build_codebook(tree)","build_huffman_tree(message)","build_huffman_tree(message):","builder","builder,","buildtre","buildtree(messag","buildtree(message)","byte","c","c)","c);","c;","c]","calcul","call","calle","calloc","calloc(0,","calloc(1,","calloc,","capacity;","case","cases,","cases.","cb","cb,","cb[char]","cf","chang","chapter","chapter:","char","char)","char)*str]","char)c];","char)tre","char*","char**","char,","charact","character.","charcount","chars.reduce((counts,","cheatsheet","check","child","child,","children","choosetreebranch(bit)","choosetreebranch(bit:","chunk","cl","class","claud","cleanup:","clear","clobber","cmovnz","cmp","cmp(&self,","code","code)","code)))))","code);","code)]","code+'0')","code+'1')","code,","code.append(0));","code.append(1));","code.deletecharat(code.length()","code.tostring());","code:","code::string,","code='')","code]","codearr","codearr)","codebook","codebook'","codebook(it","codebook)","codebook);","codebook*","codebook,","codebook.","codebook.decode(&encoded);","codebook.encode(input);","codebook.entryset())","codebook.getorelse(c,","codebook.insert(value,","codebook.put(node.letter,","codebook.put(symbol,","codebook/tre","codebook:","codebook::codebook(it","codebook::decode(it","codebook::encode(it","codebook::node::~node()","codebook;","codebook[0][0]","codebook[c]).join(\"\"),","codebook[i]","codebook[n.key]=\"0\"","codebook])","codebook_free(struct","codebook_ptr","codebook_recurse!(branch.left,","codebook_recurse!(branch.right,","codebook_recurse!(branch::branch,","codebook_recurse!(leaf::leaf,","codebook_recurse!(n,","codebook_recurse(const","codebook_recurse(tre","codebook_recurse(tree,","codebook_s","codebook_size,","codebook_size]","codebookrecurse(c,","codebookrecurse(left,","codebookrecurse(nod","codebookrecurse(node.left,","codebookrecurse(node.right,","codebookrecurse(node:","codebookrecurse(right,","codebookrecurse(root,","codebookreverse()","coder","coder))","coder]","codes(begin(s),","codes(codes),","codes,","codes.decode(begin(string),","codes;","codes[256];","codes[i]);","codeword","codeword.","collect","combin","common","compar","compareto(nod","complet","complete.","compress","compression.","comput","concat","concat(&result,","concat(char**","concat_char(char**","concat_char(result,","concaten","concatmap","conceptu","consist","console.log(decoded);","console.log(encoded.string);","const","const&","const*","const;","construct","contain","contains?","continu","convent","convert","copi","correct","count","count(&self)","count)","count,","count:","count;","counter","counter(message)","counter,","counter.","counts,","counts;","counts[(unsign","counts[256]","counts[char]","counts[i];","counts_size,","counts_size]","counts_size],","cours","crate","creat","create_codebook(huffman_tree)","create_codebook(n::node)","create_tree(phrase)","create_tree(phrase::string)","createbitstring(str","createbranch","createbranch(nod","createcodebook(mayberoot:","createcodebook(tree)","createcodebook(tree);","createdictionary(nod","createdictionary(node.leftchild,","createdictionary(node.rightchild,","createdictionary(root,","createleaf(char","createtree()","createtree(originaltext)","createtree(phrase:","createtree(str)","createtree(str);","creativ","cur","cur.char","cur.left","cur.right","current","current.left","current.right","current_nod","currentnod","c|","data","data.","data.list","data.map","data:","data;","data[index]","data[target]","datastructur","data{std::move(decoder),","david","dead","dec","decod","decode(&self,","decode(bitstring,","decode(const","decode(enc,","decode(encoded,","decode(encoded.string,","decode(encoded:","decode(huffman_tree,","decode(huffman_tree::node,","decode(it","decode(messag","decode:","decode_dfs(&self,","decode_don","decode_done:","decode_loop","decode_loop:","decode_loop_char","decode_loop_char:","decode_loop_char_branch","decode_loop_char_branch:","decode_recurse(const","decode_recurse(input","decode_recurse(input,","decode_singl","decode_single(it,","decoded()","decoded)","decoded);","decoded:","decoded_messag","decoded_message)","decoded_message.append(inverse_dict[key])","decoded_message:","decoder)","decoder))","decoder;","decoder]","decreas","decrement","def","depend","depth","dequ","dequeue!(nodes)","dequeue!(weights)[1]","dequeue()","deriv","descend","describ","destroy","devis","dfs(&self,","dict","dict((v,","dict([(v,","dict(codebook)","dict)","dict);","dict::dict{char,string})","dict;","dict[leaf.key]","dict[node.key]","dictionari","dictionary();","dictionary)","dictionary);","dictionary,","dictionary.","dictionary;","dictionary[character];","dict{char,string}()","difficult","dil","dil,","display","distinctli","divid","do","doesn't","don't","done","dst","dst,","dst;","dst_len","dump","duplicate(build","duplicate(const","duplicate(get_code(codebook,","dword","dynamic_cast(cur))","dynamic_cast(current_node))","e.g","each","earthfail","easier","easiest","ecx","ecx,","edit","educ","edx","edx,","element","elif","empti","empty()","enc)","enc,","encod","encode(\"bibb","encode(\"bibbity_bobbity\")","encode(&self,","encode()","encode(codebook,","encode(codebook::dict{char,","encode(const","encode(it","encode(messag","encode(originaltext,","encode(phrase:","encode(str)","encode:","encode_calculate_length","encode_calculate_length:","encode_calculate_new_bit_offset","encode_calculate_new_bit_offset:","encode_don","encode_done:","encode_messag","encode_message:","encode_message_bit","encode_message_bits:","encode_message_bits_qword","encode_message_bits_qword:","encode_message_bits_try_overflow","encode_message_bits_try_overflow:","encoded)","encoded);","encoded.tree);","encoded:","encoded_messag","encoded_message)","encoded_message):","encoded_message:","encoded_str","encoded_string(codebook","encoded_string(std::str","encoder;","encoder_rec(&decoder,","encoder_rec(b","encoder_t","encoder_t&","encoder_t();","encoding.","encoding:","encodingresult","encodingresult(str","end","end(code),","end(encoder))","end(encoder),","end(freq))","end(freq),","end(ret),","end(s)))","end(s)),","end(string));","end)","enough","enqueue!(nodes,","enqueue(value)","ensur","entri","enum","enumerate(encoded_message):","enumerate(trees)","eq","eq(&self,","eq)","equal","esi","esi,","exampl","example.","exist","exit","experiments.core)","explan","explanation.","explicit","extend","extern","extra","extraordinari","f'leaf({self.char},","f'node({str(self.left)},","f1)","f1+f2)","f2))","fact","fact,","fano","fano,","field","fields:","final","final_bitstr","final_str","find","first","first,","first;","firsti","fit","flatmap","flip","fmt.printf(\"i","fmt.println(\"\\nencoded:\",","fmt.println(\"codebook:\")","fmt.println(\"decoded:\",","fmt.println(string(r),","fn","follow","following:","foreach","forward_dict","forward_dict[char]","found,","free","free(heap","free(tree);","free_tre","freq","freq,","freq.emplace_back(1,","freqmap","freqmap[char]","freqmap[char].freq++","freqmap[char];","frequenc","frequencies,","frequencies.most_common()","frequency)","frequency,","frequency.","frequency;","frequency]","frequency_array(message)","frequency_array(str)","frequencymap","frequencymap.entryset())","frequent","from(input:","func","function","function(a,","function,","gathro","gener","generate_codebook","generate_codebook(*huffman_tree);","generate_codebook(const","generate_codebook:","generate_codebook_branch","generate_codebook_branch:","generate_codebook_recurs","generate_codebook_recurse:","generate_codebook_recurse_don","generate_codebook_recurse_done:","generate_tre","generate_tree(const","generate_tree(input);","generate_tree:","generate_tree_branch","generate_tree_branches:","generate_tree_count_char","generate_tree_count_chars:","generate_tree_don","generate_tree_done:","generate_tree_leav","generate_tree_leaves:","generate_tree_leaves_count","generate_tree_leaves_counters:","generate_tree_leaves_setup","generate_tree_leaves_setup:","generate_tree_one_leaf","generate_tree_one_leaf:","generate_tree_ret","generate_tree_ret:","generatecodebook(root","generatecodebook(root)","generation:","get;","get_code(codebook,","get_code(const","getfrequ","giallouraki","given","givennodes)","givennodes.tolist();","go","gotten","graphic","great","group","guarante","guston","gustorn","h","h.len()","h.pop().(*node)","h.pop().(*node),","handl","happen","hash","hashmap","hashmap)","hashmap,","hashmap::new();","hashmap<>(),","hashmap<>();","hashmap};","heap","heap'","heap)","heap*","heap,","heap.init(h)","heap.pop(h).(*node)","heap.push(h,","heap_data,","heap_data]","heap_free(&heap);","heap_free(struct","heap_len,","heap_len]","heap_len],","heap_pop","heap_pop(&heap);","heap_pop(struct","heap_push","heap_push(&heap,","heap_push(struct","heap_push:","heap_push_don","heap_push_sift_up:","heap_size,","heart","heart.","help","helper","helper::make_decoder(first,","helper::make_encoder(*decoder);","here","here'","here,","here.","himself!","hoist","hold","horribl","huffman","huffman.","huffman::encoded_string(to_be_encoded);","huffman_decode(codebook,","huffman_encode(codebook,","huffman_tre","huffman_tree,","huffman_tree:","huffmancod","huffmancoding();","huffmancoding.c","huffmancoding.decode(result);","huffmancoding.encode(\"bibb","huffmancoding.nod","huffmanencod","huffmantre","huffmantree(\"bibbity_bobbity\");","huffmantree(str","huffmantree,","huffmantree.createtree();","huffmantree.decode(encoded));","huffmantree.encode();","huffmantree::branch","huffmantree::from(input);","huffmantree::leaf","i)","i,","i.e.,","i32","i32,","icompar","idea","ignor","imag","images/graph","immedi","impl","implement","implement,","implemented.","import","inc","included\"","increas","increment","index","index)","index).","index,","index.","index:","index;","indic","indici","ineffici","inefficient,","inform","information.","initi","inlin","input","input\"),","input)","input,","input.chars().fold(hashmap::new(),","input.chars().map(|c|","input.chars().next();","input:","input;","insert","instanc","instead","instruct","int","int)","int64}()","interest","interface{}","interface{})","interleav","intern","introduc","inverse_dict","inverse_dict:","inverse_dict['']","inverse_dict[key]","invert","is:","is_leaf(const","isa(huffman_tree,","isa(n,","isleaf","it'","it,","it.","iter","itertools::itertools;","itertools;","ith","itself","j","jame","java.util.*;","jge","jl","jle","jmp","jne","jnz","julian","jz","k)","k,","keep","key","key(key)","key)","key,","key::char","key;","keyword","kid","knew","l","l)","languag","language,","last","last)","last);","last,","last;","last;)","lasty))))))","lasty]","later","lea","leader","leaf","leaf(*t))","leaf(_,","leaf(c,","leaf(char,","leaf(char:","leaf(i,","leaf(int","leaf(symbol,","leaf(t,","leaf(weight,","leaf)","leaf.","leaf;","left","left,","left.count()","left.decode_dfs(&input[1..],","left.dfs(code.clone()","left.freq","left.weight","left:","left::union{leaf,","left;","leftchild","leftchild,","leftchild.weight","leftchild;","len","len()","len(codebook)","len(encoded_message)","len(message)","len(n)","len(old)","len(trees)","length","length,","length;","length]","less","less(i,","letter","letter))","letter,","letter;","lh","lhs(std::move(lhs)),","lhs,","lhs.frequenc","lhs;","licens","license.","license.md).","like.","line","list","list();","list,","list.","littl","load","local","localdictionary)","localdictionary);","localdictionary.add(node.key[0],","longer","look","loop","lose","lossless","m","m)","m.!)","m.empti","m.fromlist","m.fromlistwith","m.getkey());","m.getvalue()));","m.getvalue());","m.tolist","made","main","main()","main():","main(args:","main(string[]","main:","make","make([]rune,","make(codebook)","make(map[rune]*node)","make_codebook(self)","make_decoder(it","make_encoder(nod","makequeue(iterable)","makequeue(nodes);","malloc","malloc(length","malloc,","manag","manipul","map","map$(forward_dict[]))","map$(t","map$(weight)","map,","map[c]","map[char,","map[rune]str","mask","mask:","match","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matthew","mayb","maybegetacharact","mayberoot.foreach(c","mayberoot.getorelse(leaf('?',","mayberoot:","member","memcpy(dst,","memori","memory,","memset","memset,","mention","messag","message)","message):","message,:cod","message:","message:',","method","method.","mid","mid)","mid))","middl","middle)))","minimum","mit","mix:","mktabl","modifi","moment,","more","mov","movap","move","movup","msg","msg)","msg_data,","msg_data]","msg_len,","mut","n","n)","n))","n),","n.count()))","n[i]","n[i],","n[i].freq","n[j]","n[j],","n[j].freq","namespac","necessari","need","needed?","never","new","new(node)","new(nodeheap)","new_freq","new_nod","new_tre","new_tree)","new_weight","newnod","newnode)","newnode.char","newnode.freq","next","next((i","next_index;","nil","node","node'","node(freq),","node(key.tostring(),","node(leaf(b,","node(left","node(leftchild.key","node(lh","node(node(leaf(o,","node(node(leaf(y,","node(str","node(tree_left,","node)","node,","node.","node.createbranch(leftchild,","node.createleaf(n.key,","node.left","node.right","node.right;","node1","node1,","node1.weight","node1[2]","node2","node2,","node2.weight)","node2[1]","node2[2]","node3","node_ptr","nodeheap","nodeheap)","nodeprioritylist","nodeprioritylist()","nodeprioritylist(list","nodeprioritylist(nodes);","nodeprioritylist.","nodeprioritylist.add(parentnode);","nodeprioritylist.pop();","nodes)","nodes.count;","non","none","noprefix","not,","note:","noth","now","now)","null","null)","null);","null,","null;","number","o","o.frequency));","object","object.entries(charcounts).map(([key,","occur","offset","offset]","ok","old","old[0","old[l","on","on.","one:p)]","onto","option","option[node]","option[node]):","ord","order","ordering,","origin","original:","originalstr","originaltext","originaltext)","other)","other.count()","other.count().cmp(&self.count())","other.count().partial_cmp(&self.count())","other.weight;","other:","otherwis","out","out)","out);","out.push_back(std::make_pair(l","output","outright","over","overflow","p","p)","p)]","p.first","p.first;","p.key","packag","pad","pair","pair:","pairs(map)","panic!(\"unexpect","paramet","params:","parent","parent_index","parent_index;","parentnod","part","partial_cmp(&self,","partialeq","partialord","partialord};","path","patholog","peek(weights)[2]","phrase","phrase)","phrase.flatmap(c","phrase::string)","place","pointer","pop","pop()","posit","possibl","practice.","principle,","print","print('codebook:","print('codebook:',","print('decod","print('encod","print('huffman","print('message:","print('message:',","print_codebook","print_messag","printcodebook()","printf","printf(\"codebook:\\n\");","printf,","println!(\"{:#?}\",","println!(\"{}\",","println(\"codebook","println(\"decod","println(\"encod","println(\"origin","prioriti","priorityqueu","priorityqueue()","priorityqueue.add(new","priorityqueue.dequeue();","priorityqueue.enqueue({","priorityqueue.remove();","priorityqueue<>(comparator.comparingint(o","priorityqueue[node]()(ordering.by(","priorityqueue{node,","priorityqueue}","privat","problem","process","professor","program","program.c","project","project!","proper,","provabl","provid","ptr","ptr,","pub","public","public:","pull","push","push(x","push/pop","put","putstrln","python","qualifi","question","queue","queue,","queue.len()","queue.pop().expect(\"th","queue.pop().unwrap();","queue.push(huffmantree::branch","quick","qword","qword]","r\"(bibbiti","r,","r10,","r10b,","r11","r11,","r11]","r12","r12,","r12:","r12d","r13","r13,","r13:","r13d","r13d,","r14","r14,","r8","r8,","r8d,","r9","r9,","r9b","r9d,","rang","range\");","rax","rax,","rax:","rax:rdx","rbp","rbp,","rbx","rbx,","rcx","rcx,","rdi","rdi,","rdx","rdx,","reach","read","readabl","readi","realli","realloc(*dst,","realloc(heap","recurs","recurse(node,","recurse(node.left,","recurse(node.right,","recurse(tree,","reduc","ref","regist","registers:","remain","rememb","remov","repeat","replac","repres","represent","request","requir","resourc","respect","restor","result","result)","result);","result.dictionary)","result.join(\"\");","result.push(node.key);","result.push(value);","result:","result;","results,","ret","ret);","ret,","ret.pop_back();","ret.push_back(p.second);","ret;","return","return:","return;","revers","reversecodebook","reversecodebook.put(m.getvalue(),","revert","rh","rhs(std::move(rhs))","rhs)","rhs.frequency;","rhs;","right","right)","right))","right));","right),","right,","right.count(),","right.decode_dfs(&input[1..],","right.dfs(code.clone()","right.freq","right.frequency,","right.weight,","right:","right::union{leaf,","right;","rightchild","rightchild)","rightchild);","rightchild.key,","rightchild.weight,","rightchild;","rip","robert","robust","root","root\")","root)","root))","root,","root.left","root.right","root;","round","rsi","rsi,","rsp","rsp,","rune","s","s\"","s)","s)))","save","scala.collection.mutable.{map,","schacher","schloss","school","scratch","scratch:","search","second","section.","see","self","self,","self.count()","self.decode_dfs(&input[start..],","self.dfs(string::from(\"\"),","self.tree.decode(input)","seq","set","set\");","set;","shannon","share","sharealik","shl","shouldn't","show","shr","simpl","simpli","singl","sit","size","size_t","sizeof(codebook","sizeof(struct","skip","small","smaller","smallest","snippet","so:","some('0')","some('1')","some(c)","somewhat","sort","sort)","space","special","specif","src)","src);","src,","src_len","st","st)))","stack","start","static","std::back_inserter(ret));","std::back_inserter(ret),","std::begin;","std::cerr","std::cmp::{ord,","std::collections::{binaryheap,","std::copy(begin(code),","std::cout","std::end;","std::find_if(","std::find_if(begin(encoder),","std::find_if(begin(ret),","std::for_each(first,","std::invalid_argument(","std::invalid_argument(\"attempt","std::make_pair(it,","std::make_pair(last,","std::make_shared(","std::make_unique(l);","std::make_unique(std::move(lhs),","std::move(bits)));","std::move(encoder)});","std::move(ret.back());","std::move(rhs));","std::pair","std::shared_ptr","std::sort(begin(freq),","std::string","std::transform(","std::vector","std::vector(),","std::vector();","std::vector;","std::vector>();","std::vector>;","step","still","store","storm,","str","str(codebook))","str(tree))","str)","str:gmatch(\".\")","str[257];","straight","straightforward","strcat(*dst,","string","string\"","string(char)","string(code)","string(code,","string(codes.encode(begin(s),","string(cur.char)","string(current.key)","string(huffman_tree.key)","string(i)","string)","string):","string,","string:","string::from(\"\");","string;","string]","string]()","string]):","stringbuild","stringbuilder());","stringbuilder();","stringtoencode)","stringtoencode;","string},","strlen(*dst);","strlen(src);","struct","sub","submit","subtract","success","such","suddenli","sum","sure","swap","swap(&heap","swap(i,","swap(struct","switch","system","system.","system.collections.generic;","system.collections;","system.console.writeline($\"{entry.key}","system.console.writeline($\"{result.bitstring}","system.console.writeline(originalstring);","system.linq;","system.out.println(\"cod","system.out.println(\"decod","system.out.println(\"encod","system.out.println();","system.out.println(m.getkey()","system;","t","t)","t1","t1)","t2","t2)","t2,","tabl","table.remove(freq)","table.remove(freq),","table.sort(arr,","take","taken","talk","target","target),","target;","temp_nod","temp_node,","temp_node.weight)","temp_str","temp_string))","templat","temporarili","termin","test","tests\"","text","text.","text:","thank","that'","theorist","thing","this.bitstr","this.data","this.data.findindex(x","this.data.push(value);","this.data.shift();","this.dictionari","this.frequ","this.key","this.left","this.leftchild","this.lett","this.nod","this.nodes.binarysearch(newnode);","this.nodes.sort();","this.right","this.rightchild","this.stringtoencod","this.tre","this.weight","this:","through","throw","time","time.","tmp","tmp;","to_be_encod","togeth","together.","together.)","too!","top","top.","top;","tosortedlist","total","touch","track","trait","traverse(node.left,","traverse(node.right,","traverse(root,","traverse(treenod","treat","tree","tree\"","tree'","tree)","tree))","tree)))))","tree));","tree))]","tree);","tree*","tree*));","tree**","tree,","tree.","tree.dequeue()","tree.headopt","tree.make_codebook();","tree:","tree:',","tree;","tree?","tree[1]","tree_count,","tree_count]","tree_count],","tree_free(struct","tree_free(tre","tree_left","tree_left,","tree_left,weight_left","tree_left]","tree_left],","tree_right","tree_right)","tree_right,","tree_right,weight_right","tree_right]","tree_right],","tree_siz","tree_size,","tree_value,","tree_value]","tree_value],","treenod","treenode(int","treenode(left.frequ","treenode(m.getkey(),","treenode(str","trees.insert(index,","trees.pop()","trees.popleft()","trees:","trees[0]","tree}","tricky.","ts","two","two_pass_huffman(\"b\")","two_pass_huffman(\"bbbbbbbb\")","two_pass_huffman(\"bibb","two_pass_huffman(phrase::string)","type","uncom","under","underlying_","underlying_;","understand","union{leaf,","uniqu","unit","unititialized,","unreachable()","unreachable();","until","up","us","use:","usiz","usual","v","val","valu","value\"","value)","value,","value.weight);","value:","value;","values.","var","vec","vec)]","vector","video","void","v}","want","way","we'll","we'r","we'v","weight","weight(leaf(char,","weight(left)","weight(new_tree))","weight(node(left,","weight(right)","weight(tree())","weight)","weight,","weight:","weight::int64","weight;","weight])","weight_left","weight_right","weights[temp_string]","weird","well,","whether","while(length(nodes)","while(length(weights)","whole","with.","with_new_bit(bits,","with_new_bit(std::move(bits),","with_new_bit(std::vector","without","word","work","world","write","written","x","x)","x.(*node);","x.weight","xmm0","xmm0,","xmm1","xmm1,","xmmword","xor","xorp","y","zero","zero:p),","zip","{","{\"\"","{:messag","{entry.value}\");","{k,","{node1[1],","{result.bitstring.length}\");","{self.n})'","{str(self.right)})'","{}","{});","|","|>","|mut","||","}","})","}));","});","},","};"],"contents/computer_graphics/computer_graphics.html":["activ","algorithm","anyth","appear","appli","applic","approxim","archive,","area","argu","around","art","art.","be.","beautifulli","between","bit","boundari","broadli","canni","change,","classifi","climate,","closest","complet","comput","consid","convolutions,","cover","creat","current","desktop","detail","details,","detect","differ","direct","distinctli","edg","effort","end,","enough","example,","eye.","fastest","feel","field","find","fluid","focus","free","further","game","good","graphic","graphics.","hand","hardwar","high","hire","however,","imag","images.","immedi","impact","instead","instead,","interest","know","known","learn","look","machin","man","mani","media,","more","movi","multimedia","none","paint","part","pixar","plot","possibl","precisely.","progress","provid","publish","purpos","rang","realist","released.","render","repres","research","research,","research;","resolut","rigor","run","scienc","scientist","section","simpli","simul","simulation.","softwar","spend","stori","studio","sub","subject","support.","tell","think!","those","though","truth!","untrain","us","vague,","via","video","visual","wavey,","wide","without","work","world.","write","year"],"contents/quantum_information/quantum_information.html":["(#560),","(found","128","3","4.0","add","adequ","advantag","ago,","agree;","algorithm","algorithm?","algorithms,","algorithms:","already.","always,","amount","ask","attempt","attribut","basically,","be","being,","bit?","bitlogic:","boast","book","build","c.","chang","chapter","chapter:","circuit","circuits:","classic","closest","code","code.","common","commun","compil","compiler,","comput","computers.","creat","creativ","current","d","deserv","differ","discuss","distil","done","exampl","exist.","expect","experiment","fact,","fantast","far","field","final","first","follow","fundament","further","futur","gate","go","graphic","hard","head","help","home.","hope","however,","ill","imagin","implement","import","imposs","impress","industri","inform","information.","initi","instead,","intense.","interfac","intern","introduct","intuit","is...","isn't","it'","item","jame","knowledg","knowledge.","languag","language.","licens","license.","license.md).","list.","look","machine,","make","mani","market","mechanics.","mit","model","modifi","more","none","note,","now,","number","numer","obviou","on","out","outdo","own.","peopl","perform","phenomen","place","point","potenti","promis","pull","purpos","purpose.","pursu","quantum","qubit","qubits!","qubits,","readi","real","realiz","realized.","realli","relat","request","requir","research","schloss","section","seem","shake","sharealik","shor'","short,","simul","simulator,","spice","start","step","strong","subject","suit","summary,","survey","system","techniqu","tell","tend","text","textbook","theori","theory,","think","through","time","time,","time:","topic","tri","true","truli","under","understand","univers","up","updat","wave,","way","we'll","wild:","work","writing,","written"],"contents/stable_marriage_problem/stable_marriage_problem.html":["!!this.fiance;","!=","!==","!haskey(pairs,","\"","\"\"\"determin","\"\"\"find","\"\"\"pick","\"\"\"propos","\"\"\"return","\"\"\"set","\"#{@name.rjust(20)}:","\"#{prefix}","\"(\"","\")\";","\".join(p.nam","\":\");","\"b\",","\"c\",","\"d\"]","\"f\",","\"g\",","\"h\"]","\"lonely\"","\"man\",","\"round","\"stable\"","\"unstable\")","\"woman\",","#","#includ","#{i}\",","#{round}\"","#{self.lonely?","$","$fianc","$groupsiz","$i","$man","$man)","$man):","$man;","$match","$match)","$match):","$match;","$men","$men,","$men;","$name;","$prefer","$preference)","$preferences):","$preferences;","$thi","$unmarri","$woman","$woman)","$woman,","$women","$women):","$women);","${girl.preferences.map(p","${guy.fiance.name}`);","${guy.preferences.map(p","%","%s',","&&","&women[man","'","'%","'__main__':","'a';","(!))","(!empty($thi","(!girl.hasfiance)","(!preferredmates.isempty())","(!prefers_partner(woman","(!woman","(#560),","($i","($man","($men","($prefer","($thi","($unmarried);","($woman","($women","((man,","(0","(20","(\\(w,","(a,","(bachelors.nonempty)","(boyfriend,","(char","(const","(elemindex)","(follow.partn","(found","(girl.prefers(guy))","(husband,","(i","(interest.partn","(jspp)","(let","(lonelyfollows.count","(m,","(m,_))","(m.fromlist","(man,","(map","(map,","(mate","(mostdesir","(ord","(person","(propos","(size_t","(size_t)rand()","(tail","(this.mat","(var","(w,","(which","(woman)","(woman.prefers(this))","(women!theone)",")","*","*/","*array,","*group,","*man","*partner;","*prefers;","*sooner*","*woman","+","++=","+=",".","...","/*","//","//alway","0","0)","0,","0;","1","1));","1);","1.step","10;","1;","1]","1];","2","2)","20","26","4.0","5","5);","5;",":","::",":id,",":name",":partner","=","==","===","=>",">",">>=",">choosematch();",">getmatch());",">getname(),",">getpreferences()));",">id,",">index++;",">index]];",">issingle())",">match",">match;",">name;",">partner",">partner)",">partner;",">prefer",">preferences))",">preferences);",">preferences;",">prefers,",">prefers[man",">propose();",">receiveproposal($this);",">setmatch($preference);",">setmatch($this);",">setpreferences($preferences);",">suitor",">suitors))",">suitors[]",">unmatch();","?","?person","@choic","@id","@name","@partner","@partner.name}\"","@partner.nil?","@partner.partn","@partner.sett","@pref","@prefs.index(partner.id)","@prefs.siz","@prefs[@choices]","@properti","[\"a\",","[\"e\",","[&]","[(a,","[(b,","[...\"abcde\"].map(nam","[...\"fghij\"].map(nam","[...iterable];","[0,","[]","[];","[a]","[a])]","[array[i],","[array[j],","[b]))","[b])]","[m","[person(name)","\\mathcal{o}(n^2)","_","__init__(self,","__name__","__str__(self):","__tostring():","`and`","`first`","`not`","`number_of_partners`.","`person`","`preference_list`","`second`","a,","a.prefer","act","again","aim","algorithm","algorithm,","algorithm.","all((man.has_partn","allow","alreadi","alway","amara","anymore.","appear","args)","around","array","array.length","array.new(size){|i|","array;","array[i]","array[i];","array[i]];","array[j]","array[j];","array[j]]","array[string]):","array_shift($thi","arraylist<>();","arraylist<>(mates);","ascii_lowercas","ascii_lowercase[:num_pairs]]","ascii_uppercase,","ascii_uppercase[:num_pairs]]","associ","assum","attempt","attr_read","attr_writ","attribut","auto","b","b)","b)]","b,","b.prefer","bachelor","bachelor,","bachelors.dequeue.propose()","bachelors.enqueue(this)","bachelors.push(girl.fiance);","bachelors.shift();","bachelors[","bachelors[bachelors_s","bachelors_size]","back","back,","base(name)","becker","becom","belt.","bool","boolean","both","boyfriend","break","break;","c","c)","c++14,","c,","c.prefer","call","candid","candidate,","carri","case","case,","chanc","chang","change.","chapter","chapter:","charact","choic","choice,","choice.","choices,","choices:","choices[currenttopchoiceindex++];","choosematch():","choosemate()","claim","class","clear,","code","collections.shuffle(preferredmates);","column","come","common","compil","conceptu","consid","console.log(\"\\ngirls\");","console.log(\"\\npairings\");","console.log(\"guys\");","console.log(`${girl.name}:","console.log(`${guy.name}:","console.println(","console.write(choice.name);","console.writeline(\"galeshapleyalgorithm\");","console.writeline();","console.writeline(man.nam","console.writeline(woman.nam","const","constructor(name)","continu","control.monad.st","copi","copy(men)","copy(women)","correctly.","counted.","coupl","creat","create_group(struct","creativ","current","currenttopchoic","currenttopchoiceindex","data.list","data.map","decreas","def","definit","delete!(mentowomen,","describ","determin","determinist","dict(map(m","dict(map(w","dictionary,","dict{string,string}","dict{string,string}()","dict{string,vector{string}}","doesn't","don't","don't.","duplicates.","each","echo","effici","elegantli","elemindex","elif","elseif","end","end(ret),","engag","equal","evalst","even","everybodi","everyon","everyone'","exampl","example.","except","explan","extend","f'{self.name}:","fals","false;","favorit","feel","female,","fianc","fiance.recieveproposal(this);","fiance:","final","find","findfirst(m","findstablemarriages(list","findstablemarriages(women,","findstablematches(men:","finished;","first","first,","follow","followit","follows)","follows,","follows:","foreach","free","free_group(men,","free_group(struct","free_group(women,","function","futur","gale","galeshapley(men,","galeshapley(men::preferences,","galeshapleyalgorithm","galeshapleyalgorithm.c","galeshapleyalgorithm.rungaleshapleyalgorithm(women,","gave","gender","gener","generators.","genpreferences(mannames::vector{string},","genpreferences(mnames,","get","get;","getclass().getname()","getmatch():","getmate()","getname():","getnexttopchoice();","getpreferences():","getpreferredmates()","girl","girl.prefer","girls)","girls);","give","given","global_random_device;","global_rng(global_random_device());","global_rng);","go","graphic","great","group","group.","groups,","guarante","gustorn","guy","guy.engageto(girl);","guy.prefer","guy.preferences)","guys)","has_partner(self):","hasfiance()","have","head","header","help","henc","here","however,","husband,","i)","i,","id","id);","id;","ilist","imagin","implement","implode(',',","import","in_array($preference,","incred","index","index;","indexerror:","individu","initi","initialize(id,","instead","int","interest","interest'","interest.choices.indexof(thi","intern","isfree(candidate,","isfree(m,","isfree(person,","islonely()","issingle():","isstable(men::preferences,","it.","iter","j","jame","java.util.arraylist;","java.util.collections;","java.util.list;","julian","keys(men)","lead,","leadit","leads'","leads)","leads,","leads;","leads_end","leads_end,","leastcommongend","left","length(bachelors)","less","licens","license.","license.md).","list","list\"\"\"","list()","list())","list(),","list();","list(a,","list(b,","list(c,","list(follows);","list(men).shuffle(random);","list(women).shuffle(random);","list(x,","list(y,","list,","list[man]","list[woman]","listextens","listextensions.c","lone","lonely!'","lonely.","lonely?","lonelyfollow","lonelyfollow.proposetonext();","lonelyfollows)","longer","look","m","m.assoc","m.empti","m.getpreferredmates());","m.insert","m.propose(women)","m.receiveoptions(women);","main()","main():","main(args:","main(string[]","make","make_person_list(size_t","male,","man","man(\"a\"),","man(\"b\"),","man(\"c\"),","man(\"d\"),","man(\"e\")","man(name:","man(str","man):","man*):","man.choic","man.choices)","man.has_partner:","man.prefer","man.propose_to_next()","man;","mani","mannames))","map","mariu","marri","marriag","marriages\"\"\"","married,","match","mate","mate)","mate,","mate.","mate.m","mate;","mates)","math.floor(math.random()","mathjax.hub.queue([\"typeset\",mathjax.hub]);","mean","member","men","men)","men)):","men);","men,","men.foreach(m","men.select(&:lonely?)","men.to[queue]","men/women","men:","men:')","men[bachelor]","men[husband]","mentowomen","mentowomen)]","mentowomen,","mentowomen::pairs,","mentowomen[bachelor]","mit","mname","modifi","more","mostdesir","msvc","much","n.","name","name)","name):","name,","name;","namespac","need","new","newlonelyfollow","newlonelyfollows.add(follow);","newlonelyfollows;","next","next_choice(self):","nil","nobodi","none","none)","none:","not.\"\"\"","noth","now","now,","npair","null","null)","null;","num_pair","number","number_of_partn","number_of_partners)","number_of_partners),","number_of_partners,","numer","object","offer","old","on","one.","onpropose(partner)","oppos","option[man]","ord","order","output","output,","over","p","p.name).join()}`)","pair","paired,","pairs)","pairs.","partner","partner(self):","partner(self,","partner.nil?","partner.partn","partners.","partners[choice].onpropose(self)","pass","peopl","person","person'","person(name));","person(str","person)","person):","person,","person.","person._partner)","person.c","person.candidates.append(self)","person.generate(4,","person.new(","person:","person{false,","php_eol;","pick","pick_preferred(self):","planb)","poor","possibl","possible.","pref","pref))","pref):bachelors)","prefer","prefer,","preference;","preference_list;","preferences.indexof(man)","preferences:","preferred\"\"\"","preferredm","preferredmates)","preferredmates.remove(0);","preferredmates;","prefers(man:","prefers(men,","prefers(other)","prefers(prefs,","prefers(women,","prefix,","prefs)","prefs[person])","print","print('\\n')","print('prefer","print('th","print()","print(f'{man.name}","print(man)","print(woman)","printf('%","printf('%s\\'","println(isstable(men,","println(mentowomen)","privat","problem","problem.","problem:","process","program","program.","program.c","propos","proposal_index","proposals(number_of_partners);","propose()","propose():","propose(partners)","propose_to_next(self):","proposetonext()","protect","provid","public","pull","put","qualifi","queue[man]()","r","r)","rais","random","random();","random.new(42)","random_pref_list","random_pref_list()};","randomli","rang","rank","receiveoptions(list","receiveproposal(person","recieveproposal(man","reject","remainingprefer","remov","request","result","ret(number_of_partners);","ret;","return","rng)","run","rungaleshapleyalgorithm(list","runtime.","scala.collection.mutable._","schacher","schloss","score(@partner)","score(partner)","second","second)","second,","see","seed","seem","select","self","self._partn","self._partner._partn","self._partner:","self.candid","self.candidates.clear()","self.candidates:","self.generate(size,","self.has_partn","self.has_partner()","self.lonely?","self.nam","self.next_choic","self.partn","self.partner:","self.pref_index","self.prefer","self.preference)}'","self.preference:","self.preference[self.pref_index]","set","set;","setmatch(person","setmate(mostdesired);","setmate(person","setpreferences($preferences);","setpreferences(array","shapley","sharealik","shuffl","shuffle($preferences);","shuffle(girls);","shuffle(guys);","shuffle(iterable)","shuffle(man.preference)","shuffle(mannames)),","shuffle(size_t","shuffle(thi","shuffle(woman.preference)","shuffle(womannames)),","simple,","simpler,","simpli","singl","singles.each","singles.empty?","size","size)","size))","size).to_a.shuffle(random:","size_t","size_t(0));","solution:')","solv","some(otherman)","some(this)","someon","someone,","sort","spacer","stabl","stable.","stable_marriage($men,","stable_marriage(array","stable_marriage(men,","stable_match(leadit","stablemarriag","stablemarriage(guys,","stablemarriage.findstablematches(a,","stablemarriage.man(\"adam\")","stablemarriage.man(\"bart\")","stablemarriage.man(\"colm\")","stablemarriage.woman(\"xena\")","stablemarriage.woman(\"yeva\")","stablemarriage.woman(\"zara\")","stablemarriageexampl","stablemarriageproblem","stablematch","state","static","stay","std::generate_n(std::back_inserter(ret),","std::iota(begin(ret),","std::mt19937","std::optional,","std::random_devic","std::shuffle(begin(ret),","std::size_t;","std::vector","still","story.","string","string,","struct","subjective.","submit","suitor","suitor)","suitors.add(suitor);","suitors.contains(mostdesired))","super(name);","symmetrical,","system.collections.generic;","system.out.println(m","system.out.println(w","system;","templat","tent","text","tfollow","that'","them.","theon","this.mat","this.mate.m","this.nam","this.preferences.indexof(other)","this;","though","thread_loc","through","tlead","tmp","tmp;","to.","to_","told","tool","top","topchoice,","tostring()","tpref","translat","tri","tricki","true","true:","true;","try:","tself","tself)","two","under","unit","unless","unmatch():","until","up","updat","upon","us","val","var","video","void","w","w))","w.fiance.getorelse(stablemarriage.man(\"nobody\")).name))","w.getmate()));","w.getpreferredmates());","w.name","w.receiveoptions(men);","want,","we'll","we'r","well\"\"\"","whether","whichev","wife","wife)","within","without","wname","wnames)","woman","woman(\"f\"),","woman(\"g\"),","woman(\"h\"),","woman(\"i\"),","woman(\"j\"),","woman(name:","woman(str","woman.choic","woman.choices)","woman.fi","woman.pick_preferred()","woman.prefer","woman;","woman?.partner.name);","womannames))","womannames::vector{string})","women","women)","women):","women,","women.","women.size()","women/men.","women:","women:')","women::preferences)","women::preferences,","womentoman::pairs)","womentoman[candidate])","womentomen","womentomen)","womentomen[candidate]","womentomen[candidate])","won't","worri","written","x","x)","x,","x.prefer","y","y)","y,","y.prefer","z","z)","z).foreach(","z,","z.prefer","{","{\",","{man.partner.name}')","|m|","|round|","||","}","});","};"],"contents/flood_fill/flood_fill.html":["\"bucket","\"circl","\"exampl","\"fill","\"grid","\"queue","\"stack","\"x","#","#includ","%","&&","'__main__':","'pass","(!queue_empty(q))","(!stack_empty(stk))","((point(0,","(auto","(c.data[cur_loc.x","(canva","(found","(grid[x][y]","(inbounds(canvas.shape,","(inbounds(size,","(int","(loc[0]","(old_val","(old_valu","(p.x","(q","(q.size()","(s.size()",")","*","*));","*/)","*=","*data;","*neighbors)","*q)","*stk)","*tmp","+","+=",".=","/*","0","0)","0))","0),","0)]","0,","0.","0.0,","0.75.","0;","0},","0}};","1","1\"","1)","1),","1,","1,1","1.0","1.0)","1.0);","1.0.","1.bucket","1;","1},","1};","2","2\"","2),","2016.","2020.2.torbert,","2;","3","3\"","4","4\"","4.0","5\"","5))","5x5","6\"","8",":",":]","=","==",">",">=",">back",">back]",">capac",">capacity)",">capacity;",">data",">data);",">data,",">data[",">data[0]));",">data[0]);",">data[q",">data[stk",">front",">front)",">front,",">front];",">top++]",">top];","?","?,","@test","@testset","[","[1].","[2].","[]","[loc","[location]","[p]","]","__add__(self,","__name__","abil","about.","abov","above.","actual","ad","add","additionally,","adequ","after,","again","again.","algorithm","alreadi","alway","anim","anoth","answer","answer_grid","answer_grid[1:3,","appli","applic","appropriately.","archiv","archive.","are:","area,","around","array","art","ask","aspect","assert(test_grid","attribut","auto","avail","back,","base","basics:","be","becom","befor","before,","before.","before;","begin","below:","beneath","best","better","between","beyond","bibliographi","bit","border","both!","bound","boundari","breadth","browser","bucket","c)","c,","c.data[cur_loc.x","c.data[p.x","c.max_i","c.max_x","c.max_x)","call","calloc((q","canva","canvas[cur_loc]","canvas[current_loc]","canvas[current_location]","canvas[loc]","canvas[location]","canvas[neighbor]","canvas[neighbour]","canvas[p]","canvas[possible_neighbor]","canvas[x]","canvas_size[1]","canvas_size[2]","capacity;","cartesianindex","cartesianindex(","cartesianindex(0,","cartesianindex(1,","cartesianindex(1,1)","cartesianindex{","case","case,","cases.","caveats.","center","center,","certain","chang","chapter","chapter,","chapter:","chapters,","chapters.","check","choos","chunks.","circl","circle,","close","cnt","coconut.","code","code,","collect","color","colored.","come","common","common,","commonli","complet","complic","compos","comput","conclus","connect","consid","consist","const","const&","constraint","consum","consume(","content","continu","correct","cover","creat","creation","creativ","cur_loc","cur_loc,","cur_loc.y]","current","current_loc","current_loc,","current_location,","data","datastructur","decid","def","defin","depth","dequ","deque()","dequeue!(q)","dequeue(&q);","dequeue(struct","describ","determin","diagon","differ","differences:","difficult","dimension","direct","directions,","dirti","discuss","disguise.","dissimilar","distinct","do","do,","do?","domain","domain,","domains\"","domains:","doubli","down,","duplic","each","easi","easier","easiest","east","east,","effici","efficient.","element","element.","element;","elements,","else:","elseif","embed","enclos","end","end='')","enough","enqueu","enqueue!(q,","enqueue!(q,neighbor)","enqueue(&q,","enqueued,","enqueued:","ensur","essenti","evenli","everyone.","exampl","example,","exclud","exclus","exist","exist,","exit_success;","explain.","explan","extent","failure_count","failure_count))","failures')","fals","false;","fashion.","featur","feel","few","fewer","fill","fill\"","fill,","fill.","fill?","filter$(x","final","final_canvas).all()","final_canvas,","find","find_neighbors(","find_neighbors(c,","find_neighbors(canvas,","find_neighbors(grid,","find_neighbors(struct","find_neighbours(canvas,","first","first.","fix","flavor.","float","floats,","flood","focu","follow","food","four","free(q","free(q.data);","free(stk.data);","free_queue(struct","free_stack(struct","front","front,","function","function(canvas)","function):","further","game,","gener","get_queue(sizeof(struct","get_stack();","gimp,","girlfriend,","glance,","go","go.","graph","grid","grid,","grid;","grid[1:2,:]","grid[2,:]","grid[3,:]","grid[neighbor_x][neighbor_y]","grid[x][y]","grid{","hand","hardwar","help","here","here,","hop","however,","iceberg","icon","idea","imag","image,","images/graph","imagin","immedi","implement","import","inbounds(canvas.shape,","inbounds(canvas_shape,","inbounds(canvas_size,","inbounds(cartesianindex","inbounds(size(canvas),","inbounds(struct","includ","increases,","incred","indic","individu","initi","initial_canva","initial_canvas.copy()","insid","instead","int","intens","intern","intuit","issue,","it!","it'","itself,","jame","journey","keep","kinda","known","languag","larg","leav","left","left,","length(q)","length(s)","less","lest","let","let'","licens","license.","license.md).","line","list","loc","loc)","loc,","loc::cartesianindex,","loc[1]","loc[1]},","loc[1]}};","locat","location!","location):","location,","location.x","long","look","lot","main()","make","manag","mani","manual","map$(location.__add__))","map$(recursive_fill$(canvas,","mask","mathjax.hub.queue([\"typeset\",mathjax.hub]);","max_x,","max_y;","maximum","me,","mean","memcpy(tmp","memcpy(tmp,","memori","method","method,","method.","methods\"","methods,","methods.","min(location)","min(p)","minesweep","minimum(tuple(loc))","mit","months,","more","n","namedtupl","namedtuple(\"point\",","namedtuple('testresults',","namely,","necessary,","need","neg","neighbor","neighbor,","neighbor_i","neighbor_x","neighbors);","neighbors,","neighbors.","neighbors.append(possible_neighbor)","neighbors.push_back(possible_neighbor);","neighbors:","neighbors;","neighbors[4];","neighbour","new_val","new_val)","new_val):","new_val:","new_val;","new_valu","new_value)","new_value))","new_value):","new_value);","new_value;","next","next.","node","node!.","node,","node.","nodes.","nodes:","north","north,","northeast,","northwest","now","now,","np","np.zeros((5,","number","numpi","obviou","old","old_val","old_val)","old_val,","old_val:","old_valu","old_value)","old_value))","old_value):","old_value,","old_value:","on","oper","optim","optimally.","other.x,","other.y)","others.","otherwise,","out","outsid","own,","p):","p);","p,","p.i","p.x","p.y),","p.y+1),","p.y]","p.y}","p.y},","parts:","pass_count","pattern","pattern.","phd,","pixel","pixel.","play","point","point(","point(0,","point(1,","point(p.x","point(p.x+1,","point(p.x,","point(self.x","point(x,","point)","point,","points[4]","pop!(s)","possibl","possible_neighbor","possible_neighbor)","possible_neighbor):","possible_neighbor,","possible_neighbors)","possible_neighbors:","possible_neighbors{","possible_neighbour","potenti","predefin","prevalent.","previou","print('.',","print('f',","print()","print(testresults(pass_count,","probabl","problem","proce","process","program","progress","properti","property.","purpos","purposes.","push","push!(neighbors,","push!(s,","push!(s,neighbor)","put:","q","q)","q.empty():","q.front();","q.get()","q.pop();","q.push(loc);","q.push(neighbor);","q.put(neighbor)","q.put(p)","queri","queue","queue()","queue.","queue.append(location)","queue.append(neighbour)","queue.popleft()","queue:","queue_fill!(canvas,","queue_fill!(grid,","queue_fill$(?,","queue_fill(","queue_fill(canvas,","queue_fill(struct","queue_fill(test_grid,","queue_test_func","queue_test_func):","queue{cartesianindex}()","quick","rang","reach","readi","realloc(stk","reasons:","recurs","recursion.","recursive_fill!(canvas,","recursive_fill!(grid,","recursive_fill$(?,","recursive_fill(","recursive_fill(canvas,","recursive_fill(grid,","recursive_fill(struct","recursive_fill(test_grid,","recursive_test_func","recursive_test_func):","red.","regularli","reiniti","remaind","replac","restrict","ret","ret;","return","return;","review","rgb.","right","row","run","s","s.pop();","s.push(loc);","s.push(neighbor);","s.top();","same","savor","scale","scanlin","scheme","schloss","science,","sections.","see","seem","select","self.i","sens","separ","set","setup","sever","shane,","share","sharealik","show","shown","side","similarli","simpl","simpler","simplest","simpli","simulation.","singl","sit","situat","six","size","size);","size,","size[0]","size[1])","size_t","sizeof(q","sizeof(stk","slightli","slower","small","so,","so:","solut","solution_grid","solution_grid);","solution_grid,","solution_grid[:3,]","solution_grid{","someon","someth","somewhat","sort","south,","southeast,","southwest,","space","space,","split","spread","springer,","stack","stack,","stack.extend(find_neighbours(canvas,","stack.pop()","stack:","stack_fill!(canvas,","stack_fill!(grid,","stack_fill$(?,","stack_fill(","stack_fill(canvas,","stack_fill(struct","stack_fill(test_grid,","stack_pop(&stk);","stack_pop(struct","stack_push(&stk,","stack_test_func","stack_test_func):","stack{cartesianindex}()","stage,","start","start_loc","start_loc,","start_loc{1,","starting_loc","starting_location,","state","static_cast(current_loc[0]);","static_cast(current_loc[1]);","static_cast(grid.size())};","static_cast(grid[0].size()),","static_cast(loc[0]);","static_cast(loc[1]);","static_cast(neighbor[0]);","static_cast(neighbor[1]);","static_cast(possible_neighbor[0]);","static_cast(possible_neighbor[1]);","std::array;","std::queue{};","std::stack{};","std::vector","std::vector>","std::vector>&","step","still","stk","stk)","stop","straightforward","straightforward.","strategi","strategy,","strategy?","struct","structure,","sub","submit","subsect","subsequ","such,","superfluid","superimpos","support","sure","surprisingli","suspect","switch","tag.","take","termin","test","test()","test():","test_grid","test_grid(grid,","test_grid(initial_canvas,","testresult","text","them.","there.","this,","this:","those","though","thought","thought:","three","threshold.","through","throughout","time","time.","tip","tmp;","top","top,","track","travel","travers","traversal,","traversal:","tree","tri","trick","true","true;","two","type","ultim","unchang","under","understand","uniqu","unit","unless","unnecessari","up","up,","us","user","usual","valu","vari","variat","vector","version","vertic","vicinity,","video","visit","void","vortic","walk","want","wasn't","way","way,","way.","way:","west","west,","west.","wherev","whose","within","without","work","worri","worth","wrap","write","write,","written","x","x)","x,","y","y\")","y):","y;","yield","zeros(5,5)","{","{0,","{1,","{loc[0]","{loc[0],","{p.x","{p.x,","|>","||","}","};"],"contents/jarvis_march/jarvis_march.html":["!(*thi","!(a","!=","!counterclockwise(p,","\"","\",","\"]\");","\"__main__\":","\"angle\"","\"check","\"find","\"fmt\"","\"return","#","#includ","${p.y})`));","&&","&[point])","'__main__':","(","(!equal(end_point,","(#560),","((ab.getx()","(*","(0,","(15,","(17","(2,","(5,","(6,","(7,","(9,","(:constructor","(>","(\\(x,y)","(ab.gety()","(ab.magnitude()","(b.i","(b.x","(compar","(curr_point","(defstruct","(defun","(double,","(endpoint","(first","(found","(gift)","(hull[i]","(i","(i64,","(if","(jspp)","(lambda","(next","(null","(on)","(p.getx()","(p.i","(p.x","(p1","(p2.0","(p2.1","(p2.i","(p2.x","(p2[0]","(p2[1]","(p3.0","(p3.1","(p3.i","(p3.x","(p3[0]","(p3[1]","(point","(pointonhul","(pointonhull.equals(hull.get(0)))","(potentialnextpointonhul","(product","(reduc","(rest","(size_t","(sort,","(var","(x","(x,",")",");","*","*first_point_it);","*points,","+","+=","/","//","//add","//find","//found","//print","//test","0","0)","0);","0,","0.0","0.0)","0.0,","0;","1","1)","1));","1),","1)]","1,","1.0","1.0,","1.jarvis,","10,","10.0,","11","11));","11),","11.0","11},","12","12));","12),","12.0","12},","14","14));","14),","14,","14.0","14.0,","14},","15","15));","15),","15);","15,","15.0","15.0,","15},","1973","1973.","1;","1]","1],","1},","2","2)","2));","2),","2,","2.0","2.0,","23","2},","4),","4.0","5","5));","5),","5,","5.0","5.0,","5},","6,","6.0,","7","7));","7),","7,","7.0","7.0,","7},","8","8)","8));","8),","8.0","8},","9","9));","9),","9,","9.0","9.0,","9},",":","::",":=",";;;;","=","==","=>",">",">=","[","[1].","[]","[](const","[];","[]point","[]point)","[]point{{","[hull_point]","[point]","[point_on_hull]","[pos(2,1.5),","\\","\\mathcal{o}(nh),","]","];","_,","__name__","__str__(self):","`on`","a,","a.","a.equals(b);","a.getx(),","a.gety());","a.x","a.x)","a.y)","a.y);","a;","a==b","a@(xa,","ab","advanc","again","algorithm","algorithm,","algorithm.","angl","angle(endpoint,","angle(point","append(hullpoints,","approxim","are:\")","are:\\n\");","args)","arr)","array","arraylist","arraylist();","attribut","auto","b)","b);","b){","b,","b.","b.getx(),","b.gety()","b.gety());","b.x","b.y;","b;","b@(xb,","base","bc","bc.getx())","bc.gety()))","bc.magnitude()));","behind","between","bibliographi","bool","boolean","break","break;","c)","c.gety()","c==b","c@(xc,","calcul","call","candid","ccw(gift[j],","ccw(p1,","chan'","chapter","chapter:","check","choos","chosen","class","clockwise?","code","common","complet","completed.","console.log(`(${p.x},","const","convex","convexhul","convexhull.foreach(p","convexhull;","convexhull[0]);","counter","counter_clockwise(p,","counter_clockwise(p1","covered.","creat","creativ","cross","curr_point","curr_point)","curr_product","curr_product)","current","current)","current))","current;","data","data.funct","data.list","def","defin","develop","dimension","dimensions.","discuss","distribut","doesn't","dot","doubl","double)","draw","due","effici","else:","elsevier,","end","end_point","end_point;","endpoint","endpoint)","endpoint)):","endpoint):","endpoint.equal(hullpoint)","endpoint.equal(hullpoints[0])","endpoint:","endpoint;","equal","equals(object","equals(point","exampl","exist,","expect,","f'({self.x},","false;","field","filter","find","finit","first","first_point_it","float64","fmt.printf(\"x=%f","fmt.println(\"th","fn","follow","foreach","forward,","forward.","func","function","gener","gethashcode()","getx()","gety()","gift","gift\"","gift)","gift))","gift)))))","gift.add(new","gift.len()","gift:","gift[0]","gift[j]","giftwrap","giftwrap)","graham","graphic","great","greater","guarante","gustorn","h","help","here,","here.","higher","hull","hull)","hull.","hull.add(pointonhull);","hull.append(point_on_hull)","hull:","hull;","hull[","hull[0]","hull[1])","hull[1],","hull[i","hull[i],","hull_point","hull_points,","hull_points;","hull_points[0]));","hull_points[15];","hullpoint","hullpoint)","hullpoints[len(hullpoints)","i++;","i64);","i;","idea","identif","if(points.empty())","implement","import","includ","incred","initi","int","interior","intern","intial","isleftof(pointonhull,","isleftof(vector","item","item.x)","j","jame","jarvi","jarvis_cross(hull[i","jarvis_cross(point1::pos,","jarvis_cross(pos(0,0),","jarvis_march(const","jarvis_march(gift):","jarvis_march(gift:","jarvis_march(point","jarvis_march(points)","jarvis_march(points);","jarvis_march(points,","jarvis_march(points::vector{pos})","jarvis_march(test_gift)","jarvismarch","jarvismarch();","jarvismarch(arraylist","jarvismarch(gift);","jarvismarch(point","jarvismarch(points)","jarvismarch(points);","jarvismarch.c","jarvismarch.run(points);","java.util.*;","julian","keep","known","largest","lefmost","left","left_most_point(point","left_most_point(points)","left_most_point(struct","leftmost","leftmost.x","leftmostpoint(point","leftmostpoint(points)","len(gift)","licens","license.","license.md).","line","list","list()","list();","list,","lowest.","magnitude()","main","main()","main():","main(string[]","make","make([]point,","mani","map$(t","march","math.acos(","math.pow(y,","math.sqrt(math.pow(x,","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matter.","maximumbi","maximumby)","min(gift)","minimum","mit","modifi","more","move","mut","n","n):","namespac","new","next","none","note,","num_hull_point","num_points)","number","obj","obj)","operator!=(const","operator!=(vector","operator==(const","operator==(vector","option>","origin","otherwis","overrid","p","p)","p.getx()","p.gety()","p.x,","p.y)","p0","p0@(x,","p1","p1))","p1)))","p1)))))","p1.0)","p1.1)","p1.x)","p1.y)","p1.y)*(p3.x","p1.y);","p1[0])","p1[1])","p2","p2\"","p2)","p2,","p2:","p3","p3)","p3):","p3:","p:","p;","packag","plane,","pm","po","point","point&","point(","point(*t))","point(0,","point(15,","point(2,","point(5,","point(6,","point(7,","point(9,","point(b.getx()","point(c.getx()","point(doubl","point(double.max_value,","point(x=0,","point)","point,","point.","point1.x,","point1.y)","point2.i","point2.x,","point2.y)","point2::pos,","point3.i","point3::pos)","point[])","point[]:","point_on_hul","pointonhul","pointonhull,","points)","points,","points.","points.aggregate((leftmost,","points.end(),","points.reduce((leftmost,","points[0]","points[0];","points[1:]","points[1])","points[2]","points[]","points[j];","pos(1,","pos(2,","pos(3,","pos(point2.x","pos(point3.x","posit","potentialnextpointonhul","potentialnextpointonhull,","potentialnextpointonhull.","potentialnextpointonhull;","print","print(\"[#]","print(\"th","print(point)","printf(\"th","println(hull)","privat","process","product","product,","program","program.c","properti","pt","public","pull","push!(hull,","r.","random","rang","range(1,","ray","readonli","realli","ref))","repeat","repres","request","ret","ret_cross","ret_cross*ret_cross","return","roughli","run(list","runtim","scan","schacher","schloss","set","setup","sharealik","simple.","simul","simulation.","size","size_t","sort","sort!(points,","start","static","std::cout","std::min_element(points.begin(),","std::vector","std::vector&","struct","submit","system.collections.generic;","system.console.writeline(\"jarvismarch\");","system.console.writeline($\"{point.x},","system.linq;","system.out.println(\"[\"","system.out.println(\"gift:\");","system.out.println(\"wrapping:\");","system;","test_gift","text","there,","theta","this.i","this.x","this.x)","this.y;","though","time.","true,","true:","true;","turn","turn_counter_clockwise(p1:","two","type","under","until","us","v","v.x","v.y;","var","vec1","vec1.x*vec2.i","vec1.y*vec2.x","vec2","vector","vector(","vector(0,","vector(15,","vector(2,","vector(5,","vector(6,","vector(7,","vector(9,","vector(int","vector{pos}()","void","whichev","while(*next_point_it","wrap","wrap.","written","x","x,","x,y;","x:","x::float64","x;","x^2+y^2","xvalue,","xvalue;","y","y)","y)))","y)=","y:","y::float64","y;","y=%f\\n\",","y=0):","ya)","yb)","yc)","yvalue)","yvalue;","{","{0,","{15,","{2,","{5,","{6,","{7,","{9,","{point.y}\");","{self.y})'","|","|>","||","}","});","},","};"],"contents/graham_scan/graham_scan.html":["!=","\"\"\"comput","\"\"\"find","\"\"\"i","\"\\n\".join(map(str,","\"calcul","\"determin","\"fmt\"","\"left\"","\"math\"","\"right\"","\"sort\"","\"the","#","#[derive(debug,","#includ","$","${p.y})`));","%","&&","&hull[hull.len()","&point)","&point,","&self)","&start);","'__main__':","(","(!(o","(#560),","((>","((and","((b.x","((wrap","(*","(+","(/","(/=p0)","(0,","(15,","(2,","(5,","(6,","(7,","(9,","(:constructor","(=","(\\(px,","(a.i","(atan","(auto","(b.i","(b.x","(c.i","(c.x","(ccw(points[m","(compar","(cond","(defstruct","(defun","(double,","(eql","(found","(i","(if","(int","(label","(length","(let","(m","(o","(on)","(p.x,","(p1","(p1:p2:ps)","(p2.i","(p2.x","(p2:ps)","(p2[0]","(p2[1]","(p3.i","(p3.x","(p3[0]","(p3[1]","(p[1],","(pa","(pi","(point","(point)o;","(point.i","(px","(rest","(s:p1:p2:ps)","(s:ss)","(size","(size_t","(sort","(sorton,","(struct","(the","(x","(xa,","(xb","(xb,","(xc","(xc,","(y","(yb","(yc",")","*","*a,","*b)","*points,","*points.iter().min().unwrap();","+","+=",".collect(collectors.tolist());",".distinct()",".sorted(comparator.comparingdouble(point","//","0","0)","0)'.","0))","0,","0;","1","1)","1));","1),","1);","1,","1.0f,","1.0f\\n\",","1.graham,","10,","10,11),","11","11));","11),","11},","12","12));","12),","12},","14","14));","14),","14,","14},","15","15));","15),","15,","15;","15},","1972.","1:length(other_points)","1:n","1;","1]","1],","1];","1},","2","2)","2))","2));","2),","2,","2;","2],","2},","4.0","5","5));","5),","5,","5,2),","5},","6,","6,15),","7","7));","7),","7,","7},","8","8));","8),","8},","8}};","9","9));","9),","9,","9},",":","::",";",";;",";;;;","=","==","===","=>",">",">=",">y",">y)","@overrid","[","[(x,y)","[...points].sort((a,","[1].","[]","[]point","[]point)","[hull[i],","[hull[m],","[p0]","[p]","[point]","[s,","[start,","\\mathcal{o}(n\\log(n)),","\\mathcal{o}(nh)","]","];","__name__","__str__(self):","`on`","a).partial_cmp(&polar_angle(&start,","a,","a.x","a.x)","a.x))","a.x)*(c.i","a.x);","a.y)","a.y)*(c.x","a.y);","a;","abc","accord","algorithm","alway","angl","angle(self,","angle.","any.","append()","are:\"","are:\")","are:\");","aren't","args)","around","array","array.","arraylist","arraylist<>();","atan(item.i","atan2","atan2(p.i","atan2(point[1]","atan2(y1","attribut","b","b)","b)).unwrap());","b,","b.x);","b.y));","b.y,","b:","b::point,","b;","back","base","basic","be","between","bibliographi","bool","boolean","bottom","bottom.","break","break;","build","b|","c)","c:","c::point)","calcul","case","ccw","ccw(a,","ccw(a::point,","ccw(const","ccw(point","ccw(struct","chapter","chapter:","circl","class","clockwis","clockwise,","clockwise?","clockwise?\"\"\"","clone)]","cmp(&self,","cmp_points(const","cmp_points);","code","colinear","collinear","collinear.","come","common","complex","concav","concern","console.log(\"th","console.log(`(${p.x},","const","continue;","convex","convex,","convexhul","convexhull.foreach(p","coordin","copy,","counter","counter_clockwise(&hull[hull.len()","counter_clockwise(a:","counter_clockwise(hull[","counter_clockwise(p1,","counterclockwise\"","counterclockwise(p1,","cover","creativ","cross","data","data.funct","data.list","def","defin","del","depend","determin","develop","distribut","doubl","double)","duplic","each","effici","element","element.","elseif","elsevier,","empti","empty,","end","end,","eq","equals(object","euclidean","exampl","expens","f'({self.x},","f64","f64,","false;","field","filter","find","finit","first","first,","float64","float64(point.x","fn","follow","form","found,","func","func(a,","function","gift","gift)","gift.","gift.get(0);","gift.remove(start)","gift.size());","gift.stream()","gift.sublist(1,","given","go","graham","graham_scan!(points)","graham_scan!(points::vector{point})","graham_scan(gift):","graham_scan(mut","graham_scan(points);","graham_scan(std::vector&","graham_scan(struct","graham_scan(test_gift)","grahamscan","grahamscan(list","grahamscan(point","grahamscan(points)","grahamscan(points);","graphic","h","hull","hull)","hull))","hull,","hull.","hull.add(0,","hull.append(point)","hull.append(pt)","hull.get(i);","hull.get(m));","hull.length;","hull.set(i,","hull.set(m,","hull.size();","hull.slice(0,","hull.sort(comparator.comparingdouble(point","hull.sublist(0,","hull.unshift(pivot);","hull:","hull[","hull[i]];","hull[m]]","i)","i);","i++;","i,","impl","implement","import","initi","instanceof","int","int)","integ","interior","intern","inward,","item","item.x","item.y)","itself","j","j)","jame","jarvi","java.util.arraylist;","java.util.comparator;","java.util.list;","java.util.stream.collectors;","key=(p","key=(point","key=lambda","know","l,","l.","leftmost","length","length(points)","licens","license.","license.md).","lisp","list","list(set(gift))","look","low_index","lowest","m","m++;","m;","main","main()","main():","main(string[]","make","map$(p","march","march,","match","math","math.atan2(a.i","math.atan2(float64(point.i","math.atan2(p.i","mathjax.hub.queue([\"typeset\",mathjax.hub]);","mean","memcpy(points,","memcpy(tmp_point","memori","min(gift,","minimumbi","minimumby)","mit","modifi","more","moreover,","mut","n","n)","nan,","negative,","never","new","none","null)","num_initial_point","number","o)","obvious","on","operation,","operations,","operator&","optimal,","option","ord","order","origin,","origin.x);","origin.y,","os","other):","other.i","other:","other_point","other_points[i]","otherwis","out","out.","output","p","p)","p.i","p.x","p.x,","p.y)))","p.y));","p0@(x,","p1","p1))","p1)))","p1)))))","p1.x)","p1.y)","p1.y)*(p2.x","p1.y)*(p3.x","p1[0])","p1[1])","p2","p2)","p2,","p3","p3)","p3):","p:","p[0]))","p]","pa","packag","partial_cmp(&self,","partialeq,","partialord","pb","pi","pi))","pivot","pivot)","pivot)));","pivot));","pivot);","pivot_angle)","place","planar","plane","point","point\"\"\"","point&","point(","point(*p))","point(0,","point(0,14),","point(15,","point(2,","point(2,8)","point(5,","point(5,7),","point(6,","point(7,","point(9,","point(9,9),","point(doubl","point(x1,","point(x=0,","point)","point))","point));","point),","point):","point*","point*)","point,","point.","point.y))","point:","point[0]","points\"\"\"","points)","points,","points.","points.add(new","points.begin()","points.is_empty()","points.retain(|a|","points.size())","points.slice(1).sort((a,","points.sort_unstable_by(|a,","points:","points[0],","points[0];","points[1:m]","points[1].x))","points[1].y,","points[1]];","points[2..points.len()].iter()","points[]","points[a].i","points[i+1]","points[i]","points[i])","points[i],","points[i];","points[j]","points[j];","points[m]","points[m]);","points[m],","polar","polar_angle(&start,","polar_angle(ref,","polar_angle(reference:","polar_angle(start,","polar_angle(struct","polar_angles_sort(point","polar_angles_sort(points,","polar_angles_sort(struct","polarangle(a,","polarangle(b,","polarangle(point","polarangle(point,","polarangle(ref,","positive,","print","print(\"th","print(point)","printf(\"points:\\n\");","println(hull)","product,","ps","pt","pt)","pt):","public","pull","py)","qsort(points,","r.","radians\"","radiu","random","ref.x))","ref.y),","ref[0])","ref[1],","refer","reference.x)","reference.y).atan2(point.x","rel","remain","remov","request","result","return","ronald","rotat","rotations,","rotations.","s","s[0],","s[1]]","s[2:]:","safe","same","save","scan","schloss","search","select","self.i","self.partial_cmp(other).unwrap()","self.x)","self.x.partial_cmp(&other.x)","self.y,","self.y.partial_cmp(&other.y)","sensitive;","set","set,","shape","sharealik","simpl","size","size)","size);","size,","size_t","sizeof(struct","snd)","so:","someth","sort","sort!(points,","sort(points[2:end],","sort.slice(points,","sorted(gift,","sortedpt","sorting,","sorton","ss","start","start.angle(point)))","static","std::cmp::ordering;","std::cout","std::ostream&","std::swap(points[i],","std::vector","std::vector(points.begin(),","struct","swap","system.out.printf(\"%","temp","temp);","test","test_gift","text","this)","this.i","this.x","this.y;","this:","three","through","throw","time","tmp","tmp;","tmp_point","tmp_points[0]","tmp_points[i]","tmp_points[i];","tmp_points[m]","tmp_points[m];","tmp_points[siz","tmp_points[size];","trigonometr","true;","turn","turn.","two","type","ultim","under","unlik","unwrap","updat","us","vec","vec![start,","vec)","vec::new();","vector","void","want","whether","within","wrap","wrap.","written","x","x)","x))","x,","x1","x:","x::float64","x;","xa)","y","y)","y)))","y)=","y1)","y:","y::float64","y;","y=0):","ya)","yb)","yc)","{","{0,","{15,","{2,","{5,","{6,","{7,","{9,","{self.y})'","{{","{}","|","|>","}","},","};"],"contents/data_compression/data_compression.html":["\"fact.\"","\"it'","\"what'","&=","(#560),","(a,","(assum","(found","(it","+",",",".1",".2",".3",".4","0","0.","0.1\\time","0.2","0.3","0.4","00","000","001","01","0100101010110100","0111101,","1","1,","1.9","10","11","2","3","4","4.0","=","\\\\","\\begin{align}","\\end{align}","\\sum_{i=0}^{n}w_i\\tim","\\text{length}(c_i)","\\time","a,","a.","abbbbab","abbbbab.","abbcccdddd","abbcccdddd.","above,","absolutes.","acknowledg","actual","add","algorithm","all.","alphabet","alphabets:","altogether,","alway","ambigu","anoth","answer","appear","ask","ask,","assum","assumpt","attribut","b","b!","b,","b.","bacccdba.","back","bag","basement","basic","basically,","be","befor","before.","better","between","binari","bit","bit,","bitlogic,","bits,","bitstr","bitstring,","bitstring?","bright","bright,","c","c,","c?","c_i","case,","case.","case:","cases,","categori","cbbbc!","certain","certainti","certainty.","chapter","chapter:","charact","character,","characters,","characters:","child","clear","clearli","code","codeword","codewords.","coding.","colloqui","combin","common","complet","compress","compression!","compression.","comput","conclud","conclusion,","consid","construct","contact.","contain","context","correspond","course,","cover","creat","creativ","d","d),","data","data;","day","day,","debat","decod","decode,","decoding.","deepli","defin","definit","definition,","degre","depth","describ","determin","development.","devic","differ","direct","discuss","distinct","distinguish","don't","door","easili","either.","encod","even","exampl","example,","exist","face","fact,","fall","fano,","far","field","field,","final","find","first","first,","first.","follow","food","free","free.","furious","further","future.","genet","get","given","go","gone","good,","graphic","great,","hand","happens).","hardwar","haven't","hear","heart","here,","honest,","hot","however,","huffman","huffman,","human","i'll","imagin","import","incred","individu","inform","information,","information.","information:","initi","intens","interact","intern","interpret","is.","it'","it,","itself","jame","kid","l","l(c(w))","l_1","l_2","learn","learning,","leav","length","less","let'","letter","letters:","level","licens","license.","license.md).","limit","logic","long","look","lossless","lot","machin","market","match","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matter","mean","measur","memori","mention","method","minim","mit","mix,","modifi","month","month,","more","mother","mother'","move","much","naiv","need","need.","new","none","notabl","now","now,","number","obviou","odd","on","on.","out","out.","outsid","overal","overcompl","overjoy","perfect","perfectli","piec","piece.","place","plenti","point,","possibl","power","prefix","pretend","probabl","programm","prospect","provid","pull","purposes,","put","quantiti","quantity:","question","question.","question:","random,","ratios.","reach","read","realiz","reason","reasons,","relat","relax!\"","repres","represent","request","requir","requires.","restrict","revolutionari","room,","said,","say,","schloss","search","second","see,","seem","set","set.","shannon,","sharealik","shorter","show","silly,","simpl","singl","slip","something,","soon!","specif","start","statements:","storage.","stori","string","summer","summer,","summer.","sunni","systems.","take","talk","techniques,","test","text","theori","thing","things,","think","third","this,","this:","those","through","thu","today","today?\"","topic,","tri","true","two","ultimately,","unawar","uncertain","under","undoubtedli","unfortunately,","uniqu","unit","unitless","until","us","usual","vague,","valid","value),","w","w_i","want","warm","warm.","wavey","way","way,","we'll","we'v","well,","without","word","word.","work","works,","written","year!"],"contents/cryptography/cryptography.html":["\"caesar","\"public","\"rijndael\"","\"rot13\"","(cipher),","(cryptosystem),","(depend","(found","(hopefully)","(i.e.","(in","(or","(probabl","(receiver).","(sender)","0","1.wikipedia:","128/192","13,","14","18","1977","2","2022.","2022.10.wikipedia:","2022.11.wikipedia:","2022.2.wikipedia:","2022.3.wikipedia:","2022.4.wikipedia:","2022.5.crypto","2022.6.wikipedia:","2022.7.wikipedia:","2022.8.wikipedia:","2022.9.wikipedia:","21","24","256","4.0","[10].","[11].","[1].","[2].","[3].","[4]","[5].","[6].","[7].","[8].","[9].","\\pi","\\pi=(3,1,2,4))","accept","accord","achiev","actual","addresses.","advanc","ae","aes.","again","again.","algorithm","algorithms,","alic","alice'","alice,","alphabet","alreadi","alter","alway","amount","analyz","ancient","anoth","another.","anymore.","anyon","anyway.","applications,","are:","art","ask","assum","asymmetr","asymmetric.","attack","attribut","b","back","banking.","base","becom","befor","behind","better.","between","beyond","bibliographi","big","bit","blowfish","blowfish:","bob","bob'","both","break","bunch","c","caesar","caeser","calcul","call","case","case,","caus","ceasar","certainli","chapter","charact","charli","chart","choos","chosen","cipher","cipher\"","cipher,","cipher:","close","code","combin","come","common","communicating.","communication,","complic","comprehension,","comput","computing.","consist","contend","context.","corner:","cornerston","correspond","couldn't","crack","creat","creativ","cryptograph","cryptographi","cryptography\"","cryptography,","cryptography.","cryptography:","current","curv","cypher.","d","damage.","data","de","dead","decod","decrypt","decrypt,","decrypting.","deem","defin","describ","determin","develop","developed.","differ","different?","digit","discuss","distance.","doesn't","doors,","e","earli","easiest","eavesdropp","eavesdropper.","ecc","effect","elabor","elementari","ellipt","encod","encrypt","encryption:","enough","entir","equal","especi","ev","even","everyth","evil","evil.","exampl","example,","extens","f","face","fact,","factor","faster","feasibl","few","field","figur","find","fine","first","follow","forg","formerli","forth","friend","future.","g","gener","general,","given","gobbledygook","good","gotten","greec","grown","h","hand.","happen","hash","have.","heart","henc","here","here,","hit","honestly,","however,","human","idea","impact","import","imposs","includ","inform","insecur","instead","instead,","interest","intern","it'","it.","j","juliu","k","keep","kept","kerckhoffs'","key","key,","key.","keys.","kid","kill","know","l","larg","layer","length","let'","letter","level","librari","licens","license.","license.md).","lie","liikt","limits.","literature,","long)","lost","m","mailman","make","manag","mani","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matter","mean","meanwhile,","messag","message,","message.","messeng","messenger'","messenger).","messenger;","method","mind:","mit","modern","n","name","near","necessari","need","negoti","never","newer","night","non","now","number","o","obsolet","obvious:","obviously,","on","onlin","oper","out","p","parti","parties.","path","peopl","permut","pk","point","posit","possible,","post","pre","prime","principl","principle,","privat","private,","problem","procedur","product","profession","progress,","progress.","properli","provid","public","purpos","q","quantum","question","r","read","reason","reason,","receiv","receiver,","receiver.","reli","remain","rememb","reorder","replac","replaced,","rijndael","robust","robust.","rome.","rot13,","rot13:","rotat","rsa","rsa:","ruse),","s","same","scheme","scheme,","school","school,","scrambl","secret","secret.","secretli","section","sections.","security.","see","seem","send","sender","sender,","sent","separ","seriou","set","share","sharealik","short)","side","signific","signing,","simple:","simpli","simplicity,","slip","smaller","sometim","spaces,","special","spy?","standard","standard,","standard:","state","stay.","stolen?","string","such","summar","supersed","supposedli","sure","symmetr","system","t","tabl","tactic","talk","technolog","technology,","tent","test","text","themselv","themselves.","there,","thing","third","time.","train","tri","trust","two","type","u","under","undergo","understand.","unscrambl","unsurprisingly,","up","us","usual","utter","v","veri","versa.","vetting.","vice","w","war","way","way,","whenev","whole","wide","wifi","won't","work","write","written","x","xor","y","z"],"contents/taylor_series_expansion/taylor_series_expansion.html":["\"taylor","&=","(#560),","(found","+","0,","1.","4.0","=","\\\\","\\begin{align}","\\end{align}","\\frac{1}{2}\\frac{d^2f(a)}{dx^2}(x","\\frac{1}{2}at^2","\\frac{d^2x(t)}{dt^2}","\\frac{df(a)}{dx}(x","\\frac{dx(t)}{dt}","\\frac{f^{(n)}(a)}{n!}(x","\\rightarrow","\\simeq","\\sum_{n=0}^{\\infty}","\\text{acceleration}","\\text{velocity}","a)","a)^2","a)^n","acceler","actual","algorithm","allow","along","approxim","approximation\"","assum","attribut","becomes!","better","between","blur","book.","boundari","bunch","chapter","chapter:","classic","close","code","common","complex","complic","consid","constant,","creat","creativ","definition:","denot","deriv","derivatives:","differ","easili","equation!","evalu","exampl","example,","expand","expans","expansion,","expansion.","f(a)","f(x)","f(x).","f^{(n)}(x)","few","figur","first","first,","follow","formal","formula","found","foundat","from,","function","function.","graphic","hand,","here","here,","higher","imag","images/graph","imagine!","include,","incomplete!","initi","intern","jame","kinemat","let'","licens","license.","license.md).","look","mani","mathemat","mathematical.","mathjax.hub.queue([\"typeset\",mathjax.hub]);","mean,","mind,","mit","modifi","more","n^{\\text{th}}","none","note","note:","obviou","on","order","perspective,","physic","physicist.","physics,","physics.","physics?","place","point","point,","power","pull","pure","quantiti","real","request","schloss","see","seem","seri","set","sever","sharealik","show","smooth","space,","strung","substitut","sum","tackl","take","taylor","technic","term","terms.","text","those","throughout","together!","told,","topic","topics.","train","true","truth","turn","under","unusu","us","v(t)","v_0t","well,","where'","why,","written","x(t)","x(t),","x_0"],"contents/convolutions/convolutions.html":["(#560),","(*)","(addition,","(get","1d","4.0","\\circ","addit","addition,","after,","algorithm.","always,","anim","anoth","answer","anyth","applic","attribut","back","basic","beyond","blend","bluntly,","brief","c,","call","chapter","chapter:","clarification.)","clear","combin","come","common","composit","comput","confusing.","convolut","convoluted!","convolutions.","convolutions?","correl","cover","creativ","definit","describ","describe,","detail","difficult","dimens","dimension","dimensions,","discuss","division),","even","example,","extend","f","f*g=c","f.","few","filters:","follow","fourier","function","function,","functions,","functions?","future.","g","g(x)","g,","g.","gaussian","go","good","graphic","great","hard","here","however,","imag","import","incred","initi","integ","interest","intern","intuit","it?","jame","joke","kernel","know","known","left","licens","license.","man","mathemat","mathjax.hub.queue([\"typeset\",mathjax.hub]);","modifi","move","multipl","multiplication,","n","near","need","needed,","needed.","none","notat","note:","now","number","numbers.","on","onc","oper","operation,","operator,","operator.","plug","possibl","power","practice,","provid","pull","put","question,","question:","reader","relat","request","schloss","section","section,","section.","see","sharealik","show","side","similar","simpl","sobel","special","standard","star","start","start.","stereotyp","subtraction,","take","talk","text","them.","theorem","third","three","told","topic","touch","transforms.","two","unclear,","under","understand","unless","up.","us","vagu","variabl","version","way","way;","wise","work","written"],"contents/convolutions/1d/1d.html":["\"applic","\"blend\"","\"blurred.\"","\"cyclic\"","\"doubl","\"full","\"gaussian","\"period","\"ramp","\"sawtooth","\"shift","\"simpl","\"squar","\"triangl","#","%","(#560),","((x","([0.5,","(a","(f*g)(x)","(f*g)[n]","(filter[i","(found","(length(filter)/2)","(sum)","(var","+","//","0","0.","0.0;","0.5]),","0;","0s","1","1)","1):","1);","1,","1.","100%","1d","1})","1},","1}}{2}","3","4.0","=","=>","\\frac{a_{n","\\frac{a_{n+1}}{2},","\\infty}^{\\infty}f(\\xi)g(x","\\infty}^{\\infty}f(x","\\infty}^{\\infty}f[m]g[n","\\infty}^{\\infty}f[n","\\int_{","\\sum_{m","\\xi","\\xi)d\\xi","\\xi)g(\\xi)d\\xi","a_{n}","abov","acceler","accelerating,","act","action","actual","ad","addition,","again","algorithm","all!","allow","along","alreadi","alway","amount","anim","animation,","animation.","animation:","animations,","animations.","anoth","appear","appli","applic","area","around","array","array,","arrays.","associ","assum","attent","attribut","base","be.","befor","before,","before.","before:","behavior","below:","best","better","between","beyond","bit","black","blend","blue","blur","blurrier","both","bound","boundari","boundaries.","boundaries:","boundary.","bring","browser","busi","c","c,","c_n","calcul","call","care","case","case,","case.","caveat","center","center,","center.","certain","certainly,","chang","chapter","chapter,","chapter.","chapter:","check,","chosen","clarity:","class","clearli","close","code","code,","common","compar","complic","comput","concept","condit","condition\"","conditions,","conditions.","constantli","continu","continuing:","contrast","convolut","convolution!","convolution\"","convolution,","convolution.","convolution1d","convolutions,","convolv","convolve_cyclic(signal,","convolve_cyclic(signal::array{t,","convolve_linear(signal,","convolve_linear(signal::array{t,","convolve_linear(x,","convolvecyclic(double[]","convolvelinear(double[]","convolvelinear(x,","copi","correct,","correlation,","count","course,","creat","createsawtooth(int","creativ","cyclic","dash","data","deal","debat","def","definit","delimitedfil","depend","descript","detail","determin","differ","dimension","directions.","directli","disappears.","discret","discuss","distinct","distinct.","distribut","domain","domain,","domain.","domain;","don't","done","double[]","double[length];","double[outputsize];","down\"","down.\"","dramat","each","easiest","edg","edge.","effect.","element","elements,","end","ensur","entir","entireti","equat","essenti","everyth","exactli","exampl","example,","example.","except","exist","expect","expect,","extend","f[n]","fact,","few","file","filter","filter)","filter,","filter,\"","filter.","filter.length);","filter:","filter::array{t,","filter?","filter_array):","filter_array,","filters,","filters.","final","finally,","first","first.","follow","form","form.","found","frequent","full","full,","full_linear_output","fulllinearoutput","function","function,","functions,","functions;","further","g[n]","gaussian","gaussian,","gaussian?","gener","general,","given","go","goe","good","graphic","greater","green","half","hand,","happen","happen!","here","here,","here.","here:","hit","honestly,","hotli","however,","i+(length(filter)/2)","i.","idea","ident","if(mod1(i","ignor","imag","image),","image,","image.","images,","images/graph","images:","images?","implement.","import","infin","initi","inner,","input","insid","instead,","instead.","int","integr","interact","interest","intern","interpret","introduc","introductori","is,","iter","itself","j","j,","j]).","jame","kernel","known","larg","larger","later","learn","leav","left","len(filter_array))","len(filter_array)),","len(x)","len(x))","len(y)","length","length(filter)","length(filter)):i","length(x)","length(x))","length(y)","length)","length,","length.","let'","licens","license.","license.md).","like:","line","line:","linear\"","linearalgebra","linger","littl","locat","location.","longer","longer.","look","loop","loop.","lot","m","m?","m]","m]g[m]","main","make","mani","math.max(0,","math.max(signal.length,","mathemat","mathematician","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matter","max(1,","max(len(signal),","mean","mention","method","middl","mind,","missed.","mit","mod(int","mod1(x,","modifi","modulu","more","move","much","multipl","multipli","multiply,","n","n,","namespac","necessarili","need","need.","neg","neighbor","neighbors,","neighbors.","new","next","nois","non","none","notat","note","note,","notic","now","np","np.zeros(output_size)","number","numpi","on","one.","opaque,","oper","operation,","operation.","operations,","opposit","origin","other,","otherwis","otherwise,","out","output","output.","output_s","output_size)","output_size):","outputs","outputsize)","outsid","over,","overlap","part","particular","particularli","past","pay","perform","period","periodic,","phase","physic","pick","place","play","point","point.","portion","posit","possibl","practic","practice,","precis","predefin","present","previou","processing),","produc","programmer,","properli","public","pull","purple,","put","questions:","random","range(max(0,","range(output_size):","read","realli","reappear","reason","reason,","red","rel","relat","rememb","request","requir","research","return","revers","right","rigorous,","s","said,","same","saniti","sawtooth","schloss","scope.","screen,","sea","second","section","section,","section.","see","seem","seemingli","seen","select","sens","sense,","separ","set","sharealik","sharp","shift","show","shown","side.","signal","signal,","signal,\"","signal.","signal?","signals,","signals.","similar","similarly,","simpl","simple_linear_output","simplelinearoutput","simplest","simpli","simul","size","slope","small","smaller","smallest","smooth","snippet,","so:","someth","somewhat","somewher","sort.","space,","spatial","specifi","squar","square,","square.","stage,","start","starts.","static","step","step,","step.","still","still,","stop","straightforward","strip","stronger","subset","subtract","such","sum","sum.","summat","support","sure","symmetr","system.io;","system;","tag.","take","talk","test","text","textbook.","that,","theorem,","therefore,","thing","think","this,","this:","those","though","through","time,","time.","together,","together:","topic","transcrib","treat","triangl","triangular,","tricki","trivial","trope","true;","two","type","typic","unbound","under","unrel","up","up\"","up,\"","us","us,","used,","user","value,","value.","var","veri","version","vertic","via","video","visual","visualization,","want","wants,","wave","wave\"","wave;","way","way,","weight","well,","whenev","white","white,","wider","wider.","wild","wise","within","without","work","worry!","worthwhil","wrap","write","written","x","x,","x.length","x.length);","y","y)","y):","y,","y.length","y;","you,","zero","{","{t"],"contents/convolutions/multiplication/multiplication.html":["&","&&&\\color{blue}6&5&4","&&&\\color{green}6&\\color{blue}5&4","&&&\\color{red}1&2&3","&&&\\color{red}1&\\color{green}2&3","&&&\\color{red}1&\\color{green}2&\\color{blue}3","&&&\\color{red}6&\\color{green}5&\\color{blue}4","&&1&2&3","&&1&\\color{green}2&\\color{blue}3&","&&6&\\color{red}5&\\color{green}4&","&1&2&\\color{blue}3&&","&4","&4&5&6","&6&5&\\color{red}4&&","&\\time","(#560),","0","0.","1","10","10,","100,","10s,","123","123,","123\\times456=56088,","13","18","18\\\\","18]=[4+1,","1s.","2","27","28","3","3+2","4","4.0","456","5","5+1","56088.","58.","6","7+1","8","8+2","8\\\\","8]=[5,8]","=","=&4+1","=&5","[4,","\\\\","\\begin{matrix}","\\color{blue}3\\times\\color{blue}6=18","\\color{green}2\\times\\color{green}6+\\color{blue}3\\times\\color{blue}5=27","\\color{red}1\\times\\color{red}5+\\color{green}2\\times\\color{green}4=13","\\color{red}1\\times\\color{red}6+\\color{green}2\\times\\color{green}5+\\color{blue}3\\times\\color{blue}4=28","\\color{red}{1}\\times\\color{red}{4}","\\end{matrix}","\\end{matrix}\\\\","\\hline","\\time","algorithm,","anoth","answer","aside,","attribut","between","blank","bound","brief","carri","case,","chapter","chapter:","column","common","consid","convolut","convolution,","convolution.","convolutions,","correct","creativ","detail","digit","discuss","each","element","elementari","end,","example,","fact","feel","follow","further","give","graphic","here,","incred","initi","integ","integers.","interest","intern","jame","know:","larg","learn","left","licens","license.","line","mathjax.hub.queue([\"typeset\",mathjax.hub]);","modifi","move","multipl","multiplication.","multiplication:","neighbor.","new","none","notat","now","number","numbers,","numbers:","oper","operations,","peopl","perform","power","pull","relat","repres","request","revers","right,","schloss","schonhag","school","second","set","sharealik","side","similar","so:","space","step:","strassen","student","such","suggest","talk","teach","text","topic:","touch","under","up","us","wise","written"],"contents/convolutions/convolutional_theorem/convolutional_theorem.html":["\"cyclic\"","\"wrap","#","(#560),","(fft)","(found","/","/=","10","10.","4.0","=","[float(i)/200","\\cdot","\\hat","\\mathcal{f}","\\mathcal{f}(f)","\\mathcal{f}(f*g)","\\mathcal{f}(g)","\\mathcal{o}(n\\log(n)).","\\mathcal{o}(n^2)","ad","add","advantag","allow","alway","anoth","around\"","array","attribut","back","base","best.","bit","blend","boundari","case","certain","chapter","chapter:","code","code,","common","complex","compos","comput","concept","condit","convolut","convolution,","convolution.","convolutions:","convolv","convolve_fft(signal1,","convolve_fft(signal1::array{t},","convolve_fft(x,","crazy,","creat","creativ","cyclic","def","delimitedfil","denot","describ","descript","differ","dimension","domain,","e^{2\\pi","each","edg","element'","equal","essenti","exampl","expand","explain,","explanation,","exponential.","exponentials,","exponentials.","extend","f(\\xi)","f(x)","fast","fft,","fft_output","fftw","first,","follow","fourier","frequenc","frequency.","function","functions.","fundament","g(\\xi),","g(x)","graphic","hard","here'","however,","idea:","ifft","ifft(np.multiply(fft(signal1),fft(signal2)))","imag","images/graph","import","incred","initi","input","inputs.","instead","intern","interpret","intuitive,","jame","k","known","lack","larg","length","licens","license.","license.md).","linearalgebra","look","magic:","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matter","mean","mention","method","method,","mit","modifi","more","move","multipl","multipli","n","n,","need","none","note","note:","now,","np","np.linalg.norm(x)","np.linalg.norm(y)","np.real(fft_output))","np.savetxt(\"fft.dat\",","numpi","n}","obviously,","on","operation,","output","output:","overal","pad","parameter","particular","particularli","peak","perform","period","process,","produc","programm","promis","pull","range(1,101)]","real","relat","rememb","request","return","revis","revised.","sawtooth","schloss","scipy.fft","section","sections!","see","seem","seen","send","seri","set","sharealik","show","side,","signal","signal.","signal2):","signal2::array{t})","signal;","singl","size","size,","smaller","someth","space","space,","space.","specifi","standard","still","take","tell","term,","text","theorem","third","this:","those","time","together.","transform","transform,","transform.","transforms!","transforms,","two","under","upon","us","valu","wave","wave.","way,","written","x","y","y)","zeros.","{t"],"contents/plotting/plotting.html":["\"2d_sample_low_res.dat\"","\"beautiful.\"","\"black\"","\"bottom\"","\"check.png\"","\"check.png\".","\"check.tex\"","\"cos(x)\"","\"exp_fn\"","\"exp_fn_log\"","\"fillsteps\"","\"gnuplot","\"gnuplot_1d_sample\"","\"gnuplot_2d_sample\"","\"gnuplot_2d_sample_colorbar\"","\"gnuplot_exp_tex\"","\"gnuplot_histogram\"","\"gnuplot_scatterplot\"","\"gnuplot_sine_cosine_customtics\"","\"gnuplot_sine_cosine_label\"","\"gnuplot_sine_cosine_linetype\"","\"gnuplot_sine_cosine_log\"","\"gnuplot_sine_cosine_movekey\"","\"gnuplot_sine_cosine_movekey2\"","\"gnuplot_sine_cosine_nokey\"","\"gnuplot_sine_cosine_notics\"","\"gnuplot_sine_cosine_square\"","\"gnuplot_sine_cosine_title\"","\"gnuplot_sine_cosine_wave\"","\"gnuplot_sine_cosine_wave_range\"","\"gnuplot_sine_wave\"","\"gnuplot_test\"","\"how","\"out.tex\"","\"purple\"","\"sample_data.dat\"","\"scatterplot_data.dat\"","\"sin(x)\"","\"sin(x)\",","\"sine","\"sine_cosine_plot.png\"","\"top\"","#","$1","'#0000ff',","'#00ff00')","'#00ff00',","'../../data/rand.dat'","'data'","'red',","(","(\"bottom\"","('#ff0000',","(0","(1","(1,0.5),","(bin($1)):(1)","(blue,","(found","(let'","(littl","(or","(read,","(to","(which",")","*","*.aux,","*.ep","+",",",".",".csv",".dat",".png",".tex",".tsv","0","0,","0.13307711243511333","0.18541942067815853","0.23648916187439406","0.23842162678327328","0.27999628668153087","0.30699091691896263","0.3548405553754319","0.35589625594005647","0.361307926046027","0.3692102429804389","0.40610861857701597","0.5","0.587785252292473","0.5877852522924731","0.5877852522924732","0.5877852522924734","0.6075688534409027","0.6338943724188091","0.6351126027850458","0.7605752608745506","0.7796784902862803","0.789554555806735","0.7972009737623846","0.8661873069668018","0.8686860241215444","0.9510565162951535","0.9510565162951536","1","1)","1,","1,0.5","1.0","1.00","1.2246467991473532e","1.williams,","10","10.","100","10cm","10cm,","12cm,","16","16:9)","17","1;","1s","2","2.0","2.4492935982947064e","2015.","2s","3","3.0","3s","4.0","480","4s,","5","5,","5.0","5.0:","6","6.0","622:","640,","6:9","7","7,","7.0","8.0","8cm","9.0","9:","=","[0:10]","[0:1]","[0:]","[1]","[n:m],","\\","\\begin{document}","\\documentclass[11pt]{article}","\\end{document}","\\input{out}","\\time","\\usepackage{gnuplottex}","abbrevi","abov","above,","above.","above:","academ","accord","actual","ad","add","addit","addition,","admittedly,","again","agnostic,","aim","algorithm","alia","alias","aliases,","allow","along","alreadi","anoth","anyon","anyth","appropri","archiv","archive,","archive.","area","argument","array","articles,","as:","ascii","ask,","aspect","associ","assum","attribut","audienc","auxiliari","avail","available.","aw","ax","axes.","axi","axis,","axis.","axis:","back","background","bar","bar.","basic","beauti","beautiful,","becom","befor","before,","begin,","behavior","beholder,","better","between","bibliographi","bin","bin(x)","bin_id(x)","bin_width","black","border","bottom,","box","bunch","c,","c.","c/c++,","cairo","call","capabl","case","case,","case:","categorized.","center","center,","certain","certainli","chang","chapter","chapter,","chapter.","chapter:","character.","check.tex","choic","choice,","choice.","choos","chore.","chosen","cleaner,","clear","clear.","clear:","clearli","cm,","code","color","colored,","column","come","command","command,","command.","command:","commands:","common","commonli","compar","comparison","complex","complic","complicated.","comput","conclus","condon","cool","coordin","copyright.","correct","correspond","cos(x)","cosin","cosine,","cover","creat","create.","creativ","cross","crosses.","current","custom","dash","dashtyp","data","data,","data.","data;","datasets.","decid","default","defin","depend","detail","determin","differ","dimens","dimension","dimension.","dimensional;","directli","discuss","do","document","document,","documentation,","documents,","don't","done","draw","each","easi","easier","easiest","easili","either:","else).","end","end,","enough","enter","entir","entri","epslatex","epslatex.","essenti","etc).","etc.),","etc.).","evaluate,","even","everyth","exact","exampl","example,","example:","exist","exist,","exp(x)","expect","expect:","explain","explan","explicitly:","extens","extern","ey","facet","fairli","fall","far","favor","featur","feel","few","file","file),","file,","file.gp","file_0000.dat,","file_0001.dat,","file_0002.dat,","files,","files;","fill","fillstep","finally,","find","first","first,","firstly,","fit","fledgl","fli","float","floor(x/bin_width)","focu","follow","following:","format","format,","fortran,","found","fractal","frequenc","frequency,","from,","from.","function","function.","futur","gener","gnuplot","gnuplot,","graphic","green,","guid","hand.","have","held","help","here","here,","here.","here:","highlight","histep","histogram","however,","html","id","ignor","imag","image,","image.","images/graph","implement","implementations.","import","inches,","includ","individu","inform","initi","input","instead","instead,","instead.","integ","intend","intens","interact","interest","intern","interpret","introduc","it!","it'","it:","iter","itself,","itself.","jame","java,","journal","julia,","keep","kelley,","key","keyword","keywords,","know","known","l","l,","label","label,","labels,","labels.","languag","languages,","larg","later.","latex","latex.","lc","learn","left","left,","legend","legend,","legend.","let'","librari","licens","license.","license.md).","like,","limit","line","line,","linecolor","littl","locat","log","logscal","look","loop","lot","m","mainli","make","mani","manually.","map","math","matlab,","matrix","matter","mean.","meant","measur","mention","method","methods.","mismatch","misrepresent","miss","missed,","mit","mode","modif","modifi","more","move","much","multipl","n","name","near","necessari","necessarili","necessary.","need","neg","new","newlin","newline,","nokey","notat","notation,","notches)","note","note,","note:","notifi","now","now,","number","number.","numbers,","numbers.","numbers?\"","object","obviously,","offici","on","on.","one...","onlin","open","option","option,","organ","otherwise,","out","out.pdf.","out.tex","output","output,","output.","output:","over","p","p,","pad","page,","pairs,","palett","paper","part,","particular","patterns,","pdf","pdflatex","peopl","perform","phrase","pixel","place","pleas","plenti","plot","plot,","plot.","plot:","plot;","plots,","plots.","plotted,","plotter","plotting,","plotting.","png","pngcairo","point","point,","pointtyp","posit","possibl","possible.","power","pr","predefin","prefer","prevent","print,","probabl","process","process,","produc","program,","project","provid","pt","pull","purpl","purpos","purpose.","purposes;","put","put,","python,","quickli","randomli","rang","rare","ratio","read","reader","reader'","real","reason,","recogn","red,","rel","relev","remov","rep","repl","replot","repositori","repres","represents,","request","requir","required.","research","resolut","rgb","rgb.","right","right,","round","rounded.","row","rows,","run","said,","same","scale","scale.","scales,","scatter","schemes.","schloss","science.","scientif","scope","screen;","script","script,","script.gp","script.gp)","script:","scripts,","section","section,","section.","see","seen","select","sens","sense,","separ","sequenti","seri","set","sever","sharealik","shell)","short","show","showcas","shown","similar,","similarly,","simpl","simplest","simpli","sin(x)","sine","singl","site.","size","skill","slowli","small","small,","smooth","so:","solid","someon","someth","sometim","space","space.","sparingly.","specif","specifi","specifiers,","splot","spot,","spruce","squar","standalon","start","state","stay","storag","store","straight","straightforward","string","strive","studi","stuff,","stun","style","such","such,","such.","sure","systems.","t","tab","tabl","take","takes.","task","tasks:","tastes.","techniqu","term","termin","terminal,","test","test\"","tex","tex,","text","text,","text.","that:","theme","themes,","thing","third,","this,","this:","though","three","through","tic","tics,","time","time,","times,","titl","title,","title.","titles,","told","tool","top","top,","tri","trouble.","turn","two","type","types.","typesetting,","u","under","understand","unit","unless","unnecessary.","unrel","unset","up","up.","updat","us","user","using,","usual","valu","value,","values,","vari","variou","vector","veri","view","visual","w","want","want.","wave","wave\",","way","way.","ways.","we'll","well","well.","whatev","whenev","widescreen","width","wish","without","word","work","work:","worse,","worth","write","written","x","x/ytic","xrang","xtic","y","yourself","yrang","ytic","z","zero","zoom"],"contents/monte_carlo_integration/monte_carlo_integration.html":["!","\"","\"\"\"return","\",","\",error:","\",our","\"check","\"error:\"","\"estim","\"fmt\"","\"how","\"math\"","\"math/rand\"","\"mont","\"percent","\"percentag","\"return","\"simplemontecarlo\"","\"squarecircle\"","\"take","\"the","\"time\"","\"world'","\"y\")(uniform01,","#","#!/usr/bin/env","#(*","#(rand","#includ","#lang","$","$(100","$2","$i","$i++)","$n","$n;","$percenterror\")","$picount","$picount++","$piestim","$piestimate\"","$piestimate\")","$positionx,","$positiony,","$radiu","$radius=1)","$x","$y","$y)","$y,","%","%))","%0.2f\\n\"","%f%%\\n\",","%f\\n\",","%lf\\n\"","🆕","🆕🌕🆕","🆕🎰🆕","🆕⏩⏩","🆕☝️🆕","🌕","🍇","🍉","🍪🔤th","🍼","🏁","🏃‍♀️","🏃‍♀️🐇🤡","🏧","🐇","👌","💯","💯samples❗️","📥","📪","📫","🔂","🔡","🔢","🔤","🔤%🔤🍪❗️","🔤run","🖍🆕","🖍radiu","😀","🤜pi_estim","🤜point_x","🤜radiu","🤡","🥧🕊💯","'__main__':","(","(#560),","($i","(($1","((ret","(*","(*'","(/","(0,","(0,0)","(100.0","(4","(>","([math]::pi))","([math]::pi))\"","([math]::pow($x,","(a","(ab","(chin123)","(dec","(defin","(defn","(defun","(displayln","(doubl","(float):","(found","(i","(if","(in","(inc","(int","(let","(like","(loop","(map","(math/ab","(mont","(n","(number","(optional)","(pi_estim","(pos_x","(println","(r,r)","(rand","(randomr","(real","(recur","(reduc","(repeatedli","(requir","(self.x,","(shown","(string","(unsign","(x","(x*x","(x*x)","(x,","(x,y)","(x:y:rest)","(y*y)","(zero?",")",");","*","**","*/","+","+))","+=",".",".count!(a",".doubl",".extern",".global",".intel_syntax",".long",".rodata",".section",".string",".take(n)",".text","/","/**","//","///return","0","0))","0..","0...n","0..n","0.0","0;","0]","1","1)","1):","1);","1.0","1.0)","10,000,000","100","100))))","100*abs(math.pi","100.0","10000000","10000000❗️","100_000","100}%\");","10❗","10❗🍪❗️","1105199103","1;","2","2)","2))","2147483647","3.141592653589793","3.14159265358979323846264338;","3jane","4","4.","4.0","4290772992","4294967295","4r^2",":","::",";",";;",";;;;","=","==","=>",">",">float",">singl",">string","?","@param","@return","[","[]","[constant","[float])","[i","[math]::abs($piestim","[math]::pow($radius,","[math]::pow($y,","[n","[pv","[r]","\\frac{\\text{area}_{\\text{circle}}}{\\text{area}_{\\text{square}}}","\\frac{\\text{count","\\pi,","\\text{area}_{\\text{circle}}","\\text{area}_{\\text{circle}}.","\\text{area}_{\\text{circle}}=\\pi","\\text{area}_{\\text{square}}","\\text{area}_{\\text{square}}=4r^2.","\\text{area}_{\\text{square}}\\times\\text{ratio}","\\text{length}","\\text{length}^2.","\\text{ratio}","\\text{ratio}?\"","\\text{width}","\\text{width}.","\\tfrac{length}{2}","\\time","]","^","^^","_","__abs__(self)","__name__","a.y));","ab","above;","abs(p","abs(p)","abs(pi_estim","abs,","ad","addsd","again","all,","anim","append","approx","approxim","approximation,","arbitrari","area","args)","array","array,","attribut","auto","bash","basic","becom","before,","below)!","below),","better","bi@","bit","bool","boolean","bunch","calcul","call","carlo","carlo\"","carlo([int]$n)","carlo.core)","case),","catch","center","chapter","chapter:","check","chinmaya","circl","circle\"","circle(1.0);","circle(doubl","circle,","circle.","circle.c","circle:","circle?","circle}}{\\text{tot","class","code","come","comisd","common","comput","constant","constexpr","coord","coordin","count","count)","count))))))","count❗️","crate","crazi","creat","creativ","crop","data","def","describ","determin","differ","dist(0,","distanc","doesn't","doubl","double)","double,","double.random(in:","drop","dup","each","easili","element","emb","embed","end","end,","engineering.","entir","equation.","error","error)))","error:","error_fmt:","estaim","estim","estimate)))","estimate))))","estimate_fmt:","exampl","exclusive\"","explan","extern","f64","f64)","f64,","fabs_const:","fact","fals","famou","feel","filter","filter$(in_circle$(?,","find","first","first.","float","float):","float64)","flonum","fn","follow","formula","four:","fprintf(\"perc","fprintf(\"th","free","fun","func","function","future!","g","get;","give","given","given_radiu","given_radius❗️","going.","graphic","guarante","here","here,","host","however,","hundred:","i)","idea","imag","images/graph","imagin","implicit","import","in_circl","in_circle()","in_circle(doubl","in_circle(float","in_circle(p","in_circle(pos_x,","in_circle(x,","in_circle(x:","in_circle(x_pos::float64,","in_circle:","incircl","incircle($x,","incircle()","incircle(a.x,","incircle(doubl","incircle(r","incircle(x,","incircle(x:","incircle(xpos,","incircle_array","inclus","increas","incred","initi","inlin","insid","instead","int","integr","integration!","integration:","intent(in)","intern","is,","is:","isinme(point","it!","it'","it,","jame","java.util.random","java.util.random;","jess","know","learn","len)","let'","licens","license.","license.md).","line","liter","local","logic","long","lower","lt","machin","mag","magic.","mahesh","main","main()","main(string[]","makepair","mani","map$(","map$(pow$(?,","margin","math","math.abs(piestim","math.abs(radius);","math.const","math.funct","math.pi","math.pi)","math.pi);","math.pow(point.x,","math.pow(point.y,","math.rang","math.sqrt","math/pi","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matter","maximum","means,","method","minimum","mit","modifi","mont","monte_carlo(10000000);","monte_carlo(samples)","montecarlo","montecarlo();","montecarlo(1000);","montecarlo(100000)","montecarlo.c","montecarlo.run(10000000);","montecarlointegr","montecarlopi","montecarlopi(100_000);","more","movsd","much","much,","mulsd","multipli","mut","n","n)","n);","n;","n_sampl","namespac","new","non","none","noprefix","not:","now,","nowadays,","number","object","objects.","obvious","on","one,","one:","otherwise.\"\"\"","output","over","p","p);","packag","percent","percent_error","percenterror","physic","pi","pi\"","pi)","pi))","pi))]","pi).abs()","pi);","pi:","pi;","pi_estim","pi_estimate)/math.pi","pi_estimate);","pi_estimate=monte_carlo(n)","pick","picount","piestim","piestimation);","place","point","point(doubl","point(random.uniform(0,","point(x,","point)","point,","point_i","point_x","point_y🤛","points,","point❗️","pos_i","pos_x,","pos_y,","possibl","pow($positionx,","pow($positiony,","power","premis","print","print(\"th","print(f\"us","printf,","println!(","println(\"estim","println(\"perc","privat","proc","produc","program","program.c","project","provid","public","pull","pv","pythagorean","quadrant","quarter","question","r","r)","r)))","r,","r]","r^2.","racket/bas","racket/local)","racket/math)","radiu","radius🤛","radius)","radius))","radius)))","radius),","radius.","radius:","radius=1)","rand","rand(2,","rand::random();","rand;","rand_max:","random","random();","random.","random.uniform(0,","randomgen","randomize()","randomli","random❗️","random❗️❗️","randx","randx:","randy:","ratio","rax","rax,","reading!","real","real(16),","repres","request","request,","requir","research,","rest","results,","ret","return","right","rough","row","run(int","same,","sampl","samples)","samples.\")","samples.\");","samples.🔤❗️","samples❗️","sampling.","save","schloss","scratch","see","seem","self.y)","set","set;","shape","shape?","shape?:","sharealik","shown","similar","simpl","simple,","simple:","simplicity,","simplicity.","slice","small","snippet","so,","someth","sort","squar","square,","square.","squares_array","srand,","start","static","std.math","std.stdio","std::f64::consts::pi;","straightforward","struct","submit","sum","sum(squares_array)","system.console.writeline(\"run","system.console.writeline($\"th","system.out.printf(\"perc","system.out.println(\"estim","system.random","system;","take","taken","technic","tell","term","test","text","thank","that'","them,","this.i","this.radiu","this.x","thm","time","time,","tool","topair","tri","trick.","true","tupl","tuple!(\"x\",","twist","two","under","uniform01))","unit","unsign","up","upper","us","used}}","using:","val","valu","value:","values?","var","vector","version","via","video","void","want","way","well,","whether","within","without","write","writeln(\"estim","writeln(\"perc","writeln;","written","x","x*x","x*x+y*i","x,","x;","x^2","x_pos^2","xam4lor","xmm0","xmm0,","xmm1","xmm1,","xor","xpo","xs","xy_array","xy_array.^2;","y","y)","y):","y*i","y*y)","y,","y:","y;","y^2","y_pos::float64)","y_pos^2","ypo","ypos)","ys","{","{:.3f}\".format(percent_error))","{:.3f}\".format(pi_estimate))","{:.3}%\",","{math.abs(piestim","{piestimate}\");","{samples:_}","|>","}","↩️","↪️","◀️","☝️","✖️","❗️","❗️🤛❗️","➕","➖","➗","➡️","⬅️"],"contents/bitlogic/bitlogic.html":["\"andgate\"","\"nandgate\"","\"norgate\"","\"notgate\"","\"orgate\"","\"roll","\"xorgate\"","(#560),","(>).","(found","(in","0","0'","0+127","0.5","0000","00000000000010100000000","00000101","00001010","0001","00010100","0010","00100100000000000000000","0011","0100","0101","01010000000000000000000","0110","0111","01111110","01111111","1","1'","1's.","1,","1.","1.00","1.00001","1.001001","10","10.25","1000","10000000","10000001","10000010","10001011","1001","1001.001","1010.01","1101:","126","127","127.","128","13,","13.","1:","1;","2","2,","2.","20","23","256","2;","2^0","2^1","2^2","2^3","2^{","2^{0}.","2^{126}","2^{130},","2^{3}","3","3+127=130,","32","3}","4","4,","4.","4.0","4096.625","5","5.25","6","7","754","8","8,","8.25","9","9.000","9.125","9.125,","=",">",">>","\\frac{1}{8}.","\\ldot","\\time","absolut","actual","ad","add","addit","alway","anoth","arises!","arithmet","attribut","available.","be","before:","bias","binari","binary,","binary:","bit","bit,","bit:","bitlogic.","bits,","bitshift","bitstr","bitstring.","bitstrings:","both","call","case","chapter","chapter:","code","code,","combin","common","compil","complic","complicated:","comput","computer.","computer?","consid","content","correspond","count","creat","creativ","cross","data","day!","deal","decim","describ","difficult","digit","digit.","discuss","divid","done","each","easiest","effect","end,","enough","essenti","exampl","example,","example:","exclus","explan","expon","exponent,","few","first","flip","float","float.","follow","gate","gate,","gate:","gates,","get","graphic","happens,","here","here'","high,","hold","however,","idea","ieee","imag","images/graph","imagin","implement","implies:","initi","input","integ","integer.","intern","interpret","it'","itself.","jame","keep","know","languag","largest","later.","lead","leav","left","left,","let'","licens","license.","license.md).","littl","logic","logic.","long,","make","mantissa","mantissa.","mathjax.hub.queue([\"typeset\",mathjax.hub]);","mean","method","mind:","mit","modifi","more","move","multipli","name","nand","natur","need","neg","negative.","new","next","none","nor:","normal","now","now,","number","number'","number.","numbers!","numbers,","numbers.","obviou","on","onto","oper","operations,","operators:","operators;","output","over\"","perform","play","point","point.","posit","power","precision)","profound","program","pull","purpos","read","realiz","reason,","redund","remov","repres","representations:","request","right,","said,","same","schloss","seem","seen","sens","sever","sharealik","shift","sign","similar","simpl","simpli","singl","smallest","so,","so:","someth","somewhat","standard.","start","still","store","straightforward","straightforward,","string","string,","structur","tabl","table:","take","talk","tell","text","that'","thing","things.","think","though","time","togeth","together.","tool!","transform","trick","truth","two","ultimately,","under","understand","understand.","us","us,","usual","valu","values:","video","way","we'll","well,","whenev","whether","whose","with.","without","work","write","written","xor"],"contents/box_muller/box_muller_rejection.html":["!=","\"","\",","\"re","#","((10,10)","(axis_num)","(found","(if","(like","(or","*","+",".+","/","0","0))","0.592m","0.618m","1","1)","1,","1.","1.273","1.9m","16","19.347","1:","1:axis_num","1]","1]^2","2","2))","2.64m","2.81m","21.46\\%","21.47\\%","256,","26.712","273.308","2]","2]^2","2d","2d,","32","32.","3700x","385.819","4)","4,","4.0","4096^2","433.644","78.54\\%,","970","=","==",">","@inbound","@index(global,","@kernel","@time","\\co","\\ell","\\ell\\tim","\\frac{1}{0.7853}","\\frac{\\pi","\\frac{pi}{4}","\\pi","\\pm","\\sim","\\sin","\\time","a[(i","abov","absolut","account","action","action,","action.","actual","again","again.","again:","allow","along","alreadi","altogether!","alway","anoth","anyon","anyway?","approach","array","array)","array,","ask","assum","at(zeros(n,","attribut","average!","aw","axi","axis_num","axis_num^2","back","bad","be","becom","befor","believ","below.","below:","benchmark","benchmarks,","benchmarktools,","best","better","between","bit","bit,","blue","both","box","box.","box—mul","bunch","calcul","call","carlo","cartesian","cartesian_box_muller!(input_pts,","cartesian_kernel!(cpu(),","cartesian_kernel!(cudadevice(),","cartesian_kernel!(input_pts,","cartesianindic","case","case,","cases,","cast","caus","ceil(int,","certain","certainli","chapter","chapter,","chosen","circl","circle,","circle.","code","code,","code:","column,","come","common","comparable.","complic","comput","computing.","configur","consid","consider:","continu","core","cos(theta)","cost","costli","cpu","cpu,","cpu.","create_grid(n,","create_rand_dist(4096^2,[0,1])","create_rand_dist(4096^2,[0,1],","create_rand_dist(n,","creativ","cuarray)","cuda","cuda.@sync.","cuda.@tim","cudakernel","dangerous!","deal","definit","depend","differ","difficult","dimens","dimension","dimensions!\")","discuss","distanc","distribut","distribution(s)","distribution,","diverg","divergence,","divid","do","don't","done","dx","each","easi","easy:","efficient.","element","elements.","else,","embed","end","endpoints;","endpoints[1]","endpoints[1])","endpoints[2]","essenti","essentially,","even","evenli","everyon","exactli","exactly.","exampl","execut","expect","expensive.","f","f(cpu(),","f(cudadevice(),","fact,","fair,","fall","fast,","fast.","faster,","few:","final","find","fine.","first","first,","firxt","for.","forev","found","full","function","fundament","gaussian","gener","given","go","gpu","gpu,","gpus)","grid","grid_ext","grid_extents/2","gtx","hand","hand,","hard","hardwar","hardware,","has_cuda_gpu()","here","here,","here:","hypothet","idea","idea,","ignor","imag","image,","imagin","implement","import","improperly,","inbuilt","includ","incred","initi","input","input_pt","input_pts[tid,","input_pts[tid,1]","insid","instead","instead?","interest","interested,","intern","is!","isa(input_pts,","issue.","it'","it.","j","j,","jame","julia","julia'","kernel","kernel!","kernel!(input_pts,","kernel,","kernel:","kernelabstract","kernelabstractions.jl,","kinda","know","larger","lead","learn","less","lesson","let'","licens","license.","license.md).","linear)","list","liter","littl","log(input_pts[tid,1]))","log(r_0)","long","look","loop","m","main()","make","mani","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matter","mean","method","method,","method:","minimum","mit","mont","more","mu","mu)","mu,","mu;","muller","multipli","n","n,","n=100)","na","nan","natur","ndrange=size(input_pts)[1])","nearest","need","new","note","now","number","numcor","numcores)","numthread","numthreads)","nvidia","odd","ok,","on","onc","onto","oper","operation,","operations.","optim","out","output","output_pt","output_pts,","output_pts[tid,1]","output_pts[tid,2]","outsid","overkill.","p1","p1^2","p2","p2^2","packag","pain","pair","parallel","parallel,","part","particl","perform","performed,","pi","pick","pink","place","platform","point","points,","points.","poison:","polar","polar_box_muller!(input_pts,","polar_muller_noreplacement!(input_pts,","polar_muller_noreplacement!)","polar_muller_replacement!(input_pts,","pre","println(\"cannot","probabl","problem","problem!","problem,","process","process,","process.","program","prohibit","provid","purpos","queu","queue","queued,","r","r^2}{(2r)^2}","r_0","r_0)","radic","ran","rand()","rand()*2","random","random?","randomli","re","read","realli","reasons.","reject","replac","replacement:","replacement?","requir","results!","results.","return","return(at(rand(n,2))","right,","right.","right?","roll\"","round","row","run","ryzen","same","sampl","sampling,","sampling?","say,","scenario","schloss","script","see","separ","set","sharealik","shouldn't","show","shown","sigma","sigma,","similar)","similar).","simulation,","sin(theta)","singl","slow","smallest","somehow","someon","someth","sometim","sometimes,","somewher","sort","specif","spend","sqrt(","sqrt(n)","sqrt(n))","squar","square.","start","statement","step","step.","step?","still","straightforward,","subsect","subsequ","subtract","such","suit","sure","sync","take","task","teach","text","there,","theta","thing","things!","things.","think","those","thread","threads,","threads.","tid","time","time,","time.","transform","transform.","tri","tricki","true","truth","tupl","type","under","unfortunately,","uniform","uniformli","unit","unlucky).","until","up","us","usual","valid","valu","values,","visual","wait(cartesian_box_muller!(input_pts,","wait(polar_box_muller!(input_pts,","want","warn","warp","warp.","way","well","well,","within","without","work","work!","worlds,","worth","write","written","||"],"contents/convolutions/2d/2d.html":["\"2d","\"8bit","\"circl","\"smeared\"","\"sobel","#","&","&=","(#560),","((i","((j","((x","(2*sigma^2))","(2d)","(a),","(array","(b),","(c)","(c),","(found","(j","(kernel_size,","(mat1.shape[0]","(normalized)","(one","(y","*","**","+","+=",".+","/","0","0.0","0.0,","0.5","1","1.0","1.0,","1.0]","1.0]*[","1.0]*[1.0","1.0],","1.0]])","1.canny,","10.","1986.","1:kernel_s","1]","2","2)","2))","2.0","2.0,","20","20\\time","2},","3","3\\time","3x3","4.0","50","50\\time","9","=","[","[0.0],","[1.0,","[1.0]],","[1].","[1~0~","[1~2~1]","[2.0],","[[","[[1.0,","\\\\","\\begin{align}","\\begin{bmatrix}","\\end{align}","\\end{bmatrix}","\\end{bmatrix}.","\\end{bmatrix}\\\\","\\frac{1}{2\\pi\\sigma^2}e^{","\\frac{1}{9}.","\\frac{x^2+y^2}{2\\sigma^2}},","\\left(","\\left(\\begin{bmatrix}","\\otim","\\right)","\\sigma","\\sigma_x","\\sigma_y.","\\sqrt{g_x^2","about,","abov","ad","add","addition,","again,","algorithm","allow","along","always,","anim","anoth","appli","approach","area","array","array.","associ","assum","attribut","axi","be.","befor","believ","below","between","bibliographi","black","blue","blur","blur\"","boundari","browser","canni","case,","center","center)^2","center)^2)","center+1)**2","center+1)**2)/(2*sigma**2))","chang","chapter","chapter,","chapter.","chapter:","circl","circle,","circle.","code","code,","color.","combin","common","complic","compon","compos","comput","compute_sobel(signal)","compute_sobel(signal):","condit","consequ","contextlib","convolut","convolution\"","convolution,","convolution:","convolutions.","convolv","convolve_linear(signal,","convolve_linear(signal::array{t,","correct","correspond","creat","create_circle(image_resolution,","create_gaussian_kernel(kernel_size)","create_gaussian_kernel(kernel_size):","create_sobel_operators()","create_sobel_operators():","creativ","cut","decid","def","definit","delimitedfil","derivatives.","detect","detection,","detector.","deviat","deviation,","diagram,","dimens","dimension","dimension)","dimensions,","direct","directions.","discuss","distribut","domain","each","edg","effect","effect,","element","elements.","ellipsoid","encourag","end","enforc","ensur","entir","essence,","essenti","essentially,","exampl","example,","examples,","exp(","expect","extens","factor","few","fill","filter","filter,","filter.","filter.shape[0]),","filter.shape[1]),","filter::array{t,","filter[i","filters\"","final","finally,","find","first","fit","float","focus","follow","formula","found","four","function","further","futur","fuzzier","g(x,y)","g_i","g_x","g_y^2}","g_{\\text{total}}","gaussian","gaussian,","gaussian.","gaussian;","gener","good","gradient","gradient.","gradient:","grant","graphic","green,","greyscal","grid.","grid_ext","grid_extents)","grid_extents,","gx","gy","gy.^2)","heart\"","here","here,","highlight","highlighted,","however,","i+1):","ieee,","imag","image,","image.","image:","image_resolution)","image_resolution))","images.","images/graph","import","independ","index","information.","initi","input","instead","integr","intern","introduc","involv","it.","iter","j","j+1):","j]","jame","john,","k","k,","kernel","kernel.","kernel[i,j]","kernel_function(x,","kernel_s","kernel_size)","kernel_size))","kernel_size*0.5","known","l","l]","larg","larger","licens","license.","license.md).","like,","linearalgebra","littl","longer","look","lot","made.","mani","mat1.shape[1]","mat2):","mat2.shape[0],","mat2.shape[1])","mathjax.hub.queue([\"typeset\",mathjax.hub]);","mean","measur","method","method:","mit","modifi","more","move","much","n","naïv","need","new","noise.","none","normalize(kernel)","note,","now","np","np.dot([[","np.dot([[1.0],","np.exp(","np.fromfunction(kernel_function,","np.linalg.norm(kernel)","np.power(gy,","np.sqrt(0.1*kernel_size)","np.sqrt(np.power(gx,","np.zeros((image_resolution,","np.zeros((kernel_size,","np.zeros(output_size)","numpi","obnoxi","off!","offset","on","onto","oper","operation.","operator.","operator:","operators,","origin","otherwis","out","out[i,","outlin","output","output_size)","output_size):","particular,","perform","place","play","point","possibl","practice:","previou","propos","pull","purpos","quadratur","radius):","random","range(image_resolution):","range(max(0,","range(output_size[0]):","range(output_size[1]):","red,","relat","rememb","reminder,","request","requir","return","right,","rule","s_i","s_x","s_x*a","s_y*a.","said,","same","sanderson","scale","schloss","section","section,","section.","sections;","see","separ","serv","set","sharealik","show","shown","sigma","signal[k,","signals,","significantli","similar","simpl","size(signal)","size(sx))","size(sy))","size,","size.","slightli","sobel","somewhat","sophist","specifi","sqrt(0.1*kernel_size)","sqrt.(gx.^2","squar","stage,","standard","start","stick","stop","such","sum","sum_matrix_dimensions(mat1,","sum_matrix_dimensions(signal,","support","suppress","suppress(indexerror):","sx","sx))","sx,","sy","sy))","sy,","tag.","talk","text","text.","that,","that:","this:","though","thought","through","thumb,","time","togeth","topic","total","tradit","two","ultim","under","us","user","valu","values).","variant","veri","video","visual","want!","way","white","whose","width","worth","write","written","x","x_posit","y","y):","y_posit","zeros(kernel_size,","{t"],"contents/cooley_tukey/cooley_tukey.html":["!","!(idx","!=","\"","\"%g\\n\"","\",","\"0.1.11\"]","\"calcul","\"combin","\"complet","\"difference:","\"dit","\"ftexample\"","\"perform","\"radix2\"","\"radix2positive\"","\"radix8\"","\"result","\"take","\"vx:\"","\"{}\",","#","#'","#'*","#'+","#(c/+","#(if","#(math/log","#c(0","#includ","#simpl","$","%","%))","%1","%1)","%2)","%2)))]","%3","%n))","&","&[complex])","'list","(","(#560),","((","((!))","((b","((dft","((fft","((stride","(*","(+","(/","(0","(0..((n","(0..n)","(0..n).step_by(strid","(1","(32","(:requir","(=","(\\cos(","(\\cos(2","(\\e","(a","(appli","(auto","(b","(bi","(c/*","(c/complex","(c/exp","(coeffici","(comp","(complex::new(0.0_f64,","(concat","(concaten","(count","(data)","(defn","(defun","(dft","(dft)","(dft),","(either","(elt","(even","(even?","(exp","(fft","(fft).","(fftw_complex*)x,","(fftw_complex*)y,","(for","(found","(i","(i.0","(if","(int","(into","(j","(k","(k)","(keep","(last","(length","(let","(let*","(like","(loop","(map","(mapcar","(mapv","(math/pow","(matrix","(mult","(n","(n)","(new_x[k","(odd","(odd?","(of","(or","(partial","(partit","(partition)","(println","(quot","(radix","(rang","(repeat","(size","(size)));","(size_t","(std::uint32_t","(stride","(time","(twiddl","*","**","*=","*x,","+","++","+=",",return",".",".*",".+","..]",".collect()",".doubl",".exp()",".extern",".fill(new",".filter(|i|",".global",".intel_syntax",".long",".map((temp,",".map(|i|",".map(|k|",".rodata",".section",".string",".sum()",".text","/","/)","//","0","0'","0)","0))","0));","0,","0..((stride","0..(n","0..64","0..n","0.0_f64));","0.0_f64);","0.0im","0:bnum","0:length(a)","0:n","0;","0s","0x00ff00ff)","0x0f0f0f0f)","0x33333333)","0x55555555)","1","1)","1)))","1)))))","1));","1)*pi*i*k/n)","1):","1,","1.","1..=((n","1.0","1.0);","1.0+0.0im","1.0+0.0im;","1.0+2.44929e","1.0_f64);","1.0im","1.0im]","1.22465e","1.83697e","1.cooley,","1105199103","16","16)","16+1.0im","16+1.0im;","16]","16im","16im;","17","1805","1965","1965.","1:digit","1:half","1:length(a)]","1:length(bit_indices)","1:length(indices)","1:length(x)]","1:length(y)","1:logn","1;","1]","1])","1e","1}","2","2)","2)))","2)));","2));","2):","2);","2**32","2*sqrt(","2,","2.","2.0","2.0_f64)","2.0j","2;","2]","2];","2^(j","2_u128.pow(i","2half","2im*pi*n*k/n)","2im*pi*n/n)","2pi","2pi*i*(k+n/2)/n=","2pi*i*k/n)","3.0","3.14159265358979323846264338327950288419716;","3.67394e","3]","4","4)","4.0","4290772992","5)","5.51091e","6.12323e","6.28318530718","8","8)","8]","8],",":+","::",":a",":depend",";;",";;els","=","=1:length(bit_indices)","=>",">",">());",">=",">>","[&","[&]","[(k","[0","[0,","[0]","[1.0+0.0im","[1].","[;;","[[w","[]","[complex","[complex(x[i])","[complex.cor","[first,","[float(i)","[i","[len","[m","[n","[r12","[r14","[r14]","[r14],","[r15","[r15]","[r15],","[rax","[rax]","[rax],","[rbx],","[rsp","[vx","[vx]","\\\\","\\cdot","\\co","\\cos(2","\\cos(\\omega","\\frac{1}{n}","\\infty}","\\int_{","\\log","\\mathcal{o}(n","\\omega","\\omega.","\\omega_2^0","\\omega_2^1","\\omega_2^1,","\\omega_n^k","\\pi","\\pm","\\rightarrow","\\sim","\\sin","\\sin(","\\sin(2","\\sin(\\omega","\\sum_{k=0}^{n","\\sum_{n=0}^{n","\\theta)","\\theta}","\\xi","\\xi)","\\xi))dx","\\xi}","])","^","^\\infti","__muldc3","__muldc3,","_i","`iterative_cooley_tukey`","a.add(b.mul(new","a[indices[i]]","a_0","a_1","abil","abov","above,","above?","accumul","accurate:","actual","add","addit","addsd","again","algorithm","algorithm.","algorithm:","allow","alreadi","alway","amaz","amount","anoth","appear","append","appli","applic","applications.","appropri","approx(y,","approx(z,","approxim","approximate.\\n\");","area","args]","arrang","array","array(n)","array(n).fill(null);","arrays.","ask","assum","attribut","auto","auto&","b","b,","b:","b[i]","b_0","b_1","back","bad","base","basically,","be","be.","be;","beauti","befor","before,","begin(initial),","behind","below","below.","better","between","bibliographi","binari","bit","bit.","bit_indic","bit_indices[i]","bit_indices[i][end","bit_reverse(x)","bit_reverse(x);","bit_reverse(x,","bit_reverse(x:","bit_reverse:","bit_reverse_entries:","bit_reverse_idxs(math.log2(n));","bit_reverse_return","bitreverse(a::array)","bitreverse(x)","bitstring(indices[i]))","bnum","bnum)","book.","both","both,","bottom","bottom;","bounc","built","butterfli","butterflies,","butterflies.","butterfly\"","butterfly(x)","butterfly(z[start_index:start_index","butterfly:","c","c/","c/*","c/+)","c/exp","c/stringifi","c]))","cabs,","calcul","calculation.","call","care","case!","case,","case.","certainli","cexp","cexp(","cexp()","cexp,","chang","chapter","chapter:","check","claim","clear,","clearli","cmath","cmp","code","code.","codebase.","coeffici","coefficients.","collect","column","column.","combin","come","common","complet","complex","complex(0,","complex(math.random(),","complex::new(1.0_f64,","complic","comput","concatenation,","console.log(\"cooley","console.log(\"it","const","constitu","convert(int,ceil(log2(length(a))))","convert(int,ceil(log2(length(x))))","cooler","cooley","cooley_tukey","cooley_tukey(&x);","cooley_tukey(&x.iter().skip(1).step_by(2).cloned().collect::>());","cooley_tukey(begin(recursive),","cooley_tukey(doubl","cooley_tukey(it","cooley_tukey(x)","cooley_tukey(x):","cooley_tukey(x);","cooley_tukey(x.filter((_,","cooley_tukey(x:","cooley_tukey(x[1:2:n])","cooley_tukey(x[2:2:n])","cooley_tukey:","cooley_tukey_end","cooley_tukey_end:","cooley_tukey_loop","cooley_tukey_loop:","cooley_tukey_mov","cooley_tukey_mov_data","cooley_tukey_mov_data:","cooley_tukey_moved:","cooley_tukey_return","cooley_tukey_return:","cooley_tukey_split","cooley_tukey_split:","cooley_tukey_spliting:","correct","correct;","correspond","course)","cover","crate","creat","creativ","cri","curv","cvtsi2sdq","cvttsd2si","cvx","cvx))","cvx)]","d\\xi","data","data)))","data.complex","data.list","data.map","data.ratio","def","defin","definit","dep","depict","describ","desire,","dft","dft(&x);","dft(doubl","dft(iter","dft(x)","dft(x):","dft(x);","dft(x:","dft.","dft:","dft:\"","dft_end_i","dft_end_i:","dft_end_j","dft_end_j:","dft_loop_i","dft_loop_i:","dft_loop_j","dft_loop_j:","dftmat","diagram","diagram:","diagrams.","didn't","differ","diffv","diffv))))","digit","digits:end]","directli","disciplin","discov","discret","distribution(0.0,","distribution(rng);","div(bnum,2)","div(n,","div(n,2)","divid","divsd","do?","does!","domain","dot","doubl","double]","during,","dx","e","e^(","e^(n*k*2*pi*(1/len)*(","e^{","e^{2","each","earli","easier","easiest","easili","effici","element","element.","elements,","elements.","end","end(initial),","end(iterative));","end(recursive));","end,","enforc","engin","entri","equal","equations:","equival","essenti","euler'","even","even[k]","evens)","everyon","exactli","exampl","example,","exist","exp","exp(","exp,","exp.(","explain","exponenti","expres","extern","f(\\xi)","f(x)","f64)","f64))","f64)).exp()","f64)).exp();","f64).log2()","f64).sqrt()).collect()","fact","factor","factor[1:half])","factor[1:half],","factors)))","far","fast","fast?","favored.","feasibl","feel","fewer","fft","fft'","fft(&x);","fft()","fft(doubl","fft(x)","fft(x:","fft)","fft))))))","fft.","fft.core","fft:\"","fft;","fftplanner::new(false);","ffts.","fftw","fftw)","fftw_destroy_plan(p);","fftw_estimate);","fftw_execute(p);","fftw_forward,","fftw_plan","fftw_plan_dft_1d((int)n,","figur","fill","find","first","first)","first,","first;","first[i]);","first[k","first[k];","firstly,","flip","fmt:","fn","follow","following:","formula:","formulas,","forth","fourier","frederick","free","freq","frequenc","friendlier,","fromintegr","front","fulli","function","function,","functions:","gathros,","gauss","glory!","go","goe","good","graphic","great","greater","half","half)","half,","half.","header","heart","help","here","here,","heroic","however,","https://github.com/alanforr/complex","i'll","i)","i))","i.1).norm()","idx","idx)","if(isapprox(y,","if(isapprox(z,","imag","images/graph","imagin","imaging,","implement","implement.","implementations.","import","imposs","imul","inclined).","independ","index","index'","index)","index))))))","indic","indices)","indices.","indices.\"","indices[i]","initi","initial;","instead","int","int(log2(n))","int)","int)time(null));","integ","integr","integrals:","intern","into:","introduc","intuit","is;","it'","it,","iter","iterative_cooley_tukey(&x);","iterative_cooley_tukey(begin(iterative),","iterative_cooley_tukey(doubl","iterative_cooley_tukey(it","iterative_cooley_tukey(x)","iterative_cooley_tukey(x):","iterative_cooley_tukey(x);","itself!","j","j*stride","j]","j]))","j]);","jame","jar","je","jle","jmp","john","jstor,","julia","julia;","k","k)","knew","know","known","landscap","languag","language,","larg","last","last)","last);","later","lay","lea","leftov","lein","len","len(x)","len)","len))))","len)]","length","length(x)","length)))","less","librari","licens","license.","license.md).","like","like:","limit","locat","log2","log_2(n)","logn","look","loop","m","m\"","m))","m.","m.fromlist","m_pi","machin","main","main()","mak","make","manag","mani","map","match","math","math,","math.floor(n","math.pi","math/ceil","math/pi","mathemat","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matmult","matrix","matrix!","matrix,","mazzuca.","mean","memcpi","memcpy,","memset(y,","memset,","mention","mentioned,","merg","mess","method","method,","method.\"","minu","miss","mit","modern","modifi","more","mov","movap","move","movq","movsd","much","much,","mulsd","mult","multipl","multipli","multiplications.","mut","n","n'","n)","n),","n).exp()));","n);","n,","n/2","n];","name","names,","necessari","necessary,","need","neg","new","new_x","new_x[k","next","nicol","non","none","noprefix","note","note,","note:","now","now,","null","number","n}","o","odd","odd[k];","odds)","odds)))","omega","on","on.","once,","one:","oper","operation.","operation:","operations.","order","order,","ordinari","oscillations.","out","output","outsider,","over","p","p;","package.\")","pad","paramet","parse(int,","particular,","particularli","parts:","peak","perfectli","perform","physic","pi","pictori","pieces.","planner","planner.plan_fft(n);","pleas","point","point,","pop","portal","posit","possible,","power","precis","preform","present","previou","primarili","principle,","print","print(all(abs([y[i]","printf(\"thi","printf,","println!(","println(\"it","println(\"recurs","problem","proce","processing.","product","prohibit","project.clj","provid","ptr","pull","push","push!(bit_indices,","put","put,","pxor","python","qualifi","quickli","qword","r12","r12,","r13","r13,","r13]","r14","r14,","r14]","r15","r15,","r15]","r15],","radic","rand(128)","rand,","rand::prelude::*;","rand;","rand_max:","random","rang","range(0,","range(1,","range(64):","range(64)][j])","range(n):","range(strid","range,","rare","rax","rax,","rbx","rbx,","rcx,","rdi","rdi,","rdx,","re","real","realli","reason","reason,","rec","recurs","recursion!","recursion,","recursion.","recursively,","reduc","relat","repl","replac","repres","request","requir","require(\"complex.js\");","research","resolut","respectively.","ret","return","return;","revers","reversal,","reverse(bit_indices[i])","right?","rng","rng.gen_range(0.0_f64,","row","row.","rsi","rsi,","rsp","rsp,","run","rustfft::fftplanner;","rustfft::num_complex::complex;","rustfft;","said,","same","save","saw","scheme,","schloss","scienc","scientif","second","section,","see","seem","seemingli","seen","sequenc","seri","series,","set","sharealik","shortcut:","show","shown","shr","shuffl","side","sign","signal","similar","simpl","simpli","singl","sinusoid","size","size_t","sizeof(y));","slow","slow,","small","snippet","so!","so,","someth","soon","sort","sort_by_bit_reverse(first,","sort_by_bit_reverse(it","soul","space","space\"","space,","space.","split","srand((unsign","srand,","stage","standard","start","start_index","static","std::array","std::begin;","std::complex;","std::cout","std::end;","std::f64::consts::pi;","std::generate(","std::size_t;","std::swap;","std::uint32_t(log2(static_cast(size))));","std::vector","std::vector(s","step,","still","straightforward","stride","stride)","stride):","string(bit_indices[i][end","strip","sub","subdivis","subdivision),","subsd","substitut","suggest","sum","summat","super","superfluid","surface,","swap","swap(first[b],","syntax,","systems;","t","t)","t)),","t));","take","tell","temp","temp[b]","temp[i]","temp[k","temp[k]","templat","term","term.","termin","terms)","terms))))","text","text,","that'","there!","thereafter.","thing","thing,","things,","this:","this_fft","this_fft.process(new_x.as_mut_slice(),","though","though,","thread_rng();","through","time","time,","time;","tmp","tmp(n);","tmp;","tmp[n];","today","together,","told,","toler","top","top;","transform","transform\"","transform,","transform.\"","transform?","transform_matrix","transform_matrix*x","transforms.","trick","truli","truth","tukey","tukey,","turn","twice.concat(twice.map(x","twiddl","two","two:","two_pi","two_pi:","u32);","ultim","ultimately,","under","understand","unnecessari","unport","until","us","used,","useful.","usiz","usize)","usize))","usize)]","usize)];","v","v))","v.iter().zip(y.iter()).all(|i|","v]","valid","valu","value:","values:","vcat(x_odd","vec![complex::new(0.0_f64,","vec::with_capacity(64);","vec>","vector","vector'","viren","void","vortex","vx","vx)","vx)))","vx)]","vx:\"","w","w))","w,","w0","w;","want","was:","wave","waveform,","way","way!","way,","well,","wikipedia)","wish","within","without","work!","work.","write","written","x","x)","x))","x);","x,","x.append(random())","x.len();","x.length;","x.map((_,","x.push(complex::new(real,","x.reduce((a,","x.to_vec();","x1","x2","x;","x[1]","x[2]","x[64],","x[b]","x[half+i]*factor[i]","x[i","x[i]","x[i];","x[indexes[i]]);","x[k","x[k]","x[n]","x[n];","x_even","x_k","x_n","x_odd","xmm0","xmm0,","xmm1","xmm1,","xmm2","xmm2,","xmm3","xmm3,","xmm6","xmm6,","xmm7","xmm7,","xmmword","xor","x}","y","y.as_mut_slice());","y.into_iter().map(|i|","y[64],","y[half+i]","y[i]","y[k]","y[n];","z","z[64];","z[i]","z[start_index+k","zero","zipwith3","{","|","}","})","});","},"],"contents/notation/notation.html":["\",","\"better\"","\"complex","\"on","#","(#560),","(a","(and","(becaus","(found","(length(a)","+","+=","0)","1","1!","1)","1.","1:length(a)","1:length(a)/2","1:size","2),","2,","2d","3","3)","3:","3d","4","4.0","4d!","8.","=",">",">=","\\log_2(8),","\\mathrm{size}\\times\\mathrm{size}","\\omega","\\omega(1)","\\omega(3)","\\omega(n)","\\omega,","\\theta","\\theta(1).","\\theta(2^n),","\\theta(3),","\\theta(\\frac{3n}{2}","\\theta(\\log(n))","\\theta(n).","\\theta(n^2)","\\theta(n^3),","\\theta.","a.","a[1])","a[2*i+1])","a[2*i]","a[2*i])","a[end])","about:","abov","acceptable,","access","access_image(img::array{float64},","action","actual","ad","addition,","advic","algorithm","algorithm.","algorithms.","alreadi","alway","anoth","answer","anyth","anything.","anyway.","arbitrari","are...\")","area","array","ask,","assum","assumption:","attribut","auxiliari","avoid","avoided,","awful,","b","b,","b::uint64)","back","bad","base","basically,","be","becom","befor","before,","below,","best","better","better:","big","book","both","breath","bunch","calcul","call","care","case","case,","case.","cases,","certain","certainli","chang","chapter","chapter:","clear","clear,","clearly,","code","come","common","compar","complet","complex","complexity.","complic","comput","concret","consid","constant","constant(a::array{float64})","constant(a::uint64,","constants!","constants,","constants.","consult","continu","convers","cover","crazi","creat","creativ","cutoff","cutoff)","cutoff::int64)","data.","decrement","definit","depend","describ","descript","descriptor","design","determin","differ","discuss","divid","doesn't","don't","done,","done.","due","each","each.","easi","easier","easili","element","element,","elements.","encourag","end","engin","entirely,","estim","even","exact,","exampl","example,","example:","examples!","examples,","exist","exist.","explain","explanation,","exponenti","exponential(value,","exponential(value::int64,","extra","fact,","factor","factors.","far","fast","fast!","faster","fastest","few","final","find","fine","finish.","first","first,","focu","follow","following:","forward","front","function","function,","function.","function:","functions,","gener","general,","geometr","go","go,","good","good!","grain","graphic","great,","great.","half","hand,","harm","haven't","here","here'","here,","histori","honest,","hour","however,","huge","hundr","i*siz","i=0:18446744073709551615","idea:","ideal","ideally,","if(a","if(n","ignor","ignored.","imag","images/graph","imagin","implement","imposs","increas","increases.","incred","index","inhibit","initi","inputs.","instead","interest","intern","intrins","intuitively,","is,","is:","issu","issue!","it!","it'","iter","j","jame","jimmi","job","keep","know","larg","larger","last","left","length","let'","librari","licens","license.","license.md).","life","like:","linear","linear(a::array{float64})","littl","logarithm","logarithmic(a::array{float64},","logarithmic(a[length(a)/2+1:end],","long","longer","look","loop","loop,","loops,","loops.","lot","love","machin","make","manag","mani","massiv","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matter","maximum","mean","mean?","measur","mind","miss","mit","modifi","more","most,","mostli","move","much","n","n)","n,","n::int64)","nearli","need","need.","nest","new","none","notat","notation","notation,","notation.","now","now,","number","o","o(1)","o(1).","o(3)","o(\\log","o(b),","o(log(n))?","o(n)","o(n),","o(n).","o(n^2)","o(n^2).","o,","obviou","obvious","obvious.","obviously,","of\"","old","older","on","on.","one,","one;","one?","ones.","oper","operation,","operation.","operations,","operations.","opposit","optim","order","others.","out","out,","outlin","over","p=np","pair","particular,","perfectli","plethora","plot","point","point,","point.","points.","polynomi","practic","practice.","pretti","print","print).","println","println(\"a","println(\"b","println(\"th","println(a[1])","println(a[2])","println(a[3])","println(a[i])","println(b)","println(img[index])","println(length(a))","println(value)","println,","probabl","problem","problem,","problem.","problems.","programming,","promis","provid","pull","put","question","question.","read","realiz","realli","reason,","reasons.","recurs","recursion.","regardless","repercussions,","request","requir","research","rid","roughli","run","run!","run,","run.","runtim","runtime,","runtime.","runtime:","rustl","said,","salt.","same,","same.","save","saw","say","scale","scaling\"","schloss","scientist","second","section","see","seem","sense,","set","sever","sharealik","should!","shouldn't","side","simpl","simpli","singl","situat","size","size.","size:","size::int64)","slowest","slowest.","small","smaller","so:","solv","solved.","someth","somewhat","space,","speaking,","speed","spend","split","square).","square,","start","statement","statements,","still","still,","stop","straightforward","strang","stupid!","sum","sure","system","system,","take","talk","task.","technic","tempt","term","territory!","text","that'","that.","that?","them,","them.","theme:","theori","theory.","there,","thing","thing:","think","thinking,","this,","those","thought","three","through","throughout","time","time,","time.","time:","time;","togeth","tool","total","total.","touch","tri","twice,","two","unclear.","under","understand","understand.","unfortunately,","unless","unlik","until","up","up,","us","useful)","useless.","vagu","vague.","valu","variabl","wait","want","warn","wasn't","wast","way","way,","way.","we'll","we'v","well","well,","whatev","whether","while,","while:","without","work","world","world;","worri","worse!","worst","worst,","write","written","wrong;","yet.","you'r","yourself"],"contents/thomas_algorithm/thomas_algorithm.html":["\"\"\"the","\"\",","\"[0.0","\"[1.0","\"[2.0","\"\\t\"))","\"divid","\"fmt\"","\"ha","\"return","\"the","\"|\",","\"~{~f","#","#(0","#(1","#(4","#(7","#a","#includ","$","$(join((\"\",","$(join((a[2],","$(join((b[1],","$a","$a,","$a[1],","$a[2],","$b","$b[0],","$b[1],","$b[2],","$c","$c,","$c[0],","$c[1],","$i","$i)","$solut","$x","$x,","$x;","$x[$i","$x[$i]","$x[0],","$x[1],","$x[2],","$y[$i]","%.1f,","%.1f][x]","%.1f][y]","%.1f][z]","%s,","%s][x]","%s][y]","%s][z]","&","&=","&[f64])","&[f64],","&b,","&c,","&x);","&x[0]);","&x[1]);","&x[2]);","'__main__':","'list))","(","(#560),","($i","((a","()","(*","(/","(0,","(0..(size","(1","(1+","(1...n).each","(a,","(a.siz","(b","(b[i]","(barely)","(c","(c',","(c,","(c_prime[i]","(coerc","(copi","(d","(d[i]","(decf","(defmacro","(defparamet","(defun","(diagon","(divf","(exclud","(format","(found","(helper","(i","(i)","(i)'","(i)^*","(in","(int","(length","(let","(loop","(n","(or","(place","(setf","(size","(size_t","(std::size_t","(svref","(thoma","(v1","(x[i]","(z[i]","(zip4)",")","*","*=","+",",divisor)))",",place",".",".266]",".5f]\".format(solution[i]))",".for_each(|i|","/","//","/=","0","0)","0))","0,","0..len(w)","0.0)","0.0);","0.0]","0.0];","0.0][x]","0.0}","0.0};","0.26666668","0.8666667","0.}","0;","0]","0][x]","0f,","1","1)","1)).rev()","1):","1,","1.","1..","1..n","1..size","1.0","1.5333333","1.upto(a.s","1:","1:1","1;","1]","1])","1]);","1]*a[i])","1];","1}","1}&","1}}","1}}{b_i","2","2)","2).downto(0)","2).downto(0).each","2,","2,0):","2.,","2.0,","2:n","3","3)","3))","3,","3.,","3.0","3.0)","3.0,","3.0]","3.0];","3.0}","3.0};","3.}","3]","4","4.0","5","5,","5.,","5.0,","5.0][y]","5][y]","6))","6.0)","6.0]","6.0];","6.0][z]","6.0}","6.0};","6.}","6]","6][z]",":","::",":=",";;",";;;;","=","==","=>",">","@[0.0,","@[1.0,","@[4.0,","@[7.0,","[","[\"\",","[%.1f]\".format(a[1],","[%.1f]\".format(b[0],","[%.1f]\\n\",","[%.1f]\\n\".format(0f,","[%s,","[%s]%s',","[.8666]","[0","[0,","[0.0,","[1","[1,","[1.0,","[1.533]","[2","[3.0]\"","[3.0]\")","[3.0]\");","[3]","[4,","[4.0,","[5.0]\"","[5.0]\")","[5.0]\");","[5]","[7,","[7.0,","[7.0]\"","[7.0]\")","[7.0]\");","[7]","[];","[]f32","[]f32)","[]f32,","[]float64","[]float64)","[]float64{0.,","[]float64{1.,","[]float64{4.,","[]float64{7.,","[a[1],","[a]","[b[0],","[double]","[double])","[double],","[i","[ratio","[{:?}]\",","\\\\","\\begin{align}","\\begin{array}{ccccccc|c}","\\begin{array}{ccccc|c}","\\ddot","\\end{align}","\\end{array}","\\frac{c_0}{b_0}","\\frac{c_i}{b_i","\\frac{d_0}{b_0}","\\frac{d_i","\\left[","\\left\\{","\\right.","\\right]","\\time","\\vdot","_,","__name__","`(setf","a'_i","a)","a))","a,","a.len();","a.length;","a.siz","a[0],","a[1],","a[2],","a[3],","a[i]","a[i])","a[i]))","a^*_i","a_0","a_0,","a_1","a_2","a_i","a_n","abov","algorithm","algorithm)","allow","allud","alreadi","analytically.","appli","args)","array)","assum","attribut","author:","auto","b","b'_i","b'_i=1","b))","b,","b:","b::vector{float64},","b[0]","b[0],","b[0];","b[1]","b[1],","b[1]}","b[2],","b[3],","b^*_i","b_0","b_0:","b_1","b_i","b_n","back","backtrack","brilliant!","c","c'","c'_0","c'_i","c'_{i","c))","c,","c.clone()","c.dup","c:","c::vector{float64},","c[0]","c[0],","c[1],","c[2],","c[i","c[i]","c[j]","c^*_i","c_0","c_1","c_i","c_in","c_in,","c_n","c_prime","c_prime[0]","c_prime[1]","c_prime[i","c_prime[i]","c_{n","calcul","call","case","cases!","certain","chapter","chapter,","chapter.","chapter:","class","code","column","column)","column)))","common","comput","console.log(\"[0.0","console.log(\"[1.0","console.log(\"[2.0","console.log(\"ha","console.log(\"th","const","const&","copi","copy(c)","copy(d)","correspond","cost","count($x));","countdown(n","course!).","course,","cprime","cprime[0]","cprime[i","cprime[i]","creat","creativ","cut","d","d')","d'_0","d'_0.","d'_i","d'_i.","d'_n.","d'_{i","d)","d))","d):","d,","d.clone()","d.count","d.dup","d.length","d:","d::vector{float64},","d[0]","d[0]].join(\"\\t\")","d[1])","d[1]),","d[1]].join(\"\\t\")","d[2])","d[2]),","d[2]].join(\"\\t\")","d[3])","d[3]),","d[i","d[i+1]","d[i]","d[j","d[j]","d^*_i","d_0","d_1","d_i","d_in","d_in:","d_n","d_{n","data.list","data.ratio","def","denomin","denominator)","denominator,","destruct","destructively\"","diagon","divf","divid","divisor\"","divisor)","don't","done","doubl","double[]","double[size];","doublearray","doublearray):","doublearray,","doublearrayof(0.0,","doublearrayof(1.0,","doublearrayof(4.0,","doublearrayof(7.0,","downto","easi","easier","echo","element","elimin","encode:","end","end.","ensur","equal","equat","equation:","equations,","even","exampl","exploit","express","factor","familiar","find","first","first,","firstly,","float","fmt.printf(\"[%f]\\n\",","fmt.println(\"[0.0","fmt.println(\"[1.0","fmt.println(\"[2.0","fmt.println(\"ha","fmt.println(\"th","fn","follow","format!(\"{:18}\",","format!(\"{:?}\",","formula,","forward","found","four","fraction","free!","fun","func","function","gammison","gaussian","goal","graphic","hand","helper","helps.","i)","i))","i))))","i)))))","i))));","implement","implementations,","import","importantly,","index","init","initi","inplac","input","instead","int","int]","intern","io","isn't","it'","it.","jame","know","last","len(d)","len(d_in)","let'","licens","license.","license.md).","lisp","local","look","main","main()","main():","main(args:","main(string[]","make","massiv","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matrix","matrix,","mayb","mechan","memset(y,","miss","mit","modifi","mut","n","n):","n:","n::int64)","neat?","need","new","new_c","new_c[0]","new_c[i]","new_d","new_d[0]","new_d[i+1]","new_d[i]","next","non","none","note","now,","number","o(n)","o(n)!","o(n^3)","obviou","on","one:","one?","overall,","packag","particular","particularli","pass","pass,","passes,","php_eol);","place","plu","print","print(\"\",","print(\"ha","print(\"th","print(a[2],","print(b[1],","print(soln)","print(table.unpack(solution))","printf('","printf('ha","printf('th","println!(\"[{:>19}]\",","println!(\"[{:?}","println!(\"ha","println!(\"th","println(","println(\"[$i]\")","println(\"[%","println(\"[%.1f,","println(\"[0.0","println(\"[1.0","println(\"[2.0","println(\"ha","println(\"solution:\")","println(\"system:\")","println(\"th","println(soln)","privat","proc","programm","project.","public","pull","put","quit","rang","range(1,","range(n","read","realli","regular","request","result","result[i","result[i]","return","right","row","row)","row)))))","rows.","same","scale","scale:","scale;","scanl","scanr","schloss","secondly,","see","separ","seq","seq[float]","seq[float]):","set","shape","sharealik","short","side","simpler:","simpli","singl","size","size)","size).","size];","size_t","sizeof(double));","soln","soln.join(\"\\t\")","soln:","soln[i]","solut","solution\");","solution.indices)","solution:\"","solution:\"\"\"","solution:\")","solution:%s',","solution:\\n\");","solution;","solution?","solution[0]","solution[i","solution[i]","solv","start","static","std::cout","std::vector","std::vector&","std::vector(a.size(),","step","steps.","substitut","system","system\"","system\")","system\");","system,\"","system,\")","system,\");","system,%s',","system,\\n\");","system.out.format(\"[%.1f,","system.out.format(\"ha","system.out.format(\"th","t","tabl","tail","tdma,","term","text","that'","this:","thoma","thomas(","thomas(&a,","thomas(a","thomas(a,","thomas(a:","thomas(a::vector{float64},","thomas(doubl","thomas_algorithm($a,","thomas_algorithm(a,","thomas_algorithm(x,","thomasalgorithm(a,","thomasalgorithm(double[]","those","time!","too,","transform","tri","two","two:","under","until","upto","v1","v2","v3","val","valu","var","vec","vec![0.0,","vec![0.0;","vec![1.0,","vec![4.0,","vec![7.0,","vec::from(x);","vector","void","w)","w:","way","we'll","well,","written","x","x)","x);","x,","x:","x[0]","x[0]))","x[0]);","x[1]","x[1]))","x[1]);","x[2]))","x[2]);","x[i","x[i+1])","x[i]","x_i","x_i.","x_n","x_{i+1}","y","y,","y.iter()","y:","y[0]","y[i","y[i]","y[size];","z","z,","z:","z[0]","z[i","z[i]","zero","zip4","{","{0.0,","{1.0,","{4.0,","{7.0,","{:?}","{:?}][x]","{c[1]","{d[1]","|i|","|j|","}","~}~%\""],"contents/IFS/IFS.html":["!)","\"$($_[0])`t$($_[1])\"","\"chao","\"if","\"out.dat\"","\"play","\"sierpinski.dat\"","\"w\")","\"yes,","\"~f~c~f\"","\"~{~a~%~}\"","#","#'format","#'make","#[derive(clone,","#\\tab","#includ","$(get","$i","$i++)","$n;","$outputpoint","$outputpoints.add($point)","$point","$shapepoint","$shapepoints)","$shapepoints.count)]","$shapepoints[$(get","$temp","$temp[0])","$temp[1])","%","&=","'list","'vector","($i","($point[0]","($point[1]","((!),","((double)","((format","()","(*","(+","(0..iters).into_iter().map(|_|","(0.0,","(0.5","(0.5,","(1","(1.0,","(1/2)","(:constructor","(appli","(auto","(auto&","(bound","(chao","(curpoint","(d,","(defparamet","(defstruct","(defun","(e)","(flet","(format","(found","(here,","(hutchinson","(ifss),","(ifss).","(int","(int)n];","(intercalate)","(iter","(lambda","(length","(loop","(make","(map","(one","(out","(p","(p)","(p.i","(p.x","(point","(rand_max));","(random","(shown","(size_t","(sqrt","(svref","(the","(with","(x","(x,","(y,",")","*","*array,","*in,","*out,","*shape","+","+=",",(sqrt",".+",".=","/","//","0)","0))))","0.,","0.0","0.0)","0.0),","0.0)]","0.0],","0.0]]","0.0},","0.0}};","0.5","0.5*(rand(shape_points)","0.5,","0.75)","0.75))","0.75_f64.sqrt()},","0.},","0;","1\"","1)","1)(rng());","1.,","1.0)","1.0)(rng());","1.0))","1.0),","1.wikipedia:","1000,","10000","1967.3.jampour,","1981.11.wikipedia:","1994.6.sanderson,","1:n","1]","2","2\"","20","200,000","2010.4.wikipedia:","2012.9.wikipedia:","2017.7.wikipedia:","2019.","2019.10.hutchinson,","2019.12.wolfram:","2019.2.mandelbrot,","2019.5.saupe,","2019.8.gneiting,","3","3\"","3blue1brown:","4","4\"","4.0","5","5\"",":","::",":direct",":if",":output",":supersede)",";",";;",";;;;","=","=>",">","@(","@($(get","@(0.0,","@(0.5,","@(1.0,","[(p","[0,","[0.5,","[1.0,","[11][12]..","[1],","[2],","[3],","[4][5].","[6][7][8].","[9][10],","[[0.0,","[math]::sqrt(0.75)),","[point(0.0,","[point]","[rand(),","[random(),","\\begin{align}","\\bigcup_{i=1}^3f_i(p)","\\bigcup_{i=1}^4f_i(p),","\\end{align}","\\frac{p","\\in","\\mathbb{r}^2","\\mathbb{r}^2)","\\mathbb{r}^n","];","_","__add__(self,","__rmul__(self,","`((0","a,","above,","accord","accordingly.","acm,","act","actual","add","addition,","advanc","again","al.,","algorithm","all,","allow","along","american","amount","anim","anoth","answer","appear","appears,","arbitrarili","archiv","aren't","array","array,","array[rand()","aspect","assess","associ","attention.","attract","attractor","attractors.","attribut","audience'","auto","avail","a}{2}\\\\","b","b,","back","backquot","becom","befor","before!","before,","before?","began","begin","below):","below:","benoit,","best","between","bewildering.","bibliographi","bit","bit.\"","blue","boggl","both","bounds,","branch","bring","britain","britain?","b}{2}\\\\","c","c,","c.","call","case","case!","catch","center","certain","chao","chaos_game(10000,","chaos_game(10_000,","chaos_game(iters:","chaos_game(n,","chaos_game(n::int,","chaos_game(struct","chaosgam","chaosgame($n,","chaosgame(10000,","chaosgame(int","chapter","chapter,","chapter.","child","children","children,","choic","choice(shape_points))","choice(shape_points))]","choice,","choos","choose(const","choose(inputpoints));","chosen,","circles?","class","clean,","clear","clearli","closer","coast","coastlin","code","collect","come","comma","common","compress","compression,","comput","computation","concept","concept,","const","constrict","context?","continu","continues.","conversation,","copy)]","costly.","count","creat","creativ","cur_point","curpoint","curpoint;","current","cut","c}{2}\\\\","d,","data","data,","data.array","data.list","day.","deal","decid","def","defin","definit","definitions,","delimitedfil","describ","detail","determin","determinist","develop","dietmar","differ","dimens","dimension","dimension,","dimension:","dimensions.","discuss","discussion.","distract","distribut","donald","dot","doubl","drand()","drand()};","draw","d}{2}\\\\","e","e))","e,","each","earlier,","easili","effici","embed","empti","end","engin","enter","entir","entirely:","equilater","escap","essenti","estim","et","evalu","everything,","exampl","example,","exist","explan","exploration,","exponenti","extend","extens","extern","f","f)","f.","f.write(\"{0}\\t{1}\\n\".format(*point))","f.write(\"{0}\\t{1}\\n\".format(p.x,","f64,","f:","f_1(p)","f_1,","f_2(p)","f_2,","f_3","f_3(p)","f_4(p)","fact,","famou","fashion,","fast","feasibl","few","file","fingerprint","first","first,","firstly,","fn","focu","follow","forego","form:","format!(\"{}\\t{}\\n\",","four","fractal","fractals,","fraction","function","function.","functions,","functions.","further","futur","future!","g","g'","g''","g'')","g')","g,","game","game\"","game,","games,","games.","gener","general,","get","glance,","go","green","h(p)","halfway","hamzaoui,","hana","happen","happens:","happili","hard","hausdorff","help","here","here,","here.","here:","hexagons?","hitch...","hutchinson","hutchinson)","idea","ident","identif","identifi","if","imag","images/graph","imagin","implement","import","in_n,","includ","incred","individu","initi","input","inputpoint","inputpoints)","inputpoints);","insert","instead","int","integ","interest","interested!","interested,","interesting?","intern","introduc","io","is!","isn't","it'","iter","iteration,","iteration.","iterations\"","iterations,","jame","java.io.filewriter;","java.util.random;","john","jstor,","k","k)","k,","keep","kinda","know","known","known:","land","languag","larg","larger","learn","let'","lhs,","lhs.i","licens","license.","license.md).","line","listarray)","literature,","load","locat","lone","long","longer","look","lower.","lt","magic","mahdi","main","main()","make","mani","math","mathemat","mathjax.hub.queue([\"typeset\",mathjax.hub]);","maximum","mean","mention","method","methodolog","methods,","midpoint","migrat","million","mind","minimum","miss","mit","modifi","more","move","movement","mut","n","n)","n,","natur","need","new","next","nil","non","none","not.","notat","note","noth","now","now,","null","number","numelem","numelems)","numoutputpoints,","object","object.","objects)","obviou","of","of!","ofs(\"sierpinski.dat\");","old_point","on","on,","onc","open","open(\"sierpinski.dat\",","oper","operator*(doubl","operator*(point","operator+(point","operator,","operator.","operators,","other)","other):","other,","other.x,","other.y)","out","out).unwrap();","out,","out_n)","outpoint","output","output_point","output_points)","output_points[i,:]","outputpoint","outputpoints(numoutputpoints);","outputpoints)","outputpoints;","outsid","overal","p","p)","p))))","p,","p.i","p.x","p.y))","p;","particular","particular.","path","pattern","pattern.","patterns,","peculiar","per","percival,","piec","plane","pleas","plenti","plot","plotter","plotter.","point","point(0.5,","point(1.0,","point(doubl","point(random(),","point(rng.nextdouble(),","point(self.x","point(x=0,","point)","point))","point)))","point))))","point,","point.x,","point.y).as_str();","point[]","point[n];","points)","points)))","points*","points*)))))","points,","points.","points:","points[randrange(points.size())];","pointvector","pointvector&","point{x:","posit","possibl","present","privat","process","provid","pseudo","pt","pt)","pt,","pt.x,","pt.y};","pt;","public","purpos","question","quick","quickli","rand","rand()","rand()]","rand::*;","rand::thread_rng();","randengine(std::random_device{}());","randengine;","random","random())","random();","random()]","random,","random_element(struct","randomgen","randomli","randomr","randrange(std::size_t","range(n):","raouf,","read","realli","red","rememb","repeat","requir","respectively.","restrict","result","retain","return","review","rhs)","rhs.x,","rhs.y};","right,","rigor","rng","rng()","rng.gen(),","rng.gen()};","rng.nextdouble());","rough","s","s)","said,","sampl","saw","scale","schloss","science,","scientific,","seconds.","section","see","seed","seem","select","self","self.i","sense,","separ","seri","set","set.","shape","shape,","shape_point","shape_points)","shape_points):","shapepoint","shapepoints)","shapes)","shapes.","shapes:","shapes[rng.gen_range(0..shapes.len())];","sharealik","show","shown","sierpinski","sierpinski.dat,","similar","similar,","similarity,","simpl","simplest","simul","simulation.","singl","size_t","slightli","so.","so:","someth","space","space,","space:","spaces;","spatial","spawn","specif","sqrt","sqrt(0.75))","sqrt(0.75)),","sqrt(0.75)],","squar","square,","square?","squares.","squares?","stage,","start","start,","start:","starts.","static","statist","std::default_random_engin","std::default_random_engine&","std::fs::write(\"./sierpinski.dat\",","std::ofstream","std::size_t","std::sqrt(0.75)},","std::uniform_int_distribution(0,","std::uniform_real_distribution(0.0,","std::vector;","step","still","still,","stori","string.","string::new();","struct","structur","structure,","structure.","structure?","subsect","subsequ","success","such","system","system.collections.arraylist","system.random","systems.","systems:","tab","take","techniqu","term","text","that:","them.","themselv","theory,","there'","therefore,","thing","this,","this.i","this.x","this:","those","though","thought,","thousand","three","through","tilmann","time","time.","tmp","tmp.x);","tmp.y);","topic","track","travers","tree","triangl","triangle,","triangle.","triangle:","triangular","tricki","truli","truth","turn","two","typic","under","underpinnings,","understand","union","until","updat","us","use)","usize,","usual","vec","vec![","vec)","vector","veri","vertic","via","video","view","visit.","visual","void","wander","wanderin","way","way.","we'll","well,","whether","why,","will","within","within.","wonder","word","world","write","writedlm(\"sierpinski.dat\",","written","x","x,","x:","x;","y","y)","y)))","y:","y;","y=0):","yield","zeros(n,2)","zip(point,","zipwith","{","{0.5,","{1.0,","{drand(),","{k","{lhs.x","{{0.0,","|","}","}).collect()","};","ševčíková,"],"contents/verlet_integration/verlet_integration.html":["!","\"[#]\\ntime","\"[#]\\nveloc","\"[#]~%time","\"[#]~%veloc","\"fmt\"","\"integr","\"~d~%\"","#","#includ","$","&=","&=x(t)","&vel,","'[#]'","'__main__':","'psetf',","'time","'veloc","(","(#560),","()","(*","(*vel)","(+","(5,","(>","(_,","(actual","(aold","(defun","(defvar","(f64,","(first","(float,","(format","(found","(incf","(list","(loop","(method","(po","(position,","(psetf","(return","(second","(show","(stormer","(tail","(time","(time,","(time:","(time:time,","(time_sv,","(time_vv,","(timesv,","(timevv,","(veloc","(verlet","(x'","(x',","(x,","(xold,","*","**","*time","*time,","*vel","*vel,","+","+=",".01)",".5*acc*dt*dt",".doubl",".extern",".global",".intel_syntax",".rodata",".section",".string",".text","/","//","0","0)","0,","0.0","0.0)","0.001","0.01","0.01)","0.01))","0.01);","0.01d0","0.0:","0.0;","0.5","0.5*acc","0.5d0","0:","0;","0d0","0d0)","1","10","10,","10.,","10.0","10.0,","10d0","2","2)","2.0","2d0","2v(t)\\delta","2x(t)","4.0","5","5.0","5.0,","5d0",":","::",":=",";;",";;;;","=","==",">","[particle]","\\\\","\\begin{align}","\\cdot","\\delta","\\end{align}","\\frac{1}{2}(a(t)","\\frac{1}{2}a(t)\\delta","\\frac{1}{2}a(t+\\delta","\\frac{1}{2}at^2","\\frac{1}{2}mv^2?","\\frac{1}{3}b(t)\\delta","\\frac{1}{6}b(t)","\\frac{1}{6}bt^3","\\frac{b(t)","\\frac{x(t+\\delta","\\mathcal{o}(\\delta","\\mathcal{o}(n\\log(n)).","\\mathcal{o}(n^2)","\\sim","^","_","_)","_,","__name__","_po","a'","a',","a(t)\\delta","a(t+\\delta","a)","a,","abov","above,","above.","aboveground","acc","acc*dt","acc*dt*dt","acc*dt;","acc,","acc:","acc::float64,","acceler","acceleration!","acceleration,","accuraci","actual","ad","add","addition,","addsd","again,","algorithm","algorithm,","algorithm.","allow","alreadi","anoth","aold,","appropriately.","approxim","approximation,","args)","array)","assum","attribut","b","ball","barn","be","befor","bodi","both","bring","calcul","calculations.\"","call","can't","case,","central","certainli","chang","chapter","chapter:","check","choice;","class","classic","close","code","code:","comisd","common","comparison","complex","console.log(`${stormer.time}`);","console.log(`${stormer.vel}`);","console.log(`${time}`);","console.log(`${velocity.time}`);","console.log(`${velocity.vel}`);","console.log(`[#]\\ntim","console.log(`[#]\\nveloc","const","constant,","creativ","current","cut","data","def","denomin","depend","describ","differ","done","doubl","double)","double):","double,","drop","dt","dt)","dt))","dt)))","dt),","dt):","dt,","dt:","dt::float64)","dt;","echo","end","energy,","equat","error","essenti","etc.","even","everyth","exampl","exit","expans","explan","f(x(t+\\delta","f64","f64)","f64,","few","final","find","first","float","float)","float):","float64)","fmt.println(\"[#]\\ntim","fmt.println(\"[#]\\nveloc","fmt.println(time)","fmt.println(vel)","fn","follow","following:","forc","forgotten","former,","freefal","fst","fun","func","function","further","get","given","go","graphic","graviti","great!","greater","ground","half","half:","handi","have.","height.","here","here'","higher","hit","hold","however,","hut","implement","implicit","import","increment","initi","instead","int","integr","integration.","integration.\"","integration:","integration:'","integration:~%\")","integrators.","intent(inout)","interfac","intern","io","is:\"","is:\")","is:\");","is:\\n\");","is:\\n%lf\\n\"","is:\\n%lf\\n[#]\\nveloc","is:`);","is:~%\")","ismainmodule:","it'","iter","ja","jame","jbe","jerk","jie","job","kinemat","kinet","know","knowledg","known","language.","last","latter","less","let'","licens","license.","license.md).","lisp","liter","look","m","magnitud","main","main()","main():","main(args:","main(string[]","main:","make","mani","mathjax.hub.queue([\"typeset\",mathjax.hub]);","mean","mention","method","method.","method.\"","mit","model","modifi","more","motion","mov","move","movsd","mulsd","mut","n","necessary!","need","new","newton'","newtonian","next","next_po","next_pos;","nextpo","none","noprefix","note","now,","object","object,","obvious","offset","old","on","order","out","output","over","p","p0","p0@(x,","p1","packag","paramet","particl","peopl","perform","physic","pinch.","play","po","poor,","pop","pos)","pos*2","pos,","pos,acc,","pos:","pos;","pos_in","pose","posist","posit","position,","prev","prev_po","prev_pos,","previou","prevpo","prevpos,","prevpos:","print","print(\"[#]\\ntim","print(\"[#]\\nveloc","print(\"\\(stormer.time)\")","print(\"\\(stormer.vel)\")","print(\"\\(velverlet.time)\")","print(\"\\(velverlet.vel)\")","print(\"\\(verlettime)\")","print(\"{:.10f}\".format(time))","print(\"{:.10f}\".format(vel))","printf","printf(\"%lf\\n\",","printf(\"[#]\\ntim","printf(\"[#]\\nveloc","println!(\"[#]\\ntim","println!(\"[#]\\nveloc","println!(\"{}\",","println(\"$(time)\")","println(\"$(vel)\")","println(\"$verlettime\")","println(\"${stormerverlet.time}\")","println(\"${stormerverlet.vel}\")","println(\"${velocityverlet.time}\")","println(\"${velocityverlet.vel}\")","println(\"[#]\\ntim","println(\"[#]\\nveloc","privat","problem;","program","public","pull","push","put","putstrln","pxor","quit","rax","rax,","rbp","rdi,","real(8)","real(8),","reference,","regist","request","requir","result","result))","ret","return","rid","said,","save","scale","schloss","sens","seri","set","sharealik","show","simpl","simpler","simpli","simul","simultan","snd","snippet","so,","solut","solv","solver","sometim","speed","speed,","split","start","static","std::cout","stormer","stormer_fmt","stormer_fmt:","stormer_verlet","stormer_verlet(&time,","stormer_verlet(5,","stormer_verlet(5.0,","stormer_verlet(doubl","stormer_verlet(mut","stormer_verlet(pos,","stormer_verlet(pos::float64,","stormer_verlet:","stormer_verlet_loop","stormer_verlet_loop:","stormer_verlet_return","stormer_verlet_return:","stormerverlet","stormerverlet(5,","stormerverlet(5.,","stormerverlet(5.0,","stormerverlet(_pos:","stormerverlet(pos,","stormerverlet(pos:","stormerverlet(pos_in,","straightforward","straightforwardli","struct","submit","subroutin","subsd","subtract","such","system.out.println(\"[#]\\ntim","system.out.println(\"[#]\\nveloc","system.out.println(stormerverlet.time);","system.out.println(stormerverlet.vel);","system.out.println(velocityverlet.time);","system.out.println(velocityverlet.vel);","system.out.println(verlettime);","t","t)","t))","t)),","t))\\delta","t),","t)\\delta","t)}{2\\delta","t,","t0","t0)","t^2","t^2)","t^2),","t^2).","t^3","t^3).","t^3.","t^3}{3","t^4)","t^4),","take","takewhil","taylor","temp","temp_po","temp_pos,","temp_pos;","temporari","temppo","temppos:","temppos;","term","term,","text","that,","there'","there.","this.tim","this.vel","this:","though","time","time)","time)))","time);","time,","time.","time:","time;","time_sv);","time_v","time_v);","time_vv);","timestep","timestep.","timesteps.","timesv","timev","timeveloc","timevv","togeth","traj","traj)","trajectori","trick","trick!","two","two:","type","typic","t}","t}.","under","unfortun","up","updat","us","v","v'","v',","v(t)","v(t),","v(t)\\delta","v(t+\\delta","v(t+\\frac{1}{2}\\delta","v)","v,","v=\\frac{\\delta","v_0t","val","valu","var","variabl","variable.","vel","vel)","vel))))","vel);","vel*dt","vel:","vel:vel)","vel;","vel_sv)","vel_sv);","vel_vv)","vel_vv);","veloc","velocity!","velocity,","velocity_fmt","velocity_fmt:","velocity_verlet","velocity_verlet(&time,","velocity_verlet(5,","velocity_verlet(5.0,","velocity_verlet(doubl","velocity_verlet(mut","velocity_verlet(pos,","velocity_verlet(pos::float64,","velocity_verlet:","velocity_verlet_loop","velocity_verlet_loop:","velocity_verlet_return","velocity_verlet_return:","velocityverlet","velocityverlet(5,","velocityverlet(5.,","velocityverlet(5.0,","velocityverlet(_pos:","velocityverlet(pos,","velocityverlet(pos:","velocityverlet(pos_in,","velsv","velsv)","velverlet","velvv","velvv)","verlet","verlet(&time,","verlet(5,","verlet(5.,","verlet(5.0,","verlet(_pos:","verlet(doubl","verlet(mut","verlet(pos,","verlet(pos:","verlet(pos::float64,","verlet(pos_in,","verlet:","verlet_fmt","verlet_fmt:","verlet_integr","verlet_loop","verlet_loop:","verlet_return","verlet_return:","verlettim","verletvalu","verletvalues(doubl","verletvalues(time,","verletvalues(v","video","void","want","ways,","well,","wide","work","worse.","write(*,*)","written","x","x'","x(t","x(t)","x(t)}{\\delta","x(t+","x(t+\\delta","x(t\\pm","x)","x,","x.","x_0","xmm0","xmm0,","xmm1","xmm1,","xmm2","xmm2,","xmm3","xmm3,","xmm4","xmm4,","xmm5","xmm5,","xmm6","xmm6,","xmm7","xmm7,","xold","xor","x}{\\delta","zero.","zero:","zipwith","{","}","};"],"contents/split-operator_method/split-operator_method.html":["!!","\"\"\"calcul","\"\"\"contain","\"\"\"initi","\",","\".dat\")","\".dat\",\"w\")","\"\\n\"","\"\\n\")","\"\\t\"","\"\\t\")","\"__main__\":","\"folder='../haskell'\"","\"imaginarysplitop\"","\"output00000.dat\"","\"output{}.dat\".format(str(i).rjust(5,","\"real","\"realsplitop\"","\"sloshing\"","\"split_op_method\"","\"w\")","\"{}\\t{}\\t{}\",","\"{}\\t{}\\t{}\\n\".format","#","#[derive(clone)]","#defin","#endif","#ifndef","#includ","$","%","&mut","&operators)","&opr)","&opr));","&par,","¶meters,","'0'","(","(\"output\"","(#560),","((/","((:+","((^","((double)i","((i","((par.x","((par.x[i]","()","(*","(*)","(+)","(.*),","(.+)","(0,","(2","(2.0","(5","(\\k","(\\mathbf{r})","(\\n","(\\x","(^","(albeit","(also","(complex","(cough","(dft,","(div","(double)i","(drop","(dt),","(dt^2)","(dx","(evol","(export","(factor","(fftw_complex*)x,","(fftw_complex*)y,","(format","(found","(granted,","(i","(i)","(i,","(intercal","(intercalate,","(invers","(inverse)","(k","(kineticop","(kstep","(like","(listarray","(map","(nlse):","(normal","(oper","(par.im_time)","(par.k","(par.timestep","(par.x","(par.x[i]","(pi","(re","(rstep","(show","(size_t","(so","(such","(t)","(the","(timestep","(wfc","(x","(x.0","(x.len()","(x.size()));","(x:xs)",")","))","));","*","*)","**","*=","*in","*k;","*ke;","*opr,","*out","*par,","*pe;","*v;","*wfc;","*x,","*x;","+","++","+=",",",".",".\"\"\"",".*",".*)",".+","..","../gnuplot/plot_output.plt","..]",".fold(0.0_f64,",".into_iter()",".zip(energy_r.into_iter())","/","//","/=","0","0)","0)))","0);","0,","0.","0..par.r","0..par.timestep","0..re","0..x.len()","0.0));","0.0,","0.01","0.05,","0.0_f64));","0.0_f64).powi(2);","0.0_f64);","0.0_f64,","0.5","0.5*opr.v*par.dt)","0.5*par.k.^2*par.dt)","0.5*wfc_c.*ifft((par.k.^2)","0.5_f64","0:","0;","1","1)","1)*pi/(xmax)),","1),","1,","1.","1.0);","1.00)","10","10.0","10.0),","10.0,","10.0/512","10.0/512,","100","100)","100,","1000","1000,","10^{","1:2","1:3","1:length(density)","1:length(energy_k)","1:length(opr.wfc)","1:par.timestep","1]","1j)","1}","1}\\left[\\hat{u}_k(dt)","2","2)","2))","2));","2),","2);","2*xmax/res,","2,","2.0","2.0);","2.0_f64","2.0_f64).exp(),","20.0/512","256,","3.14159265358979323846","35},","4","4.0","5,","5.272859","512","512,","512/2",":",":+","::","=","==","=>",">",">dk",">dt",">dx",">im_tim",">k",">k[i]",">ke",">ke[i]",">pe",">pe[i]",">re",">size",">timestep",">v",">v[i]",">v[i]);",">wfc",">wfc[i]",">x",">xmax","?","[","[0","[1","[operators]","[x","\\frac{1}{2}","\\frac{1}{2}\\hbar","\\frac{1}{2}\\hbar\\omega,","\\frac{[i\\hat{h}_r,","\\frac{\\hbar^2}{2m}\\nabla^2","\\frac{\\parti","\\frac{i(\\hat{h}_r","\\frac{i\\hat{h}_kdt}{\\hbar}},","\\frac{i\\hat{h}_kdt}{\\hbar}}e^{","\\frac{i\\hat{h}_rdt}{2\\hbar}}","\\frac{i\\hat{h}_rdt}{2\\hbar}}e^{","\\frac{i\\hat{h}_rdt}{\\hbar}},","\\frac{i\\hat{h}_rdt}{\\hbar}}e^{","\\frac{i\\hat{h}dt}{\\hbar}}\\right]\\psi(\\mathbf{r},t)","\\hat","\\hat{h}_k","\\hat{h}_k)dt}{\\hbar}}\\right]\\psi(\\mathbf{r},t)","\\hat{h}_r","\\hat{u}_k","\\hat{u}_r","\\hbar","\\hbar\\omega.","\\infty}^{+\\infty}\\psi^\\ast\\psi","\\int_{","\\left[","\\left[\\hat{u}_r\\left(\\frac{dt}{2}\\right)","\\left[\\hat{u}_r\\left(\\frac{dt}{2}\\right)\\mathcal{f}^{","\\left[e^{","\\left[v(\\mathbf{r})","\\mathcal{f}","\\mathcal{f}^{","\\mathcal{o}(dt^3)","\\nabla^2","\\omega","\\omega,","\\psi(\\mathbf{r},t","\\psi(\\mathbf{r},t)","\\psi(\\mathbf{r},t),","\\psi(\\mathbf{r},t)}{\\parti","\\psi(\\mathbf{r},t+dt)","\\psi(\\mathcal{r},","\\right]","\\right]\\psi(\\mathbf{r},t)","\\right]\\psi(\\mathbf{r},t).","\\tau","\\time","^","_","_)","__init__(self,","__name__","_dt,","_dt;","_res,","_res;","_timesteps,","_timesteps;","_xmax,","_xmax;","abov","above,","above.","above:","abs)","abs2.(opr.wfc)","acc","accru","actual","add","addition,","address","afterwards,","again","algorithm","allow","also,","ambiguous.","amount","anim","anoth","appropriately,","are;","area,","aside,","assum","atom","attribut","auto","b","back","bad","baker","base","basically,","befor","behave,","bit","bool","bool)","bool,","boolean","both","bottom","boundari","box","c","c++","calcul","calculate_energy(&par,","calculate_energy(par,","calculate_energy(par:","calculateenergi","call","campbel","carray","case","case,","cases.","center","cexp(","chang","chapter","chapter:","check","chunks,","class","close(outfile)","code","code,","coeffici","coefficients.\"\"\"","common","commonli","commut","complet","complex","complex)","complex::new(par.k[i],","complic","complicated).","compon","components,","concession,","conditions,","conj(wfc_r)","conjug","continue.","correct","cough)","cover","cpow(par.k[i],","cpow(par.x[i]","crate","creat","creativ","data","data.array.carray","data.complex","data.list","deal","decay","def","defaultparamet","definit","densiti","density,","density.iter().sum::()","density:","density[j],","density[j].real,","density[opr.size];","dependence,","describ","desir","dft","didn't","differ","differenti","dig","discontinu","display","display,","distribut","distribution.","div","div(par.timesteps,","divid","dk","dk,","dk:","dk::float64","dk;","do","do.","done","doubl","double)","doubt","dt","dt)","dt,","dt:","dt::float64","dt::float64,","dt;","dt^2","dt^3,","dtype=complex)","dure","dx","dx);","dx,","dx:","dx::float64","dx;","dynam","e","e^{","each","easier","easili","elem","element","elems)","else:","end","end).","energi","energy)","energy.","energy_fin","energy_final*par.dx","energy_k","energy_k,","energy_k[i]","energy_r","energy_r).r","energy_r[i]","energy_r[i])","enforc","enough","equat","err(why)","error","evol","evolution.","evolv","exactli","exampl","example,","exp","exp.(","expectation.","experimentalist","explan","exponenti","export","extern","f","f)","f64","f64)","f64))","f64).sqrt();","f64);","f64,","fact,","factor","false)","false);","fastest","feature!","few","fft","fft(&mut","fft(doubl","fft(opr.wfc)","fft(wfc_r)","fft(x:","fft.process(x.as_mut_slice(),","fftplanner::new(inverse);","ffts.","fftw","fftw3","fftw_backward","fftw_backward,","fftw_complex","fftw_destroy_plan(p);","fftw_estimate);","fftw_execute(p);","fftw_forward),","fftw_forward,","fftw_plan","fftw_plan_dft_1d((int)n,","fftw_plan_dft_1d(static_cast(x.size()),","fi","fi)","figur","file","file.","file.flush()","file::create(&path)","filenam","files,","final","find","fine","first","flip","float)","float,","float:","flowchart","flush","fn","follow","format","format!(\"output{}.dat\",","formula:","forth","forward","fourier","fraction","frequenc","fromintegr","front","full","function","future.","g","gaussian","gener","gif","give","gnuplot","gnuplot.","go","goe","good","good,","graphic","grid","ground","guess","g|\\psi(\\mathbf{r},t)|^2","h_r","half","hamiltonian","hamiltonian.","hamiltonians.","hard","harmon","heart,","here","here'","here,","higher","hold","honest,","hood","housdorff","however,","i'll","i)","i);","i\\hat{h}_k]dt^2}{2}}\\right]\\psi(\\mathbf{r},t)","id","ideal.","idft","idft)","ifft","ifft(opr.wfc)","im)","im*0.5*opr.v*par.dt)","im*0.5*par.k.^2*par.dt)","im;","im_tim","im_time,","im_time:","im_time::bool","im_time;","im_val","im_val::bool)","imag","images/graph","imaginari","impl","implement","implementations.","import","imtim","in,","includ","incred","index,","indic","individu","init(par,","init(par:","init(par::param,","init_operators(struct","init_params(struct","initi","instead","int","int)","int,","integr","interact","intercal","intern","interpret.","invers","inverse)","inverse:","involv","io","is:","issue,","it'","it.","it:","iter","iteration,","itself.","j","j,","jame","julian","k","k,","k.","k.push(((i","k.push((i","k.push_back((static_cast(i)","k.reserve(res);","k:","k::vector{complex{float64}}","k::vector{float64}","k;","k[i]","ke,","ke.push(complex::new(","ke.reserve(size);","ke:","kinetic","kineticop","kmax","know","known","ks","ks)","kstep","l","laplacian,","larg","left","length","let'","library.","licens","license.","license.md).","liftarray","liftarray2","line","linear","lines,","littl","locat","long","longer","look","loop","lose","lowest","luckily,","m_pi","main","main()","make","makeoper","makeparamet","malloc(sizeof(doubl","malloc(sizeof(double)","mani","map","mapm_","match","math","math.fft","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matter","mean","memset(y,","mention","method","method),","method:","mislead","mit","models)","modern","modifi","momentum","momentum,","momentum.","more","move","multipli","mut","mutabl","n","n)","n,","natur","need","new(","new(10.0,","new(par:","new(xmax:","new(zeros(res),","next","non","none","none:","nonlinear","norm","norm2","normal","notat","notation","note","note,","noth","np","np.abs(opr.wfc)","np.arange(","np.concatenate((np.arange(0,","np.conj(wfc_r)","np.empty(res,","np.exp(","np.fft.fft(opr.wfc)","np.fft.fft(wfc_r)","np.fft.ifft((par.k","np.fft.ifft(opr.wfc)","number","numbers.","numpi","o","odd","of:","offset","ok(good)","okay.","on","op","op@(oper","open(\"output\"","open(filename,","oper","operator.","operators(len(par.x))","operators(length(par.x))","operators(param","operators(res)","operators)","operators.","operators:","operators::new(&par,","opr","opr)","opr);","opr.k","opr.ke[j];","opr.pe[j];","opr.r","opr.v","opr.v[i]","opr.v[j].re)","opr.v[j].real)","opr.wfc","opr.wfc,","opr.wfc.clone();","opr.wfc.iter().map(|x|","opr.wfc[j]","opr:","opr::operators)","ops))","op}","order","oscillator,","other,","otherwis","out,","outfil","outfile.write(line)","outfile:","output","over","p","p)","p.plan_fft(x.len());","p;","pad","panic!(\"couldn't","par","par,","par.dt","par.dt)","par.dx","par.dx;","par.im_tim","par.im_time:","par.k[i].powi(2)).exp(),","par.res);","par.res;","par.res];","parallel","param","param()","param(5.0,","param(xmax::float64,","param)","param,","param:","paramet","parameter","parameters,","parameters.\"\"\"","parameters::new(5.0,","params(doubl","part","part,","particular","path","path.display();","path::new(&path_name);","path_nam","pe,","pe.push(complex::new((","pe.push(complex::new(0.0_f64,","pe.reserve(size);","pe:","perform","period","phd","phd.","physic","pi","pi/10.0),","pi/xmax,","play","plot","plot_output.plt","plotter","plotting:","posit","position),","potenti","potential","potential,","potential.","potential.\"\"\"","precis","pretti","primari","print","print(\"energi","print(\"output","printevolut","println!(\"th","println(\"energi","println(\"output","probabl","process","provid","pseudo","pub","public:","pull","purpos","quantum","quickli","quit","r","r::vector{complex{float64}}","range(len(density)):","range(par.timesteps):","re","real","real(energy_k[i]","real,","realli","realpart","realpart)","regardless,","reinterpret_cast(x.data());","reinterpret_cast(y.data());","rel","relat","renorm","renorm_factor","rep","repeat","replic","repres","request","res)","res));","res);","res,","res/2:","res:","res::int64","res::int64,","res;","res])","research","rest","results!","return","rng","rstep","run","rustfft::fftplanner;","rustfft::num_complex::complex;","rustfft;","said,","same","satisfied.","say,","scale","schacher","schloss","schrödinger","section,","see","self.dk","self.dt","self.dx","self.dx)","self.im_tim","self.k","self.r","self.timestep","self.v","self.wfc","self.x","self.xmax","seri","set","settl","sharealik","shift","shown","side","similar","simpl","simplest","simpli","simul","simulation,","simulation.","sit","size","size;","size_t","sizeof(y));","skip","slide","slight","slightli","small","smoothli","so:","solut","solv","solver...","someth","something).","somewhat","sort","space","space,","space:","spatial","specified.","spectral","split","split_op!(par,","split_op!(par::param,","split_op(&par,","split_op(par,","split_op(par:","split_op(param","split_op(struct","split_op.jl","splitop","sqrt","sqrt()","sqrt(renorm_factor)","standard","start","starting,","state","states,","states.","std::complex(0.0,","std::complex;","std::f64::consts::pi;","std::fs::file;","std::io::write;","std::path::path;","std::vector(opr.size,","std::vector;","step","step:","story.","str(0)))","straightforward","straightforward.","strang","string(0)))","string(density[j])","string(lpad(string(i","string(par.x[j])","string(real(opr.v[j]))","struct","studi","such,","sum","sum(density)","sum(energy_k","sum.sqrt();","sure","system","system!","system.","system:","systems,","t+dt)","t,","take","technic","templat","template(par.x[j],","term","term.","test","text","that'","think","this:","those","though.","through","throughout","time","time,","time.","timestep","timestep!","timestep,","timestep:","timesteps,","timesteps:","timesteps::int64","timesteps::int64,","timesteps;","too!","total","toward","transform.","transforms.","transpos","transpose)","trap","trap,","trap.","tri","trick","true","true)","true);","turbul","turn","two","type","typic","t}","u","under","understand","unit","units,","units.","unphysical,","unsign","until","us","usize,","v","v(\\mathbf{r})","v,","v.push(complex::new(","v.reserve(size);","v0","v0)","v:","v::vector{complex{float64}}","v[i]","v[i].re).exp()));","v[i].re).exp(),","v]","v_offset).powi(2),","v_offset:","valu","value.","vanish.","vec","vec![complex::new(0.0_f64,","vec,","vec::with_capacity(par.res);","vec::with_capacity(res);","vec;","vec>","vec>,","vector","vector_complex","vector_r","vector{float64}(","vector{float64}(vcat(0:512/2","vector{float64}(vcat(0:res/2","video","voffset)","voffset).^2","voffset,","voffset:","voffset::float64,","void","w","wave","wavefunct","wavefunctions.","wavevector","wavevectors,","way","way.","we'll","wfc","wfc'","wfc)","wfc.push(complex::new(","wfc.reserve(size);","wfc0","wfc0)","wfc:","wfc::vector{complex{float64}}","wfc_c","wfc_c.*opr.v","wfc_c[i]","wfc_c[i].scale(0.5_f64);","wfc_k","wfc_k)","wfc_k,","wfc_k[i]","wfc_offset).powi(2))","wfc_offset:","wfc_r","wfc_r[i].conj();","wfc_r[i];","wfcconj","wfcoffset)","wfcoffset).^2/2)","wfcoffset,","wfcoffset:","wfcoffset::float64)","whole","why)","why),","wide","work","world\"","write","write(outfile,","writefil","writeln!(file,","written","x","x))","x,","x.1).re);","x.len()];","x.norm().powi(2)).collect();","x.push(xmax","x.reserve(res);","x:","x::vector{float64}","x;","x[i]","x^2","xmax","xmax)","xmax),","xmax);","xmax+xmax/res:2*xmax/res:xmax),","xmax,","xmax:","xmax::float64","xmax;","xs)","x|","y","y(x.size(),","y.as_mut_slice());","y[i]","y[n];","zeros(res))","zeros(res),","zip","{","{wfc","{}\",","{}:","|","|\\psi(\\mathbf{r},t)|^2","|acc,","}","};"],"contents/domain_coloring/domain_coloring.html":["\"$2\\pi$\"])","\"$\\pi$\",","\"++\"","\"__main__\":","\"absz\"","\"hsv\"),","\"hsv1\"","\"hsv2\"","\"hsv3\"","\"hsv4\"","\"hsv5\"","\"im(z)\"","\"phase","\"plot","\"re(z)\"","\"rgb1\"","\"rgb2\"","\"shade\"","\"utf8\"","\"z2\"","#","&=","'++'","'2pi'","'domain.png'","'f(z)=z^2'","(","(\"0\"","(0,0)","(2*pi)","(2.0","(abs(sin(real_f(z(x,y))*pi)**thresh)","(clear)","(f(z)","(f_val_ab","(found","(hue,","(np.abs(np.sin(np.pi","(np.pi","(pi","(red).","(red,","(z","(z)",")","*","**","+","/","0","0,","0,0","0.1","0.1)","0.5","0.5*(abs(f(z(x,y)))","1","1)","1))","1,","1.","1.wikipedia:","1000","1000,","180","1:2:(color($1,$2))","1i","1j","2","2.","2.0","2.0)","2.0),","2.0,","2000","2000,","2004.","2008.4.wegert,","2012.5.poelke,","2019.3.pethick,","2020.2.schloss,","2:2]","2\\pi","2d","2i,","2pi","3.14159","3.14159)","3.14159,","4.0","4\\pi","500)","500x500","800",":","=","==","[","[1].","[2]","[3].","[4]","[5]","[6].","\\","\\&","\\\\","\\begin{align}","\\cdot","\\end{align}","\\frac12","\\frac{1}{2}","\\frac{1}{2}\\left(r","\\in","\\left(\\lfloor","\\left(f(z)=z^2\\right),","\\lfloor","\\mathbb{c}),","\\mathbb{c}.","\\mathbb{r}):","\\rfloor","\\rfloor.","\\right),","\\right).","\\sqrt{\\text{re}(z)^2","\\text{atan}\\left(\\frac{\\text{im}(z)}{\\text{re}(z)}\\right)","\\text{im}(z)^2}","\\theta","\\theta}","]","__name__","abs(sin(imaginary_f(z(x,y))*pi))**thresh)","accord","actual","ad","add","addition,","again,","along","also,","altern","alway","analyt","angle\"","angle\")","angle(x,y)","anoth","appropri","arbitrary.","around","array","aspect","aspect=\"equal\"","aspect=\"equal\")","assum","atan2","atan2(","atan2(y,x)","attribut","ax","ax=axes,","axes.get_xticklines():","axes.get_yticklines():","axes.imshow(","axes.set_title(\"$f(x)=z^2$\")","axes.set_xlabel(\"$re(z)$\")","axes.set_ylabel(\"$im(z)$\")","axi","axis,","back","bar","base","beauti","before,","below:","between","bibliographi","black","blue","blue),","border","bose","both","built.","busi","c,","calcul","cambridg","capabl","case","case,","cbar","cbar.set_ticklabels([\"$0.0$\",","cbar.set_ticks([0.0,","cblabel","cbrang","cbtic","center","certain","certainli","chang","chapter","chapter,","chapter:","choic","choos","chose","christoph","circl","clear","code","color","color(f_val,","color(x,y)","colorbar","coloring,","coloring:","colors,","common","compel","complet","complex","complic","compon","components,","components.","condens","consequ","constrain","contain","context","contour","contour.","contours.","convers","coord","coords)","corner","correspond","creat","creativ","crunching.","current","data","data.","datafil","dataset","def","defin","degre","degrees,","depend","describ","determin","diagon","differ","difficult","dilut","dimens","dimension","dimensionality,","dimensions,","directli","discontinu","distracting,","domain","draw","drop","each","easi","easier","easili","edg","edge.","einstein","elias,","ensur","equations,","essenti","essentially,","establish","exampl","example,","explan","extent=(","f(z)","f(z)!","f(z).","f(z):","f(z)=z^2.","f_val","f_val_ab","fact","feebl","feel","fig,","fig.colorbar(","fig.savefig(\"domain.png\")","figur","file","find","fix","floor","floor(abs(f(z(x,y)))))","fluctuat","fluids,","focu","follow","form","form,","form:","formula","fortran,","four","fourier","free","full","function","function'","function,","function.","function:","functions.","functions.6.lundmark,","functions:","further","g(r)","gases,","gener","gnuplot,","go","gradient,","graphic","green,","grid","gridlin","gridlines(f_val,","gridlines(x,y)","gridlines(x,y))","gridlines.","h(z)","hans,","happen","have","heat","heavili","henrik,","here","here,","hide","horizont","however,","hsl","hsv","hsv,","hsv2rgb(angle(real_f(z(x,y)),","hue","human","i\\sin(\\theta))","ideal,","imag","imag(f(z))","image.","image:","images!","images/graph","imagin","imaginari","imaginary_f(z(x,y))),","imaginary_f(z)","implement","import","improvise.","imput","incap","increas","increases.","independ","index","indic","inform","input","instead","integ","interest","intern","introduct","intuitive.","invert","inviscid","isosampl","isosamples\"","j","jame","james,","java","key","kind","konrad,","konstantin","label","label=\"phas","languag","last","lc","left","legend","let'","licens","license.","license.md).","line","line.","linearli","lines,","locat","long","look","lot","lower","magnitud","magnitude,","magnitude.","magnitude:","magnitude_shading(f_val)","magnitude_shading(f_val):","magnitude_shading(x,y)","magnitude_shading(x,y),","make","mani","map","maps,","massiv","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matplotlib.cm","matplotlib.color","matplotlib.colors.hsv_to_rgb(hsv)","matplotlib.pyplot","mean","means,","meant","media,","method","mind","mirror","mit","model","modifi","more","move","much","much,","necessari","need","new","next","nocontour","none","note","now","np","np.abs(f_val)","np.abs(np.sin(np.pi","np.angle(f_val))","np.floor(f_val_abs))","np.imag(f_val)))","np.linspace(","np.meshgrid(coords,","np.moveaxis((hue,","np.pi)","np.pi),","np.pi,","np.pi])","np.real(f_val)))","number","numpi","offset","on","onc","onto","oper","opposit","order","origin","origin,","origin.","origin;","origin=\"lower\"","origin=\"lower\",","other.","out!","outlin","output","output,","output.","overal","overall,","palett","parallel","pattern","peak","peopl","phase","phase.","pi","pi,","pixel","place","plane","play","plenti","plot","plot,","plot.","plot:","plotted:","plt","plt.subplots(1,","plug","pm3d","pngcairo","point,","polthier,","portraits,","possibl","precis","press,","problem.","process","produc","project","pull","pure","purpos","purposes,","put","quantum","r","r(\\cos(\\theta)","r(x,y)","r(x,y)*exp(theta(x,y)*sqrt(","r,","rang","rapidly,","ratio","re^{i","real","real(f(z))","real_f(z)","realli","reason,","red","remov","repres","request","requir","requires.","respectively.","return","rgb","rotat","round","sacrif","same","sampl","satur","saturation,","save","save_encod","saw","say,","scalarmapp","scalarmappable(matplotlib.colors.normalize(0.0,","scale","scheme","scheme,","schloss","scienc","script","see","seen","separ","set","shade","sharealik","sharpli","show","shown","similar","simpl","simpler","simplest","simpli","simul","singl","size","smaller","smith,","smooth","so,","so:","somewhat","sort","space","space,","space.","spatial","split","splot","springer","sqrt(x*x","squar","start","start,","step","subsequ","such","system","t","techniqu","termin","text","that,","theta(x,y)","this,","this:","those","thresh","threshold","threshold)","threshold):","through","throughout","thu","tic","tick","tick.set_visible(false)","titl","togeth","top","track","tupl","tuples,","twice,","two","types.","under","understand","unfortunately,","units,","univers","unset","us","user","valu","value)","value),","value).","value,","values,","values.","variabl","variable,","variou","vertic","video","view","visual","vortex","want","want!","wash","way","whatev","whenev","where,","wind","winding.","without","wrap","written","x","x)","x))","x,","xlabel","xrange[","xtic","xy","y","y*y)","y,","ylabel","yrange[","ytic","z","z(x,y)","z**2","z,","z.","z\\in\\mathbb{r}","z^2","z^2,","z^2.","z_imag","z_real","z_real,","zero","|\\sin(\\pi\\times\\text{re}(f(z)))^t|\\times|\\sin(\\pi\\times\\text{im}(f(z)))^t|,","|z|"],"contents/barnsley/barnsley.html":["!)","\"\\t\"","\"affin","\"fern","\"if","\"simpl","#","#[derive(clone,","#includ","$","&","&0","&0.04","&0.16","&0.22","&0.24","&0.28","&0.5","&0.85","&=","&[f64])","&[f64],","&[vec],","&barnsley_hutchinson,","&barnsley_probabilities,","'__main__':","(!))","(\"check","()","(+)","(0,","(0,0)).","(0..iters)","(0.0,","(a","(a,","(array,","(auto","(b","(double)rand()","(double,","(found","(i,","(int","(intercalate)","(name","(point","(rnd","(scale","(size_t","(step","(x","(x,","(xx,","(y,",")","*","*_","*hutchinson_op,","*probabilities,","+","++","+=","./barnsley.cpp",".collect()",".into_iter()",".map(|_|","/","//","0","0\"","0),","0.,","0.0","0.0),","0.0,","0.01","0.04","0.04,","0.07","0.07,","0.07]","0.07];","0.15","0.15,","0.16,","0.2","0.22,","0.23","0.24,","0.26","0.26,","0.28,","0.44","0.44),","0.44],","0.5","0.85","0.85,","0.],","0;","0u;","1\"","1\"));","1)","1,","1.","1.0)(rng());","1.0),","1.0,","1.6","1.60),","1.6],","1.],","1.barnsley,","10_000,","17","1994.","1:length(probabilities)","1])","1};","2\"","2014.2.wikipedia:","2019.3.saupe,","3","3\"","3d","4.0","4u;",":","::",":=","=","==","=>",">",">)","@","[","[0.,","[0.01,","[0.2,","[0.23,","[0.26,","[0.85,","[1]:","[2][3].","[point]","\\\\","\\begin{align}","\\begin{bmatrix}","\\end{align}","\\end{bmatrix}","\\end{bmatrix}p","\\frac{a}{2}","\\frac{b}{2}","\\frac{c}{2}","\\frac{p+a}{2}","\\frac{p+b}{2}","\\frac{p+c}{2}","\\frac{p+d}{2}","\\tau","]","]),","],","];","__name__","__rmatmul__(self,","a,","academ","account","acm,","act","ad","addit","advantag","affect","affin","again","align","all,","all.","along","anoth","answer","apparent.","appropri","around","array","attractor","attractor,","attractor.","attractor;","attractors,","attractors:","attribut","auto","b)","b,","back","barnsley","barnsley_hutchinson","barnsley_hutchinson,","barnsley_prob","barnsley_probabilities)","be","beauti","becom","bellow","below","between","bibliographi","big","biggest","bin","bin,","bit","bit...","both","bounds,","briefli","browser","bulk","c","c++","c,","call","case","cases,","cast","challeng","chang","chao","chaos_game(","chaos_game(initial_loc","chaos_game(point(0,","chaosgam","chapter","chapter,","check","choic","choices(hutchinson_op,","choos","chosen:","clang++","class","clear","code","code.","coeffici","come","common","common.","compil","compon","compress","compression,","const","constexpr","constitu","construct","construction,","continu","contractive.","contractivity,","convers","coordinates)","coordinates[0];","coordinates[1];","coordinates[2];","copy)]","correct.","correspond","creat","creativ","cumulprob","d","d_glibcxx_debug","data","data.array","data.list","def","definit","delimitedfil","derefer","describ","dietmar","differ","difficult","dimension","disect","distribut","don't","doubl","double)","double,","double[3];","double[]","drand();","drastic","draw","drawn.","dtor","due","e.g.:","each","easiest","effect","elem","element","elems,","end","end,","entir","essentially,","even","eventu","everyone'","everywhere,","exactli","exampl","example,","explain","explan","extend","f,","f64)","f64,","f_1","f_1(p)","f_1,","f_2","f_2(p)","f_2,","f_3","f_3(p)","f_3,","f_4","f_4(p)","f_4,","fact,","fashion","fashion,","features,","feel","fern","fern\"","fern,","fern.","fern:","few","fewer","final","find","first","flags,","fli","flip","fmap","fn","form:","format!(\"{}\\t{}\\n\",","forward.","fractal","fst","function","function.","functions,","functions:","functions?","g","g'","g''","g'')","g')","game","gdwarf","gener","general,","given","glance,","go","greater","half","halfway","hamzaoui,","hard","heart","here","here,","high","hop","hope","however,","hutchinson","hutchinson_op","hutchinson_op,","hutchinson_op[0];","idea","ident","imag","image.","images/graph","impl","implement","import","includ","incomprehens","individu","infin","initi","initial_loc","initial_location,","initial_location.x,","initial_location.y,","initial_location[1],","instead","int","interest","intern","introduc","involv","io","it'","iter","itself,","jame","java.io.filewriter;","java.io.ioexception;","java.util.random;","k","k)","k,","knob","knowledg","known","lead","leav","left","left.","length","less","let'","leverag","licens","license.","license.md).","likelihood","line.","linear","list","listarray,","literature,","location.","look","low","magic","main","main()","major","make","mani","map","mat,","mat.xi","mat.xx","mat.xz","mat.yi","mat.yx","mat.yz","mat.zi","mat.zx","mat.zz","mat:","mathematician","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matmul(struct","matrix","matrix)","matrix_mul(self,","matrixmultiplication(double[][]","me.","meant","meanwhile,","mention","mess","methods,","michael","mind","mit","modifi","more","move","mut","mystifying,","n","n,","natur","necessari","need","new","new(x:","next","no.","non","not,","notat","note","note:","now","np","np.array([","np.array([*output_gen$[:10000]])","np.array([self.x,","np.array):","np.savetxt(\"out.dat\",","num_op)","number","numpi","o3","obvious.","old_point","old_point.x,","old_point.y,","on","on,","op","op&","oper","operator*(const","operator*(doubl","operator*(std::array","operator+(std::array","operator.","opn","origin","others.","out","out).unwrap();","out;","output","output_gen","output_point","output_points)","over","p","p,","part","path","perform","pick","play","pluck","point","point(doubl","point(double[]","point(x,","point(x=0,","point)","point))","point,","point.i","point.matrix_mul(operation);","point.x","point.x,","point.y).as_str();","point.z","point.z,","point2","point2d","point3","point3::new(","point3::new(0.0,","point3::new(0.20,","point3::new(0.23,","point3::new(0.26,","point3::new(0.85,","point3d","point;","point_array","point_array))","points.","points:","posit","precis","predict","predict?","press,","privat","probabilities)","probabilities):","probabilities);","probabilities.iter().enumerate()","probabilities:","probability)","probabl","programm","promot","properti","provid","public","qualiti","question:","rand()","rand::prelude::*;","rand::thread_rng();","rand_max;","random","randomgen","randomli","randomr","raouf,","read","reconstruct","reflection,","reminder,","resolut","respectively.","result","result!","result,","ret","return","review","rhs:","rhs[0].i","rhs[0].x","rhs[0].z","rhs[1].i","rhs[1].x","rhs[1].z","rhs[2].i","rhs[2].x","rhs[2].z","right","right.","rnd","rng","rng.gen::();","rotat","row","rule,","said,","same","sampl","satisfi","scale","scanl1","schloss","see","seem","seemingli","select","select_array(","select_array(hutchinson_op,","select_array(hutchinson_op:","select_array(struct","self","self.i","self.x","self.y,","self.z;","self::new(x,","sens","sense,","sense.","separ","set","set.","shape","sharealik","shearing)","show","shown","showpoint","side","sierpinski","similar","simpl","simple,","simul","singl","size_t","slightli","smaller","snd","somewhat","soon,","space,","specif","squar","square,","stage,","start","static","std::array","std::array&","std::array;","std::fs::write(\"./out.dat\",","std::vector{};","std=c++17","stem","stem,","stem.","step","store","strategi","string","string::new();","struct","style","subtract","success","support","surpris","system","system.random","systems,","tag.","take","takewhil","templat","tend","text","them,","thing","this,","this.i","this.x","this.z","though","through","tilt","time","to_choic","toward","transform","transformation.","transforms,","translation.","triangl","triangle,","triangle.","true:","tuple(*(mat","turn","twiddl","two","under","understand","understandable.","uniform","unsettl","until","up","upon","us","v)","v,","v;","vari","variant","vec","vec![","vec![0.01,","vec)","vec2","vec3","vec3&","vec3{initial_location[0],","vec3{};","version","video","virtual","wall","want","way","wcast","wconvers","wdoubl","we'll","wextra","wformat=2","without","wnon","wnull","wold","work","works,","worry!","woverload","wpedant","written","wshadow","wsign","wunus","x","x,","x:","x;","xx","xx,","xy","xy,","xz,","y","y)","y,","y:","y;","y=0):","yield","yx","yx,","yy","yy)","yy,","yz,","z","z)","z:","z;","zipwith","zx,","zy,","zz;","{","}","})","},","};"],"contents/box_muller/box_muller.html":["!(isnan(input_x)","!=","\"affin","\"fern","\"if","\"simpl","#","&&","&=","(((x+mu[1])^2)/(2*sigma^2)","((y+mu[2])^2)/(2*sigma^2)))","(also","(axis_num)","(both","(found","(gaussian_valu","(input_i","(input_x","(j","(probabl","(to","(u_1","(yes,","(z_1","*","+","+1.","+=",".+",".=","/","0","0\"","0.1)","0.1,","0.5)","1","1\"","1)","1,","1,000","1,000,","1.","1.box,","10,000","100","1958","1958.2.wikipedia:","1:axis_num","1:size(histogram)[1]","1:size(histogram)[2]","1:size(input_pts)[1]","1;","1]","1],","2","2\"","2)","2022.","2022.3.wikipedia:","2\\ln(r_0)}\\left(\\frac{u_1}{\\sqrt{r_0}}\\right)","2\\ln(r_0)}\\left(\\frac{u_2}{\\sqrt{r_0}}\\right)","2\\ln(r_0)}{r_0}}","2\\ln(r_0)}{r_0}}.","2\\ln(u)}.","2\\ln(u_1)}","2\\pi","2\\pi,","2]","2d,","3\"","4.0",":]","=","==",">","[","[(i","[0,0],","[1].","[2].","[3].","[nan,","[sigma","\\\\","\\begin{align}","\\co","\\cos(\\theta)","\\end{align}","\\frac{r^2}{2}},","\\gt","\\mu","\\mu,","\\mu.","\\rightarrow","\\sigma","\\sigma,","\\sin","\\sin(\\theta)","\\sqrt{","\\sqrt{\\frac{","\\sqrt{u_1^2","\\theta","\\theta,","a[(i","actual","again,","all,","along","alreadi","amount","angl","angular","anyway,","applies,","are:","around","array,","as,","attribut","avoid","away","axi","axis_num","axis_num^2","backward","barnsley","basic","be.","between","bibliographi","bin","bin[1]","bin[2]","bodi","both","bottom.","bound","bounds[1,1]","bounds[1,1])","bounds[1,1])/dx),","bounds[2,1]","bounds[2,1])","bounds[2,1])/dx))","box","box—mul","bunch","calcul","call","cartesian","cartesian_box_muller(input_pts,","cartesianindex(ceil(int,","case","case,","case.","ceil(int,","ceil(int,(bounds[2,2]","chang","chapter","circl","circle,","cleanest","clear","code","code,","column,","come","common","complete,","compon","coordin","coordinates,","coordinates.","cos(theta)","costli","course,","creat","create_grid(n,","create_rand_dist(n,","creativ","debug","decent","decid","delimitedfiles,","determin","develop","deviates,","deviation,","differ","dimens","dimension","dimension:","dimensions,","discuss","distanc","distribut","distribution)","distribution,","distribution.","divid","dx","dx))","dx),","e^{","each","easiest","end","endpoints)","endpoints[1]","endpoints[1])","endpoints[1],","endpoints[1]]","endpoints[2]","entir","ep,","equat","equations,","essenti","exact","exampl","except","exp(","expect.","fairli","far","faster","fastest","fern","fern\"","few","final","finally,","first","follow","form","form,","full","function","gaussian","gaussian_valu","gener","general,","georg","given","good","grid","grid,","grid.","grid_ext","half","have,","heart","here","here,","here.","histogram","histogram[bin]","histogram[i,j])^2","hold","honest,","i*dx","idea","ident","imag","images/graph","implement","implementation,","individu","inher","initi","input","input.","input_i","input_pts[1]","input_pts[1]^2","input_pts[2]","input_pts[2]^2","input_pts[i,","input_x","instead","interest","intern","intuitive.","is_gaussian(input_pts;","isnan(input_y))","it!","it'","it.","it:","j","j*dx","j,","jame","know","larg","last","later):","let'","licens","license.","license.md).","like,","limit","linearalgebra","littl","log(input_pts[1]))","log(r_0)","logic","look","loop","main","mainli","make","marsaglia","mathjax.hub.queue([\"typeset\",mathjax.hub]);","mean","mean,","mention","mervin","messi","method","method,","mit","more","mu","mu)","mu[1],","mu[2]]","muller","multipli","n","n=100,","n=100:","name)","nan]","nearest","need","new","next","next!","nice","normal","normalize!(histogram)","note","now","number","numbers.","obviou","ok","ok,","on","onc","once.","one,","one.","oper","operations.","opt","order","origin","output","output:","outsid","over","pair","parallel,","particl","particular","particularli","peopl","percent","perform","physical,","pi","place","plot","point","points.","polar","polar_box_muller(input_pts,","practic","preform","process:","produc","purpos","question!","r","r,","r=\\sqrt{","r?","r\\cos(\\theta)","r\\sin(\\theta)","r\\sin(\\theta).","r_0","r_0)","r_0.","radial","rand()","random","random)","random,","rang","read","readi","real","redefin","reject","rel","relev","rememb","requir","research.","return","return(rand(n,2)","right,","rm","roughli","round","row","same","same,","sampl","sampling)","scale","schloss","see","seem","sense.","separ","set","shape","sharealik","shi","show","sigma","sigma,","simple.","simpli","simulation.","sin(theta)","singl","size","size,","smaller","so,","so:","solv","someth","somewhat","special","specifi","spin","sqrt(","sqrt(n)","sqrt(n))","sqrt(rms/n)","squar","stage,","standard","star","start","step","step.","straightforward:","subsections:","such","sum(histogram)","super","sure","take","techniqu","test","text","that'","theta","thing","this,","this:","threshold","transform","transform!","transform,","tri","triangl","trigonometr","turn","twiddl","two","typic","u","u_1","u_1/\\sqrt{r_0}","u_2","u_2),","u_2.","u_2/\\sqrt{r_0}.","u_2^2}.","ultim","under","uniform","uniform,","uniform.","uniform?","uniformli","unit","up","us","usual","valid","valu","value.","values,","values.","vari","version","video","walk","want","way","well,","within","without","work","works,","written","x","x,i","x\\sigma","y","y\\sigma","z_1","z_2","z_2).","zeros(ceil(int,(bounds[1,2]","zeros(n,","||"],"contents/computus/computus.html":["\"","\"#{a[i]}\\t#{servois_numbers[i]}\\t\\t#{easter_dates[i]}\"","\"$year`t$(calcul","\"%d\",(21","\"19","\"\\t\"","\"\\t\\t\"","\"a\"","\"april","\"calcul","\"full","\"march","\"meton","\"notation)","\"passover\"","\"patching\"","\"rel","\"servoi","\"synod","\"the","\"year","\"year\\tservoi","\"year`tservoi","\"you","\"{year}","\"{}\\t{:","\"~8a~18a~a~%\"","\"~{~a~%~}\"","#","#includ","$","$((21","$a","$b","$c","$d","$d)","$e","$e)","$k","$k)","$m","$m)","$n","$n)","$p","$q","$q)","$year","$year)\"","${22","${d","%","%d\",","&","&&","&e","&option","'(\"the","'april","'march","(","($d","((13","((2","((21","((22","((a","((d","()","(*","(+","(12","(13","(15","(19","(19a+m)~\\%~30","(2","(2020..2030).to_a","(21","(21+d)~\\%~31,","(22","(2b+4c+6d+n)~\\%~7.","(4","(4+k","(>","(a","(and","(b","(c","(computu","(computus)","(d","(date)","(defun","(e","(easter","(eql","(floor","(format","(found","(here","(if","(in","(int","(k","(let","(let'","(let*","(loop","(m","(mod","(modulo","(multipl","(n","(or","(orthodox)","(p","(q","(roughli","(servoi","(servois)","(setf","(solar)","(strawberry)","(such","(the","(to","(use","(valu","(var","(when","(where","(with","(within","(year",")",");","*","*/","*computus(int","*out,","+","++","..","/","/**","//","//shift","0","1","1))","1,","1.venerabilis,","10)","10))","10)))","10):","10)?","100","100)","100))","100).floor();","100).toint","100,","100.","100;","11","11~\\%~30","12","13","15","1777,","1800","1800,","1813.","1816.","1876.5.servois,","19","19)","19))","19.","1900.","1999.2.dictionary.com","19;","19a","19th","19th.","1:length(a)","1;","1st","1st,","2","2.","2000","2000,","2004.4.unknown,","2004.7.wikipedia:","2017","2018","2019","2020","2020,","2020.","2020..2030)","2020..2030:","2020..=2030;","2020.3.bien,","2020;","2021","2021;","2030","2030]","2031):","2039.","2099,","21","21st","21st).","21st,","21st.","22","22+d+e>31","22+d+e\\leq31","22nd","25","25)","25))","25).floor();","25).toint","2500","2500.","25;","25th","26","26th","27.5","28","28)","28).","29","29)","29.5","29th","2b+4c,","3","30","30)","30))","300","30;","30th","31","31)","31)))))","31).to_","31).to_string();","31).tostring()","31).tostring();","31);","31:","31}\"","354","365","365).","365.","365.2425","365.25","4","4)","4))","4).floor();","4).toint","4.0","400","400,","4200","45","4;","50%","52","52\\times7=364,","6","6)","6))","7","7)","7))","7)))","7;","8","84","9)","9))","9).to_","9);","96","97","9\\text{","9th.","9}\"","9}\".fmt","9}';","9}`;",":","::",";",";;",";;;;","=","==",">","?","@param","@return","[...]","[1]","[2020","[2],","[3].","[4].","[5].","[6].","[7].","[];","[int]","[math]::floor($k","[math]::floor($year","[math]::floor((13","[string]","[switch]$servois)","\\","\\%","\\%30","\\%~30","\\%~31","\\\\","\\begin{align}","\\end{align}","\\frac{\\pi}{4}","\\frac{\\pi}{4}).","\\left\\lfloor\\frac{13+8k}{25}\\right\\rfloor.","\\left\\lfloor\\frac{\\text{year}}{100}\\right\\rfloor,","\\left\\lfloor\\frac{k}{4}\\right\\rfloor.","\\left\\{","\\lfloor\\cdot\\rfloor","\\qquad","\\right.","\\text{","\\text{easter}","\\text{if","\\text{year}~\\%~19,","\\text{year}~\\%~4,","\\text{year}~\\%~7,","`april","`div`","`march","`mod`","a)","a,","a.each_index","a.map","a>10","abilities)","abov","above,","above.","accord","accordingly;","account","account.","accur","act","actual","ad:\"","ad:\")","ad:\");","ad:\",","ad:\\n\"","ad:\\n\");","ad:~%\"","add","addit","addition,","admittedly,","again","again,","ahead","algorithm","algorithm).","algorithm,","algorithm:","algorithm;","algorithms,","align","all,","allow","allud","along","alway","angl","annal","anoth","anyth","anything,","anywher","apparently,","appear","appliquées.6.standish,","approach","appropri","approxim","approximation,","april","april.","april}&","arbitrari","arc","arcan","archiv","archive,","arithmet","arithmetic)","arithmetic,","arithmetic.","around","array","array[string]):","ascens","astound","astrolog","astronom","attribut","auxiliari","away","axi","axis,","axis.","b","b)","b,","b:","back","background","bad","baffl","bamboozl","base","be","be,","becam","beda","bede,","befor","behind","behind.","below,","below:","best","better","between","beyond:","bibliographi","bind","birthday","bit","body.","bool","bool)","boolean","born","both","c","c)","c,","c.","calcul","calculation,","calculation.","calculator,","calendar","calendar,","calendar.","calendars.","calendrier,","call","cambridg","care","case","case;","cases,","celebr","center","center,","center.","centuri","centuries,","centuries.","century.","certain","certainli","chang","chapter","chapter.","char","chose","choseth","christendom.","christian","church","church'","circle.","clarity),","clergi","close","closer","code","code,","code.","collect(2020:2030)","color","combin","come","common","commun","compatriot","complain","complet","complex","complic","complicated.","comput","computation,","computer.","computu","computus([int]$year,","computus(int","computus(y)","computus(y,","computus(year","computus(year,","computus(year:","computus(year;","computus,","computus.(a)","computus.(a;","conc","concern","condit","conditionals,","conditions,","connect","consecut","consid","consider","console.log(","const","constrict","cooley","correct","correspond","counts,","cover","craft.","creat","creation.","creativ","current","cycl","cycle)","cycle,","d","d)","d+e","d+e+22\\text{","d+e.","d,","d,31))","d=28","d=28,","d=29","data","date","date.","dates.","day","day,","days),","days,","days.","de","decad","def","definit","delambre)","demand.","depend","describ","design","determin","devis","dictat","differ","dimension","discrep","discuss","div","divid","divis","doesn't","done","doubt","down","drama","drawn","duct","dumb","dure","e","e)","e)))","e).to_","e);","e,","e.","e=","e=6","e=6,","each","earli","earth","earth'","earth,","earth.","easili","easter","easter\"","easter\"))","easter)","easter)))","easter,","easter.","easter:","easter?","easter_d","easterd","eastern","echo","effect","electromagnetism,","element","elimination,","else:","em,","empir","encourag","end","engin","ensur","entir","eq","equinox","equival","era","era!","especi","essenti","essentially,","et","etc.","even","event","everyon","exampl","example,","except","exist","existed,","explain","explan","express","expressions.","e}\"","e}\".fmt","e}';","e}`;","f","f)","f,","fact","fact,","factor","fail","fall","false)","false):","false):6}\".fmt","false})","famou","fan","favorit","februari","feel","festival.","few","final","find","first","fld(13","fld(k,","fld(year,","fledgl","floor","fn","focu","follow","follow;","following,","for(","foreach($year","format!(\"april","format!(\"march","formula","found","found,","frederick","friday","full","fulli","func","function","funky,","further","gauss","gauss'","gauss,","gauss.","gausseast","gaussian","gem","gener","genius.\"","github)","give","given","glance,","go","go!","goe","good,","greater","greek","gregorian","grew,","grey","grumpili","gt","half","hand","happen","hard","heartili","held","here","here,","here;","hidden","higher","himself","histor","histori","history,","holiday","honest,","honestly,","horizont","host","hour","however,","hundr","hunter'","i'll","idea","if($servois)","if(($d","if(22","imag","images/graph","imagin","implement","import","includ","incorpor","increment","index","index,","indic","individually.","inform","information,","ingenu","initi","instead","instead,","int","int,","integ","integer.","interest","interestingly,","interfac","intermedi","intern","introduc","invent","investig","io","ioutputlin","ioutputline[]","is,","isiz","isize;","ismainmodule:","issu","it'","it.","itself,","itself.","jame","jan","januari","javascript/typescript","jean","jewish","johann","joseph","journal","julian","k","k)","k))","k,","keep","key","know","know!","known","lambert","languages,","larg","last","later","law","lead","leap","legend","length","less","let'","letter","licens","license.","license.md).","limit","line","liter","littl","liverpool","locat","longer","look","loop","loops,","lot","loves.","lunar","m","m)","m,","m.","made","magic,","main","main()","main(args:","make","mani","map","mapm_","march","march,","march.","march}&","mark","master","mathemat","mathjax.hub.queue([\"typeset\",mathjax.hub]);","mathématiqu","mayl","me,","mean","meaningful.","mediev","mentioned,","met","method","method'","meton","minut","missed.","mit","mod","mod(15","mod(19","mod(2","mod(4","mod(a,","mod(a:","mod(year,","mode","modern","modifi","modulo","modulu","monday","month","month)","month,","month.","months),","months:","moon","moon'","moon).","moon,","moon.","more","mother","move","much","multipl","n","n)","n,","name","namely:","names,","natur","near","nearest","necessari","need","neg","new","next","nil","nil))","nominally,","non","none","normal","notat","notation)","notation),","note,","note:","now","now,","nowadays,","number","number\"","number\":","number):","number,","number;","number\\teaster\"","number\\teaster\")","number\\teaster\");","number\\teaster\\n\")","number\\teaster\\n\");","number`teaster\"","numbers,","numbers.","object","observ","observation.","observed.","observed;","occur","off,","off.","offset","offset,","offsets,","old","on","one,","one.","ones.","onto","oper","operations,","option","orbit\"","orbits\"","origin","others,","others.","out","out;","out_size)","out_size,","outlin","outline,","output","over","p","p)","p+k","p,","partial","particular","particularli","parts:","paschal","past","paul","peopl","per","performance,","peter","phase","phase.","phases,","pictori","pink","place","place.","pleas","point","point,","point.","pope).","pope;","pose","posit","position,","positions,","possibl","power","precis","precise.","present","press,","presum","previou","print(","print(\"th","print(\"year\\tservoi","print(f\"{year}\\t{computus(year,","printf(\"th","printf(\"year\\tservoi","println!(","println!(\"year\\tservoi","println(\"$(a[i])\\t$(servois_numbers[i])\\t\\t$(easter_dates[i])\")","println(\"th","println(\"year\\tservoi","probabl","problem","problem,","programm","prolif","provid","public","publication,","publication.","pull","pure","put","put,","putstrln","q","q)","q))","q),","q)~\\%~30","q)~\\%~7.","q,","question","queues.","quot","range(2020,","re","read","real","realli","reason","reason,","reasons,","reckon","red","refer","regardless,","reinhold,","rel","relat","remark","rememb","remov","repli","replic","repres","represent","request","request.","requir","result","return","revolut","revolv","right.","roman","rotat","roughli","round","s","s\"${(21","s\"april","s\"march","said,","same","same,","saying,","schloss","scholars,","scientif","second","section,","sections,","see","seem","send","sens","sense!\"","separ","seri","servoi","servois\"","servois\",","servois'","servois)","servois)`t`t$(calcul","servois,","servois:","servois=false)","servois=false):","servois=true)","servois=true)}\\t\\t{computus(year)}\")","servois_numb","servoisnumb","servoisnumbers,","set","sever","shadows\"","sharealik","sheer","shift","shorter","show","shown","signifi","significantli","similar","simpli","simul","singl","size_t","slightli","small","snapshot","snow","snprintf(out,","so!","so,","softwar","solar","someth","sometim","somewhat","sort","space","special","split","spring","spring,","spring.","springer,","stacks,","standard","start","start,","state","static","std::cout","std::string","std::to_string((21","std::to_string(22","std::to_string(d","step","still","store","str((21","str(22","str(d","straightforward","straightforwardli","strformat","string","string(22","string(d","string(mod(21","string,","string;","student","students).","studi","subsequ","subtract","such","such,","suffic","sum","sun","sun,","sunday","support","sure,","surround","synchron","synchronized,","synod","system","systems,","systems.","t","t)","tab","tabl","table\"","table,","table:","take","tape","task","technic","techniques.","temp_","tempt","term","ters","text","text!","that'","then.","there,","thing","things:","think","this,","though","through","throughout","thus,","time","time,","time.","tittl","tmp1[9],","tmp2[9];","togeth","together,","told","track","transit","translat","tri","tricki","tricky.","trivial!","true","true)","true):14}","true,","truncat","truth","tuesday","tukey","tupl","twitch.","two","type","under","understand","understand,","understand.","undocu","unfortunately,","unit","univers","unlik","until","up","upon","us","used.","user","usize,","val","valu","values:","var","variabl","variable,","variables,","variou","video","void","wait","want","wave","way","way,","wednesday","week","week,","weekli","well","western","wish!","within","without","word","work","work,","worth","wrap","write","written","x","xadisten","y","year","year\"","year'","year,","year.","year:","years)","years,","years.","years.for_each(|year|","york","zipwith3","{","{22","{bool","{computus(year,","{d","{number}","{}\",","|","|i|","|y|","||","}","};","~a\""],"contents/gaussian_elimination/gaussian_elimination.html":["!","!=","!==","!singular","\",","\"\\n\")","\"\\t\"","\"__main__\":","\"current","\"echelon","\"fmt\"","\"game\"","\"gevis\"","\"math\"","\"origin","\"pivot\"","\"reduc","\"solut","#","#includ","$","&","&=","&[f64])","&eqns)","&f64","&matrix)","&mut","&self.data[row","&vec![2.0,","'eqns'","'rows'","(","(#560),","((1,","((i,","((r1,","()","(/)","(0);","(0..a.row","(3,","(a[(i,","(a[i","(a[i,","(a[i][col","(a[max_index,","(a[pivot","(a[pivot][col]","(a[pivot_i,","(a[r][col","(a[row,","(c,","(c1,","(col","(col+1):col","(compar","(curr_row),","(eqns[pivot][i]","(found","(fraction","(i","(i,","(i..a.rows).rev()","(instead","(int","(int,","(intercalate,","(k","(k,","(k..a.cols).rev()","(let","(no","(of","(on)","(r","(r,","(r1,","(r2,","(rn,","(row","(row+1):row","(row,","(similar","(size_t","(std::size_t","(target,","(tdma)","(the","(usize,","(v","(x,",")",");","*","*)a,","*a,","*x,","+","++row;","+=",".",".map(v","/","//","/=","0","0)","0,","0.","0..(a.col","0..min(a.cols,","0..row","0..self.col","0.0","0.0)","0.0,","0.0;","0:","0;","0x+0y+0z=1,","1","1)","1),","1)..a.col","1)..a.row","1).rev()","1):","1)]","1,","1.","1..a.row","1.0,","10","10.0],","10]","10]],","10},","10}};","11","11z","14","14.0}};","14}{11}","15","15.0},","18","1:(col","1:1","1:col","1:i","1:row","1;","1]","2","2)];","2,","2.","2.0,","2;","2x","2y","2z","3","3,","3.","3.0,","3.0},","3:","3\\\\","3d","3d,","3jane","3x","3y","3z","4","4))","4);","4,","4,],","4.","4.0","4.0,","4;","4\\\\","4y","4z","4}","4},","5","5,","5.","6","6,","6.0,","6;","6],","6},","7","8","9","::",":=",":]",":].copy()","=","==","===","=>",">",">=","[","[((r,","[(k,","[(m","[1,","[2,","[2.","[3,","[[((r2,","[];","[][]float64)","[][]float64{","[]float64","[]float64)","[ratio","[show","\\;,\\;","\\\\","\\begin{align}","\\begin{array}{ccccc}","\\begin{array}{ccc|c}","\\begin{array}{ccc}","\\begin{array}{cc}","\\begin{array}{c}","\\end{align}","\\end{array}","\\frac{","\\frac{18}{11}","\\frac{1}{3}","\\frac{1}{3}.","\\frac{1}{3}\\tim","\\left[","\\mathbf{","\\mathbf{0}","\\mathbf{10}","\\mathbf{1}","\\mathbf{2}","\\mathbf{3}","\\mathbf{4}","\\mathbf{6}","\\mathbf{\\frac{10}{3}}","\\mathbf{\\frac{2}{3}}","\\mathcal{o}(n^3).","\\quad","\\right]","\\rightarrow","\\sim","\\text{current_row}","\\text{pivot_row},","\\text{pivot}_{\\text{col}})","_),","_,","__name__","`on`","a(\\text{curr_row},","a(\\text{pivot}_{\\text{row}},","a)","a);","a,","a.col","a.length","a.length;","a.rows)","a.rows];","a.shape[0]):","a.shape[1]","a.shape[1])):","a.shape[1]:","a:","a[(a.row","a[(i,","a[(k,","a[(row,","a[0].length","a[0].length;","a[3][4]","a[col]","a[col];","a[i","a[i,","a[i,col]","a[i,col]*a[row,j]","a[i,col]/a[row,col]","a[i,j]","a[i][col]","a[i][i];","a[i][j]","a[i][j];","a[max_i,","a[max_index,","a[p]","a[p],","a[p][c]","a[pivot]","a[pivot];","a[pivot_i,","a[pivot_row,","a[r+1:]","a[r,","a[r:]","a[r]","a[r],","a[r][c]","a[r][j]","a[r][r]","a[row","a[row,","a[row,col]","a[row,i]","a[row,j]*fract","a[row][col];","a[row][i]","a[row][j];","a[rowa]","a[rowa];","a[rowb]","a[rowb];","ab","abov","above,","above.","above;","abysmal!","accum","actual","add","addition,","afterwards,","again,","algorithm","algorithm.","allow","along","alreadi","alway","ambigu","an","analog","analyt","anim","anoth","ans(rows);","ans;","answer","anything,","apply.","appropri","are:\")","argmax(abs.(a[row:end,col]))","args)","around","array","arrays.stream(a).foreach(x","assum","attribut","author","axes.","b","b:","back","back_substitution(&a);","back_substitution(a)","back_substitution(a):","back_substitution(a:","back_substitution(a::array{float64,2})","back_substitution(const","backsubs(const","backsubs(equations);","backsubstitut","backsubstitution(a","backsubstitution(a)","backsubstitution(double[][]","bases.","basic","basically,","becom","befor","before).","before,","before.","below","beneath","best.","better","beyond","boil","bottom","bound","break","browser","c","c)","c))","c)),","c))]","c),","c++","c,","c1)","c1),","call","can:","case","case,","case.","cell","cell)","chapter","chapter:","check","class","clear","clear:","clearli","cn","cn)","cn))","code","code,","code:","coeffici","col","col):","col);","col,","col]","col]))","col];","cols)","cols);","cols,","cols:","cols]","column","column,","column.","columns.","common","completeness.","complex","complic","comput","concat","conclus","conditions:","configuration:","confus","consid","consist","console.log(\"th","const","constrained,","context","continu","continue,","continue;","continuing,","contradiction.","convert","coordin","correct","correspond","course)","cover","creat","creativ","current","data.array","data.funct","data.list","data.ratio","data.to_vec(),","data:","deal","deduc","def","definit","demonstr","describ","desir","determin","diagon","differ","dimens","dimension","directli","divid","do","doesn't","done","doubl","double[]","double[][]","double[rows];","down","down.","downwards.","dtype=float)","due","dure","each","easi","easier","echelon","echelon)","either.","elem","element","element.","elimin","elimination\")","elimination,","elimination.","elimination:","elimination:\")","elimination:\");","elimination:\\n\");","encount","end","end,","enlighten","enough","ensur","entir","entri","eq","eqns.size(),","eqns.size();","eqns[0].size();","eqns[i]);","equat","equation.","equations,","equations.","equations;","equations?","equations{","essenti","evalu","even","everyth","exactli","exampl","example,","exist","exists,","exists.","exit","explan","f","f64","f64;","fabs(a[pivot","fabs(eqns[pivot][i]))","fact","fals","far","fashion.","faster","fastest","favorit","feel","find","first","first,","first.","float","fmt.print(\"[\")","fmt.printf(\"%9.4f","fmt.println(\"]\")","fmt.println(\"gauss","fmt.println(\"gaussian","fmt.println(\"origin","fmt.println(\"solut","fmt.println(\"thi","fmt.println()","fn","follow","following:","form","form\"","form,","form.","form:","found","frac","fraction","fraction,","fraction;","framework,","free","front","func","function","further","fuss!","game","game).","gauss","gauss_jordan(&mut","gauss_jordan(a:","gauss_jordan(doubl","gauss_jordan_elimination!(a)","gauss_jordan_elimination!(a::array{float64,2})","gauss_jordan_elimination(a)","gauss_jordan_elimination(a):","gaussian","gaussian_elimination!(a)","gaussian_elimination!(a::array{float64,2})","gaussian_elimination(&mut","gaussian_elimination((doubl","gaussian_elimination(a)","gaussian_elimination(a):","gaussian_elimination(a:","gaussian_elimination(doubl","gaussianelimin","gaussianelimination(a","gaussianelimination(a)","gaussianelimination(a);","gaussianelimination(double[][]","gaussianelimination(std::vector","gaussjordan","gaussjordan(a","gaussjordan(a)","gaussjordan(a);","gaussjordan(double[][]","gaussjordan(std::vector","gener","general,","give","glanc","go","goal","goe","good!","graphic","hand","happen","help","here","here'","here,","here?","higher","highest","hope","how?","however,","i)","i)]","i)];","i,","i;","i]","i];","idea","ideally,","ident","images/graph","imagin","immedi","impl","implement","implementation,","import","includ","inconsistent.","independ","index","index(&self,","index_mut(&mut","indexmut","indexmut};","inher","initi","instead","instead.","int","int)","int]","intend","intercal","intercept","interest","intern","interpret","interpretation!","intersect","introduc","invers","involv","io","is,","it'","it.","iter","itself.","j","j)","j),","j)]","j)];","j;","j]","j];","jame","java.util.arrays;","jess","jordan","jordan\")","jordan:\")","jordan:\");","k","k)]","k)].abs();","k)];","k;","keep","know","known","language.","larg","last","lead","leav","left","len(a)","len(a[0])","let'","licens","license.","license.md).","line","linearli","listarray","literature,","locat","look","loop","lower","m","m'","made","main","main()","main():","main(string[]","make","make([]float64,","mani","manipul","map","mat","math","math.abs(a[pivot][col]))","math.abs(row[c]);","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matric","matrix","matrix)","matrix,","matrix.","matrix:\"","matrix:\")","matrix::new(","matrix;","max_i","max_index","max_row","max_valu","maximum","maximumbi","maximumby)","maxval","mean","mess","method","mit","modif","modifi","moment","more","motiv","move","moves.","much","multipl","multipli","mut","name:","necessarili","necessary!","need","nevertheless,","new","new(rows:","next","next...","nice,","no.","non","none","nonzero","notat","note,","note:","now,","np","np.argmax(abs(a[pivot_row:,","np.array([[2,","np.zeros(a.shape[0]).t","number","numer","numpi","o(n)!","o(n^3),","obviou","obvious","on","opt","optim","otherwis","out","output","over","p","p,","packag","parallel","particular","particularli","parts.","perform","pivot","pivot)","pivot);","pivot,","pivot.","pivot_col","pivot_col]","pivot_col]))","pivot_i","pivot_i]","pivot_row","pivots.","plane","plane.","planes.","play","plenti","plot","plug","point","point,","possibl","precis","previou","print(\"back","print(\"gauss","print(\"gaussian","print(\"original\")","print(a,","print(back_substitution(a),","printf(\"gaussian","printf(\"th","println!(\"solution:","println(\"matrix","println(a)","println(soln)","printm","printmatrix(a","printmatrix(a)","printmatrix(const","printmatrixrow(row","printmatrixrow(row)","printmatrixrow(x)","printv","procedur","process","process,","program","properti","provid","pub","public","pull","put","putstrln","question:","quickli","r","r)","r++","r,","r1","r2","r;","random","rang","range(a.shape[0]","range(a.shape[0]):","range(min(a.shape[0],","range(pivot_i","range(pivot_row","range(row):","rank","ratio","re","reach","read","readers,","reason,","recreat","reduc","refer","remain","repeat","represent","request","resembl","reshap","respect","rest","rest.","return","right","right)","right,","rn)","roll","rounding)","row","row\"","row'","row++;","row,","row.","row:","row;","row[c]","row[j]","rowa,","rowb)","rows)","rows,","rows.","rows:","rule","s","s)","said,","same","satisfi","scale","scan","schloss","second","section","see","seem","seemingli","self,","self.col","self.data.swap(a","self.data[row","sens","separ","set","sever","sharealik","show","shown","side","sign","similar","similarly,","simpli","simplifi","simply:","singl","singular","singular!\")","singular\");","singular,","singular.\")","singular.\");","singular.\\n\");","size(a,1)","size(a,2)","size_t","skip","small","snd)","so:","sol","sol;","sol[col]","sol[i]","sol[j]","sol[pivot_i]","soln","soln);","soln[a.row","soln[i]","soln[j]","soln[j]*a[i,j]","solut","solution,","solution.","solution;","solution?","solution[i]","solution[j]","solutions.","solv","solvabl","solve,","solver","sometim","specif","split","start","start,","static","std::cmp::min;","std::cout","std::ops::{index,","std::size_t","std::swap(eqns[pivot],","std::vector","step","stop","straightforward","straightforward,","straightforward:","strategi","string","struct","submit","subrow","subsequ","subsitution\")","substitut","substitute,","substitution\"","substitution,","substitution.","substitution:","subtract","such","suggest","sum","sum'","sum)","support","sure","swap","swap_rows(&mut","swap_rows(a,","swap_rows(doubl","swaprow","swaprow(a,","swaprow(double[][]","switch","system","system.","system.err.println(\"th","system.out.println(\"\\ngauss","system.out.println(\"\\nsolutions:\");","system.out.println(\"gaussian","system.out.println(arrays.tostring(backsubstitution(a)));","system.out.println(arrays.tostring(x)));","systems,","systems.","t","t;","tag.","tediou","temp","temp;","temp_vector","term","text","that'","that,","that.","then,","there,","thing","think","this,","this:","thoma","through","thu","time,","time.","togeth","together,","top","transform","translat","treat!","tri","triangular","triangular.","tridiagon","trivial","true","two","two.","type","ultimately,","under","underneath","uniqu","unknowns,","unlin","until","up","upper","upward","us","usize)","usize))","usize,","valu","value,","value.","var","variabl","variable,","variable.","vec","vec![0.0;","vec,","vector","veri","via","video","visual","visualization,","void","want","way","way.","well,","well.","what'","what,","within","without","wobbl","words,","work","wouldn't","write","written","x","x,","x[c]","x[i]","x[j]","x[r]","y","y)","y,","y.","z","z)","z,","z.","zero","zero.","zeros(rows)","{","{1,","{2,","{2.0,","{3,","{5.0,","{:?}\",","{{3.0,","|","}","},","};","—"],"contents/quantum_systems/quantum_systems.html":["\"\"\"calcul","\"ftgaussian\"","\"the","\"wait.","#","$","&=","&opr)","&par,","(#560),","((/","(*","(\\psi_0);","(^","(found","(heat)","(inner","(k","(k_i)","(kineticop","(more","(or","(size_t","(wfc","(with","(x_i)","(|\\psi(x)|^2)","*","**","+","+=",".",".\"\"\"",".*",".+","0","0.5","0.5*wfc_c.*ifft((par.k.^2)","0;","1","1,","1.","1:length(energy_k)","1d","1}\\left(","2","2)","2))","2\\pi","4.0","::","=",">","\\\\","\\begin{align}","\\end{align}","\\frac{1}{2}\\omega","\\frac{2","\\frac{\\hbar^2}{2m}","\\frac{\\hbar}{2}","\\frac{\\parti","\\frac{\\partial\\phi(\\mathbf{r},t)}{\\parti","\\frac{h}{\\lambda}","\\frac{p^2}{2m}","\\geq","\\hat","\\hbar","\\infty}^{+\\infty}|\\psi(\\mathbf{r},t)|^2","\\int_{","\\lambda","\\lambda}","\\langl","\\left[","\\lvert","\\mathbf{r}","\\mathcal{f}\\left(","\\mathcal{f}^{","\\mu","\\mu)^2}.","\\nabla","\\nabla^2","\\omega","\\omega.","\\phi","\\phi(\\mathbf{r},t)","\\phi,","\\pi","\\psi","\\psi(\\mathbf{r},t)","\\psi(\\mathbf{r},t)^{*}\\psi(\\mathbf{r},t)","\\psi(\\mathbf{r},t)}{\\parti","\\psi(x)","\\psi(x).","\\psi(x)\\rangl","\\psi_i","\\rangl","\\rangle,","\\right)\\right)","\\right]","\\rvert","\\sigma","\\sigma_p","\\sigma_q","\\sigma_x","\\sqrt{\\frac{1}{n}\\sum_{i=1}^{n}(q_i","\\sum_i","\\textbf{k}","\\textbf{x},","abov","above.","absolut","accur","act","actual","add","advantage.","again,","again:","ahead","algorithm","algorithms.","all.","allow","alreadi","alway","always,","analog","analogu","angular","anim","anoth","answer,","area","areas.","argument","ascertain","associ","attribut","b","b.","back.","basic","basically,","be.","becom","befor","before.","behavior","behavior.","better","between","bit","blanketli","block","both","boundari","bra","braket","broader","brogli","build","c_i","c_i'","calcul","calculate_energy(par,","calculate_energy(par:","calculate_energy(param","calculate_energy(struct","calculateenergi","calculation:","call","can!","carlo,","carlo.","case","case,","cases!","cases.","certain","chang","change.","chapter","chapter.","chapter:","character","check","classic","cleaner","clear","clear,","clear:","clearli","code","collaps","column","come","common","complete.","complex","component,","comput","computation.","computations,","computer,","computers?","computers?\"","confin","conj(wfc_r)","conjug","conjugate.","consid","constant","constitu","contact","convers","convinc","cornerston","cours","course,","cover","creat","creativ","current","d","d\\mathbf{r}","de","deal","deeper","def","defin","definit","definitions:","densiti","densities.","density:","depend","depth","depth,","deriv","describ","descript","descriptions,","deserv","desired.","detail:","deviation,","devot","dft","diagonalization,","differ","difficult","diffus","discuss","distinct","distribut","distribution,","dive","dmrg,","do!","doesn't","don't","done","dot","doubl","dx","e","each","easi","easier","easiest","easili","effect","eigenst","elem","end","end,","energi","energy.","energy_fin","energy_final*par.dx","energy_k","energy_r","energy_r).r","energy_r[i])","enough","equat","equation,","equation:","essenti","even","eventu","everywher","exact","exactli","exampl","example,","exclus","exist","expect,","experi","experiment","explain:","explan","explicit","express","extra","f","fact","fact,","false);","features;","feel","fft(wfc_k,","fft(wfc_r)","find","find;","float:","focu","focus","follow","form","formal","formally):","formula:","formulations.","found","fourier","free","frequenc","full","function","function,","fundament","further","futur","f}{\\partial","gaussian","gener","general.","get","github","given","go","good","graphic","great","greatli","grid,","ground","grover'","h","hamiltonian","hamiltonian.","hamiltonians.","hand","hand,","hard","hardwar","hardware...","hardware;","harmon","have","heard,","heart","heisenberg","here","here'","here,","here.","here:","here;","hermitian","higher","however,","huge","human","h}{2","i,","i\\hbar","idea","idea.","idft","images/graph","imagin","imaginari","immedi","import","in,","includ","incred","indic","industry,","inform","inher","initi","inner","innov","instead","instead,","integr","interest","intern","interpret","interpretation,","intuit","intuitive,","invent","invers","involv","is!","isn't","issu","it!","it'","it,","itself,","jame","k","ket","kinetic","kineticop","know","know!","knowledg","knowledge;","known","laboratories,","lack","lagrangian","landscap","laplacian,","larg","larger","lead","left","less","let'","level.","licens","license.","license.md).","liftarray","literatur","locat","location,","location.","long","look","lot","lower","lowest","machines.","make","mani","map","mathemat","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matrix","me,","mean","meant","measur","mechan","mechanics!","mechanics,","mechanics.","memcpy(wfc_k,","memcpy(wfc_r,","mentioned,","method","method,","method.","methods,","methods.","miss","mit","modern","modifi","momentum","momentum,","momentum.","mont","more","more.","move","much","multipli","n","need","new","next","none","notat","notation,","notation.","note:","now","now,","np.conj(wfc_r)","np.fft.fft(wfc_r)","np.fft.ifft((par.k","number","numer","object","object,","observ","obviou","offer","on","onc","onto","op","oper","operations.","operator.","operators)","operators,","operators.","opposit","opr)","opr.size,","opr.v","opr.wfc","opr.wfc,","opr:","ops))","ourselves.","out","outer","over","p","p(\\mathbf{r},","p.","par,","par.dx","param","param)","param,","paramet","parameter","part","part,","particl","particle'","particle.","particles.","particular","particular,","particularli","parts;","perform","phenomenon.","physic","physically.","physics.","pictur","planck'","pleas","point","point,","posit","position,","possibl","potential","potential,","power","precis","pretti","principl","principle,","probability,","probabl","problem","proce","product","product)","product.","progress","properties.","provid","pull","purpos","push","put,","q","q_i","quantiti","quantum","qubit","qubits.","question","r","radic","re","readabl","real","real(energy_k[i]","real,","real.","realli","realpart","reason","reason.","reciproc","relat","replac","repres","request","research","restrict","results.","return","right","row","said,","same","sampled,","says:","scale","schloss","schrödinger","section","section,","section.","section;","see","sens","set","sever","sharealik","shor'","shown","side","side.","simpl","simpli","simplicity,","simplifi","simul","simulators.","singl","situation.","sizeof(wfc_k));","sizeof(wfc_r));","slightli","smaller","solv","someth","sometim","somewher","soon","sort","space","space,","space.","spatial","specif","specifically,","spectral","split","squar","stand","standard","start","state","state,","state.","statement","statist","steps)","sticky.","still","strengthen","struct","studi","sum","sum(energy_k","supercomput","sure","system","system'","system,","system.","systems,","systems.","t","t)","take","talk","taught","techniqu","temperature)","term","text","textbook","that!","that,","theori","theory.","thing","thinking,","thinner","this,","this:","those","though","thought","thought.","through","thu","time","time.","times,","total","transform","transform!","transform;","transformation,","transforms,","trap","trap,","tri","tricki","trivial","true:","truth","two","type","t}","t}.","ultim","ultimately,","uncertainti","under","understand","unfortunately,","unit","univers","universe.","up","updat","us","usual","v","v(\\mathbf{r},t)","valu","vector","vector.","vector_complex","want","wave","wavefunct","wavefunction,","wavefunction.","wavefunctions,","wavefunctions.","wavelength.","wavevector","wavey","way","way,","way.","we'll","weird.","well,","wfc","wfc_c","wfc_c(opr.size);","wfc_c.*opr.v","wfc_c[opr.size];","wfc_k","wfc_k(opr.wfc);","wfc_k)","wfc_k[opr.size];","wfc_r","wfc_r(opr.wfc);","wfc_r[opr.size];","wfcconj","wheel","without","words,","work","world","write:","written","x.","x^2","x}","{","|\\psi(\\mathbf{r},t)|^2"],"contents/affine_transformations/affine_transformations.html":["\"a11","\"a12","\"a13","\"a21","\"a22","\"a23","\"a31","\"a32","\"a33","\"coincidence\"","\"cosines\"","\"how","\"pseudo","\"rotat","\"scale\"","\"semi","\"shear\"","\"sines\"","\"stuff\"","&","&=","(a","(and","(at","(found","(note:","(x,y),","(yet","+","0","0!","0).","0,","0.","1","1)","1,","1.","1\\time","2","2,1],","2\\pi,","3","4","4.0","=","[","[0,0,1]","[0,0],","[1,2]","\\\\","\\begin{align}","\\begin{bmatrix}","\\cdot","\\cos(0)","\\cos(\\theta)","\\ell","\\ell.","\\end{align}","\\end{align},","\\end{array}\\right]","\\end{bmatrix}","\\end{bmatrix},\\\\","\\end{bmatrix}.","\\frac{\\vec{p_1","\\left[\\begin{array}{@{}ccc|c@{}}","\\left[\\begin{array}{@{}cc|c@{}}","\\mathbf{a}","\\mathbf{a}\\mathbf{v}_0","\\mathbf{a}\\mathbf{v}_0.","\\mathbf{a}_{\\text{rot}}","\\mathbf{v_0}","\\mathbf{v}","\\mathbf{v},","\\mathbf{v}_0","\\pi/2),","\\pi/2,","\\pi/2.","\\pm","\\rightarrow","\\sin(0)","\\sin(\\theta)","\\textbf{v}","\\theta","\\theta.","\\time","about,","about:","abov","above,","abruptli","accordingly.","act","actual","addit","affin","affine;","after.","again,","again...","ahead","algorithms.","all,","allow","along","alreadi","alway","always)","amount","angl","anim","animation:","anoth","answer","anyth","append","appli","applic","applications.","around","array,","array?","as,","assign","attribut","augment","away","back","balanc","barycent","barycenter.","basic","be:","befor","before,","before;","behaviors:","believ","between","beyond","bit","both","bottom","browser","button:","care","case,","case.","center","center),","certain","chang","chapter","circl","class","clearli","click","code","collect","collinear","combin","common","complet","complic","compon","component,","component.","components.","comput","computation:","concav","confus","confusing.","consid","continu","convex","correspond","cosin","course,","creat","creativ","cube","cube!","cube\"","cube,","cube:","decid","deeper","deepli","definit","definitions;","delv","describ","descript","dial","differ","dimens","dimension","direct","direction,","direction.","directions,","discuss","discuss.","distinct","dive","do","down","draw","dwell","each","easiest","effect,","effect.","element","emb","encompass","encourag","end","entir","equal","essenti","essentially,","even","everyon","exactly.","exampl","example.","example:","expected,","explan","extend","factor","feel","figur","finally,","find","first","flip","flip.","focus","follow","following:","formal","formalism.","found","fulli","fun","function","further","go","graphics.","grow","guarante","guess","hack:","hacki","happen","help","here","here,","hesit","honest,","hope","hopefulli","however,","hyper","ident","images/graph","imagin","implement","import","individu","initi","initially,","input","input,","instead,","interact","interest","intern","intro","intuit","is,","it).","it,","jame","keep","know","known","larg","larger","last","later","learn","leav","left.","length","less","licens","license.","license.md).","limit","line","linear","linear)","linear,","lines.","littl","locat","lot","loves:","magic","magnitud","make","manipul","mass","mathemat","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matric","matrices:","matrix","matrix,","matrix.","matter","me,","mean","meant","meanwhile,","mit","mix","modifi","more","more.","move","movements.","multipl","multipli","n","n+1","n\\time","namely,","necessarili","necessary.","need","need,","neg","never","new","next","nice","non","none","notat","note","now","now,","numer","object","ok,","on","on:","oper","opposit","origin","origin.","oscil","out","output","output,","overall,","p_1","p_2,","p_2}}{\\vec{p_3","p_3","p_4,","p_4}}","paint","parallel","parameter","particular","particularli","perform","perspective;","pictur","plane","plane.","plate.","play","point","point,","points,","points.","position,","position.","possibl","potenti","power","powerful,","practice.","practice:","preserv","previou","probabl","properti","provid","put","question","quick","quiet","ratio","ready,","realli","reason","reason,","regularli","regularly,","rel","relat","remain","represent","respectively.","result","right","right,","right?","rigor","rotat","rotate\"","rotation\"","rotation,","rotation.","rotation:","row","row?","same","same,","scale","scale?\"","scaling,","schloss","second","see","seem","seen","segments,","segments.","sens","set","sever","shape","shape.","sharealik","shear","shearing,","show","shown","side","similar","similarly,","simpli","sine","slice","slope","slowli","small","so,","someon","somewhat","space","space.","special","specifi","squar","square\"","square,","square.","stage,","start","start,","state","step","still","subsequ","such","suitabl","support","sure","surprising.","system,","tag.","take","talk","technic","terribl","text","that:","there,","thin)","think","this,","those","though","three","through","time,","time.","togeth","together.","took","top","topic,","touch","toward","transform","transformation,","transformation.","transformations,","transformations:","translat","translation,","translation.","treat","tug","turn","two","type","typic","under","underneath.","understand","unsatisfying!","us","varieti","variou","vector","vector,","vector.","vectors,","vectors.","vertic","video","video,","view","visible.","visual","visualizations,","want","watch","way","well,","well.","well...","whatev","whole","wide","within","work","worked.","works.","worth","wrap","written","x","y","y,","z","z.","z=1."],"contents/approximate_counting/approximate_counting.html":["\"!\"","\"a","\"approxim","\"count","\"delta","\"failed\"","\"finger","\"histogram","\"histograms\"","\"passed\"","#","#includ","&","&=","((1_f64","((avg","(0.4%).","(2^2","(2^{10}).","(4000)","(\\delta","(a","(a/(a+1))^j","(but","(chosen","(dot","(double)rand()","(drand()","(especi","(fingers),","(for","(found","(in","(items)","(left)","(left),","(like","(math.abs((avg","(math.pow(1","(math.random()","(maximum","(middle),","(n(v","(n)","(note:","(or","(pow((1","(pow(1","(sometim","(standard","(though","(unless","(v=2),","(variance)","(when","(which","(with","(without","*","*/","+",".average()",".getasdouble();",".limit(ntrials)",".sum::()",".take(n_trials)","/","/*","//","0","0.","0..n_item","0.025%","0.025\\%","0.037","0.053","0.25.","0.4%","0.4%).","0.42","0.42%","0.58),","00000000","00000001","00000010","00000100","00010000","01000000","0_f64;","0}","1","1)","1);","1)}","1)}{2a}.","1+1/a","1,","1,000,000","1,000,000\"","1,000,000)","1,000,000.","1.","1.0)(rng());","1.1\\time","1.71","1.85","1.sanderson,","1/(n(v","1/(n(v+1,","1/4000","1/a)**v","10","10,","10,000","10,000\"","10,000,","10,000.","100","1000","10000000","1023","1023,","1023?","10:","10^{110}.","10^{16}","10^{16},","10^{19}","10^{38}","10^{76}","10^{76}.","1110010101,","11111111","12,000,","128","130,000","130,000,","15","16","17,000).","1977","1978","1978.3.flajolet,","1985.4.bhayani,","1;","1=","1\\right).","1_f64","1_f64)","1_f64,","2","2).","2,","2.","20%","20.0","2015.2.morris,","2019.","2020.5.gundersen,","25","25%","250","255","255),","255,","255.","256","2^0","2^1","2^2","2^3","2^4","2^5","2^6","2^7","2^8","2^9","2^n","2^v","2^{10}","2^{255}","3","3.","3.36","3.40","3.84","35","35\"","3rd","3}","4","4,","4,000","4,000.","4.0","4000","4000*v.","4000,","4000.","4000:","4000th","483,200.0","499,813.2","4th","5.56","5.79","500,000","500,000\"","500,000,","511!","511,","512","512.","58%","6,","64","65535","8","8,000","8,000.0","8...","9,958.0","917","917:","961,600.0","999,466.0","=",">","[0,","[1,n]","[1]:","[2],","[2].","[3].","[4]","[5].","\\\\","\\approx","\\begin{align}","\\cdot","\\delta","\\delta,","\\delta_j","\\end{align}","\\frac{1}{(2^3","\\frac{1}{1.72","\\frac{1}{7","\\frac{1}{n_3","\\frac{1}{n_{v+1}","\\frac{\\log(1+n/a)}{\\log(1+1/a)}.","\\frac{\\log_e(n+1)}{\\log_e(2)}","\\frac{n(n","\\frac{n}{4000}","\\in","\\leq","\\log_2(1)","\\log_2(1+n),","\\log_e(1+e^v).","\\log_e(1+n).","\\neq","\\qquad","\\sigma","\\sigma(n,a)^2","\\sim","\\sum_{n=0}^9","\\text{if","\\time","_","a)","a))","a)))","a));","a),","a).powf(v)","a):","a);","a*((1","a*((1+1/a)^v","a,","a:","a=30","a=30,","a\\left(\\left(1+\\frac{1}{a}\\right)^v","abov","above:","abstract","abstractions.","access","account.","accur","acm","act","actions:","actual","ad","addit","addition,","advantage.","again,","algorithm","algorithm,","algorithm.","algorithm:","algorithm?","allow","along","also,","alway","analogy.","analysis,","anomaly:","anoth","answer","anyon","approach","appropri","approxim","approximate_count","approximatecount","approximatecount(nitems,","approximation).","arbitrari","arbitrarili","argument","around","ask","associ","attribut","auto","averag","avg","away","axi","back","bad,","bar.","base","base,","bases,","basic","be","be.","becom","befor","begin","bell","below:","better","better!","between","beyond","bibliographi","big","binari","bit","bits)","bits).","bits,","bits?","bitstr","bitstring.","black","blog","both","brought","bunch","by,","calcul","case","case,","cases,","catch","certain","certainli","chanc","chang","chapter","choos","chose","class","clear,","clearli","close","close?","closed,","closest","code","code,","come","common","comput","concret","configuration,","consequences:","consid","const","constant","constrictions.","convert","correct","correct,","correct.","correspond","count","count,","count.","counted,","counted.","counter","counter!","counter,","counter.","counting!","counting\"","counting,","counting:","counts,","counts.","counts:","cover","creat","creativ","deal","decid","decreas","def","definit","degre","delta","depend","describ","descript","detail","determin","determinist","deviation,","deviations.","differ","distanc","distinct","distribut","distribution,","distributions,","dive","do","don't","done","doubl","drand()","drawback","e","e)","e),","e,","e.","e^v","e^{255}","each","earli","effect","encount","end","engin","enough","ensur","equal","error","error,","error.","essenti","essentially,","estim","even","event","events,","events.","evid","exactli","exactly,","exampl","example,","excit","exp","expect","experi","experiment,","experiment.","experiment?","experiments,","experiments.","experiments:","explan","expon","exponentially.","express","f64","f64)","f64,","f64;","fact","fact,","factorial.)","feel","few","figur","final","finally,","find","finger","finger.","fingers?","first","fix","flajolet","flip","float","fn","follow","for)),","formula","found","fulli","function","further,","future.","g,","game","gaussian","gaussian,","gener","give","given","go","gone","good","good,","gotta","gray,","great!","guess","hairs.","half","hand","hand,","hand.","hands,","happen","hard","have,","have.","here","here,","here:","high","high!","high.","higher","higher)","higher,","highest","highlight","histogram","hold","honest,","hop","hope","however,","huge","ideal","imag","image,","images/graph","imagin","impact","implement","import","imposs","impressive!","in:","increas","increment","increment(doubl","increment(int","increment(v,","increment(v:","indic","individu","inform","initi","instead","integ","interest","intern","introduc","invent","issu","it!","it'","item","item,","item.","items,","items.","items;","items?","itself.","j","jame","java.lang.math;","java.util.stream.doublestream;","job","keep","kinda","know","known","lab","larg","largest","later","later,","learn","leav","left","less","let'","licens","license.","license.md).","lift","line","line),","line.","lines.","littl","logarithm","logarithm\"","logarithm):","logarithm,","logarithm.","logscale,","long","longer","look","loop","lot","low","lower","machin","main","make","mani","match","mathemat","mathjax.hub.queue([\"typeset\",mathjax.hub]);","maximum","mean","meaning","measur","mention","mentioned,","method","method!","method,","method.","mind","minimum","miss","mit","moder","modifi","more","morri","morris'","move","much","much,","multipl","mut","n","n(doubl","n(v,","n(v,a),","n(v:","n:","n=1","n=1.","n_2}","n_item","n_items:","n_items_float","n_items_float)","n_trial","n_trials:","n_v","n_v.","n_v:","n_{v+1}","n_{v}}","name","necessari","need","new","next","next.","nice","nitems)","non","none","not,","not.","note","note,","note:","notic","now","now,","number","number.","numbers,","numbers.","ny,","object","object,","obviou","obvious","occur","occurred.","occurs.","odd","on","on.","onlin","order","origin","out","out,","outputs.","overall,","p,","paper","paper,","paper.","paramet","parameters,","paus","peak","peopl","percent","perfect","perform","philipp","plot","plot,","point","possibl","possible,","potenti","power","practice,","pre","precis","precise)","precision.","predecessor","prefer","previou","primari","probability,","probabl","problem","problem,","problem:","process","proof","provid","pseudo","public","put,","put:","quantifi","question","question,","r","r,","rand()","rand::random::()","rand_max;","randengine(std::random_device{}());","randengine;","random","random()","random),","rang","read","real","realli","reason","reason,","regist","register,","register.","registers,","rel","rememb","reminder,","report","repres","resolut","resolution\"","resolution)","resolution,","resolv","resourc","result,","results.","return","right","right,","right.","right?","rigor","rng()","roughli","run","run,","said,","same","save","say,","scale","scale,","scale.","scales,","scheme","schloss","second","section,","section.","see","seed","seem","select","sens","sense,","separ","set","settl","sever","shade","sharealik","sheep","sheep,","sheep.","show","shown","signific","significantli","similar","similarly,","simpl","simpli","simul","situation?","size","skew","slightli","small","smaller","so)","solut","solution:","solv","some(approximate_count(n_items,","someon","someth","somewhat","space","specif","specifically:","split","springer,","stage,","standard","start","static","statistics.","std::default_random_engin","std::default_random_engine&","std::iter::from_fn(||","std::uniform_real_distribution(0.0,","step","still","stop","storage.","store","straight","straightforward","strategi","strategy:","stream","studi","such","system.","tabl","tackl","tak","take","talk","tell","term","terminolog","test","test_approximate_count(n_trials:","text","that'","that,","there'","there,","therebi","therefore,","thing","think","this,","this?","those","though","three","threshold:","thu","thumb","tick","time","time,","time.","times.","togeth","tool","top","total","track","traditionally,","trend","tri","trial","trials\"","trigger","trit","true","tune","twiddl","two","type","unaccept","under","understand","undoubtedli","unfortunately,","unpack","until","up","up,","up.","updat","updated.","upward","us","usa,","usize,","v","v\"","v(n)","v)","v,","v.","v:","v=1.","v=255.","valu","value,","value:","values.","values:","vari","variabl","varieti","veri","video","walk","want","way","way,","ways,","we'll","weight","well),","well,","what'","whether","win","wonder","work","world,","worthwhil","written","x.","y","y=x","y=x.","yes.","york,","yourself","{","}"],"contents/metropolis/metropolis.html":["\"\\n\".join(str(x)","\"__main__\":","\"adaptive\"","\"anim","\"barrier.\"","\"bins\"","\"multipl","\"plot","\"trained\"","\"w\")","\"walker\",","#","&","'''","'''iter","'''perform","'''random","'states'.","(","(#560),","(500,","(\\mathbf{x})","(a","(f(x_proposed)","(found","(n),","(np.sqrt(np.pi)","(there","(x","(x^2","(x_t","*","+","+1","+1,","+3].","+y^2",",",",x_n,",".","...","...)}.","/","/=","0","0)","0.2(x+1)^2}","0.2,","0.25","0:","1","1)","1).","1,","1,1)","1,1).","1.","1.,","1.]).reshape(3,","1.metropolis,nichola","10","10,","10^{41}","10^{50}","10d","10e^{","10}^{10}","1953.2.wikipedia:","1970.6.wikipedia:","1\\right).","1d","2","2(x","2.]).reshape(3,","2001.10.wikipedia:","2011.9.gareth","2021.","2021.3.wikipedia:","2021.4.wikipedia:","2021.5.hastings,","2021.7.wikipedia:","2021.8.rosenthal,","3","3,","3,3)","3.,","3e^{","3n","4(x+4)^2}","4.,","4.0","5)^2}.","5.]).reshape(3,","50","50_000","50_000))","50_000):","5_000,","=","==","[","[10].","[1]","[2]","[3]","[4]","[5]","[6],","[7],","[8]","[9].","\\dot","\\exp\\left[","\\exp\\left[\\frac{","\\exp\\left[{\\displaystyle\\frac{","\\frac{1}{\\sqrt{\\pi}}","\\frac{\\displaystyl","\\frac{e^{","\\frac{f(\\mathbf{x})}{\\displaystyle\\int_d","\\frac{f(x')}{f(x_t)}\\right).","\\frac{f(x)}{\\int_{","\\gt","\\infty}^{\\infty}","\\int_d","\\int_{x_1}","\\int_{x_{10}}","\\left(\\frac{f(x')}{f(x_t)},","\\leq","\\mathbf{x}","\\mathbf{x},","\\mathbf{x}.","\\min","\\min\\left(1,","\\right]","\\right].","\\right]}","\\rightarrow","_","__name__","a.","a=1","a])","abov","above,","accept","accur","achiev","act","actual","adapt","add","adjust","advanc","affect","ag","al.,","algorithm","algorithm!","algorithm,","algorithm.","algorithms,","algorithms.","allow","alreadi","although","altogeth","alway","always,","amin","analyt","anim","another,","another.","applic","applications,","approach","approxim","arbitrari","area","aris","assum","atoms,","attract","attribut","averag","away","b","bad","base","basi","be","befor","below","below.","between","between,","bibliographi","billion","bin","bin,","bin.","bin_width","bin_width)","bin_width/2,","bins=bins,","boca","boltzmann","boltzmann,","browser","built","bypass","calcul","calculate,","calculation,","call","carefulli","carlo","carlo,","case,","cases,","center","chain","chanc","chapman","chapter","chapter,","chapter:","charged,","choos","choose,","choose.","chosen","code","code!","coloss","combin","common","compar","complic","comput","computation","consid","constant,","continu","converg","coordin","coordinate,","count","coupl","creat","creativ","criterion","crucial","current","d","d\\mathbf{x}","d\\mathbf{x}.","data","data,","decis","def","defin","defined.","denomin","densiti","density=true)","depend","describ","deviat","deviation,","differ","difficult","dimens","dimension","dimension,","dimensions,","dimensions.","directly,","discov","discret","discrete,","discuss","distribut","distribution,","distribution.","distribution:","dive","divid","doesn't","domain","don't","done","dot","dramat","drastic","due","dx_1\\dot","dx_{10}.","dx}","e(\\mathbf{x})","e(\\mathbf{x})/t\\right],","e(\\mathbf{x})}{t}","e(x_1,","e(x_1,...,x_{10})","e(x_1,\\dot","e^{","each","easi","easier","effect","effici","else:","end","energi","energy,","ensur","equat","equilibrium","equival","error","error,","especi","estim","et","even","eventually,","everyth","exactly.","exampl","example,","exist","expens","explor","express","f(\\mathbf{x})","f(\\mathbf{x})d\\mathbf{x}},","f(centers,","f(x')","f(x)","f(x)).item())","f(x),","f(x).","f(x)},","f(x,","f(x_t),","f(x_t).","f=f,","fact","factor","factor,","far","fast","faster","fed","few","few.","field","figur","file","file,","finally,","first","fl,","fli","follow","footbal","form","frequenc","full","function","function,","function.","fundament","further","g","g()","g():","g,","g.","g=g):","game","gaussian","gaussian,","gaussians.","gener","give","given","global","goal","goal,","goe","good","graphic","hall/crc","hamiltonian","hand,","hast","height,","heights,","henc","high","higher","histogram","histograms\"","however,","i.","i.e.,","imag","images/graph","imagin","implement","implement.","impli","import","in!","incorpor","increas","increment","indeed.","iniit","initi","instead","instead,","institut","integ","integr","integral,","integrate,","integration.","intens","interact,","interactions.","intern","interv","intervals,","is,","is.","is:","it'","it.","iter","iterate.","iterations!","iterations,","itself.","jeffrey","k.","k.,","know","known","langevin","languag","larg","larger","later","learn","left,","length","let'","licens","license.","license.md).","line","list(metropolis_iterate(x0,","list,","locat","long","longer","look","lot","low","ludwig","machines,","made","magnitude!","make","mani","markov","mathemat","mathjax.hub.queue([\"typeset\",mathjax.hub]);","matters!","mcmc,","mean","mean_valu","mean_value)","meter","method","method.","methods,","metric","metric.","metropoli","metropolis\"","metropolis_iterate()","metropolis_iterate(x0,","metropolis_step(x)","metropolis_step(x,","min(1,","min(true_values))","mit","modifi","molecules,","mont","more","more,","move","move,","much","multidimension","multidimensional,","multipl","n","n.","name","nanosecond","nearbi","necessarili","need","new","next","next,","nmsd","none","norm","normal","normalize:","normalize=false):","normalize=true)","note","note:","noth","now","np","np.arange(xmin","np.arange(xmin,","np.array([","np.array([10.,","np.average((height","np.exp(","np.histogram(x_dat,","np.mean(true_valu","np.random.choice([x_proposed,","np.random.uniform(","np.random.uniform(xmin,","np.sqrt(b))).sum()","np.sqrt(nmsd)","nrmsd","num_step","num_steps))","num_steps):","num_steps.","number","numer","numerically.","numpi","o.","obvious!","occur","occurr","on","one.","open(\"output.dat\",","optim","order","other","other.","others,","otherwise,","out.write(\"\\n\")","out.write(output_string)","out:","output_str","over","overlap","own,","own.","p(\\mathbf{x})","p(\\mathbf{x}),","p(x)","p(x)\"","p(x),","p(x).","p=[a,","parallel","parameters,","part","particl","particles\">","particles,","particles.","particularli","peak","peopl","perform","physic","physicist","plot","point","poor","popular","posit","position,","position.","position.'''","positions.","possibl","potenti","power","practice,","practice.","pretti","print(f\"test","print(f\"{'num_steps':>10s}","print(f\"{num_steps:10d}","probability,","probabl","process","processor","processor,","program","proport","propos","proposal,","pull","put","q","q,","q.","question","quickli","quickly.","quit","random","randomli","range(num_steps):","ratio","raton,","reach","read","readi","real","realli","reduc","ref.","region","region,","reject","repeat","repel","replic","repres","request","requir","research","resolut","resolution,","respectively:","rest","restrict","result","return","right.","robert","root","rosenthal,","run","s","s.","same","same.","sampl","scale","scheme.","second","see","segment","segment.","set","setup","shall","shape","sharealik","show","shown","shudipto","similar","simpli","simplifi","singl","size","size,","size.","slightli","slowly,","small","so,","solut","someth","sometim","spatial","sped","speed,","spheric","squar","star","start","state","statist","statistics,","step","step,","steps.","still","style=\"width:80%\">","such","sum","support","symmetr","symmetric,","system","systems!","systems,","t","t,","tag.","take","target","techniqu","temperatur","term,","test","test_metropolis_iter","test_metropolis_iterate(num_steps,","testing,","text","them),","there!","thing","third","this,","three","thus,","time","times,","times.","together,","took","total","toward","transit","trial","trillion","true","true,","true_valu","true_values)**2","two","u","under","understand","unfeas","unfeasible.","unity,","univers","up","us","using,","usual","valu","values.","vari","variou","vector.'''","veri","verifi","video","visit","w.","walk","walk\"","walk,","walk.","walker","walker'","walker,","wanna","want","watch","way","well.","what'","whatev","whether","whose","wide.","width","words,","work","work.","works,","world","world,","write","written","x","x'","x,","x.","x0","x0)","x0):","x=0.","x],","x^2}","x^2}.","x^2}}{\\displaystyle\\int_{","x_0","x_0'''","x_0.","x_2,","x_dat","x_dat)","x_i,","x_new","x_propos","x_t","x_{10})}{t}\\right]\\","x_{t+1}","xmax","xmax)","xmax,","xmin,","xs","xs)**2)).sum(axis=0)","y_1,","y_2,","y_i,","y_n,","yield","you'd","z_1,","z_2,","z_i","z_n),","{'nrmsd':10s}\")","{nrmsd:5.1%}\")","{q},","{x0:5.2f}\")","}","–"],"contents/probability_distributions/distributions.html":["\"frequenc","\"n","\"not","\"probabl","\"set","&;&","(#560),","(1","(a","(also","(bi","(denot","(for","(h)","(homework","(it","(or","(popularli","(such","(t)",")","+","0.","1","1).","1,","1.","1/6,","12","12,","15,","16","16.5.","1s.","2","2,","2;","3","36","36,","3;","4.0","5","50\\%","5\\%","6","=","[\\![1,6]\\!]","[\\![2,12]\\!].","\\begin{matrix}","\\displaystyl","\\displaystyle\\frac","\\end{matrix}","\\end{matrix}.","\\frac","\\frac{1}{2}.","\\frac{1}{\\sqrt{\\pi}}","\\frac{1}{n}","\\frac{\\displaystyle\\sum_{n}f(n)}{\\displaystyle\\sum_{n}","\\frac{f(\\mathbf{x})}{\\int_d","\\frac{f(n)}{\\displaystyle\\sum_{n}","\\geq","\\in","\\in\\left\\{h,t\\right\\},","\\infty}^{\\infty}","\\int_a^b","\\int_d","\\int_{","\\int_{d}","\\int_{s}f(\\mathbf{x})d\\mathbf{x}","\\left\\{h,t\\right\\}","\\left\\{h,t\\right\\}.","\\leq","\\mathbb{p}(a","\\mathbb{p}(x_0","\\sqrt{\\pi}.","\\sum_n","\\sum_{n=a}^{b}","\\time","abov","above.","actual","again","ahead","all,","allow","allowed\"","alreadi","also.","amin","analag","answer","approach","area","as,","ask","assum","attribut","away","b","b)","b).","b,","be","becom","belong","below.","between","boring,","both","brevity,","broadli","calcul","call","candid","case","case,","case.","categori","certain","chanc","chapter","chapter:","check","classifi","clearli","coin","common","consid","construct","contain","contin","continu","count","creat","creativ","crucial","curv","curve.","d","defin","defined.","definit","denot","densiti","density\"","depend","determin","dice","dice),","dice,","dice.","die","differ","discret","distribut","distribution,","distribution.","distribution:","distribution?","distributions),","distributions.","divid","do","doesn't","domain","doubl","dx","dx)","dx,","e^{","each","easi","edge!).","edge)","electron","entir","equal","equation,","essenti","etc.","exactli","exampl","example,","except","experi","express","f(2)=1.","f(3)=2.","f(\\mathbf{x})","f(\\mathbf{x}).","f(\\mathbf{x})d\\mathbf{x}.","f(\\mathbf{x})d\\mathbf{x}}.","f(n)","f(n),","f(n).","f(n)}","f(n)}.","f(x)","f(x),","f,","fact","featur","find","finite:","first","follow","formally,","frequenc","frequencies,","function","function,","function.","function:","function?","further","gambler!","gaussian","general,","get","get,","give","go","good","googl","graphic","great","green","h","half,","happen","head","hence,","here,","hold.","i.e.,","imag","images/graph","immedi","import","impossible,","includ","inclus","incred","infinit","infinitesim","information,","initi","instead","integ","integer,","integr","interest","intern","intuit","is.","isn't","it!","it'","it,","it.","itself","k.","know","know,","land","less","let'","licens","license.","lie","look","lowest","ly","make","mani","mathemat","mathjax.hub.queue([\"typeset\",mathjax.hub]);","maximum","mean","mean?","measur","measurement,","mention","modifi","n","n,","n.","n=2","n=2,","n=3,","n=4","n=7","n=7,","necessarili","neg","next,","non","none","noon","normal","notat","notation\",","note","now","now,","number","numbers,","object,","obtain","obviou","occur.","on","onc","out","outcom","outcome,","outcome.","outcome:","outcomes.","over","p(\\mathbf{x})","p(h)","p(n)","p(n),","p(n).","p(t)","p(x)","p(x),","p(x)dx","p(x)dx,","p(x)dx.","pair","particular","pattern","physic","plot","possibilities,","possibl","previou","probabilites.","probability,","probability.","probabl","procedure,","process","proport","prospect","pull","put","quantiti","quantity,","quick","rang","range,","range.","reader!).","real","realli","region","request","result","roll","roll\"","roll.","rule","s)","same","satisfi","say","search,","second","section:","see","sens","set","sharealik","show","shown","shudipto","similar","similarly,","simpli","singl","sixes,","sliver","small,","so,","sort","speaking,","spin","still","strictli","studi","style=\"width:100%\"/>","style=\"width:80%\"/>","subset","such","sum","sum:","suppos","sure.","system,","t\".","t.","tail","take","target","technic","tell","temperatur","text","things.","thu","thus,","tomorrow","toss","toss,","total","translat","tricky)","two","under","understand","unlikely,","up","up,","us","valu","values.","vari","variabl","varies.","veri","visual","vs","want","way","way,","weight?","well,","what'","wherea","whole","within","write","written","x","x,","x.","x^2}","x^2},","x^2}.","x_0","zero!","zero):","–"]},"length":49},"tokenStore":{"root":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"1":{"0":{"1":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"1":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"1":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"docs":{}},"1":{"0":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"1":{"0":{"1":{"0":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"1":{"0":{"0":{"0":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"docs":{}},"1":{"0":{"0":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"1":{"0":{"0":{"1":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}},"1":{"0":{"0":{"0":{"0":{"0":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"1":{"0":{"0":{"1":{"0":{"1":{"1":{"1":{"0":{"1":{"1":{"1":{"1":{"0":{"1":{"1":{"1":{"0":{"0":{"0":{"1":{"0":{"0":{"1":{"0":{"1":{"1":{"1":{"0":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"1":{"0":{"1":{"0":{"1":{"0":{"1":{"1":{"0":{"1":{"0":{"0":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"1":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"1":{"0":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"1":{"0":{"0":{"1":{"1":{"1":{"1":{"0":{"1":{"1":{"0":{"0":{"1":{"1":{"0":{"1":{"0":{"1":{"1":{"0":{"0":{"0":{"0":{"1":{"1":{"1":{"1":{"0":{"1":{"1":{"0":{"0":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"1":{"0":{"1":{"0":{"1":{"1":{"0":{"0":{"0":{"0":{"1":{"0":{"0":{"1":{"0":{"0":{"1":{"1":{"1":{"1":{"1":{"0":{"1":{"0":{"1":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"1":{"0":{"1":{"docs":{},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}}},"docs":{}},"1":{"1":{"0":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581}}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0035433824937751387},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.007045797684952189},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0037199415437757406},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.010638297872340425},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00821917808219178},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.00944206008583691},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.005635919594213789},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0028782894736842104},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.010225820195994887},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0018137847642079807},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.004419191919191919},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.014613778705636743},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.014251781472684086},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.016568047337278107},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004204625087596356},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.003639149588201494},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.005200469719845663},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.006391137622496805},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0022169437846397467},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"'":{"docs":{},".":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0016280406052480367},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.001062840441078783},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0031323414252153485},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0029655990510083037},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002843216896831844},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0024422318241593085},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003289473684210526},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.004402783695497799},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0028214429665457475},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.007759303246239113},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},",":{"0":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.005338078291814947},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0014251781472684087},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0015322735108216816},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"b":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},"[":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}},"}":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643}}},"}":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},"/":{"1":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"docs":{}},"a":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"x":{"0":{"0":{"docs":{},"f":{"docs":{},"f":{"0":{"0":{"docs":{},"f":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"docs":{}},"docs":{}}}},"docs":{},"f":{"0":{"docs":{},"f":{"0":{"docs":{},"f":{"0":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}}},"docs":{}}},"docs":{}}},"1":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"3":{"3":{"3":{"3":{"3":{"3":{"3":{"3":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"5":{"5":{"5":{"5":{"5":{"5":{"5":{"5":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{},"+":{"0":{"docs":{},"y":{"docs":{},"+":{"0":{"docs":{},"z":{"docs":{},"=":{"1":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"docs":{}}}},"docs":{}}}},"docs":{}}},".":{"0":{"0":{"1":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"docs":{}},"1":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0019883539269990058}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002272404487998864}}}},"d":{"0":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"docs":{}}},"2":{"5":{"docs":{},"%":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"\\":{"docs":{},"%":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"docs":{}},"3":{"7":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"4":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}}},"5":{"3":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767}}}},"7":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}},"]":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00695923874449652},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0031656700668308124},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},";":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0028405056099985795},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}},"_":{"docs":{},"f":{"6":{"4":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"i":{"docs":{},"(":{"2":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"docs":{}}}}}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}}}},"docs":{}},"docs":{}}},"i":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}},"[":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"}":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},"1":{"3":{"3":{"0":{"7":{"7":{"1":{"1":{"2":{"4":{"3":{"5":{"1":{"1":{"3":{"3":{"3":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"5":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}},"6":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}},"8":{"5":{"4":{"1":{"9":{"4":{"2":{"0":{"6":{"7":{"8":{"1":{"5":{"8":{"5":{"3":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}}}}}},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"2":{"2":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}},"3":{"6":{"4":{"8":{"9":{"1":{"6":{"1":{"8":{"7":{"4":{"3":{"9":{"4":{"0":{"6":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"8":{"4":{"2":{"1":{"6":{"2":{"6":{"7":{"8":{"3":{"2":{"7":{"3":{"2":{"8":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}},"4":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}},"5":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"6":{"6":{"6":{"6":{"6":{"6":{"8":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0041753653444676405}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}},"7":{"9":{"9":{"9":{"6":{"2":{"8":{"6":{"6":{"8":{"1":{"5":{"3":{"0":{"8":{"7":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"8":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}},"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}},"(":{"docs":{},"x":{"docs":{},"+":{"1":{"docs":{},")":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{}}}},"docs":{}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"3":{"0":{"6":{"9":{"9":{"0":{"9":{"1":{"6":{"9":{"1":{"8":{"9":{"6":{"2":{"6":{"3":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"5":{"4":{"8":{"4":{"0":{"5":{"5":{"5":{"3":{"7":{"5":{"4":{"3":{"1":{"9":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"5":{"8":{"9":{"6":{"2":{"5":{"5":{"9":{"4":{"0":{"0":{"5":{"6":{"4":{"7":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"6":{"1":{"3":{"0":{"7":{"9":{"2":{"6":{"0":{"4":{"6":{"0":{"2":{"7":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"9":{"2":{"1":{"0":{"2":{"4":{"2":{"9":{"8":{"0":{"4":{"3":{"8":{"9":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}},"4":{"0":{"6":{"1":{"0":{"8":{"6":{"1":{"8":{"5":{"7":{"7":{"0":{"1":{"5":{"9":{"7":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"2":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"%":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"4":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}},")":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"]":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}},"%":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},")":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"5":{"8":{"7":{"7":{"8":{"5":{"2":{"5":{"2":{"2":{"9":{"2":{"4":{"7":{"3":{"1":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"2":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"4":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{},")":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"9":{"2":{"docs":{},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"docs":{}},"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.007725321888412017},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.004924375659514597},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0034086067319982955},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0058444175735590485},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0029227557411273487},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"]":{"docs":{},")":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"*":{"docs":{},"(":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}},"a":{"docs":{},"c":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"v":{"docs":{},"*":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"d":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"k":{"docs":{},".":{"docs":{},"^":{"2":{"docs":{},"*":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"d":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}},"docs":{}}}}}}}},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},"_":{"docs":{},"c":{"docs":{},".":{"docs":{},"*":{"docs":{},"i":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"k":{"docs":{},".":{"docs":{},"^":{"2":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"d":{"0":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}},"docs":{}},"_":{"docs":{},"f":{"6":{"4":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534}}},"docs":{}},"docs":{}}},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}}},"6":{"0":{"7":{"5":{"6":{"8":{"8":{"5":{"3":{"4":{"4":{"0":{"9":{"0":{"2":{"7":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"1":{"8":{"docs":{},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"docs":{}},"3":{"3":{"8":{"9":{"4":{"3":{"7":{"2":{"4":{"1":{"8":{"8":{"0":{"9":{"1":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"5":{"1":{"1":{"2":{"6":{"0":{"2":{"7":{"8":{"5":{"0":{"4":{"5":{"8":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"7":{"5":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"_":{"docs":{},"f":{"6":{"4":{"docs":{},".":{"docs":{},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}},"docs":{}},"docs":{}}}},"6":{"0":{"5":{"7":{"5":{"2":{"6":{"0":{"8":{"7":{"4":{"5":{"5":{"0":{"6":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"7":{"9":{"6":{"7":{"8":{"4":{"9":{"0":{"2":{"8":{"6":{"2":{"8":{"0":{"3":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"8":{"9":{"5":{"5":{"4":{"5":{"5":{"5":{"8":{"0":{"6":{"7":{"3":{"5":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"9":{"7":{"2":{"0":{"0":{"9":{"7":{"3":{"7":{"6":{"2":{"3":{"8":{"4":{"6":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"8":{"5":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}}},"6":{"6":{"1":{"8":{"7":{"3":{"0":{"6":{"9":{"6":{"6":{"8":{"0":{"1":{"8":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"6":{"6":{"6":{"7":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"8":{"6":{"8":{"6":{"0":{"2":{"4":{"1":{"2":{"1":{"5":{"4":{"4":{"4":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"9":{"5":{"1":{"0":{"5":{"6":{"5":{"1":{"6":{"2":{"9":{"5":{"1":{"5":{"3":{"5":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},"6":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},".":{"6":{"4":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"docs":{}},"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},".":{"docs":{},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"(":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"a":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},"w":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.003022974607013301}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"x":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"a":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}},"]":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}}}},"s":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"'":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"+":{"1":{"2":{"7":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"f":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}},"d":{"0":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},"docs":{}},"\"":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407}}},"u":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}}},"!":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"_":{"docs":{},"f":{"6":{"4":{"docs":{},";":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}}}},"1":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603}}},"docs":{}},"1":{"0":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"1":{"0":{"1":{"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}},".":{"0":{"0":{"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002843216896831844},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"%":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},",":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},".":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"*":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},".":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}},".":{"0":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"_":{"0":{"0":{"0":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"docs":{}},"docs":{}},"docs":{}},"}":{"docs":{},"%":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}},"1":{"0":{"docs":{},".":{"0":{"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}}},"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"2":{"3":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"?":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"4":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"docs":{}},"4":{"0":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"docs":{}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0014251781472684087},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"❗":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"️":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0010534380386899062}}}}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"3":{"6":{"docs":{},"a":{"docs":{},";":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"docs":{}},"docs":{}}},"docs":{}}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},",":{"0":{"0":{"0":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004905395935529082}},",":{"0":{"0":{"0":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"docs":{}},"docs":{}},"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}}},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}},"1":{"1":{"docs":{},")":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"docs":{}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002414429768498793},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},".":{"0":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0019883539269990058},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"/":{"5":{"1":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},"docs":{}},"docs":{}},"]":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"2":{"5":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}},"s":{"docs":{},",":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"c":{"docs":{},"m":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}},"d":{"0":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"^":{"docs":{},"{":{"1":{"1":{"0":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"docs":{}},"6":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"9":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"3":{"8":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"4":{"1":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{}},"5":{"0":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{}},"7":{"6":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"docs":{}},"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"_":{"0":{"0":{"0":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{}},"docs":{}},"docs":{}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"?":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"]":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"}":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"}":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"^":{"docs":{},"{":{"1":{"0":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{}},"docs":{}}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"e":{"docs":{},"^":{"docs":{},"{":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"1":{"0":{"1":{"docs":{},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"5":{"1":{"9":{"9":{"1":{"0":{"3":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"1":{"0":{"0":{"1":{"0":{"1":{"0":{"1":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"1":{"1":{"1":{"1":{"1":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"docs":{}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}},"a":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},".":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}},"docs":{}},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"~":{"docs":{},"\\":{"docs":{},"%":{"docs":{},"~":{"3":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}}}}},"z":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"2":{"3":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}},",":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"4":{"5":{"6":{"docs":{},"=":{"5":{"6":{"0":{"8":{"8":{"docs":{},",":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"docs":{}},"docs":{}}}}}}}},"6":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"7":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603}}}},"8":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.005200469719845663},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"*":{"7":{"7":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"docs":{}},"docs":{}},"/":{"1":{"9":{"2":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0010534380386899062}},"#":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"9":{"1":{"docs":{},"b":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"docs":{}},"docs":{}}},"docs":{}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}}},",":{"0":{"0":{"0":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"b":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},".":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}},"docs":{}},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"c":{"docs":{},"m":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"3":{"0":{"docs":{},",":{"0":{"0":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"a":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"b":{"docs":{},"b":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"t":{"docs":{},"b":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604}}},".":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}},"}":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"docs":{}},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}},"{":{"1":{"1":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"docs":{}},"docs":{}}}},"5":{"3":{"6":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},".":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}},"}":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"docs":{}},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"6":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009299853859439352},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0035694157430020664},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000861903849837196},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"#":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},":":{"9":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"docs":{}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"+":{"1":{"docs":{},".":{"0":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"docs":{}}},"docs":{}},"i":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},".":{"5":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"docs":{}}},"7":{"7":{"7":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},",":{"0":{"0":{"0":{"docs":{},")":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"docs":{}},"docs":{}},"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"8":{"0":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},"'":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"5":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}},"1":{"3":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"6":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"7":{"6":{"docs":{},".":{"5":{"docs":{},".":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}},"docs":{}}},"docs":{}},"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}},"\\":{"docs":{},"\\":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"]":{"docs":{},"=":{"docs":{},"[":{"4":{"docs":{},"+":{"1":{"docs":{},",":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"docs":{}}},"docs":{}}}}},"9":{"0":{"0":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"5":{"3":{"docs":{},".":{"2":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}},"docs":{}}},"8":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},".":{"2":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}}}},"docs":{}}},"docs":{}},"6":{"5":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"7":{"docs":{},".":{"3":{"docs":{},".":{"docs":{},"j":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"o":{"docs":{},"u":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}},"docs":{}}},"docs":{}},"7":{"0":{"docs":{},".":{"6":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}},"docs":{}}},"2":{"docs":{},".":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"3":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"7":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"8":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"3":{"docs":{},".":{"docs":{},"f":{"docs":{},"l":{"docs":{},"a":{"docs":{},"j":{"docs":{},"o":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}},"docs":{}}},"docs":{}},"8":{"1":{"docs":{},".":{"1":{"1":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}},"docs":{}},"docs":{}}},"5":{"docs":{},".":{"4":{"docs":{},".":{"docs":{},"b":{"docs":{},"h":{"docs":{},"a":{"docs":{},"y":{"docs":{},"a":{"docs":{},"n":{"docs":{},"i":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}},"docs":{}}},"6":{"docs":{},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"docs":{}},"9":{"4":{"docs":{},".":{"6":{"docs":{},".":{"docs":{},"s":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}},"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"9":{"docs":{},".":{"2":{"docs":{},".":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}}},"docs":{}}},"docs":{}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.004528985507246377}},".":{"3":{"4":{"7":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"docs":{}},"docs":{}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}},"a":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"t":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.005458724382302241},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0026571011026969575},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.008344923504867872},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00487408610885459},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.03287671232876712},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.010300429184549357},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0033815517565282736},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.007305194805194805},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004111842105263158},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.005681818181818182},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00870942201108472},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01952662721893491},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.010161177295024528},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.007415254237288136}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0018599707718878703},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.003355704697986577},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0020665038512117226},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0022168480451430876},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002058590657165479},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"v":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}},"*":{"docs":{},"p":{"docs":{},"i":{"docs":{},"*":{"docs":{},"i":{"docs":{},"*":{"docs":{},"k":{"docs":{},"/":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}},"/":{"docs":{},"(":{"docs":{},"x":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}},"(":{"docs":{},"r":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{},"a":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}},"r":{"docs":{},"e":{"docs":{},"v":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"{":{"2":{"docs":{},"a":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"docs":{}}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0035087719298245615},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013285505513484788},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.005369127516778523},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.006334125098970704},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"]":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011956954962136308},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0028782894736842104},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0026845637583892616},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"^":{"2":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649}}},"docs":{}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004523026315789474},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"*":{"docs":{},"a":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}}}}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"9":{"1":{"docs":{},"b":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"docs":{}},"docs":{}}},"docs":{}}}},",":{"0":{"0":{"0":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},",":{"0":{"0":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003854239663629993}},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}},"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"docs":{}},"docs":{},".":{"5":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}}},"1":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.00800711743772242},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.003691275167785235},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0034837688044338875},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},".":{"0":{"0":{"0":{"0":{"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"1":{"0":{"0":{"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"(":{"docs":{},"r":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"f":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},"]":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}},"*":{"docs":{},"[":{"1":{"docs":{},".":{"0":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"docs":{}}},"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}},"]":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852}}}}},"+":{"0":{"docs":{},".":{"0":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"docs":{}}},"2":{"docs":{},".":{"4":{"4":{"9":{"2":{"9":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"_":{"docs":{},"f":{"6":{"4":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}},"docs":{}}},"i":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"1":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}}},"2":{"2":{"4":{"6":{"4":{"6":{"7":{"9":{"9":{"1":{"4":{"7":{"3":{"5":{"3":{"2":{"docs":{},"e":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"5":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"docs":{}},"docs":{}},"docs":{}},"7":{"3":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}},"docs":{}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"5":{"3":{"3":{"3":{"3":{"3":{"3":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"6":{"0":{"docs":{},")":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}},"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0041753653444676405}},"]":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}},"7":{"1":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"8":{"3":{"6":{"9":{"7":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"docs":{}},"docs":{}},"docs":{}},"5":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"9":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},".":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}},"=":{"docs":{},"(":{"docs":{},"(":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"a":{"docs":{},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}},"b":{"docs":{},"u":{"docs":{},"c":{"docs":{},"k":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"a":{"docs":{},"r":{"docs":{},"n":{"docs":{},"s":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"o":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},"j":{"docs":{},"a":{"docs":{},"r":{"docs":{},"v":{"docs":{},"i":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"h":{"docs":{},"a":{"docs":{},"m":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"l":{"docs":{},"l":{"docs":{},"i":{"docs":{},"a":{"docs":{},"m":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"n":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"u":{"docs":{},"p":{"docs":{},"t":{"docs":{},"o":{"docs":{},"(":{"docs":{},"a":{"docs":{},".":{"docs":{},"s":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"]":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}},")":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"(":{"3":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"docs":{}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"b":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},",":{"docs":{},"n":{"docs":{},"i":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"l":{"docs":{},"a":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}}}}}},":":{"1":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},":":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"(":{"docs":{},"$":{"1":{"docs":{},",":{"docs":{},"$":{"2":{"docs":{},")":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"docs":{}}}},"docs":{}}}}}}}}}}},"3":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0013407393219689715},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},"n":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"a":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"/":{"2":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"docs":{}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}}}}}}}}},"x":{"docs":{},")":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"y":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"d":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{},"y":{"docs":{},"_":{"docs":{},"k":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"b":{"docs":{},"a":{"docs":{},"b":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"g":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"a":{"docs":{},"x":{"docs":{},"i":{"docs":{},"s":{"docs":{},"_":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}}}}}}}}},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"_":{"docs":{},"s":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}},"d":{"docs":{},"i":{"docs":{},"g":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"h":{"docs":{},"a":{"docs":{},"l":{"docs":{},"f":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}},"(":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},")":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"2":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"docs":{}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"docs":{}}}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}},"i":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},"/":{"0":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"4":{"0":{"0":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"docs":{}},"docs":{}},"6":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"docs":{},"(":{"docs":{},"n":{"docs":{},"(":{"docs":{},"v":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"+":{"1":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}}}}}},"a":{"docs":{},")":{"docs":{},"*":{"docs":{},"*":{"docs":{},"v":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"a":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"\"":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"}":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824}}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},"{":{"2":{"docs":{},"}":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"docs":{},"b":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"&":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"[":{"docs":{},"\\":{"docs":{},"h":{"docs":{},"a":{"docs":{},"t":{"docs":{},"{":{"docs":{},"u":{"docs":{},"}":{"docs":{},"_":{"docs":{},"k":{"docs":{},"(":{"docs":{},"d":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}},"(":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},"d":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":5.000555247084953},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}}},"s":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}},".":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}}}},"'":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}},"s":{"docs":{},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"j":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}},"i":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"+":{"1":{"docs":{},"/":{"docs":{},"a":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"docs":{}},"=":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"_":{"docs":{},"f":{"6":{"4":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}}}},"2":{"0":{"0":{"0":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"1":{"docs":{},".":{"1":{"0":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}},"docs":{}},"docs":{}}},"4":{"docs":{},".":{"4":{"docs":{},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"k":{"docs":{},"n":{"docs":{},"o":{"docs":{},"w":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}},"7":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}},"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"8":{"docs":{},".":{"4":{"docs":{},".":{"docs":{},"w":{"docs":{},"e":{"docs":{},"g":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}},"docs":{}}},"docs":{},",":{"0":{"0":{"0":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"docs":{}},"docs":{}},"docs":{}}},"1":{"0":{"docs":{},".":{"4":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}},"docs":{}}},"1":{"docs":{},".":{"9":{"docs":{},".":{"docs":{},"g":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"docs":{}}},"2":{"docs":{},".":{"5":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"e":{"docs":{},"l":{"docs":{},"k":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}},"9":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}},"docs":{}}},"4":{"docs":{},".":{"2":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}},"docs":{}}},"5":{"docs":{},".":{"2":{"docs":{},".":{"docs":{},"m":{"docs":{},"o":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}},"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"6":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"7":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"7":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}},"docs":{}}},"8":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"9":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"1":{"0":{"docs":{},".":{"docs":{},"h":{"docs":{},"u":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}}},"2":{"docs":{},".":{"docs":{},"w":{"docs":{},"o":{"docs":{},"l":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}},"docs":{}},"2":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"b":{"docs":{},"r":{"docs":{},"o":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}}},"3":{"docs":{},".":{"docs":{},"p":{"docs":{},"e":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"c":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"s":{"docs":{},"a":{"docs":{},"u":{"docs":{},"p":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"5":{"docs":{},".":{"docs":{},"s":{"docs":{},"a":{"docs":{},"u":{"docs":{},"p":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}},"8":{"docs":{},".":{"docs":{},"g":{"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}},"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"2":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.004347826086956522}},".":{"2":{"docs":{},".":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}},"s":{"docs":{},"c":{"docs":{},"h":{"docs":{},"l":{"docs":{},"o":{"docs":{},"s":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}},"3":{"docs":{},".":{"docs":{},"b":{"docs":{},"i":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"5":{"docs":{},".":{"docs":{},"g":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"2":{"0":{"3":{"0":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{},"=":{"2":{"0":{"3":{"0":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}}},"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"3":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}},"4":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}},"5":{"docs":{},".":{"docs":{},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}},"7":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}},"8":{"docs":{},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"h":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}},"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"2":{"docs":{},".":{"1":{"0":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}},"1":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}},"docs":{}},"2":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}},"3":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}}}},"4":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}},"5":{"docs":{},".":{"docs":{},"c":{"docs":{},"r":{"docs":{},"y":{"docs":{},"p":{"docs":{},"t":{"docs":{},"o":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}},"6":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}},"7":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}},"8":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}},"9":{"docs":{},".":{"docs":{},"w":{"docs":{},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}},"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"docs":{}},"3":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0038043478260869567}},"]":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"1":{"docs":{},")":{"docs":{},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"9":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"9":{"9":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}},".":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"/":{"5":{"1":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"%":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"1":{"4":{"7":{"4":{"8":{"3":{"6":{"4":{"7":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},".":{"4":{"6":{"docs":{},"\\":{"docs":{},"%":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}},"7":{"docs":{},"\\":{"docs":{},"%":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}},"docs":{}},"docs":{}},"s":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0034420289855072463}},")":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}},"+":{"docs":{},"d":{"docs":{},"+":{"docs":{},"e":{"docs":{},">":{"3":{"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"q":{"3":{"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}}}}}}}}},"n":{"docs":{},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"3":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"4":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"5":{"0":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"5":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}},")":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"6":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0030797101449275364},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}},"t":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"%":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"6":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261}},".":{"7":{"1":{"2":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"docs":{}},"docs":{}},"docs":{}},"t":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}},"7":{"3":{"docs":{},".":{"3":{"0":{"8":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835}},".":{"5":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}}},"8":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0019927536231884057}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"9":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0019927536231884057}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},".":{"5":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"t":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.003639149588201494},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.011126564673157162},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.006092607636068237},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00821917808219178},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.010526315789473684},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.006008583690987125},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0045087356753710315},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.007243289305496378},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0032245062474808546},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.006109979633401222},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.006017418844022169},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.00650887573964497},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002452697967764541},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.005280259951259139},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0035694157430020664},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.003022974607013301},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703696609844858},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"d":{"docs":{},"o":{"docs":{},"w":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},".":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}},"docs":{}}}}}}}}},"]":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},",":{"0":{"docs":{},")":{"docs":{},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.003371868978805395},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0026845637583892616},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},".":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004934210526315789},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.005050505050505051},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"_":{"docs":{},"f":{"6":{"4":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509}},".":{"docs":{},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}},"docs":{}},"docs":{}}},"j":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"4":{"4":{"9":{"2":{"9":{"3":{"5":{"9":{"8":{"2":{"9":{"4":{"7":{"0":{"6":{"4":{"docs":{},"e":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"6":{"4":{"docs":{},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"docs":{}},"7":{"docs":{},"+":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"8":{"1":{"docs":{},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"docs":{}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"]":{"docs":{},")":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"(":{"3":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"docs":{}}}}}}}}}}}}},":":{"2":{"docs":{},"]":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0014365064163953266}},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"b":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"+":{"4":{"docs":{},"c":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"docs":{}}},"d":{"0":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}},"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255}},"u":{"docs":{},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}},"\"":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407}}},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852}}}},"]":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004210526315789474},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465}}},"^":{"2":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649}}},"docs":{}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}},"s":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"^":{"0":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"1":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"2":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"3":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"4":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"5":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"6":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"7":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"8":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"9":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"docs":{},"{":{"0":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},"1":{"0":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}}}},"2":{"6":{"docs":{},"}":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"docs":{}},"3":{"0":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},"docs":{}},"docs":{}},"2":{"5":{"5":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}},"3":{"docs":{},"}":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"(":{"docs":{},"j":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"n":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"v":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"*":{"docs":{},"*":{"3":{"2":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"docs":{}},"docs":{}},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"x":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"/":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}},"_":{"docs":{},"u":{"1":{"2":{"8":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"(":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"docs":{}},"docs":{}},"docs":{}}},"h":{"docs":{},"a":{"docs":{},"l":{"docs":{},"f":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}}},"i":{"docs":{},"m":{"docs":{},"*":{"docs":{},"p":{"docs":{},"i":{"docs":{},"*":{"docs":{},"n":{"docs":{},"*":{"docs":{},"k":{"docs":{},"/":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"/":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}}}}}}}}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"p":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"*":{"docs":{},"i":{"docs":{},"*":{"docs":{},"(":{"docs":{},"k":{"docs":{},"+":{"docs":{},"n":{"docs":{},"/":{"2":{"docs":{},")":{"docs":{},"/":{"docs":{},"n":{"docs":{},"=":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"docs":{}}}}}},"k":{"docs":{},"/":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}}}}}}}},"v":{"docs":{},"(":{"docs":{},"t":{"docs":{},")":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}},"x":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"(":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"\\":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"l":{"docs":{},"n":{"docs":{},"(":{"docs":{},"r":{"docs":{},"_":{"0":{"docs":{},")":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"docs":{},"u":{"docs":{},"_":{"1":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"{":{"docs":{},"r":{"docs":{},"_":{"0":{"docs":{},"}":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}},"docs":{}}}}}}}}}}}},"2":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"{":{"docs":{},"r":{"docs":{},"_":{"0":{"docs":{},"}":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}},"docs":{}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}},"{":{"docs":{},"r":{"docs":{},"_":{"0":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},"docs":{}}}}}}},"docs":{}}},"u":{"docs":{},")":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"_":{"1":{"docs":{},")":{"docs":{},"}":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"docs":{}}}}}}},"y":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"z":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"(":{"docs":{},"x":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"3":{"0":{"0":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261}}},"1":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002898550724637681}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0014492753623188406}}},"t":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"1":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0019927536231884057}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},".":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"}":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"2":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002873012832790653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"5":{"4":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"}":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"6":{"5":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},")":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},".":{"2":{"4":{"2":{"5":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"docs":{}},"docs":{}},"5":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"7":{"0":{"0":{"docs":{},"x":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"docs":{}},"docs":{}},"8":{"5":{"docs":{},".":{"8":{"1":{"9":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0014365064163953266},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.005681818181818182},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.006175771971496437},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004142011834319527},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703696609844858}}}},",":{"3":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002533650039588282},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"a":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"b":{"docs":{},"b":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"l":{"docs":{},"u":{"docs":{},"e":{"1":{"docs":{},"b":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"docs":{}}}}},"t":{"docs":{},"b":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"\"":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}},"+":{"1":{"2":{"7":{"docs":{},"=":{"1":{"3":{"0":{"docs":{},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"docs":{}},"2":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}},".":{"0":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003289473684210526}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004934210526315789},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004111842105263158}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946}}}},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"1":{"4":{"1":{"5":{"9":{"2":{"6":{"5":{"3":{"5":{"8":{"9":{"7":{"9":{"3":{"2":{"3":{"8":{"4":{"6":{"2":{"6":{"4":{"3":{"3":{"8":{"3":{"2":{"7":{"9":{"5":{"0":{"2":{"8":{"8":{"4":{"1":{"9":{"7":{"1":{"6":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"3":{"6":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"4":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"6":{"7":{"3":{"9":{"4":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"8":{"4":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"s":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"j":{"docs":{},"a":{"docs":{},"n":{"docs":{},"e":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"}":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}},"\\":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"x":{"3":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}},":":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"d":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"y":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"z":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"r":{"docs":{},"d":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"e":{"docs":{},"^":{"docs":{},"{":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},";":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"4":{"0":{"0":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004204625087596356}},"*":{"docs":{},"v":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"t":{"docs":{},"h":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"9":{"6":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},".":{"6":{"2":{"5":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{}},"docs":{}},"^":{"2":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"docs":{}}},"docs":{}},"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"2":{"0":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"8":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"9":{"0":{"7":{"7":{"2":{"9":{"9":{"2":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"4":{"9":{"6":{"7":{"2":{"9":{"5":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"3":{"3":{"docs":{},".":{"6":{"4":{"4":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"5":{"6":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"8":{"0":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},"3":{"docs":{},",":{"2":{"0":{"0":{"docs":{},".":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"9":{"9":{"docs":{},",":{"8":{"1":{"3":{"docs":{},".":{"2":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.004347826086956522},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.004908946951702296},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},".":{"0":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007773459189339256},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009468917249897077},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002843216896831844},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005627857896588111},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006944444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.010862186014935505},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01242603550295858},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"*":{"docs":{},"r":{"1":{"2":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"docs":{}},"8":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"docs":{},"a":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}},"d":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"\"":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},".":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"r":{"docs":{},"^":{"2":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"docs":{}}},",":{"0":{"0":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},"docs":{}},"docs":{}},"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"]":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"d":{"docs":{},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"\\":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}},"\\":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"u":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"y":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"z":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"t":{"docs":{},"h":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"(":{"docs":{},"x":{"docs":{},"+":{"4":{"docs":{},")":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{}}}},"docs":{}}}}},"5":{"0":{"0":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"x":{"5":{"0":{"0":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"docs":{}},"docs":{}},"docs":{}},",":{"0":{"0":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002803083391730904}},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"%":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"%":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"_":{"0":{"0":{"0":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},")":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"docs":{}},"docs":{}},"docs":{}}},"1":{"1":{"docs":{},"!":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"2":{"8":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"/":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"8":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"7":{"docs":{},"=":{"3":{"6":{"4":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}}}},"6":{"0":{"8":{"8":{"docs":{},".":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"docs":{}},"docs":{}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"8":{"docs":{},".":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"%":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},":":{"0":{"0":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"docs":{}},"docs":{}},".":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.009868421052631578},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"]":{"docs":{},"[":{"docs":{},"y":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}}}}}},"2":{"5":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"7":{"2":{"8":{"5":{"9":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"5":{"1":{"0":{"9":{"1":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}},"docs":{}},"docs":{}},"6":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"7":{"9":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},"docs":{}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},"]":{"docs":{},")":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"(":{"3":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"docs":{}}}}}}}}}}}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}},"^":{"2":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"docs":{}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"\"":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"x":{"5":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"docs":{}},",":{"2":{"docs":{},")":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.003371868978805395},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"+":{"1":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}},"]":{"docs":{},"[":{"docs":{},"y":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}},"d":{"0":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}},"docs":{}},"_":{"0":{"0":{"0":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{}},"docs":{}},"docs":{}},"\\":{"docs":{},"%":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"6":{"2":{"2":{"docs":{},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"docs":{}},"3":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"4":{"0":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.006542526421741319},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"*":{"8":{"1":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"docs":{}},"docs":{}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"5":{"5":{"3":{"5":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"docs":{}},"docs":{}},"7":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"9":{"1":{"docs":{},"b":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"docs":{}},"docs":{}}},"docs":{}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0018453279651065259}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224}}}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.004528985507246377},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002533650039588282},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"\"":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"1":{"5":{"docs":{},")":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"docs":{}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.009152215799614644},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.007046979865771812},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"0":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}},"[":{"docs":{},"z":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}}}}},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}},"1":{"2":{"3":{"2":{"3":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"2":{"8":{"3":{"1":{"8":{"5":{"3":{"0":{"7":{"1":{"8":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},":":{"9":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"docs":{}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},"[":{"docs":{},"z":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"}":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"7":{"1":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"5":{"4":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"7":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"9":{"1":{"docs":{},"b":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"docs":{}},"docs":{}}},"docs":{}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844}},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}}}}},"8":{"docs":{},".":{"5":{"4":{"docs":{},"\\":{"docs":{},"%":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},"docs":{}},"docs":{}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},".":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}},"docs":{}},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}},"+":{"1":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0019927536231884057}}}},"8":{"0":{"0":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}},"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},"1":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"9":{"1":{"docs":{},"b":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"docs":{}},"docs":{}}},"docs":{}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}}}}},"4":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0014614056064833267},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.02127659574468085},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00821917808219178},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002717391304347826},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002803083391730904}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002585711549511588},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703696609844858},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438}}},"=":{"docs":{},"[":{"5":{"docs":{},",":{"8":{"docs":{},"]":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"docs":{}}},"docs":{}}}},"*":{"docs":{},"r":{"1":{"3":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}},"docs":{}},"docs":{},"a":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"c":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"d":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886}}}},".":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"2":{"5":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},".":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"}":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"+":{"2":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}},"\\":{"docs":{},"\\":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.010638297872340425}}}},"c":{"docs":{},"m":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},",":{"0":{"0":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}}},"docs":{}},"docs":{}},"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589}}}},"9":{"1":{"7":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"6":{"1":{"docs":{},",":{"6":{"0":{"0":{"docs":{},".":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"7":{"0":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"8":{"5":{"6":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"9":{"9":{"docs":{},",":{"4":{"6":{"6":{"docs":{},".":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.005150214592274678},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.004335260115606936},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0026845637583892616}}},".":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"9":{"5":{"8":{"docs":{},".":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}}},"docs":{}},"docs":{}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},".":{"0":{"0":{"0":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"docs":{}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}},"1":{"2":{"5":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.005479452054794521}},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"docs":{}},"docs":{}},"docs":{}},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465}}},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"docs":{},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"'":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"`":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"t":{"docs":{},"h":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"docs":{},"(":{"0":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},".":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"4":{"docs":{},"%":{"docs":{},")":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"5":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}},"docs":{},".":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},".":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"_":{"docs":{},"b":{"docs":{},"y":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}},"(":{"docs":{},"(":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},".":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"|":{"docs":{},"_":{"docs":{},"|":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}},",":{"0":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},")":{"docs":{},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"1":{"0":{"0":{"docs":{},".":{"0":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"docs":{}}},"docs":{}},"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"3":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854}}},"5":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0019927536231884057}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"7":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"9":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507}},"a":{"docs":{},"+":{"docs":{},"m":{"docs":{},")":{"docs":{},"~":{"docs":{},"\\":{"docs":{},"%":{"docs":{},"~":{"3":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}}}}}}}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"0":{"docs":{},".":{"5":{"docs":{},")":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"docs":{}}},"docs":{}},"+":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},".":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}},"docs":{},".":{"docs":{},".":{"docs":{},"n":{"docs":{},")":{"docs":{},".":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}},"/":{"2":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"docs":{}}},"2":{"0":{"2":{"0":{"docs":{},".":{"docs":{},".":{"2":{"0":{"3":{"0":{"docs":{},")":{"docs":{},".":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"a":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}}},"docs":{}},"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"+":{"docs":{},"d":{"docs":{},")":{"docs":{},"~":{"docs":{},"\\":{"docs":{},"%":{"docs":{},"~":{"3":{"1":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"docs":{}}}}}}}}},"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"*":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{},"^":{"2":{"docs":{},")":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}},"docs":{}}}}}}},"p":{"docs":{},"i":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"d":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":3.333333333333333}}}},".":{"0":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"docs":{}},"b":{"docs":{},"+":{"4":{"docs":{},"c":{"docs":{},"+":{"6":{"docs":{},"d":{"docs":{},"+":{"docs":{},"n":{"docs":{},")":{"docs":{},"~":{"docs":{},"\\":{"docs":{},"%":{"docs":{},"~":{"7":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}}}}}}}}}},"docs":{}}}},"docs":{}}},"^":{"2":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{},"{":{"1":{"0":{"docs":{},"}":{"docs":{},")":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"docs":{}},"docs":{}}}},"3":{"2":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"4":{"0":{"0":{"0":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}},"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507}},"+":{"docs":{},"k":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"5":{"0":{"0":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{}},"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}},"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"7":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"9":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.010597302504816955},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.011073825503355705},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0036555645816409425},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0032245062474808546},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"f":{"6":{"4":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}},"docs":{}},"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0022984102662325224},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}}}}},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{},".":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"i":{"docs":{},"f":{"docs":{},"o":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}},"l":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"[":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},".":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"a":{"docs":{},"i":{"docs":{},"l":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}},"o":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}}},"e":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}},"*":{"docs":{},"g":{"docs":{},")":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"[":{"docs":{},"n":{"docs":{},"]":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}},"f":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}},")":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"w":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},"*":{"docs":{},")":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"y":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},"(":{"docs":{},"z":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"x":{"docs":{},"_":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"i":{"docs":{},"o":{"docs":{},"s":{"docs":{},"o":{"docs":{},"s":{"docs":{},")":{"docs":{},":":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}}}},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},"(":{"docs":{},"n":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}}}}}}}}}}}},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},"/":{"2":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"docs":{}}}}}}}}},"a":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}}}}}}},"a":{"docs":{},"f":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}},"v":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002058590657165479}},"'":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"*":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"i":{"docs":{},"f":{"docs":{},"o":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"s":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}},"k":{"docs":{},"e":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"t":{"docs":{},"t":{"docs":{},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"o":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0010534380386899062},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"docs":{}}},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},"f":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"m":{"docs":{},"b":{"docs":{},"d":{"docs":{},"a":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},"p":{"1":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},":":{"docs":{},"p":{"2":{"docs":{},":":{"docs":{},"p":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},"docs":{}}}},"2":{"docs":{},".":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"1":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"docs":{},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"1":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{}},":":{"docs":{},"p":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},"3":{"docs":{},".":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"1":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"docs":{},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"1":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{}}},"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"o":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.007669365146996165}},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},")":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"u":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"_":{"docs":{},"x":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.005780346820809248},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.005704697986577181},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0045726345409778405},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}},"o":{"docs":{},"n":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"l":{"docs":{},".":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"(":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}},")":{"docs":{},"o":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},".":{"docs":{},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},"w":{"docs":{},"(":{"1":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{},"(":{"1":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"l":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}}}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"d":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"b":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}},"a":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}}}},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},".":{"docs":{},"i":{"docs":{},"m":{"docs":{},"_":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}}}}}}}},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}},"t":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},".":{"docs":{},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"x":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}}},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"[":{"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"docs":{}},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"_":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}},"x":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"l":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"f":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}}}},"#":{"5":{"6":{"0":{"docs":{},")":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"docs":{}},"docs":{}},"docs":{}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.008387854386847844},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"n":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}}},"u":{"docs":{},"t":{"docs":{},"o":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}},"&":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004361684281160879},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}},"s":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{},"*":{"docs":{},"p":{"docs":{},"i":{"docs":{},")":{"docs":{},"*":{"docs":{},"*":{"docs":{},"t":{"docs":{},"h":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"h":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"d":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}}}}}}},"l":{"docs":{},"m":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}},"b":{"docs":{},"e":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"s":{"docs":{},"o":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"s":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"o":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},"u":{"docs":{},"m":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"p":{"docs":{},"p":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},".":{"docs":{},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"t":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"a":{"docs":{},"n":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}},"x":{"docs":{},"i":{"docs":{},"s":{"docs":{},"_":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}}}}},")":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"c":{"docs":{},"t":{"docs":{},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"o":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}},"[":{"docs":{},"(":{"docs":{},"i":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"i":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"]":{"docs":{},"[":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}}}}},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}}},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"]":{"docs":{},"[":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}}}}},"_":{"docs":{},"i":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}},"r":{"docs":{},"]":{"docs":{},"[":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}},"o":{"docs":{},"w":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}},"/":{"docs":{},"(":{"docs":{},"a":{"docs":{},"+":{"1":{"docs":{},")":{"docs":{},")":{"docs":{},"^":{"docs":{},"j":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"docs":{}}}}}},"o":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},"t":{"docs":{},"h":{"docs":{},"o":{"docs":{},"d":{"docs":{},"o":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"u":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},"e":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"l":{"docs":{},"d":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124}},"u":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}}}}}}}},"p":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"d":{"docs":{},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"?":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"f":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"w":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"i":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"(":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"!":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"i":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"f":{"docs":{},"c":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"c":{"1":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}},"(":{"docs":{},"$":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"s":{"docs":{},"[":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"g":{"docs":{},"h":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"n":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"e":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742}}}}},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"m":{"docs":{},"p":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"0":{"docs":{},".":{"0":{"docs":{},"_":{"docs":{},"f":{"6":{"4":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509}}}},"docs":{}},"docs":{}}}},"docs":{}}},"docs":{}}}}}}}}}},"a":{"docs":{},"r":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"u":{"docs":{},"t":{"docs":{},"u":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},"s":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"e":{"docs":{},"f":{"docs":{},"f":{"docs":{},"i":{"docs":{},"c":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}}}},"r":{"docs":{},"c":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"p":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}}},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}},"+":{"1":{"docs":{},")":{"docs":{},":":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}},"docs":{}}}},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364}}}}},"v":{"docs":{},"a":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}},"n":{"1":{"2":{"3":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"docs":{}},"docs":{}}},"a":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},")":{"docs":{},"i":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"?":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},"o":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}},"y":{"docs":{},"p":{"docs":{},"t":{"docs":{},"o":{"docs":{},"s":{"docs":{},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},")":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}}},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},")":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"j":{"docs":{},"u":{"docs":{},"r":{"docs":{},"e":{"docs":{},".":{"docs":{},"p":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"/":{"docs":{},"p":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"/":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},"[":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}}}}}}}}}}}}},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0030201342281879194}}},"x":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0030201342281879194}}}},"c":{"docs":{},"w":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},"[":{"docs":{},"m":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}},"i":{"docs":{},"p":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"/":{"docs":{},"*":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}}}}}},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}},"'":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}},"_":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}}}}}}}}},"i":{"6":{"4":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"docs":{}},"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"n":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002533650039588282}},"e":{"docs":{},"r":{"docs":{},"m":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"v":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},".":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"r":{"docs":{},"?":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"o":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},")":{"docs":{},"n":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001583531274742676}}}},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"f":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478}}}},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"t":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"b":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{},"s":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"e":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"x":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003355141754739138},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0026845637583892616},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754}},"s":{"docs":{},"s":{"docs":{},")":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"s":{"docs":{},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},"(":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"e":{"docs":{},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"m":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},".":{"0":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"docs":{},"e":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},".":{"docs":{},"a":{"docs":{},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},")":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"v":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}}}}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},"'":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"^":{"docs":{},"*":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}},"r":{"1":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114}}}},"2":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0014251781472684087}},"e":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}},"a":{"docs":{},"r":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},"d":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"e":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"d":{"docs":{},"u":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},")":{"docs":{},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}},"p":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"e":{"docs":{},"d":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"q":{"docs":{},"u":{"docs":{},"i":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}},"o":{"docs":{},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"+":{"1":{"docs":{},")":{"docs":{},":":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}},"docs":{}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"u":{"docs":{},"g":{"docs":{},"h":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00395882818685669}},"r":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"o":{"docs":{},"m":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542}},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"_":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}},"g":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}}}},"d":{"docs":{},"i":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}},"n":{"docs":{},"d":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}},"t":{"1":{"docs":{},":":{"docs":{},"t":{"2":{"docs":{},":":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"docs":{}}}},"2":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},"o":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"p":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873}},".":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"k":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},"r":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}},"i":{"docs":{},"l":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"h":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"s":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}},"e":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"r":{"docs":{},"e":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"u":{"docs":{},"g":{"docs":{},"h":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}}}}},"_":{"docs":{},"s":{"docs":{},"v":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"v":{"docs":{},"v":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"s":{"docs":{},"v":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"v":{"docs":{},"v":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}},"w":{"docs":{},"i":{"docs":{},"d":{"docs":{},"d":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"d":{"docs":{},"m":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"!":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"_":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},"&":{"docs":{},"q":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},"q":{"docs":{},")":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"_":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{},")":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"m":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}}},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"i":{"docs":{},"s":{"docs":{},"a":{"docs":{},"(":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},"$":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{},"(":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}},"g":{"docs":{},"i":{"docs":{},"r":{"docs":{},"l":{"docs":{},".":{"docs":{},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"f":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"i":{"docs":{},"s":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"(":{"docs":{},"o":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"$":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"o":{"docs":{},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408}}}}},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}},"h":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"e":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"1":{"docs":{},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"docs":{}}}}}}},"u":{"docs":{},"n":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"e":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742}}}}}}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"(":{"1":{"0":{"docs":{},",":{"1":{"0":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"docs":{}},"docs":{}}},"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"3":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"_":{"docs":{},"f":{"6":{"4":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"docs":{}}}},"2":{"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}},"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"b":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"x":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}},"n":{"docs":{},"d":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465}}}},"v":{"docs":{},"g":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},".":{"docs":{},"x":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},"e":{"docs":{},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}},"f":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"t":{"docs":{},"m":{"docs":{},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"docs":{}}}}}},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},">":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"x":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}},"$":{"1":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"docs":{}},"r":{"1":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0014251781472684087}}}},"docs":{},"e":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},"i":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"j":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"!":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}}}}}}},"/":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},":":{"docs":{},"+":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"^":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"(":{"docs":{},"x":{"docs":{},"+":{"docs":{},"m":{"docs":{},"u":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{},")":{"docs":{},"^":{"2":{"docs":{},")":{"docs":{},"/":{"docs":{},"(":{"2":{"docs":{},"*":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{},"^":{"2":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"docs":{}}}}}}}}},"docs":{}}}}},"docs":{}}}}},"docs":{}}}}}}},"y":{"docs":{},"+":{"docs":{},"m":{"docs":{},"u":{"docs":{},"[":{"2":{"docs":{},"]":{"docs":{},")":{"docs":{},"^":{"2":{"docs":{},")":{"docs":{},"/":{"docs":{},"(":{"2":{"docs":{},"*":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{},"^":{"2":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},"docs":{}}}}}}}}},"docs":{}}}}},"docs":{}}}}},"docs":{}}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},">":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},")":{"docs":{},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"s":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"n":{"docs":{},"(":{"docs":{},"$":{"1":{"docs":{},")":{"docs":{},")":{"docs":{},":":{"docs":{},"(":{"1":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"docs":{}}}}}},"docs":{}}}}},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},".":{"docs":{},"n":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},"o":{"docs":{},"y":{"docs":{},"f":{"docs":{},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},"t":{"docs":{},"h":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},".":{"docs":{},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.003691275167785235}}},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0030201342281879194}}}},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},")":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}},"e":{"docs":{},"c":{"docs":{},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003289473684210526}}}}},"u":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"d":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0036231884057971015}},"e":{"docs":{},"f":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"u":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0010534380386899062},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"v":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}},"i":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}}},"a":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"m":{"docs":{},"a":{"docs":{},"c":{"docs":{},"r":{"docs":{},"o":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}},"p":{"docs":{},"t":{"docs":{},"h":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"c":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"f":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"n":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0013407393219689715}},"s":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"i":{"docs":{},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},"l":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}},"a":{"docs":{},"g":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"v":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"f":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}}},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"e":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}},")":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}},"e":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"^":{"2":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"docs":{}}},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}},"e":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}},"n":{"docs":{},"s":{"docs":{},"[":{"docs":{},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"]":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}}}}}},"n":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"v":{"docs":{},"i":{"docs":{},"s":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004026170105686965}},"_":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}},"*":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}},"*":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"v":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"?":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"o":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"x":{"docs":{},"p":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"c":{"docs":{},"l":{"docs":{},"u":{"docs":{},"d":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"s":{"docs":{},"p":{"docs":{},"e":{"docs":{},"c":{"docs":{},"i":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"m":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"a":{"docs":{},"k":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}},"t":{"1":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}},"docs":{}}}}}}}}},"docs":{},"h":{"docs":{},".":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}},"(":{"docs":{},"a":{"docs":{},"v":{"docs":{},"g":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"(":{"1":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}},"/":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},".":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}}}},"[":{"docs":{},"c":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"c":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}}}}},"v":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"y":{"docs":{},"b":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"x":{"docs":{},"i":{"docs":{},"m":{"docs":{},"u":{"docs":{},"m":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"o":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0014492753623188406}},"u":{"docs":{},"l":{"docs":{},"o":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"r":{"docs":{},"e":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"t":{"docs":{},"h":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},"_":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},".":{"docs":{},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"m":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},"i":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"i":{"docs":{},"d":{"docs":{},"d":{"docs":{},"l":{"docs":{},"e":{"docs":{},")":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0026300958106331017},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},"o":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"d":{"docs":{},"e":{"2":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.005362957287875886},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551}}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}},"i":{"docs":{},"s":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"m":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"_":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}},"e":{"docs":{},"g":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"?":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}},"w":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}}},"_":{"docs":{},"x":{"docs":{},"[":{"docs":{},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"x":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},")":{"docs":{},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"p":{"docs":{},".":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"n":{"docs":{},"p":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"n":{"docs":{},"p":{"docs":{},".":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}},"p":{"docs":{},"i":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"n":{"docs":{},"p":{"docs":{},".":{"docs":{},"p":{"docs":{},"i":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}}}}}}}}},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"(":{"docs":{},"v":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}}}}},"q":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}},"_":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},"q":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}},"o":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"s":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}}}}}}}},"h":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"_":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0028214429665457475},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},")":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},"m":{"docs":{},"i":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}},"_":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}},"n":{"docs":{},"d":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"d":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"a":{"docs":{},"w":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"u":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"3":{"2":{"docs":{},"_":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}},"docs":{}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"_":{"docs":{},"t":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437}}}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"e":{"docs":{},"p":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"o":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"r":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}}}}}},"p":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}},":":{"docs":{},"p":{"1":{"docs":{},":":{"docs":{},"p":{"2":{"docs":{},":":{"docs":{},"p":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},"docs":{}}}},"docs":{}},"s":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465}}}}}},"u":{"docs":{},"m":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"c":{"docs":{},"h":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"v":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004934210526315789},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"e":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"v":{"1":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"a":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0031323414252153485},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"u":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"e":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"=":{"2":{"docs":{},")":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"docs":{}}},"%":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"*":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004193927193423922},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002272404487998864},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"c":{"docs":{},"b":{"docs":{},")":{"docs":{},"[":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}},"d":{"docs":{},"s":{"docs":{},"t":{"docs":{},")":{"docs":{},"[":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},")":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"'":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"=":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"_":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"g":{"docs":{},"c":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"e":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}},"i":{"docs":{},"r":{"docs":{},"l":{"docs":{},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"(":{"docs":{},"g":{"docs":{},"u":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}},"f":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},"[":{"docs":{},"x":{"docs":{},"]":{"docs":{},"[":{"docs":{},"y":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}}}}},"j":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}},"s":{"docs":{},"p":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}},"u":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"u":{"docs":{},"b":{"docs":{},"s":{"docs":{},"a":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}},"n":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"p":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}},"_":{"1":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"docs":{}},"s":{"docs":{},"e":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0036231884057971015}}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}},"x":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"y":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"a":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"b":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"c":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"*":{"docs":{},"x":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},":":{"docs":{},"y":{"docs":{},":":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}},"x":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}},"'":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0019883539269990058}}}},"o":{"docs":{},"l":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}},".":{"0":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}},"x":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"_":{"docs":{},"i":{"docs":{},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"^":{"2":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"docs":{}}},"z":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"e":{"docs":{},"r":{"docs":{},"o":{"docs":{},"?":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"i":{"docs":{},"p":{"4":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"_":{"1":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"docs":{}}},"~":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"'":{"docs":{},"_":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}},"i":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}},"o":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}},"t":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}},"y":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}},"#":{"docs":{},"f":{"docs":{},"f":{"0":{"0":{"0":{"0":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}}}},"+":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},";":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"(":{"docs":{},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}},"t":{"docs":{},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"l":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}}},"r":{"docs":{},"e":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"u":{"docs":{},"s":{"docs":{},"b":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"l":{"docs":{},"l":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}},"e":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}},"o":{"docs":{},"p":{"docs":{},"e":{"docs":{},"f":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"w":{"docs":{},"o":{"docs":{},"r":{"docs":{},"k":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}},")":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},"y":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}},"e":{"docs":{},"p":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},".":{"docs":{},".":{"docs":{},"a":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"s":{"docs":{},")":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"v":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}}}}}},"_":{"docs":{},"i":{"docs":{},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"{":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"\\":{"docs":{},"(":{"docs":{},"w":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"p":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"c":{"docs":{},"o":{"docs":{},"s":{"docs":{},"(":{"2":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"x":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}},"n":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"_":{"0":{"docs":{},")":{"docs":{},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"docs":{}}}}},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},":":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"i":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"/":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},"=":{"docs":{},"p":{"0":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{}}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"y":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}},"b":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"c":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"*":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"a":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}},"t":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"[":{"0":{"docs":{},".":{"5":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"docs":{}}},"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"]":{"docs":{},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"i":{"docs":{},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"o":{"docs":{},"w":{"docs":{},"(":{"docs":{},"$":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}}}}}}}}}},"\"":{"0":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{},"b":{"docs":{},"o":{"docs":{},"t":{"docs":{},"t":{"docs":{},"o":{"docs":{},"m":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}},".":{"docs":{},"*":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"+":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"^":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"|":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{},"|":{"docs":{},"^":{"2":{"docs":{},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"docs":{}}}}}}}}}}}},"/":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.005280259951259139},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.00631578947368421},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.00944206008583691},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.009768927296637234},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.013569078947368422},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.012696493349455865},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.005431093007467753},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.003260869565217391},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.004433887569279493},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004905395935529082},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891}},"*":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.005614035087719298},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"*":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.009824561403508772},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}},"/":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0077192982456140355},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0021068760773798123},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.005871498070793491},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.005048492095124219},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.009005481597494126},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.005780346820809248},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.007046979865771812},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003886729594669628},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002843216896831844},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.005448055607739997},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.007386563489271896},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0025564550489987218},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0018137847642079807},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.01127348643006263},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.013768115942028985},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.009026128266033254},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.01296426068675543}},"s":{"docs":{},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},".":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"l":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"u":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}}}}}}}}},"h":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},".":{"docs":{},"d":{"docs":{},"f":{"docs":{},"s":{"docs":{},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"i":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"_":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}},"a":{"docs":{},"l":{"docs":{},"w":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"d":{"docs":{},"d":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"/":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}},"=":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003289473684210526},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"a":{"docs":{},"d":{"docs":{"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.03389830508474576},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}},"v":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"t":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"e":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"i":{"docs":{},"c":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"d":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.020833333333333332},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.017391304347826087},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0021068760773798123},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0025242460475621096},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.005479452054794521},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.005448055607739997},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002717391304347826},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"(":{"docs":{},"$":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}},"l":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"p":{"docs":{},"a":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}}}}}}}},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"s":{"docs":{},"d":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0025564550489987218}}}}},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"m":{"docs":{},"i":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"d":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},":":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},")":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"~":{"docs":{},"%":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"a":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"j":{"docs":{},"u":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{"./":{"ref":"./","tf":5.045918367346939},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.007707129094412331},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.028169014084507043},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.03389830508474576},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.02608695652173913},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":5.013085052843483},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.02702702702702703},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0234375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.011029411764705883},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.008350730688935281},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.00699876492383697},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0020665038512117226},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.030844155844155844},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":5.002055921052632},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0038043478260869567},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":3.3347348750291985},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.01129305477131564}},";":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"s":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},",":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},":":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"?":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"!":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"d":{"docs":{},"\"":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},";":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364}}},"(":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},".":{"docs":{},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"!":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"u":{"docs":{},"d":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"o":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0047522063815342835},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.013609467455621301},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"!":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"c":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371}},"e":{"docs":{},"'":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},"a":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"s":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"p":{"docs":{},"h":{"docs":{},"a":{"docs":{},"b":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"s":{"docs":{},":":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"y":{"docs":{},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}}}}},"w":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"s":{"docs":{},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},")":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"t":{"docs":{},"o":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"!":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}},"n":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"h":{"docs":{},"o":{"docs":{},"u":{"docs":{},"g":{"docs":{},"h":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}},".":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"s":{"docs":{},"o":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"m":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}},"g":{"docs":{},"u":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"o":{"docs":{},"u":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}},"a":{"docs":{},"z":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"r":{"docs":{},"a":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}}}}}},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}}}},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"y":{"docs":{},"t":{"docs":{},"h":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"o":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},"w":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"?":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"m":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},".":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"e":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"m":{"docs":{},"a":{"docs":{},"l":{"docs":{},"y":{"docs":{},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"c":{"docs":{},"i":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"i":{"docs":{},"m":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"s":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}}},"s":{"docs":{},"w":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"_":{"docs":{},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}},"[":{"1":{"docs":{},":":{"3":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"docs":{}}},"docs":{}}}}}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"(":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"g":{"docs":{},"l":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.004335260115606936},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.005704697986577181},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},"e":{"docs":{},"(":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},".":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"u":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"a":{"docs":{},"l":{"docs":{},"y":{"docs":{},"z":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"t":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"i":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"o":{"docs":{},"g":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"u":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"y":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"a":{"docs":{},"g":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"r":{"docs":{},"c":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"a":{"docs":{},"n":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"h":{"docs":{},"i":{"docs":{},"v":{"docs":{"./":{"ref":"./","tf":5.01530612244898},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.016901408450704224},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"o":{"docs":{},"r":{"docs":{},"g":{"docs":{},"/":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}},"!":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},":":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409}}},",":{"docs":{"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"s":{"docs":{},"/":{"docs":{},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"\"":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}}},"x":{"docs":{},"i":{"docs":{},"v":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},".":{"docs":{},"o":{"docs":{},"r":{"docs":{},"g":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904}}}}}}}}},"g":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"(":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},".":{"docs":{},"(":{"docs":{},"a":{"docs":{},"[":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},":":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},",":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"a":{"docs":{},"y":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002585711549511588},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004997223764575236},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.007653061224489796},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00958106331016344},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.010551948051948052},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"<":{"docs":{},">":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}}}},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},".":{"docs":{},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"l":{"docs":{},"(":{"docs":{},"n":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}}}}}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{},"{":{"docs":{},"|":{"docs":{},"i":{"docs":{},"|":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},"$":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}},"s":{"docs":{},"h":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"$":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"[":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"]":{"docs":{},")":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"i":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"]":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"j":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"s":{"docs":{},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"m":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"x":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}}}}}}}}}}}},"?":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"n":{"docs":{},"g":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"[":{"docs":{},"#":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}},"e":{"docs":{},"a":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002843216896831844},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}},".":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"s":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"\"":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},".":{"docs":{},".":{"docs":{},".":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"i":{"docs":{},"c":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"s":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"s":{"docs":{},"!":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},".":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}},"i":{"docs":{},"c":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"l":{"docs":{},"i":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"y":{"docs":{},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}},"s":{"docs":{},"s":{"docs":{},"o":{"docs":{},"c":{"docs":{},"i":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}}}}}}}}}}},"s":{"docs":{},"s":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"u":{"docs":{},"m":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703696609844858},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"p":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}}},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.018691588785046728},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"k":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},",":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"m":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}},"c":{"docs":{},"i":{"docs":{},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{},"e":{"docs":{},"r":{"docs":{},"c":{"docs":{},"a":{"docs":{},"s":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"e":{"docs":{},"[":{"docs":{},":":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"]":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"c":{"docs":{},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"[":{"docs":{},":":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"]":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"r":{"docs":{},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},"p":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"=":{"docs":{},"\"":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}},"y":{"docs":{},"m":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405}},"i":{"docs":{},"c":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}},"i":{"docs":{},"d":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"t":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"r":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"n":{"docs":{},"o":{"docs":{},"m":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"t":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"b":{"docs":{},"u":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.02040816326530612},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007773459189339256},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009057225195553726},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005627857896588111},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006944444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.010862186014935505},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01242603550295858},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}}}}},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"w":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"o":{"docs":{},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0029227557411273487}},"s":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"a":{"docs":{},"n":{"2":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"(":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"p":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"docs":{}}}}}}},"y":{"1":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"docs":{},",":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}},"(":{"docs":{},"z":{"docs":{},"e":{"docs":{},"r":{"docs":{},"o":{"docs":{},"s":{"docs":{},"(":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}}},"o":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0018137847642079807}},"s":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"v":{"docs":{},"a":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.007707129094412331},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},".":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}}}}},"o":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"e":{"docs":{},"!":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}},"g":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141}},"i":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"o":{"docs":{},"v":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002533650039588282},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"?":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"g":{"docs":{},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}},"u":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},":":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"s":{"2":{"docs":{},".":{"docs":{},"(":{"docs":{},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}},"docs":{},"(":{"docs":{},"$":{"docs":{},"a":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}},"b":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0020130850528434826}}}},":":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"b":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}},"b":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0020130850528434826}}}}},"i":{"docs":{},"n":{"1":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"2":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"docs":{}}},"p":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"i":{"docs":{},"_":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"_":{"docs":{},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{},"*":{"docs":{},"p":{"docs":{},"i":{"docs":{},")":{"docs":{},")":{"docs":{},"*":{"docs":{},"*":{"docs":{},"t":{"docs":{},"h":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"h":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}}},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}},"z":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001509813789632612}}},"c":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"c":{"docs":{},"c":{"docs":{},"c":{"docs":{},"d":{"docs":{},"d":{"docs":{},"d":{"docs":{},"d":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"v":{"docs":{},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"y":{"docs":{},"s":{"docs":{},"m":{"docs":{},"a":{"docs":{},"l":{"docs":{},"!":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"r":{"docs":{},"u":{"docs":{},"p":{"docs":{},"t":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}},"g":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},"n":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},".":{"docs":{},"\"":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}},"o":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},".":{"docs":{},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},":":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}}}},"h":{"docs":{},"e":{"docs":{},"m":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"a":{"docs":{},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},"i":{"docs":{},"x":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"(":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"[":{"docs":{},":":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"*":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}}}}}}}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}},"a":{"docs":{},"l":{"docs":{},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"s":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"r":{"docs":{},"o":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001915341888527102},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}},"x":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"i":{"docs":{},"m":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.020242914979757085},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":3.347699135715954},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},")":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"e":{"docs":{},".":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"(":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}}}}}},"(":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"z":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"l":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"c":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"q":{"docs":{},"u":{"docs":{},"é":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"6":{"docs":{},".":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"h":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}},"docs":{}}}}}}}},"y":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"i":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409}},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"r":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002898550724637681}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"}":{"docs":{},"&":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"u":{"docs":{},"t":{"docs":{},"h":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"o":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002258535937292414},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.011862396204033215},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.004592901878914405},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904}}}}},"&":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}},"d":{"docs":{},"i":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"e":{"docs":{},"'":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"x":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"g":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}}}}}}}},"w":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"a":{"docs":{},"y":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"f":{"docs":{},"u":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"c":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.021729867916489135},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"e":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.005081874647092038}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}},"s":{"docs":{},"s":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"_":{"docs":{},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"m":{"docs":{},"g":{"docs":{},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"o":{"docs":{},"n":{"docs":{},"!":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"r":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"u":{"docs":{},"r":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"c":{"docs":{},"i":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}},"m":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},"u":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}},"*":{"docs":{},"d":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}},"*":{"docs":{},"d":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0097997443544951}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0031245561709984378}},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},"docs":{}},"docs":{}}}}}}}},"r":{"docs":{},"u":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"s":{"docs":{},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"v":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002452697967764541},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}}},"h":{"docs":{},"i":{"docs":{},"e":{"docs":{},"v":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"k":{"docs":{},"n":{"docs":{},"o":{"docs":{},"w":{"docs":{},"l":{"docs":{},"e":{"docs":{},"d":{"docs":{},"g":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}}}},"a":{"docs":{},"d":{"docs":{},"e":{"docs":{},"m":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"m":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.006374769334004362},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.003371868978805395},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0021303792074989347},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"{":{"docs":{},"b":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551}}}}}},"%":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001509813789632612}},",":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0014614056064833267},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004905395935529082}},"(":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"n":{"docs":{},"e":{"docs":{},"g":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"?":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},")":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},";":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},".":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"c":{"docs":{},"m":{"docs":{},"p":{"docs":{},"(":{"docs":{},"&":{"docs":{},"p":{"docs":{},"o":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{},"_":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"w":{"docs":{},"f":{"docs":{},"(":{"docs":{},"v":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}},"^":{"2":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},"docs":{},"n":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"e":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}}}}}}}}},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"b":{"docs":{},".":{"docs":{},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"(":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}}}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"(":{"docs":{},"b":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"x":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.00436241610738255}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"*":{"docs":{},"(":{"docs":{},"c":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886}}}}},"y":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.006040268456375839}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"*":{"docs":{},"(":{"docs":{},"c":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}},"1":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},")":{"docs":{},")":{"docs":{},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"docs":{}}}}}}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"]":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005956552207428171}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.007045797684952189},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"=":{"1":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"3":{"0":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{},"$":{"docs":{},"(":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"=":{"docs":{},"b":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},">":{"1":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{},"b":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141}}}}}}}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}},"2":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}}},"*":{"docs":{},"i":{"docs":{},"+":{"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}}},"docs":{}},"]":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"3":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},"[":{"4":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"docs":{}}}},"docs":{},"(":{"docs":{},"i":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0014251781472684087}}}},"a":{"docs":{},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}}}},"k":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}}}},"i":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141}},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004111842105263158}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"[":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}}},"i":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}},"j":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"*":{"docs":{},"a":{"docs":{},"[":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},",":{"docs":{},"j":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}},"/":{"docs":{},"a":{"docs":{},"[":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},",":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}}}}}}}},"j":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"_":{"docs":{},"i":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}}}}}}}}},"p":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"[":{"docs":{},"c":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"_":{"docs":{},"i":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0023752969121140144}}}}}}}}}}}},"r":{"docs":{},"+":{"1":{"docs":{},":":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}},"docs":{}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001583531274742676}}},":":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"[":{"docs":{},"c":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"j":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"r":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"i":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"j":{"docs":{},"]":{"docs":{},"*":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}},"]":{"docs":{},"[":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}}}},"i":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}},"j":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}}}},"a":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"b":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"i":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"f":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"f":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"i":{"docs":{},"n":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.005010438413361169},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":5.0094674556213015}},"e":{"docs":{},";":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"@":{"docs":{},"(":{"docs":{},"x":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"e":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731}},"s":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},"_":{"0":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"1":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"2":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{},"{":{"docs":{},"n":{"docs":{},"}":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003700657894736842}}},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"x":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"_":{"docs":{},"x":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"k":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}},"y":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"k":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"m":{"docs":{},"s":{"docs":{},"h":{"docs":{},"o":{"docs":{},"w":{"docs":{},"(":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"_":{"docs":{},"t":{"docs":{},"i":{"docs":{},"t":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"$":{"docs":{},"f":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{},"=":{"docs":{},"z":{"docs":{},"^":{"2":{"docs":{},"$":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"docs":{}}}}}}}}}}}}}}}},"x":{"docs":{},"l":{"docs":{},"a":{"docs":{},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"$":{"docs":{},"r":{"docs":{},"e":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},"$":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}},"y":{"docs":{},"l":{"docs":{},"a":{"docs":{},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"$":{"docs":{},"i":{"docs":{},"m":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},"$":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}}}}}}}}},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"_":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814}},"^":{"2":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"docs":{}}}}}}}},"=":{"docs":{},"a":{"docs":{},"x":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},"'":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}},"_":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},"^":{"docs":{},"*":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"\\":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}},"docs":{}}},"(":{"docs":{},"t":{"docs":{},")":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}},"+":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}}}}}},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"_":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"}":{"docs":{},"_":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"}":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"l":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}},"*":{"docs":{},"(":{"docs":{},"(":{"1":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"+":{"1":{"docs":{},"/":{"docs":{},"a":{"docs":{},")":{"docs":{},"^":{"docs":{},"v":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"docs":{}}},"docs":{}}}},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"1":{"docs":{},"+":{"docs":{},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"1":{"docs":{},"}":{"docs":{},"{":{"docs":{},"a":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{},"^":{"docs":{},"v":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}},"docs":{}}}}}}}}},"docs":{}}}}}}}}}}}}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.05569535312866969},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.011101973684210526},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.004166666666666667},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"s":{"docs":{},"!":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742}}}}},"a":{"docs":{},"m":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004142011834319527},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"!":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"?":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},")":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"(":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}},"i":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"a":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"t":{"docs":{},"w":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0033944331296673455},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.00421179302045728},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.007415254237288136}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},":":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"!":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},":":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.020833333333333332},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},")":{"docs":{},"!":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"n":{"docs":{},"g":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"t":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"i":{"docs":{},"e":{"docs":{},"v":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"l":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"o":{"docs":{},"w":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"n":{"docs":{},"e":{"docs":{},"f":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125}}}}},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"c":{"docs":{},"h":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"k":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737}},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}},"t":{"docs":{},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}}}}}},"o":{"docs":{},"i":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},".":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"a":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"f":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}}},"s":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.005681818181818182},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"y":{"docs":{},"o":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"a":{"docs":{},"v":{"docs":{},"i":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"s":{"docs":{},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"e":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"o":{"docs":{},"l":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"w":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}},"d":{"docs":{},"a":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"e":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"./":{"ref":"./","tf":0.015306122448979591},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.009633911368015413},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"s":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.003371868978805395},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.008529650690495532},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0024183796856106408},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"e":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"t":{"docs":{},"h":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"!":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"t":{"docs":{},"o":{"docs":{},"m":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"\"":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"b":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.009394572025052192}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"'":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"x":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":3.3380855397148674}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"—":{"docs":{},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.008825526137135099}}}}}}},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.009994447529150472},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"y":{"docs":{},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"s":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"[":{"1":{"docs":{},",":{"1":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"/":{"docs":{},"d":{"docs":{},"x":{"docs":{},")":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}},"docs":{}}},"2":{"docs":{},",":{"1":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"/":{"docs":{},"d":{"docs":{},"x":{"docs":{},")":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}},"docs":{}}},"docs":{}}}},"c":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}},"y":{"docs":{},"f":{"docs":{},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394}}}}},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"g":{"docs":{},"g":{"docs":{},"l":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"d":{"docs":{},"i":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"y":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"s":{"docs":{},"e":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"i":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"c":{"docs":{},"a":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"l":{"docs":{},"t":{"docs":{},"z":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.003952569169960474}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}},"c":{"docs":{},"k":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003289473684210526},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"g":{"docs":{},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":5.008695652173913},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"s":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"q":{"docs":{},"u":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"_":{"docs":{},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"&":{"docs":{},"a":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"a":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"2":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"docs":{}}},"docs":{}},"docs":{}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}},"t":{"docs":{},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"a":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"[":{"docs":{},"]":{"docs":{},"[":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}}}}}}}}}}}}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.003523884103367267}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"s":{"docs":{},".":{"docs":{},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"g":{"docs":{},"i":{"docs":{},"r":{"docs":{},"l":{"docs":{},".":{"docs":{},"f":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"h":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"[":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},"_":{"docs":{},"s":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}}},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"c":{"docs":{},"c":{"docs":{},"d":{"docs":{},"b":{"docs":{},"a":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}}},"s":{"docs":{},"i":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"s":{"docs":{},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"h":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0024899444550852325},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.009058882737795673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002898550724637681},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.010861948142957253},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"(":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"s":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"g":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}},"n":{"docs":{},"k":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}},"r":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"s":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":5.005010438413361},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"_":{"docs":{},"h":{"docs":{},"u":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"b":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"a":{"docs":{},"b":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}}}}}}},"y":{"docs":{},"c":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},"e":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}}},"d":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"f":{"docs":{},"f":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"m":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"z":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"i":{"docs":{},"g":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},")":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"g":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000861903849837196},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.005579912315663611},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.013908205841446454},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":5.016438356164383},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0035502958579881655},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002803083391730904}},"s":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"_":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},"b":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0035870864886408927},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002452697967764541}},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},":":{"docs":{},":":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}},"_":{"docs":{},"b":{"docs":{},"u":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"e":{"docs":{},"r":{"docs":{},"*":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"?":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"s":{"docs":{},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}},"h":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.010958904109589041}}}}}},"?":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"m":{"docs":{},"a":{"docs":{},"s":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"?":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{},"i":{"docs":{},"c":{"docs":{},":":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"\"":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},".":{"docs":{},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"e":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"[":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}},"i":{"docs":{},"d":{"docs":{},"x":{"docs":{},"s":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},".":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"2":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"docs":{}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"a":{"docs":{},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"x":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044}}}}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{},"i":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125}}}}}}},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0037578288100208767},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.006512162420992147},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},"y":{"docs":{},"!":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"2":{"4":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"2":{"4":{"docs":{},";":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}},"_":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"_":{"docs":{},"i":{"docs":{},"d":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}}}},"w":{"docs":{},"i":{"docs":{},"d":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"/":{"2":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"docs":{}}}}}}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"[":{"1":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"2":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"docs":{}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"s":{"docs":{},"=":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"@":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"_":{"docs":{},"b":{"docs":{},"o":{"docs":{},"b":{"docs":{},"b":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"o":{"docs":{},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"h":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"(":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"a":{"docs":{},"s":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"r":{"docs":{},"t":{"docs":{},"h":{"docs":{},"d":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"l":{"docs":{},"l":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"s":{"docs":{},"f":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}}}}},"o":{"docs":{},"g":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"c":{"docs":{},"k":{"docs":{"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"w":{"docs":{},"f":{"docs":{},"i":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}},"u":{"docs":{},"r":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339}},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"\"":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"n":{"docs":{},"t":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}}}},"e":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},")":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"n":{"docs":{},"k":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}},"e":{"docs":{},"t":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}},"e":{"docs":{},"r":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004441976679622432},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.005010438413361169},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.011834319526627219},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}},"a":{"docs":{},"d":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"e":{"docs":{},"r":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"g":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"u":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"a":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0025242460475621096},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"1":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"}":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}},"k":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0010534380386899062},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124}}}}},"k":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002873012832790653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0030201342281879194}}}},"t":{"docs":{},"h":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"v":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"e":{"docs":{},"f":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}},"l":{"docs":{},"i":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"l":{"docs":{},"l":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{},"!":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"?":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"u":{"docs":{},"l":{"docs":{},"k":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013285505513484788},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"(":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}}}}}},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},"e":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"c":{"docs":{},"k":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}}},"s":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"f":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"y":{"docs":{},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"z":{"docs":{},"[":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},":":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"o":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.021976178493541353},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0024084778420038534},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"(":{"docs":{},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001677570877369569},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"(":{"docs":{},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},"{":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703696609844858}},"s":{"docs":{},"(":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},":":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"~":{"docs":{},"%":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"_":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"(":{"docs":{},"&":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"_":{"docs":{},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000861903849837196}}}}}},"y":{"docs":{},"t":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0027899561578318055}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"p":{"docs":{},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0025163563160543532},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.009046052631578948},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"e":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}}}}}}}}}},"z":{"docs":{},"e":{"docs":{},"r":{"docs":{},"o":{"docs":{},"?":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"x":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"y":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004193927193423922},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"docs":{}},"docs":{}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}},"u":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"docs":{}},"docs":{}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.007045797684952189},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"=":{"0":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{},"$":{"docs":{},"(":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"b":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}},"b":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"c":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"x":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.006578947368421052}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004111842105263158}}}}},"1":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}},"2":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946}}}}},"3":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}},"docs":{},"i":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"@":{"docs":{},"(":{"docs":{},"x":{"docs":{},"b":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"|":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"!":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"_":{"0":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"1":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"'":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"=":{"1":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}}}},"^":{"docs":{},"*":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"\\":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}},"docs":{}}}},"c":{"1":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}}}},"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.009735744089012517},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.013980263157894737},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.003985507246376811},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00395882818685669}},"h":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.004528612597776863},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},",":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},"'":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"p":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.011267605633802818},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0026690391459074734},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.01020408163265306},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0024621878297572987},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},":":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0026571011026969575},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"*":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"c":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"*":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002258535937292414}},"*":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0025242460475621096},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.013908205841446454},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731}},"e":{"docs":{},"r":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936}}},"s":{"docs":{},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},":":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"s":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"u":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731}}}},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"g":{"docs":{},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"o":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00809004572634541},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}},"s":{"docs":{},"_":{"docs":{},"g":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"(":{"1":{"0":{"0":{"0":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}}}},"docs":{}},"docs":{}},"docs":{},"_":{"0":{"0":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}},"n":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}},":":{"docs":{},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{}}}}}}}}}}}}},"g":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"e":{"docs":{},"(":{"1":{"0":{"0":{"0":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{},"$":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"i":{"docs":{},"p":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"l":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0074698333652556985},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.009864010725914576},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0045726345409778405}},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001915341888527102}},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"}":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}},"|":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"|":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"_":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}}}}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}},"}":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703696609844858}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}},"n":{"docs":{},"m":{"docs":{},"a":{"docs":{},"y":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0031323414252153485},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"e":{"docs":{},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"s":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},"[":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"+":{"docs":{},"+":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}}},"(":{"docs":{},"h":{"docs":{},"u":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},"_":{"docs":{},"o":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}}},"(":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"o":{"docs":{},"s":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0029227557411273487},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925}},"e":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"s":{"docs":{},"e":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"n":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"t":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"r":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"e":{"docs":{},"c":{"docs":{},"k":{"1":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"2":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0012449722275426163},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0018453279651065259},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0036555645816409425},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},".":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"a":{"docs":{},"t":{"docs":{},"s":{"docs":{},"h":{"docs":{},"e":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"m":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125}}}}}}}}}},"k":{"1":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"2":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"docs":{}},"u":{"docs":{},"n":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"s":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304}},"'":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"r":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"h":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{"./":{"ref":"./","tf":0.015306122448979591},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.009633911368015413},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.030985915492957747},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":5.010416666666667},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.03389830508474576},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.017391304347826087},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.023809523809523808},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.018018018018018018},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.018691588785046728},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.004251361764315132},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.011029411764705883},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004151838671411625},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.006954102920723227},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.007653061224489796},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.005479452054794521},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0068669527896995704},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.006493506493506494},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0028139289482940555},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0018137847642079807},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0047522063815342835},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.003952569169960474}},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.011267605633802818},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"/":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},"b":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.004915637039989372}},"'":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013285505513484788}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873}}}},"*":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"y":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"s":{"docs":{},"y":{"docs":{},"m":{"docs":{},"b":{"docs":{},"o":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"/":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873}},":":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},":":{"docs":{},":":{"docs":{},"~":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"[":{"0":{"docs":{},"]":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"docs":{}}}},"docs":{},"c":{"docs":{},"]":{"docs":{},")":{"docs":{},".":{"docs":{},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"i":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"n":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"]":{"docs":{},"=":{"docs":{},"\"":{"0":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"docs":{}}}}}}}}}},"]":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"_":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"p":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"!":{"docs":{},"(":{"docs":{},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},":":{"docs":{},":":{"docs":{},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},":":{"docs":{},":":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"n":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"e":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},".":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"1":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"docs":{}}}}}}}},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},"e":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}},"+":{"docs":{},"'":{"0":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"1":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"docs":{}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},":":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}},"=":{"docs":{},"'":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"s":{"docs":{},"(":{"docs":{},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"s":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},".":{"docs":{},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"[":{"2":{"5":{"6":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"docs":{}},"docs":{}},"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"w":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.011126564673157162}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"s":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}}}}}}},"!":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.016310372129849565}},"l":{"docs":{},"a":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{"./":{"ref":"./","tf":0.01020408163265306}}}}},"p":{"docs":{},"s":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"(":{"2":{"0":{"2":{"0":{"docs":{},":":{"2":{"0":{"3":{"0":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}}}},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},".":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}},"o":{"docs":{},"q":{"docs":{},"u":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"u":{"docs":{},"m":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.005067300079176564},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"s":{"docs":{},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},")":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},"o":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0050415183867141165},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.005351996706463565},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":5.015151515151516},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"(":{"docs":{},"f":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}}}}},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},":":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"s":{"docs":{},"s":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},")":{"docs":{},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0028503562945368173}},")":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"s":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"m":{"docs":{},"m":{"docs":{},"o":{"docs":{},"n":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703696609844858},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.012145748987854251},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.009439200444197668},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009468917249897077},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.005150214592274678},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005627857896588111},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006944444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.011541072640868975},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01301775147928994},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"l":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"u":{"docs":{},"n":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.011560693641618497},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},".":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"s":{"docs":{},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}},"a":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"n":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0037052284890901604}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557}}},"s":{"docs":{},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"e":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"d":{"docs":{},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"n":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"x":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":5.016233766233766},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0032245062474808546},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.015782828282828284},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0048134777376654635}},"(":{"0":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}}}},"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},".":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"1":{"docs":{},".":{"0":{"docs":{},"_":{"docs":{},"f":{"6":{"4":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}},"docs":{}}}},"docs":{}}},"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"k":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}}}}},"i":{"docs":{},"c":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},")":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"r":{"docs":{},"e":{"docs":{},"h":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}},"s":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":5.016689847009736},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"!":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"u":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.01348747591522158},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":5.0476190476190474},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":5.096045197740113},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.03676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.005479452054794521},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.00487012987012987},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.006618531889290012},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},"?":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"\"":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"?":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"_":{"docs":{},"s":{"docs":{},"o":{"docs":{},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"s":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"u":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":10.001268115942029}},"s":{"docs":{},"(":{"docs":{},"[":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"]":{"docs":{},"$":{"docs":{},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}},"y":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},".":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"a":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"t":{"docs":{},"o":{"docs":{},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"i":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"o":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339}},"i":{"docs":{},"t":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}},"n":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.007100591715976331}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"i":{"docs":{},"l":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}}}},"e":{"docs":{},"l":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.020833333333333332}}}}}},"e":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"i":{"docs":{},"s":{"docs":{},"d":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478}}}}}},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"d":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"x":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"l":{"docs":{},"i":{"docs":{},"b":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}},"?":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"r":{"docs":{},"i":{"docs":{},"b":{"docs":{},"u":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":10.011267605633803},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},"e":{"docs":{},",":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},".":{"docs":{},"m":{"docs":{},"d":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},":":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}}}}}}}},"o":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},".":{"docs":{},"m":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"d":{"docs":{},".":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"k":{"docs":{},",":{"docs":{},"v":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}}}}}}}}}}},"s":{"docs":{},"?":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"c":{"docs":{},"t":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"i":{"docs":{},"n":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"u":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0023752969121140144},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"e":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114}}},"s":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"s":{"docs":{},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}}}}},"c":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"s":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}},"p":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"a":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}},"(":{"docs":{},"&":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"*":{"docs":{},"*":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"*":{"docs":{},"*":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"v":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}}},"l":{"docs":{},"u":{"docs":{},"s":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"d":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"g":{"docs":{},"l":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}}},"s":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},":":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},"s":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"m":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"e":{"docs":{},"(":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},"o":{"docs":{},"l":{"docs":{},"e":{"docs":{},".":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{},"(":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},".":{"docs":{},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}}}}},"\"":{"docs":{},"[":{"0":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"1":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"2":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}},"\\":{"docs":{},"n":{"docs":{},"g":{"docs":{},"i":{"docs":{},"r":{"docs":{},"l":{"docs":{},"s":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"s":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"g":{"docs":{},"u":{"docs":{},"y":{"docs":{},"s":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"t":{"docs":{},"h":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"c":{"docs":{},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"h":{"docs":{},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}}}}}}}}}},"'":{"docs":{},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}}},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"(":{"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"(":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"docs":{}}}}}}}}}},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},".":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"`":{"docs":{},"$":{"docs":{},"{":{"docs":{},"g":{"docs":{},"i":{"docs":{},"r":{"docs":{},"l":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"u":{"docs":{},"y":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},"`":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"}":{"docs":{},"`":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},"`":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},"`":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"}":{"docs":{},"`":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}}}}}}}},"(":{"docs":{},"$":{"docs":{},"{":{"docs":{},"p":{"docs":{},".":{"docs":{},"x":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}}}}}}},"w":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},".":{"docs":{},"p":{"docs":{},"e":{"docs":{},"e":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},".":{"docs":{},"p":{"docs":{},"e":{"docs":{},"e":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}},"g":{"docs":{},"a":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"c":{"docs":{},"k":{"2":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"l":{"docs":{},"n":{"docs":{},"(":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.005614035087719298},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.005048492095124219},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.003915426781519186},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.010972716488730723},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0030201342281879194},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.005345394736842105},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00395882818685669},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"&":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0010534380386899062},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011956954962136308},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0029655990510083037},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}},"o":{"docs":{},"r":{"docs":{},"(":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}},"*":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.00974025974025974},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815}},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"l":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"(":{"docs":{},"a":{"docs":{},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}}},"docs":{}},"docs":{}}}}}}}}}}}},"u":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"docs":{}},"docs":{}}}}}}}}},"s":{"docs":{},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}},"c":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"v":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"x":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.036036036036036036},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"l":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"p":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"docs":{}}}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"r":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{},"c":{"docs":{},"e":{"docs":{},"i":{"docs":{},"l":{"docs":{},"(":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"2":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"x":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}},"s":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"g":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}}},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":10.053333333333333},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":5.0210993892282065},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":5.00709219858156},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":5.028061224489796},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":3.3436337625178822}},"i":{"docs":{},"o":{"docs":{},"n":{"1":{"docs":{},"d":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}},"docs":{},"s":{"docs":{},",":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},".":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}},"?":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}},":":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}},"!":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003886729594669628},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003886729594669628},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653}}},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"e":{"docs":{},"d":{"docs":{},"!":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}}}},"v":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003886729594669628},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339}},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"y":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0068669527896995704}}},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}}}}}},"x":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216}}}}}}}}}}},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"1":{"docs":{},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"t":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653}}}}}}}}}}}}}},"docs":{}}}}}}},"x":{"docs":{},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}}}}},"c":{"docs":{},"y":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"(":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"[":{"docs":{},"]":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"(":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"[":{"docs":{},"]":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}}}},"x":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"n":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"f":{"docs":{},"u":{"docs":{},"s":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"i":{"docs":{},"g":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}},"n":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"d":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"s":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"o":{"docs":{},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"j":{"docs":{},"(":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},"_":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},"u":{"docs":{},"g":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001583531274742676},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"o":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"e":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"y":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0033815517565282736},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"_":{"docs":{},"t":{"docs":{},"u":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},"(":{"docs":{},"&":{"docs":{},"x":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},".":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"s":{"docs":{},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{},"(":{"1":{"docs":{},")":{"docs":{},".":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"_":{"docs":{},"b":{"docs":{},"y":{"docs":{},"(":{"2":{"docs":{},")":{"docs":{},".":{"docs":{},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},":":{"docs":{},":":{"docs":{},">":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},")":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"x":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},".":{"docs":{},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"(":{"docs":{},"_":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}}}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"[":{"1":{"docs":{},":":{"2":{"docs":{},":":{"docs":{},"n":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"docs":{}}},"2":{"docs":{},":":{"2":{"docs":{},":":{"docs":{},"n":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"docs":{}}},"docs":{}}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"_":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},"e":{"docs":{},"d":{"docs":{},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"d":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"i":{"docs":{},"n":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"[":{"0":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"1":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"2":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"docs":{}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"s":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.008421052631578947},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0017271157167530224},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.004467912266450041},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":3.3729268862415323},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0026845637583892616},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.006657323055360897}},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"_":{"docs":{},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"k":{"docs":{},"w":{"docs":{},"i":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"1":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}}},"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"&":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"[":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}},"a":{"docs":{},":":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"[":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}}}}}}}}}}}}}}},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"k":{"docs":{},"w":{"docs":{},"i":{"docs":{},"s":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"(":{"docs":{},"p":{"1":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{}}}}}}}}}}}},"!":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"d":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"(":{"0":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}},"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"$":{"docs":{},"x":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815}}},"s":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"[":{"2":{"5":{"6":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"docs":{}},"docs":{}},"docs":{},"(":{"docs":{},"u":{"docs":{},"n":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"i":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"d":{"docs":{},"o":{"docs":{},"w":{"docs":{},"n":{"docs":{},"(":{"docs":{},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"!":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"r":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"!":{"docs":{},")":{"docs":{},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},"p":{"docs":{},"l":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"l":{"docs":{},"d":{"docs":{},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}}}}},"g":{"docs":{},"h":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}}}},"p":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"y":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"c":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"d":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},")":{"docs":{},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}}},"s":{"docs":{},"t":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"l":{"docs":{},"i":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":3.334035087719298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"y":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107}}}},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828}},"e":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.01322463768115942},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"s":{"docs":{},"p":{"docs":{},"o":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0029227557411273487},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"l":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},"e":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"e":{"docs":{},"f":{"docs":{},"f":{"docs":{},"i":{"docs":{},"c":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0013407393219689715},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0023913909924272616},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004448398576512456},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00832870627429206},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.007653061224489796},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.015232606010703994},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.008441786844882167},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.012626262626262626},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.008350730688935281},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.01493550577053632},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.014792899408284023},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005255781359495445},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"i":{"docs":{},"v":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007773459189339256},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009057225195553726},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005627857896588111},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006944444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.010862186014935505},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01242603550295858},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}},"o":{"docs":{},"n":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"e":{"docs":{},"_":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}},"e":{"docs":{},"(":{"2":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}}}},"3":{"docs":{},",":{"2":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}},"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}},"l":{"docs":{},"e":{"docs":{},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"docs":{}},"docs":{}}}}}},"s":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}},"p":{"docs":{},"h":{"docs":{},"r":{"docs":{},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},":":{"docs":{},":":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"(":{"docs":{},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"n":{"docs":{},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}},"i":{"docs":{},"r":{"docs":{},"c":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}}}}}}}}}}}}}}}}}},"g":{"docs":{},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"p":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"i":{"docs":{},"d":{"docs":{},"(":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}}},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"(":{"docs":{},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"_":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"4":{"0":{"9":{"6":{"docs":{},"^":{"2":{"docs":{},",":{"docs":{},"[":{"0":{"docs":{},",":{"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}},"docs":{}}},"docs":{}}}},"docs":{}}},"docs":{}},"docs":{}},"docs":{}},"docs":{},"n":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}}}}}}}}},"s":{"docs":{},"o":{"docs":{},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{},"_":{"docs":{},"o":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852}},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}}},"d":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"e":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}},"e":{"docs":{},"(":{"2":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"3":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"s":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"s":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"p":{"docs":{},"h":{"docs":{},"r":{"docs":{},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"y":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"s":{"docs":{},"a":{"docs":{},"w":{"docs":{},"t":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}}}}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}},"p":{"docs":{},"t":{"docs":{},"o":{"docs":{},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"h":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551}},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":10.015657620041754}}},"y":{"docs":{},"\"":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731}}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}}}}}}}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0010534380386899062},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"u":{"docs":{},"c":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"c":{"docs":{},"k":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}},"z":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"f":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"o":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"p":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.007086764987550277},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001509813789632612},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.004118506709180284},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.006263048016701462},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0035694157430020664},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0018463286464990769},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"o":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"(":{"0":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"1":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},"4":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"docs":{},"(":{"docs":{},"q":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"c":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011956954962136308},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0018463286464990769},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.010688405797101449},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.006211180124223602},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}},"u":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"s":{"docs":{},".":{"docs":{},"\"":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},":":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"e":{"docs":{},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{},"y":{"docs":{},"(":{"docs":{},"&":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"a":{"docs":{},"m":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"o":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0038043478260869567}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}},"s":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"n":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"'":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},"n":{"docs":{},"i":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"d":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0031323414252153485},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}}}}}}}},"v":{"docs":{},"a":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004151838671411625}},"s":{"docs":{},"[":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}},"u":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}},"p":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},"o":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"_":{"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}}}}}}}}}}}}}}}}},"x":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"2":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"docs":{}}}}}}}}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"!":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"s":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0035433824937751387},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0021808421405804393},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0018599707718878703},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.00974025974025974},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002803083391730904},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"s":{"docs":{},",":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"!":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"!":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0029585798816568047},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},":":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},")":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"p":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"a":{"docs":{},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}},"b":{"docs":{},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"c":{"docs":{},"a":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"m":{"docs":{},"p":{"docs":{},"\"":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"b":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},"g":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"f":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"r":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"a":{"docs":{},"y":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.006109979633401222}},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134}},"(":{"0":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}},"1":{"docs":{},",":{"1":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"c":{"docs":{},"e":{"docs":{},"i":{"docs":{},"l":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}},"{":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}},"i":{"docs":{},"c":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}},"_":{"docs":{},"b":{"docs":{},"o":{"docs":{},"x":{"docs":{},"_":{"docs":{},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"r":{"docs":{},"!":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}}}}}},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}}}}}}}}}}}}}}}}}},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"!":{"docs":{},"(":{"docs":{},"c":{"docs":{},"p":{"docs":{},"u":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}},"u":{"docs":{},"d":{"docs":{},"a":{"docs":{},"d":{"docs":{},"e":{"docs":{},"v":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":5.005686433793664},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"(":{"docs":{},"[":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"]":{"docs":{},"$":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"c":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"t":{"docs":{},"e":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428}}}}},"z":{"docs":{},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}},"c":{"docs":{},"h":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"v":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"s":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"e":{"docs":{},"s":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"e":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}}}},"u":{"docs":{},"s":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"i":{"docs":{},"r":{"docs":{},"o":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"b":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.007017543859649123},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0012449722275426163},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0017271157167530224},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.005873140172278779},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"i":{"docs":{},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0048134777376654635}}},"f":{"docs":{},"i":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"v":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}},"u":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"i":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"r":{"docs":{},"i":{"docs":{},"f":{"docs":{},"i":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{},")":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}}}}}}}}},"t":{"docs":{},"y":{"docs":{},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},")":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"n":{"docs":{},"g":{"docs":{},"+":{"docs":{},"+":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"l":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"y":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}},"n":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}},"l":{"docs":{},"i":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"u":{"docs":{},"p":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"e":{"docs":{},"r":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"s":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"r":{"docs":{},"g":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"u":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}}},"o":{"docs":{},"j":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}},"c":{"docs":{},"k":{"docs":{},"w":{"docs":{},"i":{"docs":{},"s":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604}},"e":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"?":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}},"b":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"s":{"docs":{},"e":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"s":{"docs":{},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"(":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}},"?":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"d":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"n":{"docs":{},"e":{"docs":{},")":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}}}},"c":{"docs":{},"k":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"+":{"docs":{},"+":{"1":{"4":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"docs":{}},"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0234375},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"l":{"docs":{},"i":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"y":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"t":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"y":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}}}}}}}}},"l":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551}},"(":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"s":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}}}}}}}}}}}}}}}}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"e":{"docs":{},"b":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}}}}}},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.006008583690987125},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},")":{"docs":{},"^":{"2":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"docs":{}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"+":{"1":{"docs":{},")":{"docs":{},"*":{"docs":{},"*":{"2":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}},")":{"docs":{},"/":{"docs":{},"(":{"2":{"docs":{},"*":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{},"*":{"docs":{},"*":{"2":{"docs":{},")":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}},"docs":{}}}}}}}}}},"docs":{}}}}},"docs":{}}}}},"docs":{}}}},"r":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"u":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.007608695652173913}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"y":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"a":{"docs":{},"s":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}}}},"i":{"docs":{},"l":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407}},"(":{"docs":{},"b":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{},"s":{"docs":{},"[":{"2":{"docs":{},",":{"2":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"docs":{}}},"docs":{}}}}}}}}}}}}}}}},"x":{"docs":{},"p":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},"(":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"p":{"docs":{},"p":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},"u":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}},"r":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}}}}},"o":{"docs":{},"w":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"k":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}},"x":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}}}}}},"u":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0014365064163953266},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0027899561578318055},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.011029411764705883},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00274079874706343},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}},".":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"_":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},"e":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0035587188612099642}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"e":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}},"r":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},".":{"docs":{},".":{"docs":{},".":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}},".":{"docs":{},"y":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}},"v":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"m":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}}}},"d":{"docs":{},"a":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},".":{"docs":{},"@":{"docs":{},"s":{"docs":{},"y":{"docs":{},"n":{"docs":{},"c":{"docs":{},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}}},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}},"t":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"o":{"docs":{},"f":{"docs":{},"f":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}},":":{"docs":{},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"docs":{}},"docs":{}}}}}}}}}},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"b":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}}}}}},"b":{"docs":{},"e":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},"!":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.005917159763313609}}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"#":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}},"i":{"docs":{},"c":{"docs":{},"c":{"docs":{},"o":{"docs":{},"t":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}}},"r":{"docs":{},"c":{"docs":{},"u":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588}},"s":{"docs":{},":":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}}}},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.01462225832656377},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.00631578947368421},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"e":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295}}},"(":{"1":{"docs":{},".":{"0":{"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"docs":{}}},"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"c":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"?":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}},"}":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"t":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}},"s":{"docs":{},"?":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"p":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}},"\"":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731}}},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}}}}}},"d":{"docs":{},"q":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}},"m":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002011108982953457},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.001062840441078783},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0024422318241593085}},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}},"o":{"docs":{},"v":{"docs":{},"n":{"docs":{},"z":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002533650039588282}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"b":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009299853859439352}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"[":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"b":{"docs":{},"b":{"docs":{},"c":{"docs":{},"!":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"a":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},".":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"_":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"k":{"docs":{},"l":{"docs":{},"a":{"docs":{},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{},"s":{"docs":{},"(":{"docs":{},"[":{"docs":{},"\"":{"docs":{},"$":{"0":{"docs":{},".":{"0":{"docs":{},"$":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"docs":{}}},"docs":{}}}}}}}}}}},"s":{"docs":{},"(":{"docs":{},"[":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}}},"docs":{}}}}}}}}}}}}}}},"l":{"docs":{},"a":{"docs":{},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}}},"f":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"|":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},"[":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}}}}}}}},"p":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},"u":{"docs":{},"p":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0026690391459074734}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.008634868421052632},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124}}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}},"=":{"docs":{},"=":{"docs":{},"b":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"@":{"docs":{},"(":{"docs":{},"x":{"docs":{},"c":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"c":{"docs":{},"w":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.003355704697986577}},"(":{"docs":{},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},"[":{"docs":{},"j":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}},"p":{"1":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},"a":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}},":":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}},":":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}},"?":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"_":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"1":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"'":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"n":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"1":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}}}}}}},"{":{"docs":{},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"y":{"docs":{},"p":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"c":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.003985507246376811}},"i":{"docs":{},"c":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653}}}},"e":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002898550724637681}}}}}}},"/":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}},"c":{"docs":{},"+":{"docs":{},"+":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"*":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}},"+":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}}}}}}}}}}},"v":{"docs":{},"t":{"docs":{},"s":{"docs":{},"i":{"2":{"docs":{},"s":{"docs":{},"d":{"docs":{},"q":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368}}}}}},"docs":{}}},"t":{"docs":{},"s":{"docs":{},"d":{"2":{"docs":{},"s":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}}}}},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"'":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"_":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579}}},"{":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.005756578947368421}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}}}}},"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946}}}}},"2":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003289473684210526}}}},"j":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"^":{"docs":{},"*":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"\\":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}},"docs":{}}}},"d":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.006954102920723227},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.011513157894736841},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0125},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"i":{"docs":{},"f":{"docs":{},"f":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844}},"e":{"docs":{},"r":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.006493506493506494},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.006618531889290012},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003153468815697267},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"i":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"?":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}},"i":{"docs":{},"c":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}}}}},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}}},"v":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"u":{"docs":{},"s":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}},"s":{"docs":{},"c":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"v":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{},"u":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255}}}}}}}},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.017777777777777778},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.009533898305084746}},"e":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"p":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"i":{"docs":{},"p":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}}}}},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"b":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.018018018018018018},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.007017543859649123},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.009504412763068567},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.007905138339920948},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":5.008474576271187}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}}},"docs":{},"s":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"r":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"s":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},")":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"?":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"l":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"g":{"docs":{},"u":{"docs":{},"i":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}},"l":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"(":{"0":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}}},"g":{"docs":{},"u":{"docs":{},"i":{"docs":{},"s":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"s":{"docs":{},"i":{"docs":{},"m":{"docs":{},"i":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112}}},"y":{"docs":{},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"l":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"y":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"t":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"v":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},"i":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},"s":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"o":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"\"":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}}}}}},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}},"e":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"r":{"docs":{},"g":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}},"(":{"docs":{},"b":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},",":{"2":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}}}}}},"n":{"docs":{},",":{"2":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}}},"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},"f":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"a":{"docs":{},"g":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.006167763157894737},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"z":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"s":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"l":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0035502958579881655}}}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.005763688760806916},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0068669527896995704},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0053254437869822485},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"s":{"docs":{},",":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"!":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"a":{"docs":{},"l":{"docs":{},";":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},"(":{"docs":{},"(":{"docs":{},"v":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"[":{"docs":{},"(":{"docs":{},"v":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"w":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},":":{"docs":{},":":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"{":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"[":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0015942606616181746}}},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"[":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}},"{":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"}":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"}":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"e":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}},")":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"u":{"docs":{},"t":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"g":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"i":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"s":{"docs":{},":":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"d":{"docs":{},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"e":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}},"t":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}},"a":{"docs":{},"y":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.01956521739130435}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"!":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"s":{"docs":{},")":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0014492753623188406}}}}},"r":{"docs":{},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}},"t":{"docs":{},"a":{"docs":{"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":5.0508474576271185},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0035087719298245615},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0035433824937751387},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0015942606616181746},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":5.015299026425591},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.012350761630300536},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}},"e":{"docs":{},"t":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"s":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"f":{"docs":{},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},".":{"docs":{},"c":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"[":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}},"{":{"docs":{},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"e":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.010326086956521738}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"s":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"v":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"s":{"docs":{},"h":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"t":{"docs":{},"y":{"docs":{},"p":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}}}},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"s":{"docs":{},"!":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}}},"e":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},".":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"\"":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"l":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"m":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"l":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}},"v":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"e":{"docs":{},"t":{"docs":{},"e":{"docs":{},"!":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}},"i":{"docs":{},"m":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"d":{"docs":{},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}}}},"a":{"docs":{},"m":{"docs":{},"b":{"docs":{},"r":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"t":{"docs":{},"a":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.00350385423966363}}}}},"v":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}},"i":{"docs":{},"c":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"a":{"docs":{},"t":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"s":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}},"o":{"docs":{},"t":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"p":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}},"t":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.003639149588201494},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703696609844858}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"s":{"docs":{},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},",":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}},":":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"o":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}},"r":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002717391304347826},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}},"f":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.009824561403508772},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0037349166826278492},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0036906559302130517},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0029228112129666534},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00822239624119029},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004744958481613286},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.004026845637583893},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.004061738424045491},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.011158798283261802},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0028139289482940555},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0018463286464990769},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.004517221908526256}},"a":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.006954102920723227},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}},"i":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},":":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},"s":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},":":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},";":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}},"q":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"e":{"docs":{},"u":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"q":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},"!":{"docs":{},"(":{"docs":{},"q":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"docs":{}}}}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}},"(":{"docs":{},"[":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},".":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}},"r":{"docs":{},"i":{"docs":{},"v":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.020242914979757085},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}}},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"s":{"docs":{},"c":{"docs":{},"r":{"docs":{},"i":{"docs":{},"b":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0048134777376654635},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"e":{"docs":{},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}},"p":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"o":{"docs":{},"r":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}},"t":{"docs":{},"r":{"docs":{},"o":{"docs":{},"y":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"_":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},"\"":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"e":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"d":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"k":{"docs":{},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}}},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"i":{"docs":{},"s":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":5.02803738317757},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"m":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603}}}},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0035870864886408927},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731}},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},".":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"_":{"docs":{},"d":{"docs":{},"f":{"docs":{},"s":{"docs":{},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"o":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"e":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"_":{"docs":{},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"d":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"_":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873}},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},".":{"docs":{},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"_":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"[":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}},"r":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"y":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}},"a":{"docs":{},"y":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},"b":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"u":{"docs":{},"g":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"n":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0028214429665457475},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0048134777376654635},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.01059322033898305}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"y":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},".":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"s":{"docs":{},"u":{"docs":{},"m":{"docs":{},":":{"docs":{},":":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"[":{"docs":{},"j":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}},"=":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"\"":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"d":{"docs":{},"u":{"docs":{},"c":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"o":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"l":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0050335570469798654},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.008529650690495532},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0035174111853675696},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.01406050276949297},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.012293430068520758},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.004592901878914405},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005606166783461808},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"e":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0015622780854992189},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},"[":{"3":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"docs":{},"]":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004997223764575236},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004523026315789474},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}},"[":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.004061738424045491},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.004118733134497941},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}},".":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}},"o":{"docs":{},"f":{"docs":{},"(":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"1":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"4":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"7":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"docs":{}}}}}}}}}}}}},"c":{"docs":{},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}},"u":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}}}}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}},"e":{"docs":{},"s":{"docs":{},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"!":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"m":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0026690391459074734},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":5.005681818181818},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653}}},"s":{"docs":{},"\"":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},";":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}},"w":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"t":{"docs":{},"o":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}},"n":{"docs":{},"e":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"'":{"docs":{},"t":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"a":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"?":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"o":{"docs":{},"r":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},"s":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"!":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0032560812104960733}},"s":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},":":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011492051331162612}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011492051331162612}}}}},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}}},"~":{"docs":{},"%":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}}},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}},".":{"docs":{},".":{"docs":{},".":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"e":{"docs":{},"(":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},"_":{"docs":{},"b":{"docs":{},"t":{"docs":{},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"0":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"1":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"2":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"docs":{}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"_":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0012449722275426163}},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},"_":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"docs":{}},"{":{"1":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}},"2":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"docs":{}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"2":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"docs":{}}}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"e":{"docs":{},"(":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"docs":{}}}}}}}}}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},"_":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}},"b":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"&":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}}}}}}}}},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"e":{"docs":{},"(":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"(":{"docs":{},"&":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}},".":{"docs":{},".":{"docs":{},".":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"_":{"docs":{},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0016280406052480367}},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},"_":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},"docs":{}}}}}}}}}}}}}}}},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703696609844858}},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},"c":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"e":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}}}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"i":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"!":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"e":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}},"1":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},"docs":{}}}}}}}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000861903849837196}}}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}},"e":{"docs":{},".":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},"c":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"e":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}}}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}},")":{"docs":{},"]":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.005635919594213789},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"(":{"docs":{},"&":{"docs":{},"x":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}},"x":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"j":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"p":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"j":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}}}},"w":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.004788354721317755},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002258535937292414}}}}},"e":{"docs":{},"l":{"docs":{},"l":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"a":{"docs":{},"w":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"m":{"docs":{},"a":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"}":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"u":{"docs":{},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"b":{"docs":{},"u":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"m":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"b":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"e":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"e":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"c":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}},"y":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"i":{"docs":{},"c":{"docs":{},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}}}}}}}}}}}}}}}}}}}}}}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004523026315789474},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"x":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0047522063815342835},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},")":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{}},"docs":{}}}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"_":{"1":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"docs":{},"{":{"1":{"0":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"docs":{}},"docs":{}}},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"\\":{"docs":{},"x":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"x":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}},"'":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},"_":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"n":{"docs":{},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"{":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}}},",":{"3":{"1":{"docs":{},")":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"docs":{}},"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}},".":{"docs":{},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"d":{"docs":{},"u":{"docs":{},"p":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003700657894736842}},"]":{"docs":{},".":{"docs":{},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"]":{"docs":{},".":{"docs":{},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}}}}},"2":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"]":{"docs":{},".":{"docs":{},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}}}}},"3":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}},"+":{"1":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"docs":{}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946}}}},"j":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"^":{"docs":{},"*":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"_":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"1":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"{":{"docs":{},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"g":{"docs":{},"l":{"docs":{},"i":{"docs":{},"b":{"docs":{},"c":{"docs":{},"x":{"docs":{},"x":{"docs":{},"_":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"u":{"docs":{},"g":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"\\":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"docs":{}}},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.036074421246981965},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0028214429665457475}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.008237466268995882},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0031245561709984378},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0039767078539980115},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},"docs":{}}}}}}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.011362022439994318},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}},"^":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"3":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"docs":{}},"y":{"docs":{},"p":{"docs":{},"e":{"docs":{},"=":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534}}}}}}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}},"o":{"docs":{},"r":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{}},"docs":{}}}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}},"+":{"docs":{},"e":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"+":{"2":{"2":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"docs":{}},"docs":{}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"=":{"2":{"8":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"9":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}},"m":{"docs":{},"r":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"e":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.011231884057971014},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"f":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}},"i":{"docs":{},"c":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},",":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"i":{"docs":{},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"v":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},")":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"m":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}},"e":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.018245614035087718},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001723807699674392},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013285505513484788},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.005338078291814947},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004441976679622432},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0028782894736842104},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.004433887569279493},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},"s":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}}},"'":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"s":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"g":{"docs":{},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"c":{"docs":{},"t":{"docs":{},"r":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"n":{"docs":{},"e":{"docs":{},"t":{"docs":{},"i":{"docs":{},"s":{"docs":{},"m":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}},"n":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}},"i":{"docs":{},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":5.003008709422011}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"\"":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"\"":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}}}},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"a":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"l":{"docs":{},"i":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731}}},"s":{"docs":{},"o":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}},"n":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0093851752537828},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.009058882737795673},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0037199415437757406},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.009397024275646046},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.010083036773428233},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.004697986577181208},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.016842105263157894},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.005150214592274678},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.004320871688897238},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.011363636363636364},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.005756578947368421},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00710126402499645},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.004635227730753728},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.012219959266802444},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0019927536231884057},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.005067300079176564},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"h":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}}},"=":{"docs":{},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0024899444550852325}},"'":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}}}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"f":{"docs":{},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}}},"i":{"docs":{},"f":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"w":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}},"s":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0052986512524084775}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},")":{"docs":{},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},".":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{},"(":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"s":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"docs":{}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"s":{"docs":{},";":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}},"[":{"1":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}},"2":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}}},"docs":{}},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}}}}}}}}},"j":{"docs":{},"o":{"docs":{},"y":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}},"t":{"docs":{},"r":{"docs":{},"y":{"docs":{},".":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"i":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643}},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"q":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"!":{"docs":{},"(":{"docs":{},"q":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"_":{"docs":{},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428}}},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}},"a":{"docs":{},"g":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}}}},"c":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":5.005447057260529},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}},"e":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"b":{"docs":{},"i":{"docs":{},"b":{"docs":{},"b":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"_":{"docs":{},"b":{"docs":{},"o":{"docs":{},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},":":{"docs":{},":":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"{":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"p":{"docs":{},"h":{"docs":{},"r":{"docs":{},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"c":{"docs":{},"u":{"docs":{},"l":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"_":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"_":{"docs":{},"o":{"docs":{},"f":{"docs":{},"f":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"e":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"e":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"_":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"s":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"_":{"docs":{},"q":{"docs":{},"w":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"t":{"docs":{},"r":{"docs":{},"y":{"docs":{},"_":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},".":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"_":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394}},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}},"r":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"(":{"docs":{},"&":{"docs":{},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"b":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},"&":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}},"u":{"docs":{},"r":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"n":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"m":{"docs":{},"p":{"docs":{},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"l":{"docs":{},"o":{"docs":{},"s":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"r":{"docs":{},"y":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.015657620041753653}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"g":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"s":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"u":{"docs":{},"m":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},"_":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},")":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"c":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"_":{"docs":{},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}},"a":{"docs":{},"l":{"docs":{},"*":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"d":{"docs":{},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}}},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},")":{"docs":{},".":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.003022974607013301},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.006618531889290012},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}}}},"l":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}},"s":{"docs":{},"s":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"c":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}},"p":{"docs":{},"e":{"docs":{},"c":{"docs":{},"i":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703696609844858},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"b":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"_":{"docs":{},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"x":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.03389830508474576},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.017391304347826087},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.023809523809523808},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.018018018018018018},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.018691588785046728},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.01020408163265306},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.00487012987012987},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0028782894736842104},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0033944331296673455},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.006211180124223602},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"e":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002803083391730904},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.006355932203389831}}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"c":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"l":{"docs":{},"i":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},"y":{"docs":{},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"c":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"e":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"n":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}},"l":{"docs":{},"u":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"s":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}},"p":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"s":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},":":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"i":{"docs":{},"c":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"l":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"y":{"docs":{},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}},"o":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"s":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"c":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"?":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"c":{"docs":{},"t":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003854239663629993}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"n":{"docs":{},"s":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.012145748987854251},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},"s":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.024291497975708502},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},".":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}}}},"o":{"docs":{},"n":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00684931506849315},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.005681818181818182},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"a":{"docs":{},"l":{"docs":{},".":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},"s":{"docs":{},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},".":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}},"(":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}},":":{"docs":{},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"docs":{}},"docs":{}}}}}}}}}}}},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}},"r":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"(":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"x":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047}}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},".":{"docs":{},"(":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534}}}}},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.013333333333333334},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}},"=":{"docs":{},"(":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}}},"r":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"r":{"docs":{},"a":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"s":{"docs":{},"!":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"_":{"docs":{},"s":{"docs":{},"u":{"docs":{},"c":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649}}}}}}},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011956954962136308},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0023492560689115116},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0026690391459074734},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004441976679622432},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.004116920543433511},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0028139289482940555},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0041753653444676405},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0038043478260869567},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003167062549485352},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.00700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002011108982953457}}}},"r":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304}},"f":{"docs":{},"a":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"'":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}},"l":{"docs":{},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"s":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"l":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}},"e":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.01177536231884058}},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},")":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},")":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"?":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"_":{"docs":{},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}}}},"y":{"docs":{},":":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}},"v":{"docs":{},"e":{"docs":{},"s":{"docs":{},"d":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"p":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"e":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0022984102662325224},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001677570877369569},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.006017418844022169}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}}},"c":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}},"r":{"docs":{},"a":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"!":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"r":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005956552207428171},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"2":{"4":{"docs":{},";":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}},"(":{"docs":{},"\"":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"s":{"docs":{},"!":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}},"_":{"docs":{},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"(":{"docs":{},"w":{"docs":{},"h":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}}}}}}},"v":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"e":{"docs":{},"r":{"docs":{},"y":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},"e":{"docs":{},"'":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"t":{"docs":{},"h":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"b":{"docs":{},"o":{"docs":{},"d":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"w":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.004696599661844825},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925}},"l":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"[":{"docs":{},"k":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}},"s":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003854239663629993}},"u":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"s":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"o":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"v":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904}}}}}},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"u":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}},"i":{"docs":{},"l":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"d":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"c":{"docs":{},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},")":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},")":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"m":{"docs":{},"o":{"docs":{},"j":{"docs":{},"i":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}}}},"p":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000861903849837196},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}}},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}},"i":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"b":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"e":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"u":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.03125},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0019883539269990058},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0026920031670625497},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"?":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"{":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},",":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"!":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"s":{"docs":{},"(":{"docs":{},"o":{"docs":{},"b":{"docs":{},"j":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}},"i":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"l":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0024621878297572987}}}}}},"i":{"docs":{},"b":{"docs":{},"r":{"docs":{},"i":{"docs":{},"u":{"docs":{},"m":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"x":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"n":{"docs":{},"s":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}},"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}},"d":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"u":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},"g":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.005150214592274678},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},"e":{"docs":{},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"!":{"docs":{},")":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},")":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224}},"%":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}},"'":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"(":{"docs":{},"$":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"_":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001509813789632612}},"(":{"0":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844}}},"docs":{}},"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"docs":{}},"docs":{}}}}}}},"b":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}},"i":{"docs":{},"n":{"1":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}}}}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"_":{"docs":{},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"m":{"docs":{},"(":{"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}},"(":{"0":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}}},"docs":{}},"docs":{}},"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"docs":{}},"docs":{}}}}}}},"i":{"docs":{},"n":{"1":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}}}}},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"x":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"_":{"docs":{},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}},"e":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":5.011407481966113},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"o":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},".":{"docs":{},"c":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"(":{"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"(":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},"(":{"6":{"4":{"docs":{},"*":{"6":{"7":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"docs":{}},"docs":{}}},"docs":{}},"docs":{},"a":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}},"b":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844}},"(":{"1":{"2":{"8":{"docs":{},"*":{"1":{"2":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"docs":{}},"docs":{}}},"docs":{}},"docs":{}},"docs":{},"a":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}},"b":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"r":{"docs":{},"'":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"i":{"docs":{},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428}}}}}},"s":{"docs":{},"t":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}}}}}}},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},".":{"docs":{},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"y":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}},"e":{"docs":{},".":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}},"^":{"docs":{},"{":{"2":{"5":{"5":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}},"\\":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}},"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}}},"(":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}},"n":{"docs":{},"*":{"docs":{},"k":{"docs":{},"*":{"2":{"docs":{},"*":{"docs":{},"p":{"docs":{},"i":{"docs":{},"*":{"docs":{},"(":{"1":{"docs":{},"/":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},"*":{"docs":{},"(":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}},"docs":{}}}}}}},"docs":{}}}}}},"v":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"p":{"docs":{},"s":{"docs":{},"l":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},".":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"=":{"6":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"}":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"docs":{},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"'":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"`":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"x":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"/":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}},"}":{"docs":{},"{":{"docs":{},"t":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}}}}}}}}}}}}}}},"x":{"docs":{},"_":{"1":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{},".":{"docs":{},".":{"docs":{},",":{"docs":{},"x":{"docs":{},"_":{"docs":{},"{":{"1":{"0":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"docs":{}},"docs":{}}}}}}}},"\\":{"docs":{},"d":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"docs":{}}}}},"f":{"1":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"+":{"docs":{},"f":{"2":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"docs":{}}}},"2":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"6":{"4":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0028214429665457475},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0029227557411273487},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},".":{"docs":{},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}},".":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"2":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"docs":{}}}},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},"docs":{}},"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.013333333333333334},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"a":{"docs":{},"v":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"i":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},"o":{"docs":{},"r":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"[":{"1":{"docs":{},":":{"docs":{},"h":{"docs":{},"a":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}},"docs":{}},"s":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},".":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}},"e":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"t":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}}},"o":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}},"q":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},"r":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"l":{"docs":{},"s":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"e":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},":":{"6":{"docs":{},"}":{"docs":{},"\"":{"docs":{},".":{"docs":{},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"}":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"l":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"i":{"docs":{},"l":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"u":{"docs":{},"r":{"docs":{},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}},")":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}},"s":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},"r":{"docs":{},",":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"l":{"docs":{},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},"s":{"docs":{},"t":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.007653061224489796},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"?":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"h":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}},"b":{"docs":{},"s":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}},"(":{"docs":{},"a":{"docs":{},"[":{"docs":{},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}},"e":{"docs":{},"q":{"docs":{},"n":{"docs":{},"s":{"docs":{},"[":{"docs":{},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"]":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}}}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"u":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}},"e":{"docs":{},"e":{"docs":{},"l":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.007707129094412331},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"b":{"docs":{},"l":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"w":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00684931506849315},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},":":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"a":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"!":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"s":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},"s":{"docs":{},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"m":{"docs":{},"a":{"docs":{},"l":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"r":{"docs":{},"n":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":5.005845511482255},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}},"\"":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}},"b":{"docs":{},"r":{"docs":{},"u":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"d":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"i":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}},"n":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0029655990510083037},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002843216896831844},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.005150214592274678},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0034420289855072463},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.005384006334125099},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"f":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}},"_":{"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},"(":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"c":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518}}},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0035587188612099642}}}}}}}}},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518}}}}}}}}}}}}}}}}}}}}},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"a":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"_":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873}}}}},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},")":{"docs":{},".":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"g":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003854239663629993}},"t":{"docs":{},"i":{"docs":{},"p":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"s":{"docs":{},"?":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"i":{"docs":{},"s":{"docs":{},"h":{"docs":{},"e":{"docs":{},"d":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"e":{"docs":{},":":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"e":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}},"l":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":5.0094899169632265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}},"\"":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},"?":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}}}},"e":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009880609304240428},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0031656700668308124},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},")":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},"g":{"docs":{},"p":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"f":{"docs":{},"l":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"_":{"0":{"0":{"0":{"0":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"1":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"2":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},";":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},":":{"docs":{},":":{"docs":{},"c":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"p":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.012215435868961688},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852}},"$":{"docs":{},"(":{"docs":{},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},"i":{"docs":{},"n":{"docs":{},"_":{"docs":{},"c":{"docs":{},"i":{"docs":{},"r":{"docs":{},"c":{"docs":{},"l":{"docs":{},"e":{"docs":{},"$":{"docs":{},"(":{"docs":{},"?":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}}},"s":{"docs":{},":":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},"\"":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004441976679622432},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232}},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},")":{"docs":{},";":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412}}}}}}}}}},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}},"docs":{}}}}}}}},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}},"?":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},")":{"docs":{},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}}},"[":{"docs":{},"i":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.011228070175438596},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.005362957287875886},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0017271157167530224},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0050415183867141165},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00684931506849315},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0035174111853675696},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0019927536231884057},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013285505513484788},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"]":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},"x":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"u":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{},"(":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}},"s":{"docs":{},"a":{"docs":{},"v":{"docs":{},"e":{"docs":{},"f":{"docs":{},"i":{"docs":{},"g":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},".":{"docs":{},"p":{"docs":{},"n":{"docs":{},"g":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.022598870056497175},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"s":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},"e":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"i":{"docs":{},"e":{"docs":{},"v":{"docs":{},"e":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"a":{"docs":{},"l":{"docs":{},"(":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"o":{"docs":{},"c":{"docs":{},"u":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"s":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"r":{"docs":{},"t":{"docs":{},"u":{"docs":{},"n":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"h":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"_":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"[":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0013407393219689715},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.005090054815974941},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"(":{"docs":{},"$":{"docs":{},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}},"v":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"g":{"docs":{},"o":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"m":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00332541567695962},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}}},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"a":{"docs":{},"l":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},"l":{"docs":{},"y":{"docs":{},")":{"docs":{},":":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"i":{"docs":{},"s":{"docs":{},"m":{"docs":{},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.004116920543433511},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"!":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"{":{"docs":{},":":{"1":{"8":{"docs":{},"}":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"docs":{}},"docs":{},"?":{"docs":{},"}":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"}":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"{":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"{":{"docs":{},"}":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}},"a":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}},"u":{"docs":{},"l":{"docs":{},"a":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"s":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}}},"\"":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"g":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"o":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}},"(":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00274079874706343},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.006175380815150268},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.005050505050505051},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0038043478260869567},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"a":{"docs":{},"t":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.025510204081632654},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00507232763479241},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976}}}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"o":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"t":{"docs":{},"b":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0012449722275426163},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"l":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657}}}},"(":{"docs":{},"q":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"_":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"e":{"docs":{},"(":{"docs":{},"q":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"e":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"_":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"k":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}},"g":{"docs":{},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"p":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"!":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"f":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0015942606616181746},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},".":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"_":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"1":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"docs":{}}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"[":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},".":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"+":{"docs":{},"+":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"u":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0026571011026969575},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.02295918367346939},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0026300958106331017},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},".":{"docs":{},"m":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"m":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}}}}}}}}},"y":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},".":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"r":{"docs":{},"y":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0035087719298245615}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004912280701754386}},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}},"e":{"docs":{},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"m":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"g":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"a":{"docs":{},"c":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114}},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0028503562945368173}},"s":{"docs":{},")":{"docs":{},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"a":{"docs":{},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.004924375659514597},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}},"s":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}}}}}}}},"m":{"docs":{},"e":{"docs":{},"w":{"docs":{},"o":{"docs":{},"r":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}},"i":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"l":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}},"d":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}},"u":{"docs":{},"n":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"d":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.011029411764705883},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0022026431718061676},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0021808421405804393},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0019928258270227183},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0028405056099985795},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141}},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.006033326948860372},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.006710283509478276},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002258535937292414},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.007047768206734534},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004448398576512456},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.004697986577181208},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.020242914979757085},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.013333333333333334},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004997223764575236},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.02040816326530612},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002881844380403458},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.006904955320877335},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.008421052631578947},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.005150214592274678},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0045087356753710315},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.012987012987012988},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":3.342126861296752},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0021303792074989347},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0022168480451430876},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.018308080808080808},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.013778705636743214},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.008146639511201629},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0014492753623188406},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002533650039588282},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005606166783461808},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.010163749294184076},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.013771186440677966}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"(":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}},")":{"docs":{},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},".":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"s":{"docs":{},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"?":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},";":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},".":{"6":{"docs":{},".":{"docs":{},"l":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}},"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},":":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"'":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"?":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"(":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"k":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},"!":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},".":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125}}}}}}},"r":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}},"i":{"docs":{},"o":{"docs":{},"u":{"docs":{},"s":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"l":{"docs":{},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004997223764575236},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.011231884057971014},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"_":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"_":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}}}}}},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"z":{"docs":{},"z":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}},"s":{"docs":{},"s":{"docs":{},"!":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}},"d":{"docs":{},"g":{"docs":{},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"p":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"a":{"docs":{},"t":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"v":{"docs":{},"o":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"g":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"j":{"docs":{},"o":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"u":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"s":{"docs":{},"h":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"c":{"docs":{},"t":{"docs":{},"u":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}}}}},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478}}}},"docs":{}},"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0050415183867141165},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.015068493150684932},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0036926572929981537},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"o":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":5.0056346381969155}}},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"(":{"docs":{},"x":{"docs":{},"/":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"_":{"docs":{},"w":{"docs":{},"i":{"docs":{},"d":{"docs":{},"t":{"docs":{},"h":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}}},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"w":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"d":{"docs":{},"(":{"1":{"3":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{},"k":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"n":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.008421052631578947},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011492051331162612},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0015942606616181746},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0014251781472684087},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},"m":{"docs":{},"t":{"docs":{},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"f":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"%":{"9":{"docs":{},".":{"4":{"docs":{},"f":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"docs":{}}},"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0013407393219689715}}}},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"x":{"docs":{},"=":{"docs":{},"%":{"docs":{},"f":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"[":{"docs":{},"%":{"docs":{},"f":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}},"l":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}},"[":{"0":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"1":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"2":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}},"\\":{"docs":{},"n":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},":":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},":":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},":":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"h":{"docs":{},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"]":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"g":{"docs":{},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"c":{"docs":{},"k":{"1":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"2":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"docs":{}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},"r":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"(":{"docs":{},"\"":{"docs":{},"[":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0013407393219689715}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"a":{"docs":{},"p":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"f":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"n":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"c":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"t":{"docs":{},"h":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"'":{"docs":{},"%":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011492051331162612}}}},"\\":{"docs":{},"n":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"b":{"docs":{},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"d":{"docs":{},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}}}}}}},"'":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},"(":{"docs":{},"{":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"{":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}},"{":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"(":{"docs":{},"{":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"x":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}},"(":{"2":{"docs":{},")":{"docs":{},"=":{"1":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"docs":{}}}},"3":{"docs":{},")":{"docs":{},"=":{"2":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"docs":{}}}},"docs":{},"a":{"docs":{},")":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}},"x":{"docs":{},")":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.016194331983805668},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},")":{"docs":{},".":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"}":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"(":{"docs":{},"t":{"docs":{},"+":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}},"'":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"_":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"\\":{"docs":{},"x":{"docs":{},"i":{"docs":{},")":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"x":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"d":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"x":{"docs":{},"}":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}},"c":{"docs":{},"p":{"docs":{},"u":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}},"u":{"docs":{},"d":{"docs":{},"a":{"docs":{},"d":{"docs":{},"e":{"docs":{},"v":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"z":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.008207070707070708}},"!":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255}}},":":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"=":{"docs":{},"z":{"docs":{},"^":{"2":{"docs":{},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}}}}}},"n":{"docs":{},")":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.006355932203389831}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},"}":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"^":{"docs":{},"{":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},"}":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}}}}}},"*":{"docs":{},"g":{"docs":{},"=":{"docs":{},"c":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}}},".":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"w":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"{":{"0":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"{":{"1":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"*":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}},"p":{"docs":{},".":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}}}}}}},"docs":{}}}}}},"docs":{}}}}}}}}}},"[":{"docs":{},"n":{"docs":{},"]":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"f":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":10.00638737554011},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},"_":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}}}}},"w":{"3":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"_":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"o":{"docs":{},"y":{"docs":{},"_":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{},"(":{"docs":{},"p":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}}}}}}}}}}},"x":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"_":{"docs":{},"d":{"docs":{},"f":{"docs":{},"t":{"docs":{},"_":{"1":{"docs":{},"d":{"docs":{},"(":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},"x":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}},"'":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"(":{"docs":{},"&":{"docs":{},"x":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"x":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},"_":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"k":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}}}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"c":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"(":{"docs":{},"x":{"docs":{},".":{"docs":{},"a":{"docs":{},"s":{"docs":{},"_":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"s":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}}}}}},":":{"docs":{},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},"f":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"_":{"1":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"(":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0037578288100208767}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}}},"2":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"(":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0037578288100208767}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}}},"3":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"(":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0037578288100208767}}}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}},"4":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"(":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845}}}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"_":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}},"=":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"g":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0031656700668308124},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.003952569169960474}},"i":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}},"h":{"docs":{},"u":{"docs":{},"b":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}},"v":{"docs":{},"e":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"_":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"r":{"docs":{},"a":{"docs":{},"d":{"docs":{},"i":{"docs":{},"u":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"s":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},".":{"docs":{},"t":{"docs":{},"o":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}},"f":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"t":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":5.027027027027027},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.004335260115606936},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.003355704697986577}},"\"":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},".":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0072254335260115606}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"docs":{}}}}},"r":{"docs":{},"e":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"1":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{}}}}}}}}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}},"docs":{},"j":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"u":{"docs":{},"r":{"docs":{},"a":{"docs":{},"k":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"r":{"docs":{},"l":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"f":{"docs":{},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}},"m":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"o":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001723807699674392},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003642121931908155},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002452697967764541},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"a":{"docs":{},"l":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"a":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"o":{"docs":{},"d":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"g":{"docs":{},"l":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"n":{"docs":{},"e":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"b":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"d":{"docs":{},"y":{"docs":{},"g":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"!":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"h":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"i":{"docs":{},"c":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":5.03954802259887},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"s":{"docs":{},".":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"h":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":5.002013422818792}},"_":{"docs":{},"s":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"!":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},":":{"docs":{},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}}}}}}}}}},"(":{"docs":{},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{},":":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}}}}},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"&":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}},"s":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604}},"(":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"s":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}},"d":{"docs":{},"i":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.006008583690987125}},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"n":{"docs":{},"t":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"i":{"docs":{},"n":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"v":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"y":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001509813789632612}}}},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"l":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"!":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"e":{"docs":{},"c":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"n":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"k":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"y":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"s":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002717391304347826}}}}}}}},"w":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"o":{"docs":{},"w":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"s":{"docs":{},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"n":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"c":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"u":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"s":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"n":{"docs":{},"d":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"'":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"i":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.004419191919191919},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0026690391459074734},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}},"[":{"1":{"docs":{},":":{"2":{"docs":{},",":{"docs":{},":":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},"docs":{}}},"2":{"docs":{},",":{"docs":{},":":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"3":{"docs":{},",":{"docs":{},":":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},"_":{"docs":{},"x":{"docs":{},"]":{"docs":{},"[":{"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},"_":{"docs":{},"y":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}}}}}}}}}},"x":{"docs":{},"]":{"docs":{},"[":{"docs":{},"y":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643}}}}}}}},"{":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"_":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.005431093007467753}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},"/":{"2":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"docs":{}},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}}},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"f":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}}}}},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"u":{"docs":{},"m":{"docs":{},"p":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"u":{"docs":{},"i":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}},"e":{"docs":{},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}}},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}}}},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"r":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}},"y":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593}},".":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"o":{"docs":{},"(":{"docs":{},"g":{"docs":{},"i":{"docs":{},"r":{"docs":{},"l":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004210526315789474},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0045726345409778405},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.003952569169960474}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"e":{"docs":{},"(":{"2":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"3":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"_":{"docs":{},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"s":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"e":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"v":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"(":{"docs":{},"*":{"docs":{},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"_":{"docs":{},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},"e":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"_":{"docs":{},"d":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"e":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"(":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"l":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}},"u":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},":":{"docs":{},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"u":{"docs":{},"s":{"docs":{},".":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.006355932203389831}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.001062840441078783},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}},"_":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"_":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"o":{"docs":{},"f":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"_":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"o":{"docs":{},"f":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}},"l":{"docs":{},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},".":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"h":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}},"x":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},"i":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":5.011904761904762}}},"y":{"docs":{},".":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.023809523809523808}}}}}}}},"r":{"docs":{},"g":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}},"m":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"n":{"docs":{},"u":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.007822149032523672},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002881844380403458},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}},"c":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003355141754739138}},"_":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{},"u":{"docs":{},"s":{"docs":{},"(":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"docs":{},"a":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"(":{"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{},"a":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}}},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"x":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"r":{"docs":{},"o":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"s":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"e":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.005479452054794521}},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603}}},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"s":{"docs":{},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589}}}}}},"m":{"docs":{},"e":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005979599015124868},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}},"\"":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542}}},"s":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},")":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"m":{"docs":{},"i":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"r":{"docs":{},"!":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}},"l":{"docs":{},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},".":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"r":{"docs":{},"u":{"docs":{},"n":{"docs":{},"g":{"docs":{},"a":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{},"(":{"docs":{},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001583531274742676}},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004441976679622432},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.007725321888412017},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":5.002375296912114},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"?":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},";":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},"e":{"docs":{},"l":{"docs":{},"i":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"!":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"2":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"docs":{}}},"docs":{}},"docs":{}}}}}}}}}}}}}}}}},"(":{"docs":{},"&":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"(":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"a":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"l":{"docs":{},"i":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"a":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"[":{"docs":{},"]":{"docs":{},"[":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}},"'":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002536231884057971}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"_":{"docs":{},"j":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"a":{"docs":{},"n":{"docs":{},"(":{"docs":{},"&":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"a":{"docs":{},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}},"_":{"docs":{},"e":{"docs":{},"l":{"docs":{},"i":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"!":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"2":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"docs":{}}},"docs":{}},"docs":{}}}}}}}}}}}}}}}}},"(":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}}}}}}}}}}}}}},"j":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},"(":{"docs":{},"a":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"[":{"docs":{},"]":{"docs":{},"[":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"l":{"docs":{},"o":{"docs":{},"b":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"_":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"_":{"docs":{},"d":{"docs":{},"e":{"docs":{},"v":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},"g":{"docs":{},"l":{"docs":{},"o":{"docs":{},"b":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"_":{"docs":{},"d":{"docs":{},"e":{"docs":{},"v":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"r":{"docs":{},"y":{"docs":{},"!":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"e":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},",":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"\\":{"docs":{},"x":{"docs":{},"i":{"docs":{},")":{"docs":{},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}}},"r":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},".":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"[":{"docs":{},"n":{"docs":{},"]":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"p":{"docs":{},"u":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004210526315789474}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}},"s":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},"_":{"docs":{},"i":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"x":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"y":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"docs":{}}},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"t":{"docs":{},"o":{"docs":{},"t":{"docs":{},"a":{"docs":{},"l":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}}}}}}}}},"x":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339}}},"y":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339}},".":{"docs":{},"^":{"2":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"docs":{}}}},"'":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"'":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"|":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{},")":{"docs":{},"|":{"docs":{},"^":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"f":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"=":{"docs":{},"g":{"docs":{},")":{"docs":{},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"i":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"s":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"a":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"r":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"e":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},".":{"docs":{},".":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},"s":{"docs":{},"h":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},"m":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},"o":{"docs":{},"n":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"s":{"docs":{},"k":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},"l":{"docs":{},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002125680882157566},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"<":{"docs":{},">":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}},"}":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},"c":{"docs":{},"u":{"docs":{},"d":{"docs":{},"a":{"docs":{},"_":{"docs":{},"g":{"docs":{},"p":{"docs":{},"u":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}}}}}}}}},"f":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"v":{"docs":{},"e":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"i":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"r":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"s":{"docs":{},")":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"!":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"l":{"docs":{},"f":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0020665038512117226},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0018137847642079807},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"w":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"l":{"docs":{},"/":{"docs":{},"c":{"docs":{},"r":{"docs":{},"c":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"m":{"docs":{},"z":{"docs":{},"a":{"docs":{},"o":{"docs":{},"u":{"docs":{},"i":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}},"i":{"docs":{},"l":{"docs":{},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"s":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"d":{"docs":{},"o":{"docs":{},"r":{"docs":{},"f":{"docs":{},"f":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}},"c":{"docs":{},"k":{"docs":{},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"i":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"e":{"docs":{},"l":{"docs":{},"p":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},":":{"docs":{},":":{"docs":{},"m":{"docs":{},"a":{"docs":{},"k":{"docs":{},"e":{"docs":{},"_":{"docs":{},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"f":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"*":{"docs":{},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"d":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"r":{"docs":{},"e":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011492051331162612},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178}},"'":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002881844380403458},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.005681818181818182},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002536231884057971},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0035502958579881655},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002452697967764541},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},":":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"?":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"o":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}},"i":{"docs":{},"c":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"m":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}}}}},"a":{"docs":{},"v":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"t":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0030556662681015014}},"'":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"*":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},".":{"docs":{},"i":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"(":{"docs":{},"h":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},"h":{"docs":{},")":{"docs":{},".":{"docs":{},"(":{"docs":{},"*":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"h":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}},"_":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}},"(":{"docs":{},"&":{"docs":{},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"(":{"docs":{},"&":{"docs":{},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"_":{"docs":{},"d":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"s":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},"_":{"docs":{},"u":{"docs":{},"p":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"r":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"\"":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"d":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}},"d":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"n":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"r":{"docs":{},"i":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"x":{"docs":{},"a":{"docs":{},"g":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"?":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"s":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}}}}},"s":{"docs":{},"e":{"docs":{},"n":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488}}}}}}}}}}},"o":{"docs":{},"p":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"f":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"i":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"y":{"docs":{},",":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}}}}},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248}},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}}},"n":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"k":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}},"u":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"d":{"docs":{},"o":{"docs":{},"r":{"docs":{},"f":{"docs":{},"f":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"w":{"docs":{},"e":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.007707129094412331},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.005681818181818182},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.005415162454873646},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"?":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"l":{"docs":{},"d":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0031245561709984378},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"i":{"docs":{},"d":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}},"i":{"docs":{},"z":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}}},"m":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},"l":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"o":{"docs":{},"d":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"t":{"docs":{},"t":{"docs":{},"p":{"docs":{},"s":{"docs":{},":":{"docs":{},"/":{"docs":{},"/":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"c":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},".":{"docs":{},"g":{"docs":{},"g":{"docs":{},"/":{"docs":{},"p":{"docs":{},"r":{"2":{"docs":{},"e":{"9":{"docs":{},"s":{"6":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}},"docs":{}}},"docs":{}}},"docs":{}},"b":{"9":{"7":{"6":{"docs":{},"s":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}},"docs":{}},"docs":{}},"docs":{}}}}}}}}}}}}}},"g":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"u":{"docs":{},"b":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"/":{"docs":{},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}}}},"a":{"docs":{},"n":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"r":{"docs":{},"/":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"w":{"docs":{},"w":{"docs":{},"w":{"docs":{},".":{"docs":{},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}}}}}},"t":{"docs":{},"w":{"docs":{},"i":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},".":{"docs":{},"t":{"docs":{},"v":{"docs":{},"/":{"docs":{},"l":{"docs":{},"e":{"docs":{},"i":{"docs":{},"o":{"docs":{},"s":{"docs":{},"l":{"docs":{},"a":{"docs":{},"b":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}}}}}}}}}}}}}}},"y":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"u":{"docs":{},"b":{"docs":{},"e":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"/":{"docs":{},"u":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"/":{"docs":{},"l":{"docs":{},"e":{"docs":{},"i":{"docs":{},"o":{"docs":{},"s":{"docs":{},"o":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"m":{"docs":{},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003854239663629993},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"s":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.004908946951702296},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}},"l":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"!":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002717391304347826}},"i":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"y":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891}},"[":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},"i":{"docs":{},",":{"docs":{},"j":{"docs":{},"]":{"docs":{},")":{"docs":{},"^":{"2":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"docs":{}}}}}}}},"s":{"docs":{},"\"":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}}},"e":{"docs":{},"p":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"m":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"!":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"r":{"docs":{},"e":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"c":{"docs":{},"h":{"docs":{},".":{"docs":{},".":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"d":{"docs":{},"e":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"d":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"u":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"l":{"docs":{},"l":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.02702702702702703},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.014932562620423893},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.015771812080536914}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"o":{"docs":{},"n":{"docs":{},"_":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}}}}}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},"t":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},"i":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"m":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},"i":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"m":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{}}}}}},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{}}}}}}}}},"u":{"docs":{},"n":{"docs":{},"s":{"docs":{},"h":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0026845637583892616}},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"]":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}},"]":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"m":{"docs":{},"]":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828}},"s":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"1":{"5":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"docs":{}},"docs":{}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}},"s":{"docs":{},"[":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"n":{"docs":{},"g":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364}}}}}}}},"d":{"docs":{},"r":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"d":{"docs":{},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"'":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":5.003587086488641},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},":":{"docs":{},":":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},"_":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"b":{"docs":{},"e":{"docs":{},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"_":{"docs":{},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009299853859439352}},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},".":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"b":{"docs":{},"i":{"docs":{},"b":{"docs":{},"b":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0014614056064833267}},"e":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"b":{"docs":{},"i":{"docs":{},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"_":{"docs":{},"b":{"docs":{},"o":{"docs":{},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},".":{"docs":{},"c":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},":":{"docs":{},":":{"docs":{},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}}}}}}}}}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}},"s":{"docs":{},"b":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}},"g":{"docs":{},"e":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005627857896588111},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0041753653444676405}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"_":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}},"[":{"0":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"docs":{}}}}}}}}}}}}},"e":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255}}}},"s":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}},"l":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"v":{"2":{"docs":{},"r":{"docs":{},"g":{"docs":{},"b":{"docs":{},"(":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}}}}}}}}}}},"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.004419191919191919}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"(":{"docs":{},"*":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}},"y":{"docs":{},"p":{"docs":{},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"(":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"z":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}},"_":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"}":{"docs":{},"{":{"2":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"docs":{}}}},"i":{"3":{"2":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},"e":{"docs":{},".":{"docs":{},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"4":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"5":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"6":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"docs":{}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"4":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"5":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"6":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"docs":{}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},"docs":{}},"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}},"docs":{}},"docs":{},"m":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}},"p":{"docs":{},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.015306122448979591},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.005614035087719298},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"s":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"i":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},"c":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"'":{"docs":{},",":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004912280701754386},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.001062840441078783},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.004306969459671104},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0026690391459074734},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0030201342281879194},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.007653061224489796},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0037052284890901604},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00487408610885459},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0035174111853675696},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0041753653444676405},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0029585798816568047},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}},"s":{"docs":{},"s":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"v":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657}},"i":{"docs":{},"s":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"!":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"u":{"docs":{},"t":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"a":{"docs":{},"g":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.007653061224489796},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.015644298065047343},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00821917808219178},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":3.3496423462088694},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0045726345409778405},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.007575757575757576},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.003340292275574113},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004204625087596356},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"i":{"docs":{},"n":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"e":{"docs":{},"!":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}},"g":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0024183796856106408},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006313131313131313},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"y":{"docs":{},"_":{"docs":{},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}},"e":{"docs":{},"s":{"docs":{},"/":{"docs":{},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}},".":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"?":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"!":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},")":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394}}},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}}}}}}}},"(":{"docs":{},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"u":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}}},"*":{"0":{"docs":{},".":{"5":{"docs":{},"*":{"docs":{},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"v":{"docs":{},"*":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"d":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"k":{"docs":{},".":{"docs":{},"^":{"2":{"docs":{},"*":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"d":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}},"docs":{}}}}}}}}}},"docs":{}}},"docs":{}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"_":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},"e":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}},":":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},":":{"docs":{},":":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534}}}}}},"n":{"2":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873}},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"a":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.007708479327259986},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"(":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"v":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},")":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"u":{"docs":{},"d":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"d":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}},"s":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},"e":{"docs":{},"!":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}},"r":{"docs":{},"e":{"docs":{},"h":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"r":{"docs":{},"p":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"n":{"docs":{},"s":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}},"h":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"i":{"docs":{},"r":{"docs":{},"c":{"docs":{},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}},"e":{"docs":{},"(":{"docs":{},"$":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"a":{"docs":{},".":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}}}}}},"a":{"docs":{},"p":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"d":{"docs":{},"i":{"docs":{},"v":{"docs":{},"i":{"docs":{},"d":{"docs":{},"u":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0028179597971068945},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}}}}}}}},"e":{"docs":{},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0017271157167530224},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00507232763479241},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"r":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"'":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"_":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{},"(":{"docs":{},"&":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"}":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"u":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},"y":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"?":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}},"a":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409}}},"n":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"e":{"docs":{},"v":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}},"o":{"docs":{},"f":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"i":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737}}}}},"t":{"3":{"2":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"docs":{}},"6":{"4":{"docs":{},"}":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"docs":{}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.008421052631578947},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0022984102662325224},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.013252809931219594},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0025242460475621096},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.00771055753262159},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0026845637583892616},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.004635227730753728},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.004710144927536232},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003800475059382423}},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007773459189339256},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009057225195553726},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.005150214592274678},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005979599015124868},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006944444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.010862186014935505},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01242603550295858},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"'":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"o":{"docs":{},"f":{"docs":{},"(":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"!":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"?":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"f":{"docs":{},"a":{"docs":{},"c":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"{":{"docs":{},"}":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"i":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"v":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"!":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"e":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"m":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"s":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"v":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"g":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.010638297872340425},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.01643835616438356},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.005681818181818182},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"(":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},">":{"docs":{},">":{"docs":{},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}}}}}},"s":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}}}},"r":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":5.010367845476495},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.003952569169960474},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"!":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"'":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449}}},"~":{"docs":{},"%":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"\"":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"e":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"l":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0012782275244993609}}}}}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}},"s":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}},"d":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"r":{"docs":{},"o":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"d":{"docs":{},"u":{"docs":{},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":10.001926782273603},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"u":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649}}},"_":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},".":{"docs":{},"e":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"4":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"5":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"9":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"docs":{}}}}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},".":{"docs":{},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"4":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"5":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"9":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"docs":{}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},"e":{"docs":{},".":{"docs":{},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"4":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}},"5":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}},"9":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}},"docs":{}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"4":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}},"5":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}},"9":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}},"docs":{}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0018453279651065259},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001583531274742676}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"(":{"docs":{},"n":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"(":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"2":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"docs":{}}}}},"o":{"docs":{},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"i":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003289473684210526},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.006683081252198382},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},"@":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"d":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"s":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"p":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},".":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"y":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"[":{"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"docs":{}}}}}}}}}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"(":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},":":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}},"_":{"docs":{},"o":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},"s":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"b":{"docs":{},"e":{"docs":{},"t":{"docs":{},"w":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{},"s":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124}}}}}}}}},"_":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}},"r":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},")":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}},"u":{"docs":{},"i":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002681478643937943}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"a":{"docs":{},"r":{"docs":{},"g":{"docs":{},"u":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"c":{"docs":{},"e":{"docs":{},"p":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"'":{"docs":{},"n":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},"_":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"[":{"docs":{},"'":{"docs":{},"'":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"n":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"g":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"o":{"docs":{},"l":{"docs":{},"v":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"i":{"docs":{},"s":{"docs":{},"c":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"(":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}}}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":5.014705882352941},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.015299026425591099},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},":":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"i":{"docs":{},"t":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003355141754739138},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"o":{"docs":{},"v":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.037383177570093455},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.005050505050505051},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.005431093007467753},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"l":{"docs":{},"d":{"docs":{},"(":{"docs":{},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"h":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"|":{"docs":{},"c":{"docs":{},"|":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"s":{"docs":{},".":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}},"s":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}},"^":{"2":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"docs":{}}}},"2":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}},"^":{"2":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"docs":{}}}},"docs":{},"t":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"1":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649}}}},"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.009122807017543859}}}}}},"i":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}}},"i":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"x":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"s":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}},"l":{"docs":{},"a":{"docs":{},"c":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}},"e":{"docs":{},"f":{"docs":{},"f":{"docs":{},"i":{"docs":{},"c":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}}},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"(":{"docs":{},"$":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}},"c":{"docs":{},"i":{"docs":{},"r":{"docs":{},"c":{"docs":{},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295}},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"p":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"o":{"docs":{},"s":{"docs":{},"_":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0036555645816409425}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},":":{"docs":{},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"docs":{}},"docs":{}}}}}}}}}}}}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}},"n":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},"h":{"docs":{},"i":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"e":{"docs":{},"r":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"u":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"!":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0035433824937751387},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"e":{"docs":{},"a":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.009633911368015413},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"l":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},":":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"n":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}},"i":{"docs":{},"f":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"i":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000861903849837196}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000861903849837196},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},"docs":{}},"docs":{}}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"i":{"docs":{},"v":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"f":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"g":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}},"s":{"docs":{},")":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0035087719298245615}}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}},"m":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.004061738424045491},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.00487012987012987},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"\"":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0021303792074989347}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.003550632012498225}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449}}}}},"%":{"docs":{},"l":{"docs":{},"f":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}}}}}}}}},"`":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449}}}}},"~":{"docs":{},"%":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}}}},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"g":{"docs":{},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},";":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"(":{"docs":{},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"n":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"f":{"docs":{},"t":{"docs":{},"o":{"docs":{},"f":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"a":{"docs":{},"n":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"m":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}},"u":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"e":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"i":{"docs":{},"n":{"docs":{},"m":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}}}},"z":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},"e":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"!":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"o":{"docs":{},"s":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},"e":{"docs":{},"s":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}},"t":{"docs":{},"!":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"'":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.008116883116883116},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0033944331296673455},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002803083391730904},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}},"e":{"docs":{},"m":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003153468815697267}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"x":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"y":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"s":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178}}},";":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"?":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0017271157167530224},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":3.3372024856372375},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.007098121085594989},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"t":{"docs":{},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{},"s":{"docs":{},":":{"docs":{},":":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{},"s":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},"_":{"docs":{},"t":{"docs":{},"u":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"(":{"docs":{},"&":{"docs":{},"x":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},")":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"x":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"s":{"docs":{},"\"":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"!":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"e":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"z":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"!":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"?":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},")":{"docs":{},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"'":{"docs":{},"l":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"m":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0035087719298245615}}}}}},"f":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},"e":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}},"f":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}},"t":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},"(":{"docs":{},"n":{"docs":{},"p":{"docs":{},".":{"docs":{},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},"i":{"docs":{},"p":{"docs":{},"l":{"docs":{},"y":{"docs":{},"(":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"1":{"docs":{},")":{"docs":{},",":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"2":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}},"docs":{}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}},"(":{"2":{"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"docs":{}},"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},".":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"1":{"docs":{},"(":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}},"docs":{}}}},"i":{"docs":{},"s":{"docs":{},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"x":{"docs":{},"(":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"z":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}},"a":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"n":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"$":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"(":{"docs":{},"$":{"docs":{},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"{":{"1":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408}}}}},"docs":{}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0028782894736842104},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"o":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"[":{"docs":{},"]":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}},"z":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0025163563160543532}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"1":{"docs":{},")":{"docs":{},".":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},".":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}}}}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"n":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"e":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"l":{"docs":{},"l":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}}}}},"+":{"1":{"docs":{},")":{"docs":{},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}},"docs":{},"+":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604}}}},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},"/":{"2":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"docs":{}}}}}}}}}}}}}}}}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002533650039588282}}},"e":{"docs":{},"e":{"docs":{},"e":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"*":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"d":{"docs":{},"x":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"=":{"0":{"docs":{},":":{"1":{"8":{"4":{"4":{"6":{"7":{"4":{"4":{"0":{"7":{"3":{"7":{"0":{"9":{"5":{"5":{"1":{"6":{"1":{"5":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"\\":{"docs":{},"h":{"docs":{},"a":{"docs":{},"t":{"docs":{},"{":{"docs":{},"h":{"docs":{},"}":{"docs":{},"_":{"docs":{},"k":{"docs":{},"]":{"docs":{},"d":{"docs":{},"t":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"docs":{}}}},"docs":{}}}}}}}}}}}},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"j":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.006107717934480844},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0068669527896995704},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0030058237835806877},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0032245062474808546},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.006809184481393508},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}},"m":{"docs":{},"e":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007773459189339256},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009057225195553726},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005627857896588111},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006944444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.010862186014935505},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01242603550295858},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719}},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"v":{"docs":{},"a":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"s":{"docs":{},"c":{"docs":{},"r":{"docs":{},"i":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"/":{"docs":{},"t":{"docs":{},"y":{"docs":{},"p":{"docs":{},"e":{"docs":{},"s":{"docs":{},"c":{"docs":{},"r":{"docs":{},"i":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}}}}}}}}}}}}}},".":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"l":{"docs":{},".":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},"s":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"n":{"docs":{},"k":{"docs":{},"e":{"docs":{},"d":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"m":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"m":{"docs":{},";":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}}}}}}}},"*":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"m":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}},"i":{"docs":{},"o":{"docs":{},".":{"docs":{},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"e":{"docs":{},"w":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}},"i":{"docs":{},"o":{"docs":{},"e":{"docs":{},"x":{"docs":{},"c":{"docs":{},"e":{"docs":{},"p":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},";":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"v":{"docs":{},"i":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":5.001926782273603},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}},"s":{"docs":{},"_":{"docs":{},"c":{"docs":{},"r":{"docs":{},"o":{"docs":{},"s":{"docs":{},"s":{"docs":{},"(":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"[":{"docs":{},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"1":{"docs":{},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"docs":{}}}},"s":{"docs":{},"(":{"0":{"docs":{},",":{"0":{"docs":{},")":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}},"docs":{}}},"docs":{}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"s":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},":":{"docs":{},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.003371868978805395}},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"s":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}},".":{"docs":{},"c":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"r":{"docs":{},"u":{"docs":{},"n":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"u":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754}}}}}}}},"o":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"a":{"docs":{},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"y":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904}}},"b":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"k":{"docs":{},"e":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}},"h":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"a":{"docs":{},"n":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"s":{"docs":{},"e":{"docs":{},"p":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"r":{"docs":{},"d":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001583531274742676}},"\"":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},":":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}},"r":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},"u":{"docs":{},"l":{"docs":{},"i":{"docs":{},"a":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"'":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"u":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001819574794100747},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0020665038512117226}},"s":{"docs":{},"s":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"r":{"docs":{},"k":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},"a":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"w":{"docs":{},"i":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"f":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}},"m":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002011108982953457},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0020130850528434826},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0014614056064833267},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298}}}},"n":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"z":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}}},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"z":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}},"z":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009299853859439352}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001677570877369569},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},"e":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"g":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"]":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},")":{"docs":{},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}},"+":{"1":{"docs":{},")":{"docs":{},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}},"docs":{}},"*":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"d":{"docs":{},"x":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"i":{"docs":{},"m":{"docs":{},"m":{"docs":{},"i":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"e":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"b":{"docs":{},"e":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"k":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.005823783580687582},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.007971014492753623},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"n":{"docs":{},"o":{"docs":{},"w":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"l":{"docs":{},"e":{"docs":{},"d":{"docs":{},"g":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488}},"e":{"docs":{},",":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044}}},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},":":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"!":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"b":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"e":{"docs":{},"w":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"e":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}}}},"y":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002125680882157566},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.012526096033402923},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"(":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},":":{"docs":{},":":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"w":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"s":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}},"=":{"docs":{},"(":{"docs":{},"p":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}},"l":{"docs":{},"a":{"docs":{},"m":{"docs":{},"b":{"docs":{},"d":{"docs":{},"a":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}}}}}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405}}}},"p":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"r":{"docs":{},"c":{"docs":{},"k":{"docs":{},"h":{"docs":{},"o":{"docs":{},"f":{"docs":{},"f":{"docs":{},"s":{"docs":{},"'":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004912280701754386},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.015450643776824034}},"!":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649}},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}}}}}}}}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737}}},":":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{},"j":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}},"[":{"docs":{},"i":{"docs":{},",":{"docs":{},"j":{"docs":{},"]":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}},"_":{"docs":{},"f":{"docs":{},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}},"s":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852}}}},"*":{"0":{"docs":{},".":{"5":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}},"docs":{}}},"docs":{}}}}}}}}}}},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},".":{"docs":{},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"t":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}}}},"o":{"docs":{},"t":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},".":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"e":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"r":{"docs":{},"a":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}},"t":{"docs":{},"h":{"docs":{},"x":{"docs":{},"b":{"docs":{},"y":{"docs":{},"e":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"i":{"docs":{},"c":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"o":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},"d":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"a":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"l":{"docs":{},"l":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},".":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"(":{"docs":{},"(":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"_":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},"i":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"s":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}}}}}}},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009299853859439352},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002881844380403458},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}},"u":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.01971830985915493},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002881844380403458},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},",":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"s":{"docs":{},".":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"'":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},":":{"docs":{},"\"":{"docs":{},"j":{"docs":{},"u":{"docs":{},"l":{"docs":{},"i":{"docs":{},"a":{"docs":{},"\"":{"docs":{},"]":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"/":{"docs":{},"j":{"docs":{},"u":{"docs":{},"l":{"docs":{},"i":{"docs":{},"a":{"docs":{},"/":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"v":{"docs":{},".":{"docs":{},"j":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"=":{"docs":{},"\"":{"docs":{},"j":{"docs":{},"l":{"docs":{},"\"":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}},"e":{"docs":{},"v":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}},"d":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"s":{"docs":{},"c":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}}}},"b":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"v":{"docs":{},"i":{"docs":{},"e":{"docs":{},"w":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}},"e":{"docs":{},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394}},"_":{"0":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"1":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"2":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"docs":{}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}},"=":{"docs":{},"\"":{"docs":{},"p":{"docs":{},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}},"c":{"docs":{},"k":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},")":{"docs":{},":":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"x":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002881844380403458}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"s":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004912280701754386},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0028782894736842104},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011956954962136308},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"y":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"r":{"docs":{},"g":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"r":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"y":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"e":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"c":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"w":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}},"e":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0012449722275426163},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0039856516540454365},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0026300958106331017}},"r":{"docs":{},"n":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.01348747591522158},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"!":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"i":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"s":{"docs":{},"'":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.001062840441078783}},"(":{"docs":{},"*":{"docs":{},"t":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"_":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"c":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"i":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"s":{"docs":{},"y":{"docs":{},"m":{"docs":{},"b":{"docs":{},"o":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"v":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"p":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.008333333333333333}}},"s":{"docs":{},"t":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"m":{"docs":{},"o":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"c":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"s":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}}}},"f":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0026571011026969575},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.003371868978805395},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"?":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009299853859439352},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"_":{"docs":{},"d":{"docs":{},"f":{"docs":{},"s":{"docs":{},"(":{"docs":{},"&":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"[":{"1":{"docs":{},".":{"docs":{},".":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"docs":{}}}}}}}}}}}}}}}}}},"f":{"docs":{},"s":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},":":{"docs":{},"u":{"docs":{},"n":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"{":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}},".":{"docs":{},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"_":{"docs":{},"m":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"s":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.003371868978805395},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},".":{"docs":{},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"s":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"v":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"m":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"s":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"r":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0030058237835806877}},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},".":{"docs":{},"_":{"docs":{},"_":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}},"n":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}}}}}}}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},"_":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"o":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}}}}}}},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412}}}}}}}}}}}}}}}}},"x":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"y":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"d":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"a":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}},"docs":{}}}},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0031885213232363493},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}}}},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"q":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"s":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}},")":{"docs":{},":":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}}}},"x":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"y":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"d":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125}}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0020665038512117226}},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"s":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"(":{"docs":{},"i":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"o":{"docs":{},"n":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"s":{"docs":{},":":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"'":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.009735744089012517},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.005479452054794521},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.00487012987012987},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}}}},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.004116920543433511},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{"./":{"ref":"./","tf":0.03571428571428571},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.009633911368015413},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.016901408450704224},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.0847457627118644},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0035087719298245615},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.043478260869565216},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000861903849837196},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.044642857142857144},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.05952380952380952},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.04504504504504504},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.04672897196261682},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0390625},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.01838235294117647},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004151838671411625},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0024084778420038534},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.006954102920723227},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.024291497975708502},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.013333333333333334},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.009994447529150472},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.010638297872340425},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.015306122448979591},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009880609304240428},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002843216896831844},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.015068493150684932},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.007725321888412017},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.00487012987012987},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.006683081252198382},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.008838383838383838},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.007933194154488519},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.012898845892735914},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.014201183431952662},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005606166783461808},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.005081874647092038},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}},"e":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007773459189339256},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009057225195553726},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005627857896588111},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006944444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.010862186014935505},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01242603550295858},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"m":{"docs":{},"d":{"docs":{},")":{"docs":{},".":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},";":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},":":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}}}}},"n":{"docs":{},"k":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}},"s":{"docs":{},":":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}},"e":{"docs":{},"d":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.007410456978180321},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.005050505050505051},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004142011834319527},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"a":{"docs":{},"r":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004142011834319527}},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"e":{"docs":{},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"(":{"docs":{},"a":{"docs":{},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047}}}}}}},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},")":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"g":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"t":{"docs":{},"t":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},",":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}},"e":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"a":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"m":{"docs":{},":":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"r":{"docs":{},"p":{"docs":{},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002125680882157566},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.005090054815974941},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"$":{"docs":{},"b":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"a":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"b":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"c":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"f":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"x":{"0":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"docs":{}}}}}}}}}}}}}}}}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}},"x":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}},"y":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}}}}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004210526315789474}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},"[":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}},"p":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"f":{"docs":{},"e":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0024183796856106408},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}}}}},"k":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"l":{"docs":{},"i":{"docs":{},"h":{"docs":{},"o":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"m":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"s":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"y":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"e":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"i":{"docs":{},"k":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}}}},"o":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},"o":{"docs":{},"k":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011956954962136308},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.00699876492383697},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003153468815697267},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"s":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"s":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"s":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"v":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.007707129094412331},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},"s":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}},"a":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001677570877369569},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.001062840441078783},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002843216896831844},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003700657894736842}},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},".":{"docs":{},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0035587188612099642},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0024621878297572987},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"!":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},")":{"docs":{},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0035587188612099642}}},":":{"docs":{},":":{"docs":{},"c":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643}}}}}}}}}}}}}}}}}}},"[":{"1":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}},"}":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},"}":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}},"docs":{}}},"l":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"m":{"docs":{},"r":{"docs":{},"o":{"docs":{},"f":{"docs":{},"l":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"n":{"docs":{},"l":{"docs":{},"o":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"g":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},")":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"l":{"docs":{},"y":{"docs":{},"!":{"docs":{},"'":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"?":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"f":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"w":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"s":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}},"a":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0015942606616181746},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"g":{"2":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}},"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047}},"i":{"docs":{},"c":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":5.004109589041096},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},"s":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557}},"e":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}},"docs":{},"t":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"1":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},"docs":{}}}}}}}}}}}}}}},"r":{"docs":{},"_":{"0":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}}},"docs":{}}}},"_":{"2":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"docs":{}},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.005681818181818182},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.01051156271899089}},"i":{"docs":{},"c":{"docs":{},"(":{"docs":{},"a":{"docs":{},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}},"[":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},"/":{"2":{"docs":{},"+":{"1":{"docs":{},":":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}},"docs":{}}},"docs":{}}}}}}}}}}}}}}}},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},")":{"docs":{},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}},"u":{"docs":{},"a":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}},"c":{"docs":{},"k":{"docs":{},"i":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.003985507246376811}}}}},"d":{"docs":{},"w":{"docs":{},"i":{"docs":{},"g":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}},":":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003355141754739138}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003355141754739138}}},"c":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"s":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"l":{"docs":{},"h":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},".":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"i":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535}}},".":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"(":{"docs":{},"c":{"docs":{},"(":{"docs":{},"w":{"docs":{},")":{"docs":{},")":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}},"_":{"1":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"2":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}},"docs":{}},"c":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"]":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852}}},"y":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"m":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0018599707718878703},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.010738255033557046},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.009184481393507521}},"a":{"docs":{},"t":{"1":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}},"docs":{}}}}}}}}},"2":{"docs":{},")":{"docs":{},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}},"docs":{}}}}}}}}},"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0022169437846397467}},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593}},"r":{"docs":{},"i":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}},"a":{"docs":{},"l":{"docs":{},";":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742}},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"h":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"e":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":5.034782608695652},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.026785714285714284},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"i":{"docs":{},"c":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044}}},",":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364}}}},"a":{"docs":{},"l":{"docs":{},".":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}},".":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044}},"a":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},"s":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001677570877369569}}}},"[":{"docs":{},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"]":{"docs":{},"[":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}}}}}}}}}}}}}},"b":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001677570877369569}}}}},"p":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"d":{"docs":{},"i":{"docs":{},"u":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}},"o":{"docs":{},"w":{"docs":{},"[":{"docs":{},"c":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"s":{"docs":{},"(":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"t":{"docs":{},"a":{"docs":{},"n":{"2":{"docs":{},"(":{"docs":{},"a":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}},"docs":{}},"docs":{}}}}}},"p":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},"docs":{}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},".":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"f":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"(":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"y":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}}}}}},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"j":{"docs":{},"a":{"docs":{},"x":{"docs":{},".":{"docs":{},"h":{"docs":{},"u":{"docs":{},"b":{"docs":{},".":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},"[":{"docs":{},"\"":{"docs":{},"t":{"docs":{},"y":{"docs":{},"p":{"docs":{},"e":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"j":{"docs":{},"a":{"docs":{},"x":{"docs":{},".":{"docs":{},"h":{"docs":{},"u":{"docs":{},"b":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"/":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}},"c":{"docs":{},"e":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"é":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"q":{"docs":{},"u":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"s":{"docs":{},"!":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"h":{"docs":{},"e":{"docs":{},"w":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"l":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"c":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.001062840441078783},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"r":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.026785714285714284},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428}}},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"x":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":5.017857142857143},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.01393507521773555},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.008284023668639054}},"!":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002533650039588282},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828}}},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}},"_":{"docs":{},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},"i":{"docs":{},"p":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"[":{"docs":{},"]":{"docs":{},"[":{"docs":{},"]":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}}}}}}}}}}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}}},":":{"docs":{},"\"":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{},"l":{"docs":{},"i":{"docs":{},"b":{"docs":{},".":{"docs":{},"c":{"docs":{},"m":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"s":{"docs":{},".":{"docs":{},"h":{"docs":{},"s":{"docs":{},"v":{"docs":{},"_":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"r":{"docs":{},"g":{"docs":{},"b":{"docs":{},"(":{"docs":{},"h":{"docs":{},"s":{"docs":{},"v":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"y":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},".":{"docs":{},"x":{"docs":{},"i":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"x":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"z":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"y":{"docs":{},"i":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"x":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"z":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"z":{"docs":{},"i":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"x":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"z":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"i":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.005614035087719298},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0018453279651065259},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0012782275244993609},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"[":{"docs":{},"]":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}},"a":{"docs":{},"r":{"docs":{},"g":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"l":{"docs":{},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"l":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"n":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.005873140172278779},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}},"a":{"docs":{},"g":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0234375},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.011029411764705883},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0037052284890901604},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"p":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.026785714285714284},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"(":{"docs":{},"\"":{"docs":{},"a":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"b":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"c":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"d":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"e":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"*":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"_":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"t":{"docs":{},"i":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"s":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"i":{"docs":{},"v":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"y":{"docs":{},"b":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"e":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},"(":{"docs":{},"'":{"docs":{},"?":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},"s":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},"e":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"(":{"docs":{},"[":{"docs":{},"]":{"docs":{},"r":{"docs":{},"u":{"docs":{},"n":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"docs":{}},"docs":{}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"[":{"docs":{},"r":{"docs":{},"u":{"docs":{},"n":{"docs":{},"e":{"docs":{},"]":{"docs":{},"*":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},"_":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"_":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767}}}}}}}},"r":{"docs":{},"k":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"d":{"docs":{},"o":{"docs":{},"w":{"docs":{},"n":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}},"e":{"docs":{},"t":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}},"o":{"docs":{},"v":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"c":{"docs":{},"h":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":5.0014450867052025},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.004166666666666667}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"}":{"docs":{},"&":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"i":{"docs":{},"u":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742}}}},"r":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}},"a":{"docs":{},"g":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":3.3348995040459406}},"e":{"docs":{},"s":{"docs":{},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{},"l":{"docs":{},"i":{"docs":{},"a":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}}}},"d":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},"(":{"4":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"o":{"docs":{},"f":{"docs":{},"(":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}},"e":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}}}}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"e":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0018599707718878703},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"$":{"docs":{},"(":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{},"_":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"[":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{},"_":{"docs":{},"_":{"docs":{},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"_":{"docs":{},"_":{"docs":{},")":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"_":{"docs":{},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"l":{"docs":{},"$":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"o":{"docs":{},"w":{"docs":{},"$":{"docs":{},"(":{"docs":{},"?":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"[":{"docs":{},"c":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}}},"r":{"docs":{},"u":{"docs":{},"n":{"docs":{},"e":{"docs":{},"]":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"m":{"docs":{},"_":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"h":{"docs":{},"e":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"d":{"docs":{},"i":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"x":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"_":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"y":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"i":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}}}},"i":{"docs":{},"m":{"docs":{},"u":{"docs":{},"m":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"b":{"docs":{},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"y":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"(":{"1":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}},"z":{"docs":{},"z":{"docs":{},"u":{"docs":{},"c":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"g":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{},"d":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006313131313131313},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},":":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"_":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"d":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},"f":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},":":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}},"!":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}},"i":{"docs":{},"c":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},":":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"j":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"e":{"docs":{},"a":{"docs":{},"n":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.009122807017543859},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.007305194805194805},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.00421179302045728},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.00350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.006211180124223602},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"f":{"docs":{},"u":{"docs":{},"l":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"w":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"s":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"?":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"s":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.004698512137823023}},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}}},"o":{"docs":{},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},")":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"[":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}}}}}}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"(":{"docs":{},"&":{"docs":{},":":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},"?":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"[":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"/":{"docs":{},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742}},"'":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"[":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"h":{"docs":{},"u":{"docs":{},"s":{"docs":{},"b":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},"s":{"docs":{},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}},"c":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"y":{"docs":{},"(":{"docs":{},"t":{"docs":{},"m":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}},"d":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},"_":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"r":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"y":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"(":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"h":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000861903849837196},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":5.044642857142857},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0234375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013285505513484788},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004744958481613286},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.009824561403508772},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0021303792074989347},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":3.335147118097541},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.005431093007467753},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.00350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.003952569169960474}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},"s":{"docs":{},".":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"\"":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"'":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"!":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"o":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.006884057971014493}}}},"e":{"docs":{},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"r":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":10.010163749294184}},"s":{"docs":{},"\"":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"x":{"0":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"docs":{}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},"s":{"docs":{},"s":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0039856516540454365},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.021920668058455117}},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},":":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.001062840441078783}},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}}}},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405}},"e":{"docs":{},"r":{"docs":{},"'":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},")":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},";":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}},"i":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"e":{"docs":{},"v":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.005415162454873646}},"i":{"docs":{},"c":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},"!":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}}}}}},"r":{"docs":{},"g":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"v":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"i":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"n":{"docs":{},"d":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"e":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"s":{"docs":{},"w":{"docs":{},"e":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"i":{"docs":{},"m":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581}},"u":{"docs":{},"m":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"(":{"docs":{},"t":{"docs":{},"u":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},")":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}},"b":{"docs":{},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"y":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}},"(":{"1":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}},"p":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}}}},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"e":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}},"u":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"s":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"r":{"docs":{},"e":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"n":{"docs":{},"i":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"d":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"e":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}}}}}}}},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}},"o":{"docs":{},"d":{"1":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0055359838953195776},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507}},"e":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}},"r":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488}}}},"l":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"s":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"i":{"docs":{},"f":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0029585798816568047},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"(":{"1":{"5":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"9":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"4":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{},"a":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"b":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}}}}}},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}},"u":{"docs":{},"l":{"docs":{},"o":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754}},"(":{"docs":{},"a":{"docs":{},",":{"docs":{},"b":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"s":{"docs":{},".":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}},"r":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.03389830508474576},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.023809523809523808},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.001062840441078783},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003855278766310795},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0037052284890901604},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.005681818181818182},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.004220893422441084},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.005415162454873646},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0035502958579881655},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004204625087596356},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"r":{"docs":{},"i":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}},"s":{"docs":{},"'":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005956552207428171}}}}}}},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"o":{"docs":{},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029}}}}},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"'":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}}}}}},"v":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.020206856923960927},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004361684281160879},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.012222665072406005},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.007702423445425512},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0035502958579881655},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}},"s":{"docs":{},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"s":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157}}}},"u":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},"i":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}},"s":{"docs":{},"d":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0030058237835806877},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.005823036500497088}}}},"q":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0037572797294758596}}}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"u":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.004433696090286175},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.01263537906137184}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"l":{"docs":{},"i":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":5.006092607636068},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891}},"h":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.004166666666666667}},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},")":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"r":{"docs":{},"l":{"docs":{},"o":{"docs":{},"(":{"1":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{},"s":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"r":{"docs":{},"l":{"docs":{},"o":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}},"(":{"1":{"0":{"0":{"0":{"0":{"0":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},".":{"docs":{},"c":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"r":{"docs":{},"u":{"docs":{},"n":{"docs":{},"(":{"1":{"0":{"0":{"0":{"0":{"0":{"0":{"0":{"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"g":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}}}}}},"p":{"docs":{},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"(":{"1":{"0":{"0":{"docs":{},"_":{"0":{"0":{"0":{"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}},"docs":{}},"docs":{}}}}}}}}}}},"d":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"o":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.01213768115942029}},"'":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},")":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}},"u":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.007017543859649123},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"c":{"docs":{},"h":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},".":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"l":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}},"i":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":5.0177304964539005},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.007653061224489796},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002803083391730904},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}},".":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},":":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"s":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"y":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"m":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}}}},"d":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}},"s":{"docs":{},"d":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0028405056099985795}}}},"l":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":3.3374066530889337}}}}}},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0019883539269990058},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.004635227730753728},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}},";":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}},"[":{"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}}}},"2":{"docs":{},"]":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}}}},"docs":{}}},"y":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"t":{"docs":{},"i":{"docs":{},"f":{"docs":{},"y":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}},":":{"docs":{},":":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}},"k":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001677570877369569}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"!":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"m":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"w":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"e":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"o":{"docs":{},"p":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"(":{"docs":{},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"_":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"v":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"+":{"docs":{},"+":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465}}}}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"?":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"]":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"g":{"docs":{},"[":{"docs":{},"m":{"docs":{},"]":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"_":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0028214429665457475}}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}},"'":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}},"c":{"docs":{},"m":{"docs":{},"c":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.011482254697286013},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.007653061224489796},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.004061738424045491},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.00631578947368421},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.013150479053165508},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.008116883116883116},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0038691523039043265},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0047522063815342835},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0019927536231884057},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.025423728813559324}},"e":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},".":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"!":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"l":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}},"e":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.017391304347826087},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.001062840441078783},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.013333333333333334},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.004528612597776863},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00684931506849315},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0077192982456140355},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.005681818181818182},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0029585798816568047},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891}},"e":{"docs":{},"d":{"docs":{},"?":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}},".":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}},"a":{"docs":{},"r":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"l":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"b":{"docs":{},"i":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}},"t":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009}},"?":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"w":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.005614035087719298},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.017391304347826087},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0033518483049224286},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0038527965989105886},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.01096319498825372},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.011078998073217727},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.004924375659514597},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005606166783461808},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"(":{"1":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}}},"docs":{}},"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"}":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"x":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"z":{"docs":{},"e":{"docs":{},"r":{"docs":{},"o":{"docs":{},"s":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"_":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"e":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004744958481613286}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.009489916963226572}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518}}},"u":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004744958481613286}},"e":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0035587188612099642}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643}}}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643}}}}}}}},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}},"[":{"docs":{},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}}}}},"c":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"docs":{},"i":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"d":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"docs":{},"i":{"docs":{},"+":{"1":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},"f":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"s":{"docs":{},".":{"docs":{},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"f":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"e":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{},"'":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}},"x":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011956954962136308},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.005797101449275362},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},"_":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},"e":{"docs":{},"s":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0038346825734980826}},"s":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}}}},"(":{"docs":{},"(":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"p":{"docs":{},"o":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002272404487998864}}}},"!":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"g":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001509813789632612},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603}}}}}}}},"o":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.011269276393831554},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"_":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"_":{"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"_":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"_":{"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}},"[":{"4":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518}}}}},"docs":{}}},".":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"u":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935}}}}},"o":{"docs":{},"t":{"docs":{},"e":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"h":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"a":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":5.013798701298701},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854}}}},"\"":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}},"b":{"docs":{},"l":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}},"_":{"docs":{},"b":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"i":{"docs":{},"c":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"f":{"docs":{},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002898550724637681},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.023809523809523808},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"m":{"docs":{},"e":{"docs":{},"r":{"docs":{},"c":{"docs":{},"i":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},"z":{"docs":{},"e":{"docs":{},"r":{"docs":{},"o":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"w":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"a":{"docs":{},"d":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}},"s":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"d":{"docs":{},"e":{"1":{"0":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"1":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"2":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"}":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},".":{"docs":{},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}},"[":{"2":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"docs":{}}},"2":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},".":{"docs":{},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}},"[":{"1":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"2":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"docs":{}}},"3":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"}":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"4":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"}":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},"5":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"6":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"}":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"7":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"8":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"}":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"9":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"}":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.00631578947368421},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.010055544914767286},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00810415836322572},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0050415183867141165}},"(":{"0":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}},"1":{"0":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"1":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"2":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"2":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"3":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"4":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"5":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"6":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"7":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"8":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"9":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}},"i":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"docs":{}},"docs":{}}}}}}},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"s":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},"(":{"docs":{},"o":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"y":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},".":{"docs":{},"t":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},"(":{"docs":{},"b":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002681478643937943},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}},"s":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"*":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"q":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"(":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.001062840441078783},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"!":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"docs":{}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}},".":{"docs":{},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"{":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}},"?":{"docs":{},".":{"docs":{},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}},"1":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"docs":{}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},"(":{"docs":{},"n":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}}}}}},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},">":{"docs":{},">":{"docs":{},"b":{"docs":{},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},"f":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}}}}}}}},"[":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"_":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},"(":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"{":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}},"p":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394}}}}}},"{":{"docs":{},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},")":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}}}},"'":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}}}}}}}}}}}}}}}}},"!":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"i":{"docs":{},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}},"b":{"docs":{},"o":{"docs":{},"d":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"r":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124}}},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"w":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"m":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"a":{"docs":{},"l":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.006355932203389831}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}},"!":{"docs":{},"(":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}}}},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"=":{"docs":{},"f":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},")":{"docs":{},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}},"i":{"docs":{},"s":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"e":{"docs":{},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"o":{"docs":{},"n":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"a":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}}},"m":{"docs":{},"e":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.004306969459671104},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"\"":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0023492560689115116},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742}}},"d":{"docs":{},"t":{"docs":{},"u":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"e":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}},"'":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},"s":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"n":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"d":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"i":{"docs":{},"v":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}},"ï":{"docs":{},"v":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339}}}}},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"o":{"docs":{},"l":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"m":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}}},"p":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"m":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409}}},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},".":{"docs":{},"z":{"docs":{},"e":{"docs":{},"r":{"docs":{},"o":{"docs":{},"s":{"docs":{},"(":{"docs":{},"(":{"5":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"docs":{},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}}}}}}}}}}},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}},"a":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},".":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}},"docs":{}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},".":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}},"y":{"docs":{},")":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}}}}}},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"l":{"docs":{},"(":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},"_":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},")":{"docs":{},")":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}}}}}}}}},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},"[":{"docs":{},"x":{"docs":{},"_":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"n":{"docs":{},"i":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"(":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"x":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"a":{"docs":{},"v":{"docs":{},"e":{"docs":{},"t":{"docs":{},"x":{"docs":{},"t":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}}}},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},".":{"1":{"docs":{},"*":{"docs":{},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}}}},"docs":{}}},"docs":{},"n":{"docs":{},"p":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"g":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}},"m":{"docs":{},"s":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"b":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},".":{"docs":{},"s":{"docs":{},"u":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"t":{"docs":{},"(":{"docs":{},"[":{"docs":{},"[":{"1":{"docs":{},".":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}},"docs":{}}},"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"(":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"m":{"docs":{},"f":{"docs":{},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"_":{"docs":{},"f":{"docs":{},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"f":{"docs":{},"t":{"docs":{},".":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},"_":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}},"i":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},"(":{"docs":{},"f":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"g":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}},"i":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"]":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"f":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"n":{"docs":{},"p":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"n":{"docs":{},"p":{"docs":{},".":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},"x":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"(":{"docs":{},"[":{"1":{"0":{"docs":{},".":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}},"docs":{}},"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"*":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"$":{"docs":{},"[":{"docs":{},":":{"1":{"0":{"0":{"0":{"0":{"docs":{},"]":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}}}}}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}},"[":{"2":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"docs":{}}}},")":{"docs":{},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"(":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"a":{"docs":{},"[":{"docs":{},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"_":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},":":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"f":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"docs":{},"(":{"docs":{},"h":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"(":{"docs":{},"n":{"docs":{},"p":{"docs":{},".":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}}}}}}}}}}}}}}}}}}}}},"j":{"docs":{},"(":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},"_":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"(":{"docs":{},"f":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"h":{"docs":{},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}},"a":{"docs":{},"n":{"docs":{},"(":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"e":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"a":{"docs":{},"x":{"docs":{},"i":{"docs":{},"s":{"docs":{},"(":{"docs":{},"(":{"docs":{},"h":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},"(":{"docs":{},"x":{"docs":{},"_":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011956954962136308},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},"p":{"docs":{},"t":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}},"m":{"1":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00536822680758262}}},"2":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004361684281160879}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844}},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001509813789632612},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.014184397163120567},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.005763688760806916},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.019178082191780823},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004210526315789474},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.006493506493506494},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.005845511482254697},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.005978260869565218},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.010161177295024528},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.009034443817052512},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00847457627118644}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},"e":{"docs":{},".":{"docs":{},"e":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"4":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"5":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"9":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"docs":{}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},".":{"docs":{},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"4":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"5":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"9":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"docs":{}}}}}}}}}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.005479452054794521},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},":":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"?":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"!":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603}}}},"_":{"docs":{},"o":{"docs":{},"f":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"'":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},")":{"docs":{},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}},"`":{"docs":{},"t":{"docs":{},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"docs":{}},"docs":{}}}}}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"s":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"{":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},".":{"docs":{},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},"}":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}}},"o":{"docs":{},"r":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}},"s":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"i":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},"s":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"p":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"t":{"docs":{},"h":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}},"s":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0015322735108216816},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},".":{"docs":{},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000861903849837196}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"_":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"i":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408}}}}}}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},".":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"j":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},".":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"^":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"t":{"docs":{},"h":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}}}}}}}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.006355932203389831}}},"}":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"_":{"2":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{},"s":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"s":{"docs":{},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"_":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"s":{"docs":{},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"v":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"{":{"docs":{},"v":{"docs":{},"+":{"1":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"}":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"=":{"1":{"0":{"0":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},":":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}},"docs":{}},"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"2":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"3":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"4":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"7":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"docs":{}},"d":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"=":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}},"v":{"docs":{},"i":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}},"/":{"2":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}},"docs":{}},"]":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}},"docs":{}}}}}},"+":{"1":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"docs":{}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}}}}}},"(":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}}}}}},"v":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002803083391730904}},"a":{"docs":{},")":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}}}}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"y":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"m":{"docs":{},"s":{"docs":{},"d":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"r":{"docs":{},"m":{"docs":{},"s":{"docs":{},"d":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}}}}},"o":{"3":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"b":{"docs":{},"v":{"docs":{},"i":{"docs":{},"o":{"docs":{},"u":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"s":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"!":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"j":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"(":{"docs":{},"[":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002717391304347826},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"x":{"docs":{},"i":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011956954962136308},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.012145748987854251},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002717391304347826},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002452697967764541},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.006775832862789385},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}},"e":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"p":{"docs":{},")":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},";":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"?":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"s":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"g":{"docs":{},"o":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"c":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"e":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"t":{"docs":{},"o":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"u":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0022026431718061676},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.006954102920723227},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0024621878297572987},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"s":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"_":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"m":{"docs":{},"a":{"docs":{},"k":{"docs":{},"e":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{},"(":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"f":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"w":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.0138811771238201},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.013174145738987238},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.004924375659514597},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.003022974607013301},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.010732323232323232},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"s":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}},".":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394}}},"_":{"docs":{},"s":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}},"t":{"docs":{},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"p":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.011929824561403509}}},"[":{"docs":{},"t":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"1":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004912280701754386}}}},"2":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004912280701754386}}}},"docs":{}}}}}}}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"s":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"[":{"docs":{},"i":{"docs":{},",":{"docs":{},":":{"docs":{},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},":":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}},"s":{"docs":{},"(":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}}}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}}},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}}}}},"(":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}},"t":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"d":{"docs":{},"o":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}},"[":{"docs":{},"i":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}},"e":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"_":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}}}}}},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"e":{"docs":{},".":{"docs":{},"w":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}},"!":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"e":{"docs":{},"r":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.007415254237288136}},"e":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},":":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"s":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"v":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}},"f":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"n":{"docs":{},"d":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428}}}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0016280406052480367},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011956954962136308},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.006521739130434782}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"s":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"i":{"docs":{},"c":{"docs":{},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"!":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"\"":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"!":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"s":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"s":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{},"p":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"k":{"docs":{},"i":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"w":{"docs":{},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{},"m":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}},"a":{"docs":{},"l":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"l":{"docs":{},",":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"j":{"docs":{},"o":{"docs":{},"y":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"l":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"\"":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"k":{"docs":{},"i":{"docs":{},"l":{"docs":{},"l":{"docs":{},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"m":{"docs":{},"l":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}},"s":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0022168480451430876},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}},"t":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"[":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},">":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"m":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.013333333333333334},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.010300429184549357},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.008116883116883116},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0028139289482940555},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":3.3411930673115675},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.007933194154488519},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.00842358604091456},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004733727810650888}},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"!":{"docs":{},"=":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}},"=":{"docs":{},"=":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}},"&":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}}},".":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"s":{"docs":{},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767}},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},"&":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}},";":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"x":{"docs":{},")":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"x":{"docs":{},")":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"*":{"docs":{},"(":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}},"+":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}},"s":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"(":{"docs":{},"\"":{"docs":{},"s":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{},"p":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"k":{"docs":{},"i":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"i":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828}}}}}}},"a":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}},"@":{"docs":{},"(":{"docs":{},"o":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.007053607416364369}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},".":{"docs":{},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0026199113260781943}},"e":{"docs":{},"[":{"docs":{},"j":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"p":{"docs":{},"e":{"docs":{},"[":{"docs":{},"j":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0034260378879484078}}},"v":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0018137847642079807},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"j":{"docs":{},"]":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"a":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0068520757758968156},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},".":{"docs":{},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"|":{"docs":{},"x":{"docs":{},"|":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},"[":{"docs":{},"j":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},":":{"docs":{},"o":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"}":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"&":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"n":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"r":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"e":{"docs":{},"r":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0013407393219689715},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"2":{"4":{"docs":{},";":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}},")":{"docs":{},".":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}},".":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"i":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"a":{"docs":{},"l":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},"x":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"y":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},";":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"=":{"docs":{},"\"":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}},"g":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"s":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"w":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"h":{"docs":{},"i":{"docs":{},"p":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"l":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"[":{"0":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.010676156583629894}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"u":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}},"e":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0071174377224199285}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},".":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"y":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},":":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},".":{"docs":{},"c":{"docs":{},"m":{"docs":{},"p":{"docs":{},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"c":{"docs":{},"m":{"docs":{},"p":{"docs":{},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"x":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"y":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},"w":{"docs":{},"i":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}},"e":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},".":{"docs":{},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}},"s":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}},"i":{"docs":{},"c":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"(":{"docs":{},"g":{"docs":{},"o":{"docs":{},"o":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"a":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"s":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"c":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"l":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"o":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}},"d":{"docs":{},"d":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0061995115536351685},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"[":{"docs":{},"k":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}}},"s":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},"m":{"docs":{},"e":{"docs":{},"g":{"docs":{},"a":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0020665038512117226}}}}}},"(":{"1":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"3":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}},"docs":{},"\\":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"b":{"docs":{},")":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},")":{"docs":{},"?":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}}},"n":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"!":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"^":{"2":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"3":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"docs":{}}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"p":{"0":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}},"@":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"1":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},")":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},")":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}},".":{"0":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}},"1":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}},"docs":{},"x":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0024084778420038534},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465}}}},"y":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"*":{"docs":{},"(":{"docs":{},"p":{"2":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"3":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"docs":{}}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}},"docs":{}},"^":{"2":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}},"docs":{}}},"2":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}},"\"":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"^":{"2":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}},"docs":{}}},"3":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.004528612597776863},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0038691523039043265},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0015622780854992189},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0022168480451430876},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.004166666666666667},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.014084507042253521},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.020833333333333332},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"e":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},"u":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"t":{"docs":{},"h":{"docs":{},"o":{"docs":{},"r":{"docs":{},"a":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"n":{"docs":{},"b":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"e":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"s":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"a":{"docs":{},"r":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},".":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}},"c":{"docs":{},"k":{"docs":{},"'":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}},"y":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"t":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},"e":{"docs":{},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"u":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"g":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"i":{"docs":{},"n":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}},"c":{"docs":{},"k":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}},"o":{"docs":{},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":10.031700288184439},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0035174111853675696},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0018137847642079807},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.013257575757575758},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},";":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}},"t":{"docs":{},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},":":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"r":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"_":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},".":{"docs":{},"p":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}},"t":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},".":{"docs":{},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{},"s":{"docs":{},"(":{"1":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}}}}}}}}}}}}},"r":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"e":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}},"o":{"docs":{},"b":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.017391304347826087},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.011126564673157162},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.007220216606498195},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005606166783461808},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.009034443817052512},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":5.052966101694915}}},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},".":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"e":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}}},"y":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":5.046728971962617},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":3.335291046724093},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"!":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"s":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"c":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"e":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"s":{"docs":{},"s":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002058590657165479},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},".":{"docs":{},"w":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},":":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"o":{"docs":{},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"d":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"e":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.007707129094412331},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"m":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},",":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044}}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}},"j":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.02040816326530612},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},"s":{"docs":{},".":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}},"!":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"c":{"docs":{},"l":{"docs":{},"j":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}},"f":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}},"s":{"docs":{},"p":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"!":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}}},"v":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.006954102920723227},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"y":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"l":{"docs":{},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"o":{"docs":{},"s":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.004306969459671104},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}},"s":{"docs":{},"(":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"_":{"docs":{},"o":{"docs":{},"f":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"_":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"r":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}}},"d":{"docs":{},"u":{"docs":{},"k":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"c":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.003371868978805395},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"m":{"docs":{},"i":{"docs":{},"s":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"o":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"t":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}}}}},"h":{"docs":{},"i":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"l":{"docs":{},"i":{"docs":{},"f":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"o":{"docs":{},"f":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"f":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.008613938919342208},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"_":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"s":{"docs":{},".":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"o":{"docs":{},"f":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"docs":{}}}}}}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}},"s":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},":":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"i":{"docs":{},"x":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"[":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},"s":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"r":{"docs":{},"v":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"u":{"docs":{},"m":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"t":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"c":{"docs":{},"i":{"docs":{},"s":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"?":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"v":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478}},"a":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"i":{"docs":{},"o":{"docs":{},"u":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0015622780854992189},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.015054679732992472}},"s":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0026984803294986506}}}}}}},"p":{"docs":{},"o":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.005681011219997159}},"s":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}}}},"m":{"docs":{},"i":{"docs":{},"s":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.004596820532465045},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009299853859439352},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"(":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},".":{"docs":{},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}},"\"":{"docs":{},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"\\":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000861903849837196}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}},"t":{"docs":{},"h":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"\"":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"h":{"docs":{},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"\\":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}}}},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}}}}},"{":{"docs":{},":":{"docs":{},".":{"1":{"0":{"docs":{},"f":{"docs":{},"}":{"docs":{},"\"":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}}}}}}}}},"docs":{}},"docs":{}}}},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}}}}}}}}},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"g":{"docs":{},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}},"'":{"docs":{},"i":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"\\":{"docs":{},"n":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}},"t":{"docs":{},"h":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},".":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}},"f":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0014365064163953266},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}}}}}}}}}}}}}},"f":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},"q":{"docs":{},")":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}},"'":{"docs":{},"{":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"\"":{"docs":{},"u":{"docs":{},"s":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"{":{"docs":{},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"{":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"u":{"docs":{},"s":{"docs":{},"(":{"docs":{},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}}}}}}}}},"'":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"s":{"docs":{},"'":{"docs":{},":":{"docs":{},">":{"1":{"0":{"docs":{},"s":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"s":{"docs":{},":":{"1":{"0":{"docs":{},"d":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"docs":{}},"docs":{}}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"n":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011492051331162612}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551}}}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},".":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},"s":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},"s":{"docs":{},")":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}}}}}}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551}}}}}}}},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"_":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"(":{"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"docs":{}},"docs":{}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"(":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"docs":{}},"docs":{}},"docs":{}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"(":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"(":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"(":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"[":{"docs":{},"y":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}},"[":{"2":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"b":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"_":{"docs":{},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},"l":{"docs":{},"n":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935}},"!":{"docs":{},"(":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"\"":{"docs":{},"{":{"docs":{},":":{"docs":{},"?":{"docs":{},"}":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004210526315789474}}}}}},"#":{"docs":{},"?":{"docs":{},"}":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"}":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449}}}}}},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}},"{":{"docs":{},":":{"docs":{},">":{"1":{"9":{"docs":{},"}":{"docs":{},"]":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"docs":{}},"docs":{}},"?":{"docs":{},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}}}},"h":{"docs":{},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"t":{"docs":{},"h":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}}}}}},"(":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"\"":{"docs":{},"[":{"0":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"1":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"2":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}}}}}}}},"$":{"docs":{},"i":{"docs":{},"]":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"%":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},".":{"1":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}},"docs":{}}}},"n":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"a":{"docs":{},"n":{"docs":{},"n":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"c":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"i":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"a":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"b":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"t":{"docs":{},"h":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"h":{"docs":{},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},":":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},":":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}},"$":{"docs":{},"(":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}},"a":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"$":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{},"s":{"docs":{},"_":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"$":{"docs":{},"(":{"docs":{},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"_":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}},"{":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}}}}}}}}}}}}},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}}},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"_":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"(":{"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"(":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"docs":{}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"(":{"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"(":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"docs":{}}}}}}}}}}},"i":{"docs":{},"s":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"m":{"docs":{},"g":{"docs":{},"[":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},"a":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}}},"2":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"3":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"b":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"!":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"{":{"docs":{},"}":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0013407393219689715}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}}},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0016280406052480367},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}},"(":{"docs":{},"\"":{"docs":{},"%":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703696609844858}}},"l":{"docs":{},"f":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449}}}}}}}}},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}}}}}}},"t":{"docs":{},"h":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},":":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},":":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}}},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}},"g":{"docs":{},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}},"'":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"'":{"docs":{},".":{"docs":{},"p":{"docs":{},"h":{"docs":{},"p":{"docs":{},"_":{"docs":{},"e":{"docs":{},"o":{"docs":{},"l":{"docs":{},".":{"docs":{},"'":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}}}}}}}}}}},"%":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"s":{"docs":{},"\\":{"docs":{},"'":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}},"h":{"docs":{},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"t":{"docs":{},"h":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"f":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"e":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"i":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},")":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"e":{"docs":{},"v":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}}}}}}}},"m":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{},"(":{"docs":{},"a":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"(":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"x":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}},"v":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"c":{"docs":{},"i":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0016280406052480367},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0014614056064833267},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"e":{"docs":{},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"l":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"e":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"y":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},".":{"docs":{},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},"{":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}}}}}}}},"<":{"docs":{},">":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},"o":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"[":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"]":{"docs":{},"(":{"docs":{},")":{"docs":{},"(":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{},"b":{"docs":{},"y":{"docs":{},"(":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}},"{":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"}":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.03389830508474576},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.017391304347826087},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.023809523809523808},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.018018018018018018},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.018691588785046728},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.008344923504867872},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}},"r":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},".":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"s":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}},";":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"e":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"s":{"docs":{},"u":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}},"e":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"b":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.015438596491228071},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0046925876268914},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0018453279651065259},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0035870864886408927},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.015661707126076743},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.008670520231213872},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.005280259951259139},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"s":{"docs":{},"h":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}}}},"s":{"docs":{},"h":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0061290940432867265},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004529441368897836},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0019928258270227183},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.004696599661844825},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"(":{"docs":{},"&":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"!":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}},"s":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}},"/":{"docs":{},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"z":{"docs":{},"z":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0013407393219689715},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0028782894736842104},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"l":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141}}}}}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"a":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"g":{"docs":{},"e":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}},"s":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005255781359495445}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.004433696090286175}},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"c":{"docs":{},"u":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"l":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"l":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0012782275244993609},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.00421179302045728},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925}},"e":{"docs":{},"'":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"s":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"\"":{"docs":{},">":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"a":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"_":{"docs":{},"c":{"docs":{},"m":{"docs":{},"p":{"docs":{},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}},"e":{"docs":{},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"}":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.005873140172278779}},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},".":{"docs":{},"n":{"docs":{},"i":{"docs":{},"l":{"docs":{},"?":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"s":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"[":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},".":{"docs":{},"o":{"docs":{},"n":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"a":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.005441354292623942},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"e":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.004635227730753728},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"r":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},".":{"docs":{},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"5":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"docs":{}}},"docs":{}}}}}}}}}}}},"s":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"(":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}},"(":{"5":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}}},"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"x":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},":":{"docs":{},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},"docs":{}}}}}}}}}}}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0026199113260781943},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004210526315789474},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}},"_":{"docs":{},"c":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"l":{"docs":{},"{":{"1":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"docs":{}}}}}},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{},"d":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.004030632809351068}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"i":{"docs":{},"m":{"docs":{},"_":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},"e":{"docs":{},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}},"k":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"i":{"docs":{},"(":{"2":{"docs":{},")":{"docs":{},")":{"docs":{},".":{"docs":{},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}}}},"docs":{}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"]":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}}}}}}}}},"s":{"docs":{},"s":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}}}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.004710144927536232}}}}}}},"c":{"docs":{},"k":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"e":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},".":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"i":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0023492560689115116},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"s":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"n":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"n":{"docs":{},"i":{"docs":{},"c":{"docs":{},"!":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"u":{"docs":{},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"l":{"docs":{},"d":{"docs":{},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}}}}}}}}}}}}}},"t":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.001062840441078783},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},".":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},"&":{"docs":{},"p":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"_":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}}}}},"_":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"y":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394}}}}}},"u":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"s":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"e":{"docs":{},"o":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"f":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"l":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.01773049645390071},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004210526315789474},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0026300958106331017},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.014487079091620987}},"'":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}},"(":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"4":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}},"docs":{}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"{":{"docs":{},"f":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"p":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},";":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}}},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731}}}}},"i":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"i":{"docs":{},"c":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}},"c":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178}},"_":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}}}}}},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}},"i":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"e":{"docs":{},"k":{"docs":{},"(":{"docs":{},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},"[":{"2":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"docs":{}}}}}}}}}}}}},"a":{"docs":{},"k":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925}}}},"c":{"docs":{},"u":{"docs":{},"l":{"docs":{},"i":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},".":{"docs":{},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"0":{"docs":{},".":{"0":{"docs":{},"_":{"docs":{},"f":{"6":{"4":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},"docs":{}}}},"docs":{}}},"docs":{},"(":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"h":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"y":{"docs":{},"s":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":5.0625},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"s":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},"?":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}},"p":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},"_":{"docs":{},"e":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593}}},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},".":{"docs":{},"f":{"docs":{},"l":{"docs":{},"a":{"docs":{},"t":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},":":{"docs":{},":":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.00946969696969697},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"s":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"p":{"docs":{},"p":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.010154346060113728},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0033815517565282736},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0022168480451430876},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}},"e":{"docs":{},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"e":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"s":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}},"x":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}},"e":{"docs":{},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"c":{"docs":{},"k":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"_":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"u":{"docs":{},"r":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}}}}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"]":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},".":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.004697986577181208},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.010926365795724466}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0023752969121140144}},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"_":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0014251781472684087}},")":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}},"i":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"s":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"_":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},")":{"docs":{},"/":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},".":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"=":{"docs":{},"m":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"r":{"docs":{},"l":{"docs":{},"o":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"k":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"c":{"docs":{},"h":{"docs":{},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"/":{"1":{"0":{"docs":{},".":{"0":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"docs":{}}},"docs":{}},"docs":{},"x":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}},"o":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.038630876295980686}},"i":{"docs":{},"n":{"docs":{},"t":{"1":{"docs":{},".":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"y":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"2":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}},".":{"docs":{},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"x":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"y":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"d":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"3":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}},".":{"docs":{},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845}}}},"2":{"0":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"3":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"6":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{}},"8":{"5":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{}},"docs":{}}},"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}}}}},"d":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}}},"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.009786476868327402},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.03757225433526012},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.03959731543624161},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.012185215272136474},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0136986301369863},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.014035087719298246},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.037636299683432996},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.014196242171189978},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002355072463768116},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.00650887573964497},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"e":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0016280406052480367},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394}}}},"s":{"docs":{},".":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.018018018018018018},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},"a":{"docs":{},"g":{"docs":{},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"g":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"m":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0050335570469798654}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"u":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"m":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"|":{"docs":{},"a":{"docs":{},"|":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}},"i":{"docs":{},"s":{"docs":{},"_":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"1":{"docs":{},")":{"docs":{},".":{"docs":{},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"(":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}},"docs":{}}}}}},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"_":{"docs":{},"u":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"_":{"docs":{},"b":{"docs":{},"y":{"docs":{},"(":{"docs":{},"|":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}},"1":{"docs":{},":":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"m":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"]":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},".":{"docs":{},"x":{"docs":{},")":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"y":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"]":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"2":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},".":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{},"]":{"docs":{},".":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}}}}}}}}},"4":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"j":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"a":{"docs":{},"]":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"i":{"docs":{},"+":{"1":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{}},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"m":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}}}}}}}}}}}}}}}}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}},")":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},":":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"*":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"(":{"0":{"docs":{},",":{"1":{"4":{"docs":{},")":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"docs":{}},"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},".":{"5":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}}},"1":{"5":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},".":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}}},"2":{"docs":{},",":{"8":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"5":{"docs":{},",":{"7":{"docs":{},")":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"6":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"7":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"9":{"docs":{},",":{"9":{"docs":{},")":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.005369127516778523}},"p":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"+":{"1":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"docs":{}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}}}}}},"x":{"1":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"=":{"0":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{}}},"*":{"docs":{},"t":{"docs":{},")":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"p":{"docs":{},")":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}},"b":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"x":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}},"c":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"x":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"e":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}},"[":{"docs":{},"]":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"i":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}}}}}}}}}},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}},"n":{"docs":{},"g":{"docs":{},".":{"docs":{},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}}}}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0028139289482940555},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},":":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}}},"&":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"y":{"docs":{},")":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},".":{"docs":{},"a":{"docs":{},"s":{"docs":{},"_":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}},"x":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"i":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{},"_":{"docs":{},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"(":{"docs":{},"o":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}}}}}}}}},"z":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"docs":{},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"n":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}},"_":{"docs":{},"o":{"docs":{},"n":{"docs":{},"_":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624}}}}}}}},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}},"x":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}},"y":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"9":{"1":{"docs":{},"b":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},"docs":{}},"docs":{}}},"docs":{}}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},")":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"o":{"docs":{},"n":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657}},"l":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"*":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},":":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}},"t":{"docs":{},"y":{"docs":{},"p":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0024621878297572987}},"&":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}}}}}}}}},"{":{"docs":{},"x":{"docs":{},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848}}}}},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}},"o":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"r":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904}}},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"a":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"r":{"docs":{},"a":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002452697967764541},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.006355932203389831}},"e":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},"_":{"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.009489916963226572}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}},"s":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"{":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}},"u":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}}}}}}}}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}}}}}}}}}}}},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}},"s":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001723807699674392}},"e":{"docs":{},"r":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002982530890498509},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0030797101449275364},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.009626955475330927},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.007340485601355167}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"'":{"docs":{},"'":{"docs":{},"'":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"v":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}},"(":{"1":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"2":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"3":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"2":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"3":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"docs":{}}}}}}},"_":{"docs":{},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"y":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}}}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}}},"*":{"2":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002272404487998864}}},"docs":{}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.004970884817497514}},"a":{"docs":{},"c":{"docs":{},"c":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0018463286464990769}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.005681011219997159}}},"e":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"w":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00684931506849315},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"s":{"docs":{},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}},"f":{"docs":{},"u":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"(":{"docs":{},"$":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"y":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}},"p":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.005458724382302241},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0023913909924272616},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0037572797294758596},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"(":{"docs":{},"&":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},"!":{"docs":{},"(":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},"e":{"docs":{},")":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"u":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0018137847642079807},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"a":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"l":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0077192982456140355},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0033944331296673455}},"_":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}},"s":{"docs":{},"_":{"docs":{},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},"s":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}}}}}}}}},"b":{"docs":{},"o":{"docs":{},"x":{"docs":{},"_":{"docs":{},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"r":{"docs":{},"!":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}}}}}},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}}}}}}}}}}}}}}}}}},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"r":{"docs":{},"_":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"!":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}}}}}}}}},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"!":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}}},"b":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}}},"y":{"docs":{},"n":{"docs":{},"o":{"docs":{},"m":{"docs":{},"i":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247}}}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"s":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}},"e":{"docs":{},"u":{"docs":{},"d":{"docs":{},"o":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}}}}},"y":{"docs":{},"t":{"docs":{},"h":{"docs":{},"o":{"docs":{},"n":{"3":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"a":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}}}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.003691275167785235},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.010821681670178126},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.009432708914574199},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.010332519256058614}},"[":{"docs":{},"r":{"1":{"2":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"docs":{}},"docs":{}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},":":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},".":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"y":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"f":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},".":{"docs":{},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{},"}":{"docs":{},"`":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}}}}}},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"y":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"+":{"1":{"docs":{},")":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"docs":{}},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"}":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"x":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312}}}}}}}},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"x":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004151838671411625},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"m":{"3":{"docs":{},"d":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"docs":{}},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"b":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"k":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"d":{"docs":{},"f":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535}},"l":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}}}}}},"n":{"docs":{},"g":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"c":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{},"o":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},"v":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"x":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0019883539269990058}}}}},"=":{"docs":{},"n":{"docs":{},"p":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"[":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"+":{"docs":{},"k":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"x":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}},"x":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.006355932203389831}},"\"":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}},"d":{"docs":{},"x":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}}}},"h":{"docs":{},")":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"n":{"docs":{},")":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00847457627118644}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}}}}},"t":{"docs":{},")":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"_":{"1":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"2":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"}":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"{":{"docs":{},"p":{"docs":{},"_":{"3":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"docs":{}}}}}}}}}}}},"3":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"4":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"}":{"docs":{},"}":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"docs":{}}},"r":{"1":{"0":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009299853859439352}}},"b":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"1":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"2":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.006990997893123923},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0033213763783711972},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0031936877700544804}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002873012832790653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011956954962136308},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"3":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.005362957287875886},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002258535937292414},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.004696599661844825}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0033518483049224286},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"4":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0032560812104960733},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011956954962136308},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.005260191621266203}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0015322735108216816},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0030058237835806877}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438}}},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}},"5":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000861903849837196},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0028179597971068945}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0033815517565282736}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"d":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}},"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}},"2":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}},"8":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011956954962136308}}},"d":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"9":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013285505513484788}}},"b":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"d":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00268411340379131},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.004061738424045491},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.003787878787878788},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.005431093007467753},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003800475059382423},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"e":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.005239822652156389},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"a":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"r":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"'":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"s":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"!":{"docs":{},")":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"m":{"docs":{},"e":{"docs":{},".":{"docs":{},"m":{"docs":{},"d":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}},"o":{"docs":{},"n":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}},"i":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"l":{"docs":{},"i":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125}}}},"n":{"docs":{},"g":{"docs":{},"!":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"y":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0038291011688835145},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.007575757575757576},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"s":{"docs":{},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588}}}},"z":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}}}},"l":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"y":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},"o":{"docs":{},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"*":{"docs":{},"d":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"(":{"1":{"6":{"docs":{},")":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},"docs":{}},"8":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0012782275244993609}}}}},"docs":{},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{},"y":{"docs":{},"_":{"docs":{},"k":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"_":{"docs":{},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"s":{"docs":{},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"r":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737}},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}},"c":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412}}}}}}}},"g":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.006657323055360897}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}},"o":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"u":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"l":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"y":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}},"p":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"o":{"docs":{},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"y":{"docs":{},":":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"r":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00821917808219178},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.008838383838383838},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.011126564673157162},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}}}}}}}}}},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"r":{"docs":{},"c":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}}}}},"l":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"a":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},":":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737}}},"?":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}}},"o":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.03389830508474576},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.017391304347826087},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.023809523809523808},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.018018018018018018},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.018691588785046728},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},".":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"i":{"docs":{},"r":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.034782608695652174},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"d":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"(":{"docs":{},"\"":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},".":{"docs":{},"j":{"docs":{},"s":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"o":{"docs":{},"u":{"docs":{},"r":{"docs":{},"c":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002803083391730904},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"v":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.03389830508474576},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},",":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},";":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}},"m":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"i":{"docs":{},"z":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"r":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"o":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013285505513484788},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}},"'":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},".":{"docs":{},"p":{"docs":{},"h":{"docs":{},"p":{"docs":{},"_":{"docs":{},"e":{"docs":{},"o":{"docs":{},"l":{"docs":{},".":{"docs":{},"'":{"docs":{},"%":{"docs":{},"s":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}}}}}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"$":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"c":{"docs":{},"k":{"1":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}},"2":{"docs":{},")":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}},"docs":{}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}},"%":{"docs":{},"d":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}},"{":{"docs":{},"}":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}},"`":{"docs":{},"n":{"docs":{},"$":{"docs":{},"(":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}},"~":{"docs":{},"%":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}},"=":{"docs":{},"$":{"docs":{},"(":{"docs":{},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"_":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}},".":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}},"s":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"!":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"[":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}},"!":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"p":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}}}}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737}}},"/":{"2":{"docs":{},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},"docs":{}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534}}},"]":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"d":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},"u":{"docs":{},"c":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003167062549485352},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"n":{"docs":{},"d":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"m":{"docs":{},"e":{"docs":{},"m":{"docs":{},"b":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}},"o":{"docs":{},"v":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004210526315789474},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0026845637583892616},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"f":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}},"r":{"docs":{},"k":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"v":{"docs":{},"i":{"docs":{},"e":{"docs":{},"w":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":5.052083333333333},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"s":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}},"e":{"docs":{},"d":{"docs":{},"o":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},".":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"(":{"docs":{},"m":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}}}}}},"(":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}}}},"v":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}},"c":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"e":{"docs":{},"i":{"docs":{},"v":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.006263048016701462}},"e":{"docs":{},"o":{"docs":{},"p":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"(":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"a":{"docs":{},"l":{"docs":{},"(":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}},"r":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.003830683777054204},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0030058237835806877},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"!":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"v":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"\\":{"docs":{},"n":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"_":{"docs":{},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"l":{"docs":{},"!":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}}}}}},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},"$":{"docs":{},"(":{"docs":{},"?":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"(":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}}}}}},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"f":{"docs":{},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},")":{"docs":{},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"e":{"docs":{},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"o":{"docs":{},"m":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904}}}}}}},"g":{"docs":{},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"i":{"docs":{},"e":{"docs":{},"v":{"docs":{},"e":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"a":{"docs":{},"l":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"k":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"f":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}},"e":{"docs":{},"r":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},".":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"y":{"docs":{},")":{"docs":{},".":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},"n":{"2":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}},"docs":{}}}}}}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}},")":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"x":{"docs":{},")":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"y":{"docs":{},")":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"docs":{}},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002681478643937943},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0023913909924272616},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002414429768498793},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.037192982456140354},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0043095192491859795},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.011575239053850024},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.010096984190248438},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.011746280344557557},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.009489916963226572},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.012524084778420038},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.015436241610738255},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.015028432168968318},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.014592274678111588},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.004320871688897238},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003700657894736842},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00809004572634541},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.007811390427496095},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.003787878787878788},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.006109979633401222},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.006884057971014493},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.008759635599159075},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.004517221908526256}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"(":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"n":{"docs":{},",":{"2":{"docs":{},")":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}},"docs":{}}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"n":{"docs":{},",":{"2":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}},"docs":{}}}}}}}}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"=":{"docs":{},"$":{"1":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}}},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"v":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}}}}}},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"_":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"_":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},"p":{"docs":{},".":{"docs":{},"s":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}},"(":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"_":{"docs":{},"o":{"docs":{},"f":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}},"_":{"docs":{},"c":{"docs":{},"r":{"docs":{},"o":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},"*":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"_":{"docs":{},"c":{"docs":{},"r":{"docs":{},"o":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"l":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"e":{"docs":{},"v":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}}}}},"a":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"x":{"docs":{},"!":{"docs":{},"\"":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"u":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588}}}}},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767}},"_":{"docs":{},"f":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}}}}},"j":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":3.340350877192982},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}}}},"i":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},"x":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}},"y":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}}},"h":{"docs":{},"o":{"docs":{},"l":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"^":{"docs":{},"{":{"docs":{},"i":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0031885213232363493},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"_":{"docs":{},"d":{"docs":{},"f":{"docs":{},"s":{"docs":{},"(":{"docs":{},"&":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"[":{"1":{"docs":{},".":{"docs":{},".":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"docs":{}}}}}}}}}}}}}}}}}},"f":{"docs":{},"s":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"u":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},"!":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},":":{"docs":{},"u":{"docs":{},"n":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"{":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"?":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}},"o":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"o":{"docs":{},"u":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"c":{"docs":{},"h":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009}}}},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"j":{"docs":{},"n":{"docs":{},"d":{"docs":{},"a":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}},"u":{"docs":{},"n":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.01461038961038961},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"g":{"docs":{},"a":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{},"(":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.00974025974025974}},"e":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},":":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"(":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935}}}},"b":{"docs":{},"i":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}},"s":{"docs":{},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},":":{"docs":{},":":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},":":{"docs":{},":":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"l":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"e":{"docs":{},")":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"l":{"docs":{},"e":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"/":{"docs":{},"b":{"docs":{},"a":{"docs":{},"s":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}},"n":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"g":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009299853859439352},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.007415254237288136}},"e":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"1":{"docs":{},",":{"1":{"0":{"1":{"docs":{},")":{"docs":{},"]":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653}}}}},"docs":{}},"docs":{}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"2":{"0":{"2":{"0":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"docs":{}},"docs":{}},"6":{"4":{"docs":{},")":{"docs":{},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"]":{"docs":{},"[":{"docs":{},"j":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"docs":{}},"docs":{},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"s":{"docs":{},")":{"docs":{},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}}}}}},")":{"docs":{},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}}},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852}}}},"docs":{}}}},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"a":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"docs":{}}}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824}}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}},"docs":{}}}}}}}}}}}}},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},"d":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},")":{"docs":{},")":{"docs":{},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"s":{"docs":{},")":{"docs":{},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}},"a":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},")":{"docs":{},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"docs":{}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},")":{"docs":{},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"d":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542}},"o":{"docs":{},"m":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0023492560689115116},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003886729594669628},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.006904955320877335},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.009145269081955681},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.008768267223382045},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.00350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.007340485601355167}},"(":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"4":{"2":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"docs":{}},"docs":{}}}}},"u":{"docs":{},"n":{"docs":{},"i":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}}}}}}}}}},"_":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"_":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"(":{"docs":{},")":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"?":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"(":{"1":{"2":{"8":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}},"docs":{}},"2":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"*":{"2":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649}}},"docs":{}},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},":":{"docs":{},":":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},":":{"docs":{},":":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"l":{"docs":{},"u":{"docs":{},"d":{"docs":{},"e":{"docs":{},":":{"docs":{},":":{"docs":{},"*":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}},"*":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"t":{"docs":{},"h":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{},"_":{"docs":{},"r":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"_":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"x":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"y":{"docs":{},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"_":{"docs":{},"d":{"docs":{},"e":{"docs":{},"v":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"{":{"docs":{},"}":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}}}}}}}}}}}}},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"_":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}}}}}}}},"k":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.003639149588201494},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0038584130179500084},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0033213763783711972},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.003926450871480559},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004193927193423922},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011956954962136308},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.004133007702423445},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"r":{"docs":{},"d":{"docs":{},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}}},"i":{"docs":{},"s":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"y":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"s":{"docs":{},"\"":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"l":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}},"u":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00934199837530463}},"s":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"9":{"1":{"docs":{},"b":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},"docs":{}},"docs":{}}},"docs":{}}}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0036555645816409425}}},"=":{"1":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"docs":{}}}},"c":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"s":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"r":{"docs":{},"e":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"o":{"docs":{},"u":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"p":{"docs":{},"i":{"docs":{},"d":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},"]":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"b":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0028179597971068945}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298}}}}},"c":{"docs":{},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011956954962136308}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0019928258270227183},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"d":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.003830683777054204},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00268411340379131},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0018599707718878703},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.006607929515418502},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.004118506709180284},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0017271157167530224},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001819574794100747},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0029228112129666534},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}},"_":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}},"b":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"y":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}},"\"":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"m":{"docs":{},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.030720506730007917},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"s":{"docs":{},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"}":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"\"":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"'":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"+":{"docs":{},"+":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"[":{"docs":{},"c":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}},"j":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}},"a":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"b":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"?":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"l":{"docs":{},"l":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}},"\"":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"t":{"1":{"3":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"docs":{}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},"a":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.007692307692307693}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},".":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"e":{"docs":{},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"u":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0033944331296673455},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}},"g":{"docs":{},"h":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"l":{"docs":{},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}}}}}}},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}},"m":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"a":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"s":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"h":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0030645470216433632},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002258535937292414},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.004213752154759625},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003355141754739138},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0033213763783711972},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438}}}},"a":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}}}}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}}},"?":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}}}}},"\"":{"docs":{},"(":{"docs":{},"b":{"docs":{},"i":{"docs":{},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"s":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"r":{"docs":{},"h":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},".":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"y":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"x":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"y":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"[":{"0":{"docs":{},"]":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"x":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"z":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"1":{"docs":{},"]":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"x":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"z":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"2":{"docs":{},"]":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"x":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"z":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"docs":{}}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}}},"n":{"docs":{},"g":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"_":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"0":{"docs":{},".":{"0":{"docs":{},"_":{"docs":{},"f":{"6":{"4":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}},"docs":{}}}},"docs":{}}},"docs":{}}}}}}}},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"}":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}},":":{"docs":{},":":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}},"(":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"d":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}}}},"g":{"docs":{},"b":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"^":{"2":{"docs":{},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"}":{"docs":{},"{":{"docs":{},"(":{"2":{"docs":{},"r":{"docs":{},")":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"docs":{}}}}},"docs":{}}}}},"docs":{}},"_":{"0":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.009824561403508772},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0047522063815342835}},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"docs":{}},"y":{"docs":{},"z":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},":":{"docs":{},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}}}}}}}}}},"(":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"s":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"*":{"docs":{},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"(":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{},"*":{"docs":{},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}}}}}}}}}}},"=":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"{":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}},"?":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"s":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}}}}},"m":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"+":{"docs":{},"+":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"a":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.006775832862789385}},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},".":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"2":{"4":{"docs":{},";":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"d":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},"?":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":3.333333333333333}}},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}},"e":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000861903849837196},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003886729594669628},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004733727810650888},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"v":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0018599707718878703},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},"o":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"e":{"docs":{},"m":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}}},"f":{"docs":{},"e":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}}},"y":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}}}},"s":{"docs":{},":":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}},"w":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"t":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653}}}}}}}},"l":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"t":{"docs":{},"i":{"docs":{},"s":{"docs":{},"f":{"docs":{},"i":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"u":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.004419191919191919}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394}}}}}}}}}}},"c":{"docs":{},"r":{"docs":{},"i":{"docs":{},"f":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"c":{"docs":{},"h":{"docs":{},"l":{"docs":{},"o":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007773459189339256},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009057225195553726},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005627857896588111},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006944444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.010862186014935505},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01242603550295858},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719}},".":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}},".":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044}}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},"n":{"docs":{},"h":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}}}},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"s":{"docs":{},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"r":{"docs":{},"ö":{"docs":{},"d":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147}}}}}}}}}}},"i":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.007707129094412331},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.022598870056497175},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"e":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}},"t":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"f":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"i":{"docs":{},"c":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}},"p":{"docs":{},"y":{"docs":{},".":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}}}}},"a":{"docs":{},"l":{"docs":{},"a":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},".":{"docs":{},"{":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"_":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{},"l":{"docs":{},"i":{"docs":{},"b":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},".":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002881844380403458},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.01069078947368421},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.008284023668639054},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005956552207428171},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},"?":{"docs":{},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"\"":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"n":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":5.001677852348993},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"l":{"1":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"i":{"docs":{},"n":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"r":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094}}}}}}},"o":{"docs":{},"n":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}},"r":{"docs":{},"e":{"docs":{},"(":{"docs":{},"@":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}},"p":{"docs":{},"e":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"m":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},";":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"i":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.004528612597776863},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},".":{"docs":{},"g":{"docs":{},"p":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"e":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{},"o":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}},"e":{"docs":{},"e":{"docs":{"./":{"ref":"./","tf":0.01020408163265306},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0022168480451430876},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004733727810650888},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.003952569169960474},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"m":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"n":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}}},"r":{"docs":{},"v":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},"e":{"docs":{},"r":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}},":":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}},"o":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.005253623188405797}},"s":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},"'":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002355072463768116}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"`":{"docs":{},"t":{"docs":{},"`":{"docs":{},"t":{"docs":{},"$":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"c":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754}}},"=":{"docs":{},"f":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"}":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"{":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"u":{"docs":{},"s":{"docs":{},"(":{"docs":{},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},")":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"_":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}},"i":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":5.02834008097166},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"o":{"docs":{},"u":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.023809523809523808},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.018691588785046728},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}},".":{"docs":{"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"s":{"docs":{},".":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"!":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},";":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},":":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"o":{"docs":{},"r":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904}}}}},"o":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}}}}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"s":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"l":{"docs":{},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"u":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}},"l":{"docs":{},"f":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},"_":{"docs":{},"_":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},".":{"docs":{},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0023492560689115116}},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}}}}}}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},".":{"docs":{},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"l":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"_":{"docs":{},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"_":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},"?":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"c":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},".":{"docs":{},"s":{"docs":{},"w":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"a":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"[":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"_":{"docs":{},"d":{"docs":{},"f":{"docs":{},"s":{"docs":{},"(":{"docs":{},"&":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"[":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},".":{"docs":{},".":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}}}}}},"f":{"docs":{},"s":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},":":{"docs":{},":":{"docs":{},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"v":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},".":{"docs":{},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}},"e":{"docs":{},"r":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"c":{"docs":{},"m":{"docs":{},"p":{"docs":{},"(":{"docs":{},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},")":{"docs":{},"}":{"docs":{},"'":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"[":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}},"m":{"docs":{},"_":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},".":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"c":{"docs":{},"m":{"docs":{},"p":{"docs":{},"(":{"docs":{},"&":{"docs":{},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"y":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},".":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"c":{"docs":{},"m":{"docs":{},"p":{"docs":{},"(":{"docs":{},"&":{"docs":{},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}}}}}}}}}}}}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"z":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}}}},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"(":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"h":{"docs":{},"u":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},"_":{"docs":{},"o":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}}}},"a":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"n":{"docs":{},"s":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"e":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},",":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"!":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}},"d":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.006263048016701462}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"t":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.003915426781519186},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.013908205841446454},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.02099629477151091},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003700657894736842},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0035174111853675696},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.021464646464646464},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0041753653444676405},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003167062549485352},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0035502958579881655},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.001062840441078783},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},".":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"e":{"docs":{},"(":{"docs":{},"m":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"$":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"p":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263}},"u":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"c":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}}}}},"[":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003289473684210526}},")":{"docs":{},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}},"g":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"s":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405}},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"k":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007773459189339256},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009057225195553726},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.009589041095890411},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005627857896588111},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.006944444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.010862186014935505},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01242603550295858},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}}}}}},"p":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"l":{"docs":{},"i":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"m":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"p":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0045726345409778405},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"?":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}},"s":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"s":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}},"s":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"[":{"docs":{},"r":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"_":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"0":{"docs":{},".":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"n":{"docs":{},"n":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"e":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"k":{"docs":{},"e":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}},"d":{"docs":{},"e":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"l":{"docs":{},"l":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"o":{"docs":{},"w":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.004291845493562232},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0010534380386899062},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"n":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"o":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}}}},"c":{"docs":{},"a":{"docs":{},"s":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}}}}},"u":{"docs":{},"l":{"docs":{},"d":{"docs":{},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"r":{"docs":{},"'":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},"e":{"docs":{},"r":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},")":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"c":{"docs":{},"u":{"docs":{},"t":{"docs":{},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"i":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"f":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261}}}}},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"l":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"e":{"docs":{},"(":{"docs":{},"$":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},"g":{"docs":{},"i":{"docs":{},"r":{"docs":{},"l":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"u":{"docs":{},"y":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"_":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"i":{"docs":{},"p":{"docs":{},"t":{"docs":{},"o":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}}}}}}},"e":{"docs":{},"l":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"a":{"docs":{},"r":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.009467455621301775}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"p":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.00350385423966363}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"e":{"docs":{},":":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"u":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"?":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}},"z":{"docs":{},"e":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004912280701754386},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0013407393219689715},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0037052284890901604},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0033815517565282736},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925}},",":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004210526315789474}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}},"x":{"docs":{},")":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}},"y":{"docs":{},")":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"a":{"docs":{},",":{"1":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}},"2":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}},"docs":{}}}},"_":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0015942606616181746},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.003915426781519186},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.003355704697986577},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0022169437846397467}},"(":{"0":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"docs":{}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"a":{"docs":{},".":{"docs":{},"s":{"docs":{},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"o":{"docs":{},"f":{"docs":{},"(":{"docs":{},"q":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}},"y":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},"_":{"docs":{},"k":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"r":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"docs":{}},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},":":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"docs":{}},"docs":{}}}}}},"]":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"g":{"docs":{},"n":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"i":{"docs":{},"f":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},"i":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"a":{"docs":{},"l":{"2":{"docs":{},")":{"docs":{},":":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"{":{"docs":{},"t":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653}}}}}}}}}}}}}},"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.012770682953914493},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.01020408163265306},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824}},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},"?":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},"s":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},";":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},"[":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}},"m":{"docs":{},"a":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.007017543859649123},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0033944331296673455}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.00631578947368421},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}}}}},"d":{"docs":{},"e":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}},"f":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.006954102920723227},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.006107717934480844},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815}},"i":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0037052284890901604},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0029585798816568047},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"c":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"f":{"docs":{},"i":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"s":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"_":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"_":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}}}}}}},"y":{"docs":{},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"u":{"docs":{},"l":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0035174111853675696},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0038291011688835145},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.009626955475330927},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"o":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},"s":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},"t":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"i":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"l":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"y":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"?":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"u":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114}},"!":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},".":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}}}},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094}}}},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}}}},"e":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828}}},"u":{"docs":{},"s":{"docs":{},"o":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"e":{"docs":{},"r":{"docs":{},"p":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"k":{"docs":{},"i":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005979599015124868},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848}}}}}}}}}}}}}}}},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"h":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004210526315789474},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{},".":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},")":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},"i":{"docs":{},"m":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}},"o":{"docs":{},"n":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"(":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"'":{"0":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"1":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"docs":{}},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"x":{"docs":{},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},"n":{"docs":{},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"w":{"docs":{},"h":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},"e":{"docs":{},"r":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}},"h":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}},"v":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.018018018018018018},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.046875},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0028503562945368173},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},";":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"r":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":5.0078125},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"s":{"docs":{},".":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125}}}},".":{"docs":{},".":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"d":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"u":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003700657894736842},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00332541567695962},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"'":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"\"":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},"\"":{"docs":{},"\"":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}},"%":{"docs":{},"s":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}}}},"_":{"docs":{},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}},"[":{"docs":{},":":{"3":{"docs":{},",":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"docs":{}}},"{":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"?":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"j":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"s":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"i":{"docs":{},"d":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"n":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0028782894736842104},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001583531274742676}},".":{"docs":{},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}},"a":{"docs":{},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}},"j":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"*":{"docs":{},"a":{"docs":{},"[":{"docs":{},"i":{"docs":{},",":{"docs":{},"j":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"a":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}}}},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"[":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"i":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"j":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}},"r":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013285505513484788},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.004697986577181208},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"s":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"!":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},"[":{"2":{"docs":{},":":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}},"docs":{}}}}}}}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"s":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}},"e":{"docs":{},"d":{"docs":{},"(":{"docs":{},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}}}}},"p":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}},"o":{"docs":{},"n":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"_":{"docs":{},"b":{"docs":{},"y":{"docs":{},"_":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"f":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"r":{"docs":{},"c":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"t":{"docs":{},"h":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"w":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"f":{"docs":{},"t":{"docs":{},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"o":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"!":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.008583690987124463}}}}},"p":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}},"!":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"p":{"docs":{},"e":{"docs":{},"c":{"docs":{},"i":{"docs":{},"f":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"i":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"r":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}},"a":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"t":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044}}}}}}}},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}}},"n":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}},"a":{"docs":{},"k":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}}}}},"e":{"docs":{},"d":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"d":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.017857142857142856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.007255139056831923},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.010830324909747292},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.00421179302045728}}},"s":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},".":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.005415162454873646},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"y":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}},"w":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}}},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}},"n":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":3.3359532446594113},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"_":{"docs":{},"o":{"docs":{},"p":{"docs":{},"!":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}},"(":{"docs":{},"&":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}}},"a":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}},".":{"docs":{},"j":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},"o":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}},"o":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"e":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"u":{"docs":{},"c":{"docs":{},"e":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"y":{"docs":{},"?":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"o":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.005415162454873646},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"s":{"docs":{},":":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}},"i":{"docs":{},"c":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011492051331162612},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.003523884103367267},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.003371868978805395},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.002348993288590604},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}},":":{"docs":{},":":{"docs":{},"d":{"docs":{},"f":{"docs":{},"s":{"docs":{},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"$":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"(":{"docs":{},"$":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"$":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},"docs":{}}}}}}}}}}}}},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}},"docs":{}}}}}},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}}},"docs":{}}}}},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},"docs":{}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"_":{"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"c":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"g":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"r":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011956954962136308},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004210526315789474},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0031656700668308124},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002898550724637681},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004142011834319527},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}},"{":{"1":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"docs":{}}}}},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}}}}}}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},".":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}},"s":{"docs":{},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"n":{"docs":{},"d":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}},":":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557}}}}}}}},"c":{"docs":{},"k":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":5.016842105263158},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.008044435931813828},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003855278766310795}},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"c":{"docs":{},"[":{"docs":{},"t":{"docs":{},"]":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}},"\"":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},".":{"docs":{},".":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"?":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"x":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"&":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"_":{"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408}}}}},"l":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},"!":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"(":{"docs":{},"&":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},".":{"docs":{},".":{"docs":{},".":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}}}}}}},"c":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}},"<":{"docs":{},">":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"1":{"docs":{},":":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"s":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"2":{"4":{"docs":{},";":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},"\\":{"docs":{},"n":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"c":{"docs":{},"a":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"_":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"_":{"docs":{},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"f":{"docs":{},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},")":{"docs":{},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"l":{"docs":{},"!":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},"$":{"docs":{},"(":{"docs":{},"?":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"(":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}}}}}},"{":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"}":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"}":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}}}}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}}}}}},"y":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"b":{"docs":{},"l":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":3.337248760114852}},"e":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"_":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"docs":{},"$":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},"e":{"docs":{},"(":{"docs":{},"g":{"docs":{},"u":{"docs":{},"y":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},".":{"docs":{},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"a":{"docs":{},"d":{"docs":{},"a":{"docs":{},"m":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"m":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"x":{"docs":{},"e":{"docs":{},"n":{"docs":{},"a":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"y":{"docs":{},"e":{"docs":{},"v":{"docs":{},"a":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"z":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},"e":{"docs":{},"x":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742}}}}}}}}}}}}}}},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}},"i":{"docs":{},"l":{"docs":{},"l":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0029585798816568047},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"c":{"docs":{},"k":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},"y":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"y":{"docs":{},"t":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"e":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003854239663629993}}},"m":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"e":{"docs":{},"r":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.005965061780997018}},"_":{"docs":{},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}},"(":{"5":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},".":{"0":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}},"docs":{}}},"docs":{},"&":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}}},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}}},":":{"docs":{},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},"docs":{}},"docs":{}}}}}}}}}}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}},"(":{"5":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},".":{"0":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"g":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"e":{"docs":{},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"p":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"?":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},",":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"l":{"docs":{},"i":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},":":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"y":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"?":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"s":{"docs":{},"s":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}}}},"n":{"docs":{},"g":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"e":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}}},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002777245738364298},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.005845622425933307},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.010379596678529062},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0063758389261744965},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0028139289482940555},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0036275695284159614},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0037578288100208767},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"u":{"docs":{},"r":{"docs":{"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":5.033898305084746},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"?":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"n":{"docs":{},"g":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}},"(":{"0":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"2":{"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"_":{"docs":{},"_":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"(":{"2":{"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"\"":{"docs":{},".":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"n":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0038527965989105886},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0023492560689115116},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0014492753623188406},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"(":{"0":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"2":{"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"s":{"docs":{},".":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"s":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"r":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}}}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}},"i":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},"[":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"[":{"docs":{},"j":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}},"l":{"docs":{},"p":{"docs":{},"a":{"docs":{},"d":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"x":{"docs":{},"[":{"docs":{},"j":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"l":{"docs":{},"(":{"docs":{},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"v":{"docs":{},"[":{"docs":{},"j":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"(":{"2":{"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},":":{"docs":{},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},")":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"b":{"docs":{},"u":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}},"}":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"p":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"v":{"docs":{},"e":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}},"d":{"docs":{},"e":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"[":{"2":{"5":{"7":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"docs":{}},"docs":{}},"docs":{}},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"*":{"docs":{},"d":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},"*":{"docs":{},"d":{"docs":{},"s":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}},"s":{"docs":{},"r":{"docs":{},"c":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}},"o":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}},"e":{"docs":{},"r":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"u":{"docs":{},"d":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"o":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"s":{"docs":{},")":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"f":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"p":{"docs":{},"i":{"docs":{},"d":{"docs":{},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"y":{"docs":{},"l":{"docs":{},"e":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},":":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},"=":{"docs":{},"\"":{"docs":{},"w":{"docs":{},"i":{"docs":{},"d":{"docs":{},"t":{"docs":{},"h":{"docs":{},":":{"1":{"0":{"0":{"docs":{},"%":{"docs":{},"\"":{"docs":{},"/":{"docs":{},">":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"docs":{}},"docs":{}},"8":{"0":{"docs":{},"%":{"docs":{},"\"":{"docs":{},">":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"/":{"docs":{},">":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"docs":{}},"docs":{}}}}}}}}}}}},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},":":{"docs":{},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}},"{":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000861903849837196},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"p":{"docs":{},"y":{"docs":{},"(":{"docs":{},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"(":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"docs":{}}},"docs":{}}}}}}}},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"m":{"docs":{},"p":{"docs":{},":":{"docs":{},":":{"docs":{},"{":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"k":{"docs":{},"e":{"docs":{},"_":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},">":{"docs":{},"(":{"docs":{},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}},"(":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"u":{"docs":{},"n":{"docs":{},"i":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},">":{"docs":{},"(":{"docs":{},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}},"(":{"docs":{},"l":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"l":{"docs":{},"h":{"docs":{},"s":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"l":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"_":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},"}":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},".":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}}},"h":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"t":{"1":{"9":{"9":{"3":{"7":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"i":{"docs":{},"n":{"docs":{},"_":{"docs":{},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},".":{"docs":{},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},">":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737}}}}}}}}}}},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"_":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"{":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}},"w":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}},"e":{"docs":{},"q":{"docs":{},"n":{"docs":{},"s":{"docs":{},"[":{"docs":{},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}}}}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},".":{"7":{"5":{"docs":{},")":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"docs":{}},"docs":{}}},"docs":{}}}}}},"u":{"docs":{},"n":{"docs":{},"i":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"r":{"docs":{},">":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"b":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"b":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"3":{"2":{"docs":{},"_":{"docs":{},"t":{"docs":{},"(":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"2":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}},"docs":{}},"docs":{}}}}},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"_":{"docs":{},"n":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},")":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"(":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"{":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},".":{"docs":{},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}},"s":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"a":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},">":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"&":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}}},"&":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"{":{"docs":{},"}":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}},"b":{"docs":{},")":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}}}},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}},"&":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}}}}}}},"e":{"docs":{},"x":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"docs":{},"b":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}}}},"n":{"docs":{},"d":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"f":{"6":{"4":{"docs":{},":":{"docs":{},":":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},"s":{"docs":{},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"i":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}},"docs":{}},"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"_":{"docs":{},"i":{"docs":{},"f":{"docs":{},"(":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"_":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"f":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}}}}}},"s":{"docs":{},":":{"docs":{},":":{"docs":{},"w":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"\"":{"docs":{},".":{"docs":{},"/":{"docs":{},"s":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{},"p":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"k":{"docs":{},"i":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}}}}},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"g":{"docs":{},"u":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"\"":{"docs":{},"a":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"t":{"docs":{},"a":{"docs":{},"(":{"docs":{},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},":":{"docs":{},":":{"docs":{},"w":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},":":{"docs":{},":":{"docs":{},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"m":{"docs":{},"_":{"docs":{},"f":{"docs":{},"n":{"docs":{},"(":{"docs":{},"|":{"docs":{},"|":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"t":{"docs":{},"h":{"docs":{},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"s":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"(":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"o":{"docs":{},"_":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"2":{"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{},"(":{"2":{"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"s":{"docs":{},":":{"docs":{},":":{"docs":{},"{":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"m":{"docs":{},"&":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}},"f":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"_":{"docs":{},"d":{"docs":{},"e":{"docs":{},"v":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"f":{"docs":{},"a":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},"_":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"&":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}}}}}}}}}}}},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},"i":{"docs":{},"o":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}},"=":{"docs":{},"c":{"docs":{},"+":{"docs":{},"+":{"1":{"7":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"docs":{}},"docs":{}}}}}},"e":{"docs":{},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0034260378879484078},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001751927119831815},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.010163749294184076}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},"s":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"?":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"r":{"docs":{},"e":{"docs":{},"o":{"docs":{},"t":{"docs":{},"y":{"docs":{},"p":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}}}}},"m":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000861903849837196},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0026690391459074734}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},".":{"docs":{},"c":{"docs":{},"a":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"u":{"docs":{},"b":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0050327126321087065},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438}},"m":{"docs":{},"i":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},"s":{"docs":{},";":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}}}}}}},"j":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"c":{"docs":{},"l":{"docs":{},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0021808421405804393},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0022169437846397467}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}}}}}}}},"(":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"*":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}}},"s":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}},"q":{"docs":{},"u":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"t":{"docs":{},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}},"e":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},":":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}},"d":{"docs":{},"i":{"docs":{},"v":{"docs":{},"i":{"docs":{},"s":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0025564550489987218}}}}}},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141}}}}}},"m":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004441976679622432},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.00944206008583691},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.004117181314330958},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.009533898305084746}},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"y":{"docs":{},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"e":{"docs":{},"r":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}}}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"(":{"docs":{},"s":{"docs":{},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{},"y":{"docs":{},"_":{"docs":{},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}}},"_":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{},"_":{"docs":{},"d":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"s":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"1":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}},"docs":{}}}},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852}}}}}}}}}}}}}}}}}}}}}}}}}}}},"'":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114}}},":":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"p":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"d":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"r":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004441976679622432},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.005010438413361169},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.011834319526627219},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},".":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{},":":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"(":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}},"f":{"docs":{},"l":{"docs":{},"u":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"i":{"docs":{},"m":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"s":{"docs":{},"e":{"docs":{},"d":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.018691588785046728},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"s":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}},"f":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}}},"c":{"docs":{},"h":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.004517221908526256},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},",":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}}}},"d":{"docs":{},"d":{"docs":{},"e":{"docs":{},"n":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"o":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"s":{"docs":{},".":{"docs":{},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"s":{"docs":{},"u":{"docs":{},"i":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"(":{"docs":{},"m":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"s":{"docs":{},"p":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754}},"n":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"d":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.005978260869565218}}}}}},"g":{"docs":{},"g":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"f":{"docs":{},"f":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"l":{"docs":{},"i":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"y":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"e":{"docs":{},"r":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"s":{"docs":{},"t":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"p":{"docs":{},"e":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"l":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"p":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"c":{"docs":{},"e":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"d":{"docs":{},"e":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}}}},"m":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"t":{"docs":{},"a":{"docs":{},"s":{"docs":{},"k":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"l":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"y":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.007725321888412017}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0234375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.014705882352941176},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":3.335092038926017},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003642121931908155},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":5.007220216606498},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.003952569169960474}},"s":{"docs":{},";":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},".":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"!":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"l":{"docs":{},"n":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},".":{"docs":{},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}},"\"":{"docs":{},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}},"\"":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},":":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},":":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}},"\\":{"docs":{},"n":{"docs":{},"g":{"docs":{},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},":":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}}}}}},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"(":{"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"(":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"docs":{}}}}}}}}}}},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"w":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},".":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"s":{"docs":{},".":{"docs":{},"t":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"t":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}}}}}}}}}}}},"x":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}}}}}}}}}}}}}}},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},".":{"docs":{},"p":{"docs":{},"e":{"docs":{},"e":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},".":{"docs":{},"p":{"docs":{},"e":{"docs":{},"e":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}},"f":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"%":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"c":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"[":{"docs":{},"%":{"docs":{},".":{"1":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}},"docs":{}}}},"h":{"docs":{},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"t":{"docs":{},"h":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"c":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"n":{"docs":{},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"e":{"docs":{},".":{"docs":{},"w":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"(":{"docs":{},"$":{"docs":{},"\"":{"docs":{},"{":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"r":{"docs":{},"y":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"}":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},".":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"}":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"x":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}},"t":{"docs":{},"h":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}},"\"":{"docs":{},"j":{"docs":{},"a":{"docs":{},"r":{"docs":{},"v":{"docs":{},"i":{"docs":{},"s":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}},"r":{"docs":{},"u":{"docs":{},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"l":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"n":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"t":{"docs":{},"h":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"q":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}},"i":{"docs":{},"o":{"docs":{},";":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"\"":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"%":{"docs":{},"s":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},"\"":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"!":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"'":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"m":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"i":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"n":{"docs":{},"c":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"h":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"o":{"docs":{},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002173913043478261}}}}},")":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339}}}},"n":{"docs":{},"i":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}},"d":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"a":{"docs":{},"p":{"docs":{},"s":{"docs":{},"h":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"o":{"docs":{},"w":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"f":{"docs":{},"(":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}}}}}}}}}}}},"w":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0010534380386899062},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}},"a":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0030087094220110845}},"(":{"docs":{},"&":{"docs":{},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}}},"i":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"f":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{},"[":{"docs":{},"b":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}},"_":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},"(":{"docs":{},"&":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"a":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}},"(":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"[":{"docs":{},"]":{"docs":{},"[":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}}}}}}},":":{"docs":{},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"c":{"docs":{},"k":{"docs":{},"_":{"1":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"2":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"docs":{}}}}}}},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"_":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"(":{"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{},"a":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"(":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"docs":{},"a":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}}}}}}}},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"$":{"docs":{},"{":{"docs":{},"(":{"2":{"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}}}},"a":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"k":{"docs":{},"i":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"l":{"docs":{},"l":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"e":{"docs":{},"w":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"r":{"docs":{},"c":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"(":{"docs":{},"(":{"docs":{},"u":{"docs":{},"n":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}},"1":{"docs":{},"]":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}},"2":{"docs":{},":":{"docs":{},"]":{"docs":{},":":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}}},"docs":{}},"s":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003886729594669628},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.004220893422441084},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0033944331296673455},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"e":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"s":{"docs":{},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"?":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},")":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"?":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004142011834319527}}}}}}},"r":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"(":{"0":{"docs":{},".":{"1":{"docs":{},"*":{"docs":{},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}}}}}}}},"7":{"5":{"docs":{},")":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"]":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}},"docs":{}},"docs":{}}},"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.00631578947368421},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814}},"n":{"docs":{},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}},")":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"_":{"docs":{},"f":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}}}}}}},"m":{"docs":{},"s":{"docs":{},"/":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}},"x":{"docs":{},"*":{"docs":{},"x":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},".":{"docs":{},"(":{"docs":{},"g":{"docs":{},"x":{"docs":{},".":{"docs":{},"^":{"2":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"docs":{}}}}}}}}}},"_":{"docs":{},"i":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}},"x":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}},"*":{"docs":{},"a":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}},"y":{"docs":{},"*":{"docs":{},"a":{"docs":{},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}},"x":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339}},")":{"docs":{},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.007725321888412017}}}}},"t":{"0":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"1":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"2":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.009824561403508772},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0024899444550852325},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002470152326060107},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.004402783695497799},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"e":{"docs":{},"x":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535}},"t":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.007707129094412331},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.014084507042253521},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.05084745762711865},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.02608695652173913},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.026785714285714284},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.03571428571428571},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.02702702702702703},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.028037383177570093},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0234375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0014614056064833267},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.011029411764705883},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.012145748987854251},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.013333333333333334},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.010638297872340425},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.007653061224489796},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}},"!":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"e":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}},"n":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"s":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0021068760773798123},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0014614056064833267},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"s":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}}}}},"(":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"_":{"docs":{},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}},"(":{"docs":{},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}}}},"i":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"x":{"docs":{},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},"n":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}},"m":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0031603141160697185},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0036906559302130517},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0026300958106331017},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}},"l":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"x":{"docs":{},"[":{"docs":{},"j":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},".":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},"!":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},".":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"{":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"_":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0014492753623188406}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},".":{"docs":{},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"p":{"docs":{},"o":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0051129100979974435}},"s":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002272404487998864}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}}}}}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0020130850528434826},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"o":{"docs":{},"r":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},"l":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"[":{"docs":{},"b":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"i":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}}}},"t":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"p":{"docs":{},"o":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478}},"s":{"docs":{},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}}}}}},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"e":{"docs":{},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}},"r":{"docs":{},"m":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"i":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},":":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0013407393219689715}}}}}}},"l":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"s":{"docs":{},".":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"y":{"docs":{},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"b":{"docs":{},"l":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"s":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"l":{"docs":{},"l":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"c":{"docs":{},"h":{"docs":{},"n":{"docs":{},"i":{"docs":{},"q":{"docs":{},"u":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"c":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"y":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}},"d":{"docs":{},"i":{"docs":{},"o":{"docs":{},"u":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"h":{"docs":{},"a":{"docs":{},"n":{"docs":{},"k":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"t":{"docs":{},"'":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"?":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"!":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"'":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"e":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"!":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"a":{"docs":{},"f":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"b":{"docs":{},"i":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"m":{"docs":{},"e":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},":":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"v":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},")":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"y":{"docs":{},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"e":{"docs":{},"m":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":5.017857142857143}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}},"t":{"docs":{},"a":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}},"(":{"docs":{},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},"n":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"i":{"docs":{},"n":{"docs":{},"k":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004142011834319527},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}},"!":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"s":{"docs":{},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"!":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},":":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},")":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"s":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}},".":{"docs":{},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"h":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"t":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"o":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"f":{"docs":{},"s":{"docs":{},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},".":{"docs":{},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"(":{"docs":{},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"s":{"docs":{},"h":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"i":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"a":{"docs":{},"d":{"docs":{},"i":{"docs":{},"u":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"s":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"a":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"i":{"docs":{},"m":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"e":{"docs":{},".":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"o":{"docs":{},"f":{"docs":{},"(":{"docs":{},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}}},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"y":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"z":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.005763688760806916},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001583531274742676},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"_":{"docs":{},"f":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"(":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"_":{"docs":{},"x":{"docs":{},".":{"docs":{},"a":{"docs":{},"s":{"docs":{},"_":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"s":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"?":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"r":{"docs":{},"d":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}}},"u":{"docs":{},"g":{"docs":{},"h":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"s":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"m":{"docs":{},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":5.003289473684211},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"s":{"docs":{},"(":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"&":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.006167763157894737}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},"_":{"docs":{},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{},"(":{"docs":{},"$":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"a":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"x":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}}}},"a":{"docs":{},"l":{"docs":{},"g":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"m":{"docs":{},"(":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"[":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"g":{"docs":{},"h":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703696609844858},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0024621878297572987},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.003340292275574113},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001583531274742676},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"w":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"e":{"docs":{},"e":{"docs":{"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.018018018018018018},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0031656700668308124},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"a":{"docs":{},"d":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0077192982456140355}},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}},"r":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},"s":{"docs":{},"h":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"o":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},":":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}},":":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}}}}},"u":{"docs":{"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"m":{"docs":{},"b":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}},"s":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"o":{"docs":{},"p":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001819574794100747},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"(":{"docs":{},"&":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004210526315789474}},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0035087719298245615}},"e":{"docs":{},"r":{"docs":{},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}},"e":{"docs":{},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"i":{"docs":{},"c":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"s":{"docs":{},".":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}},":":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}}},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"r":{"docs":{},":":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"!":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}},"o":{"docs":{},"l":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}}},"s":{"docs":{},",":{"docs":{"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044}}}},"!":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"!":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"k":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},"d":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"?":{"docs":{},"\"":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"u":{"docs":{},"r":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428}}},"c":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"_":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"b":{"docs":{},"e":{"docs":{},"_":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}}}}},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"e":{"docs":{},"d":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"s":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"t":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"l":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"e":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}},"m":{"docs":{},"o":{"docs":{},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}},"r":{"docs":{},"i":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},"c":{"docs":{},"k":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"y":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},")":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"!":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"g":{"docs":{},"o":{"docs":{},"n":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003886729594669628},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.010903974674639466},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"e":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},":":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848}}}}},"u":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"l":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"s":{"docs":{},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"v":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"!":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},"g":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"l":{"docs":{},"l":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"c":{"docs":{},"k":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"n":{"docs":{},"s":{"docs":{},"c":{"docs":{},"r":{"docs":{},"i":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0010534380386899062},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}},"b":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"l":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.005917159763313609},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.02040816326530612},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0045087356753710315},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003700657894736842},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.007933194154488519},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":3.35234215885947},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.00421179302045728},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":5.021893491124261}},"s":{"docs":{},".":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"!":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},",":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},".":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"?":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}},"_":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"*":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"s":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},":":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}}}}}}}},"!":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"e":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":5.000861903849837},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004448398576512456},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"a":{"docs":{},"l":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"2":{"4":{"docs":{},";":{"docs":{},"️":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"e":{"docs":{},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}},"d":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}},"j":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}}}}},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}},"e":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"p":{"docs":{},"e":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"u":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203}}}},"e":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.004061738424045491},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002452697967764541},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},":":{"1":{"4":{"docs":{},"}":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"docs":{}}},"_":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},"*":{"docs":{},"*":{"2":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"docs":{}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.011029411764705883},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"t":{"docs":{},"h":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"!":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}},"n":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"!":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":5.008331737215093},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.008901288694034807},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"!":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}},"'":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"(":{"2":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"3":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"docs":{},"$":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"o":{"docs":{},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0017271157167530224}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873}},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}},"\"":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}},"b":{"docs":{},"f":{"docs":{},"s":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"d":{"docs":{},"f":{"docs":{},"s":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"f":{"docs":{},"s":{"docs":{},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"i":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}},"j":{"docs":{},"a":{"docs":{},"v":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{},"o":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"k":{"docs":{},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394}},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"~":{"docs":{},"%":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"\\":{"docs":{},"n":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}}}}}}}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"a":{"docs":{},"l":{"docs":{},".":{"docs":{},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"_":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}}}}}},"s":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},".":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"docs":{}}},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}},"a":{"docs":{},"l":{"docs":{},":":{"docs":{},":":{"docs":{},"d":{"docs":{},"f":{"docs":{},"s":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},"$":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"$":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"(":{"docs":{},"$":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"$":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},"$":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"*":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0026571011026969575}},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"*":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}},"?":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"[":{"1":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"docs":{}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009299853859439352}},"e":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},".":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"m":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"}":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"n":{"docs":{},"d":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"y":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"w":{"docs":{},"i":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"c":{"docs":{},"e":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"t":{"docs":{},"w":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"d":{"docs":{},"d":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"o":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0021808421405804393},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.018018018018018018},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0017271157167530224},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0024084778420038534},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.017777777777777778},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004441976679622432},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.015306122448979591},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0068669527896995704},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0014251781472684087},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.008875739644970414},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.01059322033898305}},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{},"_":{"docs":{},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"b":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"i":{"docs":{},"b":{"docs":{},"b":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"p":{"docs":{},"h":{"docs":{},"r":{"docs":{},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{},":":{"docs":{},":":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"b":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"l":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0030797101449275364},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}},"e":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}},"k":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.008116883116883116},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005255781359495445},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"s":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"w":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}},"s":{"docs":{},"k":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},".":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"s":{"docs":{},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"l":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}},"r":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.003952569169960474},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"g":{"docs":{},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004441976679622432},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.005010438413361169},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.011834319526627219},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"y":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":5.0242914979757085},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"i":{"docs":{},"l":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"p":{"docs":{},"e":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"u":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.005780346820809248},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.00974025974025974},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.029967334185485018},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0024183796856106408},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.006493506493506494},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.008095440988495952},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0019883539269990058},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0032245062474808546}},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}},"s":{"docs":{},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},"docs":{}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}},"!":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"v":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},":":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0012782275244993609}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0015622780854992189}}},"!":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449}},")":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}},"_":{"docs":{},"s":{"docs":{},"v":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"v":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"v":{"docs":{},")":{"docs":{},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"v":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}},"v":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"t":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0037052284890901604},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394}},"e":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"t":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"p":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"c":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},"s":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}},"k":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"_":{"docs":{},"v":{"docs":{},"i":{"docs":{},"s":{"docs":{},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"f":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615}}},"l":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"y":{"docs":{},"p":{"docs":{},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0032935364347468094},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0012782275244993609},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"s":{"docs":{},"c":{"docs":{},"r":{"docs":{},"i":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"e":{"docs":{},"t":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"r":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"t":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}},"i":{"docs":{},"c":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"&":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004210526315789474}}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004210526315789474},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0039767078539980115},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}},"}":{"docs":{},"{":{"2":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}},"docs":{}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"m":{"docs":{},"p":{"1":{"docs":{},"[":{"9":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"docs":{}}},"2":{"docs":{},"[":{"9":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"docs":{}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0024422318241593085},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}},"x":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},"y":{"docs":{},")":{"docs":{},";":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},")":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"s":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{},"i":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"m":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"e":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}},"[":{"docs":{},"n":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551}}},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"u":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}}}}}}},"*":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}},"!":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"x":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},"s":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"r":{"docs":{},"n":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"_":{"docs":{},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"k":{"docs":{},"w":{"docs":{},"i":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"1":{"docs":{},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"docs":{}}}}}}}}}}}}}}}}}}}}},".":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"b":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0035694157430020664},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"e":{"docs":{},"s":{"docs":{},"d":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"g":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"n":{"docs":{},"e":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"b":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"f":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}},"d":{"docs":{},"m":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"^":{"2":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"3":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},")":{"docs":{},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"}":{"docs":{},"{":{"3":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"docs":{}}}},"4":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"docs":{}},"}":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"+":{"docs":{},"d":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"\"":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"u":{"3":{"2":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}},"6":{"4":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}},"docs":{}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"i":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{"./":{"ref":"./","tf":0.015306122448979591},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.011267605633802818},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.03389830508474576},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.017391304347826087},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.023809523809523808},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.018018018018018018},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.018691588785046728},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.015625},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003855278766310795},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0041753653444676405},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.012145748987854251},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00832870627429206},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.007653061224489796},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.009468917249897077},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.010958904109589041},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.005150214592274678},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.005979599015124868},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.007575757575757576},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.007098121085594989},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.011541072640868975},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0014492753623188406},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.01301775147928994},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004905395935529082},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.007707129094412331},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.017391304347826087},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.007352941176470588},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0020584602717167557},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.006618531889290012},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"o":{"docs":{},"o":{"docs":{},"d":{"docs":{},"!":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}}},"l":{"docs":{},"y":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"_":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"g":{"docs":{},"o":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"p":{"docs":{},"i":{"docs":{},"n":{"docs":{},"n":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"e":{"docs":{},"d":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"c":{"docs":{},"u":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"u":{"docs":{},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}},"a":{"docs":{},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}},"c":{"docs":{},"c":{"docs":{},"e":{"docs":{},"p":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"i":{"docs":{},"q":{"docs":{},"u":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0234375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}}},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.005280259951259139},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"y":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},"o":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"{":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"0":{"1":{"docs":{},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"docs":{}},"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004912280701754386},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0047522063815342835}},"l":{"docs":{},"i":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"?":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"m":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428}}}}}}},"h":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},"t":{"docs":{},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"i":{"docs":{},"k":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"u":{"docs":{},"c":{"docs":{},"k":{"docs":{},"y":{"docs":{},")":{"docs":{},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}}}}},"t":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002717391304347826},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"r":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}}}}},"w":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"y":{"docs":{},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}},"s":{"docs":{},"c":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}},"u":{"docs":{},"r":{"docs":{},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}}}}}},"e":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"t":{"docs":{},"l":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0028214429665457475}}}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"s":{"docs":{},"f":{"docs":{},"y":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"!":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"u":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}},"b":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216}}}}}}},"p":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"h":{"docs":{},"y":{"docs":{},"s":{"docs":{},"i":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"k":{"docs":{},"n":{"docs":{},"o":{"docs":{},"w":{"docs":{},"n":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}},"s":{"docs":{"./":{"ref":"./","tf":0.015306122448979591},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0035087719298245615},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0022026431718061676},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00268411340379131},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.017857142857142856},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0234375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.004118506709180284},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.005090054815974941},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.004744958481613286},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.006263048016701462},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.013333333333333334},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007218212104386452},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.02040816326530612},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.018526142445450804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.005280259951259139},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.005479452054794521},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0068669527896995704},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.012175324675324676},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0024621878297572987},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002414429768498793},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0068520757758968156},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.010732323232323232},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0041753653444676405},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.010862186014935505},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.007821901323706379},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004733727810650888},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005956552207428171},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.010163749294184076},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}},"e":{"docs":{},"r":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0019927536231884057}}},"f":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"d":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"}":{"docs":{},"}":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},"z":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"e":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428}}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}},"p":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003153468815697267},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"!":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"o":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"t":{"docs":{},"o":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}},"r":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}},"t":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},".":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"_":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"k":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}},"s":{"docs":{},"u":{"docs":{},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}}}}}},"l":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}}}}}}}},"_":{"1":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}},"/":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"{":{"docs":{},"r":{"docs":{},"_":{"0":{"docs":{},"}":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"docs":{}}}}}}}}}}},"2":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}},")":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"/":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"{":{"docs":{},"r":{"docs":{},"_":{"0":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"docs":{}}}}}}}}}},"^":{"2":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}},"docs":{}}},"docs":{}}},"v":{"0":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"1":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"2":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},"3":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0026199113260781943},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.007358093903293623}},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"f":{"docs":{},"i":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"s":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"s":{"docs":{},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}},"a":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":5.016758983098992}},"(":{"5":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}},".":{"0":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"docs":{},"&":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}}},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},"docs":{}},"docs":{}}}}}}}},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}},"_":{"docs":{},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"g":{"docs":{},"r":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0015622780854992189}},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}}}}}}},"v":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0031656700668308124},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"c":{"1":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}},".":{"docs":{},"x":{"docs":{},"*":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"2":{"docs":{},".":{"docs":{},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"docs":{}}}}}},"y":{"docs":{},"*":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"2":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"docs":{}}}}}}}},"2":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}},"3":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"&":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"{":{"docs":{},"i":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"docs":{}}}}}}}}}}}}}}}}}},"}":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}},"w":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"docs":{},"_":{"docs":{},"c":{"docs":{},"a":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"6":{"4":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}},"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}}}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},"e":{"docs":{},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}},"!":{"docs":{},"[":{"0":{"docs":{},".":{"0":{"1":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"docs":{}}},"1":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"4":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"7":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}},"]":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"n":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"0":{"docs":{},".":{"0":{"docs":{},"_":{"docs":{},"f":{"6":{"4":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}},"docs":{}},"docs":{}}}},"docs":{}}},"docs":{}}}}}}}}}}}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0036275695284159614},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0053254437869822485}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"'":{"docs":{},"'":{"docs":{},"'":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}},"(":{"0":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"1":{"5":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"docs":{}},"2":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"5":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"6":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"7":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"9":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"{":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"}":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},"(":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},"v":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},":":{"5":{"1":{"2":{"docs":{},"/":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{}}},"docs":{}},"docs":{}},"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"/":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{}}}}}}},"docs":{}}}}}}}}},"docs":{}},"docs":{}}}}}}},"'":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488}}}}}}}}},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}},"s":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}}}}}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},">":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0018137847642079807}}}}},"t":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.02371822184348814}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002982530890498509}},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},"*":{"docs":{},"d":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}}}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0015622780854992189}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}}}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}}},"_":{"docs":{},"s":{"docs":{},"v":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"v":{"docs":{},"v":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},";":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0097997443544951}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"!":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}},"_":{"docs":{},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}},"(":{"5":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},".":{"0":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}},"docs":{}}},"docs":{},"&":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}}},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}}},":":{"docs":{},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},"docs":{}},"docs":{}}}}}}}}}}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}},"(":{"5":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},".":{"0":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"v":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"v":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"i":{"docs":{},"a":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},"l":{"docs":{},"l":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}},"d":{"docs":{},"e":{"docs":{},"o":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00832870627429206},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0027397260273972603},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.004220893422441084},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.010855949895615866},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.008146639511201629},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.02485207100591716},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"e":{"docs":{},"w":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"s":{"docs":{},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"i":{"docs":{},"z":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"s":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}}}}}},"i":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"b":{"docs":{},"l":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},"e":{"docs":{},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"m":{"docs":{},"l":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}},"c":{"docs":{},"i":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"e":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"t":{"docs":{},"u":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}}}}}},"a":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0038584130179500084},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0018599707718878703},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.003915426781519186},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0024084778420038534},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007218212104386452},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.005965061780997018},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"e":{"docs":{},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"s":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"n":{"docs":{},"t":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"o":{"docs":{},"u":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"e":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"s":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"_":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965}}}}},"l":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013285505513484788},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0023492560689115116},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003700657894736842},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}},"u":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002777245738364298},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0023913909924272616},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.002881844380403458},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0028179597971068945},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0019883539269990058},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.011363636363636364},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.005431093007467753},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.004908946951702296},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.019271198318149965},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.006355932203389831}},"e":{"docs":{},"(":{"docs":{},"v":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"|":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"_":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551}}}}}}}}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"s":{"docs":{},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"?":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},":":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},")":{"docs":{},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}},"g":{"docs":{},"u":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}},"e":{"docs":{},",":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"n":{"docs":{},"i":{"docs":{},"s":{"docs":{},"h":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"o":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004210526315789474},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.005937559854434017},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002258535937292414},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00822239624119029},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003855278766310795},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0023752969121140144}}}},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},"e":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}}},"f":{"docs":{},"f":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},".":{"docs":{},"^":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},"docs":{}}}}}}}}}}}}}},"}":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},"x":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"y":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"z":{"docs":{},"i":{"docs":{},"p":{"docs":{},"(":{"docs":{},"y":{"docs":{},".":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},".":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{},"(":{"docs":{},"|":{"docs":{},"i":{"docs":{},"|":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},"(":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}}}}},"+":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}}},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"1":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}}}}}},"docs":{}}}},"docs":{}}}}}}}}},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},",":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488}}}}}}}}}}}}}}},"n":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"_":{"0":{"docs":{},"t":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"docs":{},"o":{"docs":{},"f":{"docs":{},"f":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"i":{"docs":{},"(":{"2":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"docs":{}}}}}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"x":{"docs":{},"_":{"docs":{},"o":{"docs":{},"d":{"docs":{},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}}},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368}},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}},":":{"docs":{},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"'":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0019883539269990058}}}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178}}},"=":{"1":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"2":{"5":{"5":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}},"docs":{},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004555010511562719}},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}}}}}}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},")":{"docs":{},".":{"docs":{},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"s":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"w":{"0":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}},"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.005763688760806916},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0028179597971068945},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009299853859439352},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.008344923504867872},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.004528612597776863},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"s":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"!":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},"i":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"n":{"docs":{},"a":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"i":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"b":{"docs":{},"o":{"docs":{},"x":{"docs":{},"_":{"docs":{},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"r":{"docs":{},"!":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{},"_":{"docs":{},"b":{"docs":{},"o":{"docs":{},"x":{"docs":{},"_":{"docs":{},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"r":{"docs":{},"!":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}},"y":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.005563282336578581},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00410958904109589},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.004419191919191919},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002803083391730904},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.005296610169491525}},"s":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},".":{"docs":{"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},";":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}},"!":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"m":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}},"p":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.005614035087719298}},".":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}},"v":{"docs":{},"e":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.004441976679622432},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.01020408163265306},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"y":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},",":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}}},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},";":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},".":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0032245062474808546},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.006016847172081829}},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}},"l":{"docs":{},"k":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891}},"\"":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"e":{"docs":{},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891}},"'":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}}}},"l":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"s":{"docs":{},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"t":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"h":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"e":{"docs":{},"'":{"docs":{},"l":{"docs":{},"l":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.00684931506849315},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013285505513484788},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"v":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"b":{"docs":{},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},":":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}}}}}}}},"l":{"docs":{},"l":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},")":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0015942606616181746},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"a":{"docs":{},"f":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"f":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}},":":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"6":{"4":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"docs":{}},"docs":{}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"]":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"s":{"docs":{},"[":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"_":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}}}}}},"?":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}},"r":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"s":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}}}}}},"x":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"d":{"docs":{},"n":{"docs":{},"e":{"docs":{},"s":{"docs":{},"d":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}}}},"e":{"docs":{},"k":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"l":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002355072463768116}}}}}}},"i":{"docs":{},"k":{"docs":{},"i":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"i":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}},"s":{"docs":{},"h":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"!":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"e":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"t":{"docs":{},"h":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"i":{"docs":{},"n":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.004210526315789474},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}},"_":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"_":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"(":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"s":{"docs":{},"t":{"docs":{},"d":{"docs":{},":":{"docs":{},":":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.011299435028248588},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"r":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}},".":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"s":{"docs":{},"c":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"t":{"docs":{},"h":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}}},"l":{"docs":{},"d":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},":":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}},"l":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"f":{"docs":{},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"n":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"d":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"k":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.011560693641618497},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.008888888888888889},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"s":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},":":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"!":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"e":{"docs":{},"d":{"docs":{},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"l":{"docs":{},"d":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294}}},"s":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},";":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"t":{"docs":{},"h":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828}},"w":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"s":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"r":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"y":{"docs":{},"!":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"s":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"!":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"t":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.003246753246753247}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"u":{"docs":{},"l":{"docs":{},"d":{"docs":{},"'":{"docs":{},"v":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"n":{"docs":{},"'":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.005873140172278779}},"(":{"docs":{},"\"":{"docs":{},"f":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"g":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"h":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"i":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"j":{"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"f":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}},"p":{"docs":{},"i":{"docs":{},"c":{"docs":{},"k":{"docs":{},"_":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},"?":{"docs":{},".":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},":":{"docs":{},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.006656225528582615}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"/":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}},"'":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},":":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},":":{"docs":{},":":{"docs":{},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"[":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},"[":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"d":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"d":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}},"b":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"r":{"docs":{},"i":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{"./":{"ref":"./","tf":0.00510204081632653},"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.005633802816901409},"contents/data_structures/data_structures.html":{"ref":"contents/data_structures/data_structures.html","tf":0.01694915254237288},"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/matrix_methods/matrix_methods.html":{"ref":"contents/matrix_methods/matrix_methods.html","tf":0.008928571428571428},"contents/computational_geometry/computational_geometry.html":{"ref":"contents/computational_geometry/computational_geometry.html","tf":0.011904761904761904},"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009},"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/physics_solvers/physics_solvers.html":{"ref":"contents/physics_solvers/physics_solvers.html","tf":0.0078125},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.003131524008350731},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}}}}},"e":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.005479452054794521},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"(":{"docs":{},"*":{"docs":{},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}},"'":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}}}},"*":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0021303792074989347}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}},"l":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"c":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"!":{"docs":{},"(":{"docs":{},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"d":{"docs":{},"l":{"docs":{},"m":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"s":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{},"p":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"k":{"docs":{},"i":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}}}}}}}}}}}},"f":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},":":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}}}}}}},"o":{"docs":{},"n":{"docs":{},"g":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}},";":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}}}},"a":{"docs":{},"p":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":5.027027027027027},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.003371868978805395},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.004697986577181208},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},".":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}},"h":{"docs":{},"a":{"docs":{},"t":{"docs":{},"'":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"e":{"docs":{},"v":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339}},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"v":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},"q":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"s":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"*":{"docs":{},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}},"f":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},":":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}},"e":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/decision_problems/decision_problems.html":{"ref":"contents/decision_problems/decision_problems.html","tf":0.009345794392523364},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"r":{"docs":{},"e":{"docs":{},"v":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},"'":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"a":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"n":{"docs":{},"e":{"docs":{},"v":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001665741254858412},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"e":{"docs":{},"l":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"o":{"docs":{},"l":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"s":{"docs":{},"e":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"y":{"docs":{},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"f":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"l":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"n":{"docs":{},"o":{"docs":{},"b":{"docs":{},"o":{"docs":{},"d":{"docs":{},"y":{"docs":{},"\"":{"docs":{},")":{"docs":{},")":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"e":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"o":{"docs":{},"p":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"(":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"s":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"o":{"docs":{},"n":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"_":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"f":{"docs":{},"c":{"0":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0026199113260781943},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"'":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}}},".":{"docs":{},"p":{"docs":{},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},":":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}}}}}}}}}},"_":{"docs":{},"c":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}},".":{"docs":{},"*":{"docs":{},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"v":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},".":{"docs":{},"s":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"0":{"docs":{},".":{"5":{"docs":{},"_":{"docs":{},"f":{"6":{"4":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"docs":{}},"docs":{}}}},"docs":{}}},"docs":{}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}},"(":{"docs":{},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}}},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}},"(":{"docs":{},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},")":{"docs":{},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}},"o":{"docs":{},"f":{"docs":{},"f":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"i":{"docs":{},"(":{"2":{"docs":{},")":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"docs":{}}}}}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"j":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}},"(":{"docs":{},"o":{"docs":{},"p":{"docs":{},"r":{"docs":{},".":{"docs":{},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{},")":{"docs":{},";":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"j":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488}}}}}},"o":{"docs":{},"f":{"docs":{},"f":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}},".":{"docs":{},"^":{"2":{"docs":{},"/":{"2":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}}},"docs":{}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"=":{"2":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"docs":{}}}}}}}},"c":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"o":{"docs":{},"n":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"p":{"docs":{},"e":{"docs":{},"d":{"docs":{},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"d":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"u":{"docs":{},"n":{"docs":{},"u":{"docs":{},"s":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}},"y":{"1":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.004335260115606936},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0063758389261744965},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.007410456978180321},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.01868399675060926},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0028139289482940555},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0031565656565656565},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0033944331296673455},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.005917159763313609},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"u":{"docs":{},"b":{"docs":{"./":{"ref":"./","tf":0.00510204081632653}},"e":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0038535645472061657}}}}}}},"!":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.020833333333333332},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"'":{"docs":{},"r":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},"d":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"r":{"docs":{},"k":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computer_graphics/computer_graphics.html":{"ref":"contents/computer_graphics/computer_graphics.html","tf":0.005649717514124294},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.020471014492753622}},"s":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"_":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"|":{"docs":{},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"|":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}}}},"!":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"'":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002355072463768116}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0018115942028985507}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0012681159420289854}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"t":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"s":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.00277623542476402},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00934199837530463},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0029227557411273487},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}},")":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"=":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003331482509716824},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0036555645816409425},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465}}}},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.005871498070793491}},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0016467682173734047}},"e":{"docs":{},"[":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}},"a":{"docs":{},"s":{"docs":{},"_":{"docs":{},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"s":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"|":{"docs":{},"i":{"docs":{},"|":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}},"\"":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}},"i":{"docs":{},"e":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0072254335260115606},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.005369127516778523},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.002110446711220542},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845}},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"docs":{}},"docs":{}}}}}}}},"=":{"0":{"docs":{},")":{"docs":{},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"docs":{},"%":{"docs":{},"f":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"x":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"b":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"c":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"*":{"docs":{},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"y":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"^":{"2":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"docs":{}},"_":{"1":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"2":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},":":{"docs":{},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"docs":{}},"docs":{}}}}}}}},"^":{"2":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"docs":{}},"i":{"docs":{},"t":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}},"i":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"n":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"p":{"docs":{},"o":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}},"s":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}},"s":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579}}}},"6":{"4":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}},"docs":{},"h":{"docs":{},"a":{"docs":{},"l":{"docs":{},"f":{"docs":{},"+":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"k":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"n":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}},"(":{"docs":{},"x":{"docs":{},".":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}},"l":{"docs":{},"a":{"docs":{},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"x":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}},"y":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"z":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"\\":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}},"\"":{"0":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},".":{"1":{"docs":{},".":{"1":{"1":{"docs":{},"\"":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}},"docs":{}}},"docs":{}}},"1":{"9":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"2":{"docs":{},"d":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},"_":{"docs":{},"s":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"w":{"docs":{},"_":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}}}}}}}}}}}}},"8":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.006990997893123923},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0014614056064833267},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.003915426781519186},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0036231884057971015}},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"u":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}}},"e":{"docs":{},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"s":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"f":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},"\"":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"\"":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"h":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0014492753623188406},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"d":{"docs":{},"\"":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}},"a":{"docs":{},"k":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}}},"y":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}},"o":{"docs":{},"p":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"_":{"docs":{},"_":{"docs":{},"m":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},"_":{"docs":{},"_":{"docs":{},"\"":{"docs":{},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649}}},"c":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"e":{"docs":{},"s":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}},"e":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}},".":{"docs":{},"p":{"docs":{},"n":{"docs":{},"g":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},".":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535}}}}}}}}}},"a":{"docs":{},"o":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0035174111853675696}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"o":{"docs":{},"d":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{},".":{"docs":{},".":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"n":{"docs":{},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"/":{"docs":{},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"s":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535}}}}}},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"m":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"x":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"i":{"docs":{},"n":{"docs":{},"c":{"docs":{},"i":{"docs":{},"d":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}}}},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"\"":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"i":{"docs":{},"r":{"docs":{},"c":{"docs":{},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"y":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}}}},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"m":{"docs":{},"i":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}},"a":{"docs":{},"k":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"t":{"docs":{},"h":{"docs":{},"\"":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"/":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}}}}}},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"e":{"docs":{},"t":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},"i":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}},"\"":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551}}},"c":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}},"n":{"docs":{},"t":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}},"a":{"docs":{},"l":{"docs":{},"c":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},"d":{"docs":{},"e":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}},"p":{"docs":{},"i":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}}}}}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"i":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},":":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}},"}":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"#":{"docs":{},"{":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{},"}":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{},"}":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}}},"@":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},".":{"docs":{},"r":{"docs":{},"j":{"docs":{},"u":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"2":{"0":{"docs":{},")":{"docs":{},"}":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"docs":{}},"docs":{}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"i":{"docs":{},"x":{"docs":{},"}":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"a":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"#":{"docs":{},"{":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{},"s":{"docs":{},"_":{"docs":{},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"#":{"docs":{},"{":{"docs":{},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"_":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},"}":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"%":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"\"":{"docs":{},",":{"docs":{},"(":{"2":{"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}}}}},"s":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}},"g":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002681478643937943}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0029687799272170084}}},"\"":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0033518483049224286},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.004058441558441558},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"r":{"docs":{},":":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},"o":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"[":{"0":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"1":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"2":{"docs":{},".":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{}}},"docs":{},"#":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001342056701895655}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}}}}},"~":{"docs":{},"%":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}},"`":{"docs":{},"n":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}},"a":{"1":{"1":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},"2":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},"3":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},"docs":{}},"2":{"1":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},"2":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},"3":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},"docs":{}},"3":{"1":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"2":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"3":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"docs":{}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011492051331162612},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"d":{"docs":{},"g":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}}},"i":{"docs":{},"m":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}},"p":{"docs":{},"p":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"r":{"docs":{},"o":{"docs":{},"x":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}}}}}}},"r":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}}}}}},"b":{"docs":{},"s":{"docs":{},"z":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"f":{"docs":{},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.003340292275574113},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.005431093007467753}}}}}},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"d":{"docs":{},"a":{"docs":{},"p":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}},"b":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"f":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"b":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"i":{"docs":{},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}},"y":{"docs":{},"_":{"docs":{},"b":{"docs":{},"o":{"docs":{},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}},"n":{"docs":{},"s":{"docs":{},"\"":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"u":{"docs":{},"c":{"docs":{},"k":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},".":{"docs":{},"\"":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}}}},"e":{"docs":{},"a":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"f":{"docs":{},"u":{"docs":{},"l":{"docs":{},".":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}},"o":{"docs":{},"t":{"docs":{},"t":{"docs":{},"o":{"docs":{},"m":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"\"":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}},"e":{"docs":{},"p":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"f":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}},"\"":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"i":{"docs":{},"f":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},":":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"v":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"f":{"docs":{},"m":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"g":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"l":{"docs":{},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"s":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}},"\"":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{},".":{"docs":{},"\"":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"i":{"docs":{},"l":{"docs":{},"e":{"docs":{},"d":{"docs":{},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}},"g":{"docs":{},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}},"o":{"docs":{},"l":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"=":{"docs":{},"'":{"docs":{},".":{"docs":{},".":{"docs":{},"/":{"docs":{},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"k":{"docs":{},"e":{"docs":{},"l":{"docs":{},"l":{"docs":{},"'":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}}}},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"t":{"docs":{},"e":{"docs":{},"g":{"docs":{},"r":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}}},"t":{"docs":{},"'":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}},"f":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0038691523039043265},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"n":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"o":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"g":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}}}}}}}}},"r":{"docs":{},"g":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}}}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"g":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}}}}}},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}},"a":{"docs":{},"l":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"d":{"docs":{},"u":{"docs":{},"c":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"t":{"1":{"3":{"docs":{},"\"":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}},"docs":{}},"docs":{},"a":{"docs":{},"t":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}}}},"l":{"docs":{},"l":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}},"j":{"docs":{},"n":{"docs":{},"d":{"docs":{},"a":{"docs":{},"e":{"docs":{},"l":{"docs":{},"\"":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}}}}}},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216}}}},"d":{"docs":{},"i":{"docs":{},"x":{"2":{"docs":{},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}},"8":{"docs":{},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}}}}},"g":{"docs":{},"b":{"1":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"2":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}}}},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},".":{"docs":{},"h":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}},"f":{"8":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}}},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"~":{"8":{"docs":{},"a":{"docs":{},"~":{"1":{"8":{"docs":{},"a":{"docs":{},"~":{"docs":{},"a":{"docs":{},"~":{"docs":{},"%":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"docs":{}},"docs":{}}}},"docs":{},"%":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}}}}},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0013407393219689715}}},"d":{"docs":{},"~":{"docs":{},"%":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449}}}}}},"{":{"docs":{},"~":{"docs":{},"f":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"a":{"docs":{},"~":{"docs":{},"%":{"docs":{},"~":{"docs":{},"}":{"docs":{},"\"":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"f":{"docs":{},"~":{"docs":{},"c":{"docs":{},"~":{"docs":{},"f":{"docs":{},"\"":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"$":{"1":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"2":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"\\":{"docs":{},"p":{"docs":{},"i":{"docs":{},"$":{"docs":{},"\"":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}},"docs":{},"a":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}},"(":{"docs":{},"$":{"docs":{},"_":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},"`":{"docs":{},"t":{"docs":{},"$":{"docs":{},"(":{"docs":{},"$":{"docs":{},"_":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{},")":{"docs":{},"\"":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"docs":{}}}}}}}}}}},"docs":{}}}}},"\\":{"docs":{},"p":{"docs":{},"i":{"docs":{},"$":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"`":{"docs":{},"t":{"docs":{},"$":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"c":{"docs":{},"u":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"e":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"\"":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"d":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"x":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"p":{"docs":{},"_":{"docs":{},"f":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"_":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"r":{"docs":{},":":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"c":{"docs":{},"h":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}},"g":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/gift_wrapping/gift_wrapping.html":{"ref":"contents/gift_wrapping/gift_wrapping.html","tf":0.009009009009009009}}}}}}},"\"":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821}}}}},"a":{"docs":{},"u":{"docs":{},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}},"m":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"n":{"docs":{},"u":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}},"_":{"1":{"docs":{},"d":{"docs":{},"_":{"docs":{},"s":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}},"2":{"docs":{},"d":{"docs":{},"_":{"docs":{},"s":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}}}}}}}}}},"docs":{},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"_":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}},"s":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"u":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"m":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"s":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}},"l":{"docs":{},"a":{"docs":{},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"t":{"docs":{},"y":{"docs":{},"p":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}},"o":{"docs":{},"g":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"2":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"s":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}},"s":{"docs":{},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}},"t":{"docs":{},"i":{"docs":{},"t":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}},"w":{"docs":{},"a":{"docs":{},"v":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"_":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}}}}}}}}},"w":{"docs":{},"a":{"docs":{},"v":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}}},"e":{"docs":{},"v":{"docs":{},"i":{"docs":{},"s":{"docs":{},"\"":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"(":{"docs":{},"b":{"docs":{},"i":{"docs":{},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"\"":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"?":{"docs":{},"\"":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"\\":{"docs":{},"\"":{"docs":{},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{},".":{"docs":{},".":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},".":{"docs":{},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}},"t":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}},"\\":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"\"":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"o":{"docs":{},"w":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},"s":{"docs":{},"v":{"1":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"2":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"3":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"4":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"5":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{},"\"":{"docs":{},")":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"o":{"docs":{},"g":{"docs":{},"r":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178}},"s":{"docs":{},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"g":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}}},"u":{"docs":{},"t":{"docs":{},".":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"p":{"docs":{},"u":{"docs":{},"t":{"0":{"0":{"0":{"0":{"0":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}},"docs":{},"{":{"docs":{},"}":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"(":{"docs":{},"i":{"docs":{},")":{"docs":{},".":{"docs":{},"r":{"docs":{},"j":{"docs":{},"u":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"5":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},".":{"docs":{},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"p":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},",":{"docs":{},"\"":{"docs":{},"w":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}},":":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"c":{"docs":{},"k":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"a":{"docs":{},"w":{"docs":{},"t":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}}}}}}},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"_":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}}}}}}}}}}}}}},"h":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"a":{"docs":{},"d":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"i":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}},"e":{"docs":{},"m":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"c":{"docs":{},"a":{"docs":{},"r":{"docs":{},"l":{"docs":{},"o":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}}},"n":{"docs":{},"(":{"docs":{},"x":{"docs":{},")":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"e":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{},"_":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{},".":{"docs":{},"p":{"docs":{},"n":{"docs":{},"g":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}},"e":{"docs":{},"r":{"docs":{},"p":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"k":{"docs":{},"i":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"e":{"docs":{},"c":{"docs":{},"i":{"docs":{},"r":{"docs":{},"c":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{},"_":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"m":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"\"":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"s":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}},"p":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"_":{"docs":{},"o":{"docs":{},"p":{"docs":{},"_":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"h":{"docs":{},"o":{"docs":{},"d":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0009057971014492754}}}}}},"m":{"docs":{},"i":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"t":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"y":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"r":{"docs":{},"l":{"docs":{},"d":{"docs":{},"'":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"h":{"docs":{},"a":{"docs":{},"t":{"docs":{},"'":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}},"\"":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"a":{"docs":{},"i":{"docs":{},"t":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"l":{"docs":{},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"o":{"docs":{},"r":{"docs":{},"g":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}}}}}}},"]":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}},"p":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}}},"r":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}}}}},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"o":{"docs":{},"d":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"c":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"a":{"docs":{},"g":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}}}}},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"o":{"docs":{},"t":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"e":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"e":{"docs":{},"d":{"docs":{},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"\"":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"s":{"docs":{},"e":{"docs":{},"u":{"docs":{},"d":{"docs":{},"o":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}},"r":{"docs":{},"o":{"docs":{},"b":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}},"y":{"docs":{},"\"":{"docs":{},")":{"docs":{},"(":{"docs":{},"u":{"docs":{},"n":{"docs":{},"i":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"0":{"1":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"docs":{}}}}}}}}}}},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"a":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"\\":{"docs":{},"t":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}}}}}}}},"`":{"docs":{},"t":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}},"o":{"docs":{},"u":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"v":{"docs":{},"x":{"docs":{},":":{"docs":{},"\"":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"{":{"docs":{},"}":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"\\":{"docs":{},"t":{"docs":{},"{":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"{":{"docs":{},"}":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},":":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"}":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"|":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003700657894736842}}}}},"+":{"docs":{},"+":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"z":{"2":{"docs":{},"\"":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}},"!":{"docs":{},"\"":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"q":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0022984102662325224},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.00741399762752076},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.002898550724637681},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.003952569169960474}},"u":{"docs":{},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{},"u":{"docs":{},"m":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/mathematical_background/mathematical_background.html":{"ref":"contents/mathematical_background/mathematical_background.html","tf":0.008695652173913044},"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":5.084558823529412},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":5.038507821901324}}}},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"y":{"docs":{},":":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"f":{"docs":{},"i":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}}}}}},"l":{"docs":{},"i":{"docs":{},"f":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"t":{"docs":{},"i":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"d":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}}}},"r":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}},":":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"s":{"docs":{},":":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"!":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}},"u":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"e":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":5.013333333333334},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.008619038498371959},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002105263157894737},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"g":{"docs":{},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"c":{"docs":{},"[":{"docs":{},"t":{"docs":{},"]":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}}}}}}},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}},"<":{"docs":{},">":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"1":{"docs":{},":":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"]":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"s":{"docs":{},",":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"{":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"}":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"}":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}}}}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"2":{"4":{"docs":{},";":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"c":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"r":{"docs":{},"o":{"docs":{},"o":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"u":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"?":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},"c":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}},"x":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"&":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"p":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},".":{"docs":{},"e":{"docs":{},"x":{"docs":{},"p":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"u":{"docs":{},"n":{"docs":{},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}}}},"_":{"docs":{},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"(":{"docs":{},"&":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},".":{"docs":{},".":{"docs":{},".":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}}}}}}},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},":":{"docs":{},":":{"docs":{},"b":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}},"_":{"docs":{},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"a":{"docs":{},"t":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}},"s":{"docs":{},"h":{"docs":{},"i":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},"\\":{"docs":{},"n":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"c":{"docs":{},"a":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"i":{"docs":{},"l":{"docs":{},"l":{"docs":{},"!":{"docs":{},"(":{"docs":{},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},"$":{"docs":{},"(":{"docs":{},"?":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"(":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"c":{"docs":{},"a":{"docs":{},"n":{"docs":{},"v":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"g":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"(":{"docs":{},"q":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"f":{"docs":{},"u":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},")":{"docs":{},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}}}}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"d":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}},"r":{"docs":{},"i":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}},"i":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"l":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/introduction/introduction.html":{"ref":"contents/introduction/introduction.html","tf":0.0019267822736030828}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"i":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"t":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"e":{"docs":{},"t":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"s":{"docs":{},"!":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},",":{"docs":{"contents/quantum_information/quantum_information.html":{"ref":"contents/quantum_information/quantum_information.html","tf":0.003676470588235294}}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"o":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.003260869565217391}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"~":{"docs":{},"\\":{"docs":{},"%":{"docs":{},"~":{"3":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"7":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}}}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"c":{"docs":{},"a":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}}}}},"t":{"docs":{},"(":{"docs":{},"n":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}}}},"p":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},"w":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.004022217965906914},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.004782781984854523},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.006763103513056547}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}},"_":{"docs":{},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"%":{"0":{"docs":{},".":{"2":{"docs":{},"f":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"docs":{}}},"1":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"2":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"3":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00536822680758262},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0036555645816409425},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.011594202898550725}},"}":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112}}},"%":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"s":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}},"'":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}},"]":{"docs":{},"[":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"y":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"z":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"t":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"f":{"docs":{},"%":{"docs":{},"%":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"l":{"docs":{},"f":{"docs":{},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"n":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}},".":{"1":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946}}},"]":{"docs":{},"[":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"y":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"z":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}}}},"docs":{}},"d":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}},">":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.02456140350877193},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0043095192491859795},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.012246267404797853},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.005978477481068154},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.005873140172278779},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003262158956109134},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.005780346820809248},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.012080536912751677},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002843216896831844},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.004320871688897238},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0035174111853675696},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.01562278085499219},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.010882708585247884},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.005010438413361169},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.005615942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.008076009501187649},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},">":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"=":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}},")":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"+":{"docs":{},"+":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}},"v":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649}}},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"=":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}}},"b":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"c":{"docs":{},"a":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703696609844858},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124}},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},"[":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},"i":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}}}}}},"o":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"docs":{},"(":{"docs":{},"u":{"docs":{},"n":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}}},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009299853859439352}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},"q":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},"s":{"docs":{},"t":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}},"]":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},"y":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408}},")":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},"docs":{}}}}}}}}}}}},"i":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0013407393219689715}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"+":{"docs":{},"+":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}},"]":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"s":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}},"m":{"docs":{},"_":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"+":{"docs":{},"+":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"]":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}},"\"":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"e":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"y":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"+":{"docs":{},"+":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"h":{"docs":{},"s":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"r":{"docs":{},"h":{"docs":{},"s":{"docs":{},".":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"e":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"c":{"docs":{},"e":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"a":{"docs":{},"l":{"docs":{},"(":{"docs":{},"$":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"d":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"t":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"$":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"$":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"[":{"docs":{},"b":{"docs":{},"u":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}},"u":{"docs":{},"i":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"[":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}},"z":{"docs":{},"e":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00274079874706343}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0023492560689115116}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"s":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"[":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"e":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}},"u":{"docs":{},"n":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"y":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},")":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"[":{"0":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},",":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},",":{"1":{"docs":{},"]":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"docs":{}}},"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},":":{"1":{"0":{"docs":{},"]":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}},"docs":{},"]":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}},"docs":{},"]":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},".":{"0":{"1":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{},"]":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946}}}},"2":{"3":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"6":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"5":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"8":{"5":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{}},"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845}}}}},"1":{"0":{"docs":{},"]":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"1":{"docs":{},"]":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}},"[":{"1":{"2":{"docs":{},"]":{"docs":{},".":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"docs":{}},"docs":{}}}},"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"]":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},":":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},".":{"0":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"]":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852}}}}},"+":{"0":{"docs":{},".":{"0":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}}},"docs":{}}},"5":{"3":{"3":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"docs":{}},"docs":{}},"docs":{}},"~":{"0":{"docs":{},"~":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"2":{"docs":{},"~":{"1":{"docs":{},"]":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"docs":{}}},"docs":{}},",":{"2":{"docs":{},"]":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"n":{"docs":{},"]":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"2":{"0":{"2":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}},"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},"]":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"[":{"3":{"docs":{},"]":{"docs":{},".":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"docs":{}}},".":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}},"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"3":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},".":{"0":{"docs":{},"]":{"docs":{},"\"":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"docs":{}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"4":{"docs":{},"]":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"[":{"5":{"docs":{},"]":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"docs":{}},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},",":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946}}}},"docs":{}}},"5":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},".":{"0":{"docs":{},"]":{"docs":{},"\"":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"docs":{}}},"6":{"4":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"docs":{},"]":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"[":{"7":{"docs":{},"]":{"docs":{},"[":{"8":{"docs":{},"]":{"docs":{},".":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"docs":{}}}},"docs":{}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"7":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946}}},"]":{"docs":{},"\"":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"docs":{}}},"8":{"docs":{},"]":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},"9":{"docs":{},"]":{"docs":{},".":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"[":{"1":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}},"docs":{}},"docs":{}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0021068760773798123},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004361684281160879},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"i":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"m":{"docs":{},"p":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},":":{"1":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.0028169014084507044}}},"docs":{}}}}}}},"t":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"n":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"]":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0015322735108216816},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"*":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"{":{"docs":{},"n":{"docs":{},"}":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}}}},"(":{"docs":{},"a":{"docs":{},"u":{"docs":{},"t":{"docs":{},"o":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"r":{"docs":{},"u":{"docs":{},"n":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"{":{"docs":{},"{":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"f":{"3":{"2":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}},"docs":{}},"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"{":{"0":{"docs":{},".":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"1":{"docs":{},".":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"4":{"docs":{},".":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"7":{"docs":{},".":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}},"docs":{}},"docs":{}}}}}},"[":{"docs":{},"]":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}},"{":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"docs":{}},"docs":{}}}}}}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004210526315789474}}}}}}}}}}}}},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}},"$":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"&":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"]":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},".":{"8":{"6":{"6":{"6":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{},".":{"docs":{},".":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},".":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"s":{"docs":{},"(":{"docs":{},")":{"docs":{},"]":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"]":{"docs":{},".":{"docs":{},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"(":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"]":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"c":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},".":{"docs":{},"s":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"0":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"docs":{}}}}}}}}}}}}}}}}},"\"":{"docs":{},"a":{"docs":{},"b":{"docs":{},"c":{"docs":{},"d":{"docs":{},"e":{"docs":{},"\"":{"docs":{},"]":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}},"f":{"docs":{},"g":{"docs":{},"h":{"docs":{},"i":{"docs":{},"j":{"docs":{},"\"":{"docs":{},"]":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},"]":{"docs":{},".":{"docs":{},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"docs":{},"(":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}},"]":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579}},")":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"j":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"[":{"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}},"l":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},"]":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}}},"f":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}}}}}},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{},"[":{"docs":{},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{},"[":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{},"[":{"docs":{},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"c":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0013407393219689715}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},"?":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"e":{"docs":{},"w":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"_":{"docs":{},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{},"]":{"docs":{},"(":{"docs":{},"a":{"docs":{},"u":{"docs":{},"t":{"docs":{},"o":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}},":":{"docs":{},"m":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"a":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}},"r":{"1":{"0":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"1":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"2":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.00450105343803869},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009299853859439352},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0010534380386899062},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}},"3":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0012449722275426163},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}}}},"4":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"5":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"docs":{}},"8":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"9":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}},"docs":{},"a":{"docs":{},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0015942606616181746},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}},"b":{"docs":{},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"]":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}}},"d":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009299853859439352}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.001062840441078783}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}},"c":{"docs":{},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"s":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0019928258270227183},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}},"]":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"]":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"r":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}}}}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"]":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{},"[":{"docs":{},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}}}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}}}}}}}}}},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.001509813789632612}}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"i":{"docs":{},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0027155465037338763}}}}}},"w":{"docs":{},"i":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"]":{"docs":{},"$":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"o":{"docs":{},"i":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}},"h":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}},"t":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}},"_":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{},"[":{"docs":{},"l":{"docs":{},"f":{"docs":{},"]":{"docs":{},"[":{"docs":{},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{},"[":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}}}}}}}}}}},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{},"[":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{},"[":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{},"[":{"docs":{},"s":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}}}},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982}}}}}}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"]":{"docs":{},"(":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408}}}},"'":{"docs":{},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"b":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"t":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"(":{"docs":{},">":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"e":{"docs":{},"q":{"docs":{},"?":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"o":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"'":{"docs":{},"b":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}},"a":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742}}}},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"i":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"t":{"1":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"docs":{}},"b":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"p":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},"(":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"m":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"e":{"docs":{},"l":{"docs":{},"s":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"c":{"docs":{},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"m":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"]":{"docs":{},":":{"docs":{},":":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"$":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"b":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"p":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"(":{"docs":{},"$":{"docs":{},"r":{"docs":{},"a":{"docs":{},"d":{"docs":{},"i":{"docs":{},"u":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}},"y":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},".":{"7":{"5":{"docs":{},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"docs":{}},"docs":{}}},"docs":{}}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},"(":{"docs":{},"$":{"docs":{},"k":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"(":{"1":{"3":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}}}}}}}}}}}}}},"i":{"docs":{},"d":{"docs":{},"d":{"docs":{},"l":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"[":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"docs":{}}},"1":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}},"docs":{}}},"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}},"[":{"docs":{},"'":{"docs":{},"_":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{},"]":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"w":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"(":{"docs":{},"(":{"docs":{},"r":{"2":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"docs":{}}}}},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}},"c":{"docs":{},"]":{"docs":{},"(":{"docs":{},"a":{"docs":{},"u":{"docs":{},"t":{"docs":{},"o":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438}},"(":{"docs":{},"x":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}},"\"":{"docs":{},"a":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"e":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"\"":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"p":{"0":{"docs":{},"]":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},"(":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}}}}}},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"_":{"docs":{},"o":{"docs":{},"n":{"docs":{},"_":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414}}}}}}}}}}},"(":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}}},"docs":{}}}}},"s":{"docs":{},"(":{"2":{"docs":{},",":{"1":{"docs":{},".":{"5":{"docs":{},")":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"docs":{}}},"docs":{}}},"docs":{}}}},"v":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"l":{"docs":{},"e":{"docs":{},"]":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}},"m":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"i":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"/":{"2":{"0":{"0":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653}}},"docs":{}},"docs":{}},"docs":{}}}}},"]":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},";":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"%":{"docs":{},".":{"1":{"docs":{},"f":{"docs":{},"]":{"docs":{},"\"":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"a":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}},"b":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}}}}}}}}}}},"\\":{"docs":{},"n":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}}}}}}}}}}}}}},"docs":{}},"s":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}},"]":{"docs":{},"%":{"docs":{},"s":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}}}}}}},"{":{"docs":{},":":{"docs":{},"?":{"docs":{},"}":{"docs":{},"]":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}}}}}}}}}}}},"\\":{"docs":{},"!":{"docs":{},"[":{"1":{"docs":{},",":{"6":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"!":{"docs":{},"]":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"docs":{}}},"2":{"docs":{},",":{"1":{"2":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"!":{"docs":{},"]":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}},"docs":{}},"docs":{}}},"docs":{}}}}},"{":{"0":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}},"5":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}}},"1":{"5":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}}},"2":{"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}},".":{"0":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"docs":{}}},"3":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"4":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}},"docs":{}}},"5":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},".":{"0":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"docs":{}}},"6":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"7":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}},"docs":{}}},"9":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.05754385964912281},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.027197854817084848},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.02549907733601745},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.03228377839776803},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.04463586530931871},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.019572953736654804},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.05250481695568401},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.03791946308724832},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.003886729594669628},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.01949634443541836},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.009205335337215856},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.010279605263157895},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.012310939148786493},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.016332907257491834},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.017331721080209594},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.013361169102296452},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.008514492753623188},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.024228028503562947},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005255781359495445}},"%":{"docs":{"contents/how_to_contribute/how_to_contribute.html":{"ref":"contents/how_to_contribute/how_to_contribute.html","tf":0.008450704225352112}}},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"_":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"s":{"docs":{},"{":{"docs":{},":":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"1":{"0":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},"[":{"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"docs":{}}},"2":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"5":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"6":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"docs":{},"_":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"{":{"docs":{},":":{"docs":{},"}":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"}":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}}}}}},"}":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}},"r":{"docs":{},"m":{"docs":{},"s":{"docs":{},"d":{"docs":{},":":{"5":{"docs":{},".":{"1":{"docs":{},"%":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"docs":{}}},"docs":{}}}}}}},"{":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}}},"3":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"docs":{}}},"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}},"}":{"docs":{},"}":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0012449722275426163}}}}}}},"}":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0011956954962136308},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},"\"":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}},"\"":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},":":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}},".":{"3":{"docs":{},"f":{"docs":{},"}":{"docs":{},"\"":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"c":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}},"i":{"docs":{},"_":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}}}}}}}}}}}},"}":{"docs":{},"%":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"docs":{}},"?":{"docs":{},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},"]":{"docs":{},"[":{"docs":{},"x":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}}},"\"":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"r":{"docs":{},"y":{"docs":{},".":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}},"k":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},".":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"n":{"docs":{},"}":{"docs":{},")":{"docs":{},"'":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"y":{"docs":{},"}":{"docs":{},")":{"docs":{},"'":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{},"}":{"docs":{},")":{"docs":{},"'":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},":":{"docs":{},"_":{"docs":{},"}":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},".":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"h":{"docs":{},".":{"docs":{},"a":{"docs":{},"b":{"docs":{},"s":{"docs":{},"(":{"docs":{},"p":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}}}},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"[":{"0":{"docs":{},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}},"docs":{}}}},"h":{"docs":{},"s":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"p":{"docs":{},".":{"docs":{},"x":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216}}}}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},".":{"docs":{},"y":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}},"t":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}},"c":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"u":{"docs":{},"s":{"docs":{},"(":{"docs":{},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}}}}}}}}}}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"[":{"1":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},")":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}}}}}}}},"w":{"docs":{},"f":{"docs":{},"c":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"'":{"docs":{},"n":{"docs":{},"r":{"docs":{},"m":{"docs":{},"s":{"docs":{},"d":{"docs":{},"'":{"docs":{},":":{"1":{"0":{"docs":{},"s":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"docs":{}},"docs":{}}}}}}}}},"q":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"x":{"0":{"docs":{},":":{"5":{"docs":{},".":{"2":{"docs":{},"f":{"docs":{},"}":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"docs":{}}},"docs":{}}},"docs":{}}},"@":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}},"a":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.020833333333333332}},"s":{"docs":{},",":{"docs":{},"@":{"docs":{},"p":{"docs":{},"e":{"docs":{},"a":{"docs":{},"n":{"docs":{},"u":{"docs":{},"t":{"docs":{},"b":{"docs":{},"u":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"i":{"docs":{},"o":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.052083333333333336}}}}}},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"l":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.020833333333333332}},"e":{"docs":{},",":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.020833333333333332}},"@":{"docs":{},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"d":{"docs":{},"o":{"docs":{},"w":{"docs":{},"m":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}},",":{"docs":{},"@":{"docs":{},"a":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"s":{"docs":{},",":{"docs":{},"@":{"docs":{},"p":{"docs":{},"e":{"docs":{},"a":{"docs":{},"n":{"docs":{},"u":{"docs":{},"t":{"docs":{},"b":{"docs":{},"u":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"s":{"docs":{},"h":{"docs":{},"a":{"docs":{},"d":{"docs":{},"o":{"docs":{},"w":{"docs":{},"m":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"a":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.041666666666666664}},",":{"docs":{},"@":{"docs":{},"p":{"docs":{},"e":{"docs":{},"a":{"docs":{},"n":{"docs":{},"u":{"docs":{},"t":{"docs":{},"b":{"docs":{},"u":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"w":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"(":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"5":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}}},"1":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{}}},"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271}},"a":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551}}}},"k":{"docs":{},",":{"docs":{},"v":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}},"$":{"docs":{},"(":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}},"o":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}}}}},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245}}}}}},"i":{"docs":{},"d":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"n":{"docs":{},"b":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.014035087719298246}}}}}}},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"(":{"docs":{},"g":{"docs":{},"l":{"docs":{},"o":{"docs":{},"b":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615}}}}}}}}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},"\"":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"i":{"docs":{},"l":{"docs":{},"?":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"t":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"a":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"s":{"docs":{},".":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},".":{"docs":{},"i":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"[":{"docs":{},"@":{"docs":{},"c":{"docs":{},"h":{"docs":{},"o":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},"]":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"o":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615}}}}}}}},"[":{"0":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"1":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"4":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"7":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}},"docs":{}}},"x":{"0":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.00282326369282891}},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},":":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"1":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"2":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}},"6":{"4":{"docs":{"contents/code_reviews/code_reviewers.html":{"ref":"contents/code_reviews/code_reviewers.html","tf":0.010416666666666666}}},"docs":{}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0021068760773798123},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004697198456634793},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.002372479240806643},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.004697986577181208},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.006587072869493619},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.017871649065800164},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.004884463648318617},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.006167763157894737},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0031656700668308124},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0019883539269990058},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.003787878787878788},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0037578288100208767},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0033944331296673455},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.007100591715976331},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.007340485601355167},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00847457627118644}},"m":{"docs":{},"m":{"0":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0035694157430020664},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0034086067319982955}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0024422318241593085},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.004970884817497514}}}},"1":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0028405056099985795}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0030058237835806877},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029}}}},"2":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0036926572929981537}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0033815517565282736},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}},"3":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002272404487998864}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002272404487998864}}}},"4":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}}}},"5":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002272404487998864}}}},"6":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0025564550489987218}}}},"7":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0025564550489987218}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},"docs":{},"w":{"docs":{},"o":{"docs":{},"r":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0022543678376855157}}}}}}},"a":{"docs":{},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00826279725916969},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}},"+":{"docs":{},"x":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"/":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},":":{"2":{"docs":{},"*":{"docs":{},"x":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},"/":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},":":{"docs":{},"x":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},")":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}},":":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{}},"docs":{}}}}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0032245062474808546}}}}},"i":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}}}}}},"o":{"docs":{},"r":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001819574794100747},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0021808421405804393},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0015942606616181746},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.005219206680584551},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"l":{"docs":{},"d":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"a":{"docs":{},"m":{"4":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"docs":{}},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308}}},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},".":{"1":{"docs":{},")":{"docs":{},".":{"docs":{},"r":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"(":{"docs":{},"*":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},":":{"docs":{},":":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}},"x":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},")":{"docs":{},";":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}}}}}},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0013150479053165509}}},"]":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"(":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"(":{"docs":{},"_":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"u":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},"(":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"p":{"docs":{},"o":{"docs":{},"w":{"docs":{},"i":{"docs":{},"(":{"2":{"docs":{},")":{"docs":{},")":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.004467912266450041},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.003340292275574113},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"y":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}},"i":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},":":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0072254335260115606},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.005369127516778523},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}},":":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},"docs":{}},"docs":{}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"a":{"docs":{},"t":{"6":{"4":{"docs":{},"}":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}},"docs":{}}}}}}}}}}}}}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"^":{"2":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"+":{"docs":{},"y":{"docs":{},"^":{"2":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"docs":{}}}},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"y":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\\":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"{":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}}}}}}}},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"docs":{}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}},"(":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}},")":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}},",":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}},"+":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}}}}},"\\":{"docs":{},"p":{"docs":{},"m":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"_":{"0":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"'":{"docs":{},"'":{"docs":{},"'":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"2":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{},"^":{"2":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"docs":{}},"i":{"docs":{},"t":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}}},"r":{"docs":{},"o":{"docs":{},"p":{"docs":{},"o":{"docs":{},"s":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"e":{"docs":{},"v":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438}}}}}},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"e":{"docs":{},"w":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}},"o":{"docs":{},"d":{"docs":{},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}}}}},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"{":{"1":{"0":{"docs":{},"}":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"t":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"]":{"docs":{},"\\":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}},"docs":{}},"docs":{},"i":{"docs":{},"+":{"1":{"docs":{},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"docs":{}}},"t":{"docs":{},"+":{"1":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"docs":{}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}},"/":{"docs":{},"y":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535}},"e":{"docs":{},"[":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"*":{"docs":{},"x":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"+":{"docs":{},"y":{"docs":{},"*":{"docs":{},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}},"p":{"docs":{},"o":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}}},"s":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"*":{"docs":{},"*":{"2":{"docs":{},")":{"docs":{},")":{"docs":{},".":{"docs":{},"s":{"docs":{},"u":{"docs":{},"m":{"docs":{},"(":{"docs":{},"a":{"docs":{},"x":{"docs":{},"i":{"docs":{},"s":{"docs":{},"=":{"0":{"docs":{},")":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}},"docs":{}}}}}}}}}}}}}},"docs":{}}}}},"y":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},"_":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},".":{"docs":{},"^":{"2":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"docs":{}}}}}}}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004111842105263158}},")":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"1":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},")":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"2":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},")":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"6":{"4":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}},"docs":{},"b":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"h":{"docs":{},"a":{"docs":{},"l":{"docs":{},"f":{"docs":{},"+":{"docs":{},"i":{"docs":{},"]":{"docs":{},"*":{"docs":{},"f":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}}}}}}}}}}}}},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0020665038512117226},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0028782894736842104},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"e":{"docs":{},"s":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}},"+":{"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0009393199323689649}}}},"n":{"docs":{},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"c":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"j":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"r":{"docs":{},"]":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}},"}":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"{":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}},"'":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}}},"|":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"l":{"docs":{},"a":{"docs":{},"b":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"x":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"z":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"\\":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}},"=":{"0":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{}},"]":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"!":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003642121931908155}},"=":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0013407393219689715},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.008387854386847844},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0013285505513484788},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.002533650039588282}},"=":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0011742996141586982},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"[":{"docs":{},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},".":{"docs":{},".":{"docs":{},"]":{"docs":{},".":{"docs":{},"i":{"docs":{},"s":{"docs":{},"_":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},".":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}}},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"!":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"f":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"h":{"docs":{},"a":{"docs":{},"s":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"(":{"docs":{},"p":{"docs":{},"a":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"(":{"docs":{},"*":{"docs":{},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}},"a":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}},"i":{"docs":{},"d":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},"s":{"docs":{},"n":{"docs":{},"a":{"docs":{},"n":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"_":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"k":{"docs":{},"w":{"docs":{},"i":{"docs":{},"s":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}}}}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"u":{"docs":{},"l":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}}},"#":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0168550086190385},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.006542526421741319},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.027633851468048358},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.012137823022709476},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.00771055753262159},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.006262042389210019},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.008053691275167786},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.002220988339811216},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.012755102040816327},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0037052284890901604},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.007311129163281885},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.009824561403508772},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.012962615066691715},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.013569078947368422},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.012310939148786493},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.013776452208493111},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.012898024989923419},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.025252525252525252},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.003340292275574113},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.01322463768115942},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.010292953285827395},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.00421179302045728},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.005956552207428171},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.002258610954263128}},"!":{"docs":{},"/":{"docs":{},"u":{"docs":{},"s":{"docs":{},"r":{"docs":{},"/":{"docs":{},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"/":{"docs":{},"e":{"docs":{},"n":{"docs":{},"v":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"c":{"docs":{},"l":{"docs":{},"u":{"docs":{},"d":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.004210526315789474},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0015322735108216816},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002125680882157566},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.005090054815974941},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0026690391459074734},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.002890173410404624},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0030201342281879194},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0028179597971068945},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.002055921052631579},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0028139289482940555},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0026199113260781943},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.001266825019794141},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.003153468815697267}}}}}}},"f":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},"[":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"(":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"u":{"docs":{},"g":{"docs":{},")":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}},"c":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282}}},")":{"docs":{},"]":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"f":{"docs":{},"i":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"f":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}},"l":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"(":{"0":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"1":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"4":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"7":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{},"+":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"l":{"docs":{},"i":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}},"*":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}},"c":{"docs":{},"/":{"docs":{},"+":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"i":{"docs":{},"f":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"/":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"e":{"docs":{},"q":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"{":{"docs":{},"i":{"docs":{},"}":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{},"}":{"docs":{},"\"":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"y":{"docs":{},"?":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}},"'":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}},"*":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"+":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"m":{"docs":{},"a":{"docs":{},"k":{"docs":{},"e":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"c":{"docs":{},"(":{"0":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"docs":{}}},"s":{"docs":{},"i":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"a":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}},"\\":{"docs":{},"t":{"docs":{},"a":{"docs":{},"b":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"&":{"0":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.003340292275574113}},".":{"0":{"4":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}},"docs":{}},"1":{"6":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}},"docs":{}},"2":{"2":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}},"4":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}},"8":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}},"docs":{}},"5":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}},"8":{"5":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}},"docs":{}},"docs":{}}},"1":{"docs":{},"&":{"2":{"docs":{},"&":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"3":{"docs":{},"&":{"docs":{},"&":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}}},"docs":{}}}}}}}}}}}}}}},"docs":{}}},"4":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}},"&":{"5":{"docs":{},"&":{"6":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835}}},"docs":{}}},"docs":{}}},"6":{"docs":{},"&":{"5":{"docs":{},"&":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"}":{"4":{"docs":{},"&":{"docs":{},"&":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}}},"docs":{}}}}}}}}}}}}}},"docs":{}}},"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.09929078014184398},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.010300429184549357},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.021792763157894735},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0025052192066805845},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.029453681710213776},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.014201183431952662},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"&":{"1":{"docs":{},"&":{"2":{"docs":{},"&":{"3":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835}}},"docs":{}}},"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"2":{"docs":{},"&":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"3":{"docs":{},"&":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"docs":{}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}},"6":{"docs":{},"&":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"}":{"5":{"docs":{},"&":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"4":{"docs":{},"&":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"docs":{}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.001062840441078783},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0024084778420038534},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.003985507246376811}},"&":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"6":{"docs":{},"&":{"5":{"docs":{},"&":{"4":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}}},"docs":{}}},"docs":{}}}}}},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"6":{"docs":{},"&":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"5":{"docs":{},"&":{"4":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}}},"docs":{}}}}}}}}}}}}}}},"docs":{}}}}}}},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"}":{"1":{"docs":{},"&":{"2":{"docs":{},"&":{"3":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}}},"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"2":{"docs":{},"&":{"3":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"3":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}},"6":{"docs":{},"&":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"5":{"docs":{},"&":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"4":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"1":{"9":{"4":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}}}},"5":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"3":{"1":{"5":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"1":{"9":{"5":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}},"docs":{}},"3":{"2":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"1":{"9":{"5":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}},"⭐":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"docs":{}},"docs":{},"b":{"0":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"1":{"9":{"5":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}},"docs":{}}},"docs":{}}},"docs":{}}}},"⏩":{"docs":{},"⏩":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"⏹":{"docs":{},"⏫":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}},"☝":{"docs":{},"️":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"1":{"9":{"5":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}}}},"docs":{}},"docs":{}},"3":{"0":{"0":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}},"docs":{},"c":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"4":{"1":{"5":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}}},"1":{"5":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"3":{"2":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"docs":{}},"4":{"6":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}},"7":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.004022217965906914},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.005280259951259139}}}},"9":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.003830683777054204},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0023485992283173965},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.005280259951259139}}}},"docs":{}},"6":{"5":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}},"8":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"3":{"4":{"6":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"docs":{}},"docs":{}},"4":{"1":{"docs":{},"a":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"3":{"3":{"2":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"3":{"4":{"6":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}}},"docs":{}},"docs":{}}},"docs":{}}}}}},"docs":{},"c":{"docs":{},";":{"docs":{},"⏹":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"d":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"4":{"3":{"docs":{},"d":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}},"docs":{}},"docs":{}}},"docs":{}}}},"b":{"docs":{},"i":{"docs":{},"n":{"docs":{},"a":{"docs":{},"r":{"docs":{},"y":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}},"a":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"2":{"4":{"docs":{},";":{"docs":{},"t":{"docs":{},"h":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}}},"7":{"docs":{},"c":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},"docs":{},"c":{"1":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"3":{"docs":{},";":{"docs":{},"‍":{"docs":{},"♀":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"4":{"0":{"7":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"9":{"2":{"1":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}}}}},"docs":{}},"e":{"2":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}},"7":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}},"docs":{}}},"4":{"0":{"7":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0008387854386847844},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}}},"docs":{}},"1":{"4":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551}}}},"5":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}}}},"docs":{}},"2":{"8":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}},"docs":{}},"3":{"docs":{},"b":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}},"d":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}},"4":{"docs":{},"c":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}},"docs":{},"a":{"docs":{},"d":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"f":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00487408610885459}},"s":{"docs":{},"a":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"s":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}},"d":{"7":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001915341888527102}}}},"docs":{}},"e":{"5":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}},"docs":{},"a":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}},"b":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}}}},"5":{"0":{"1":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"2":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"1":{"0":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"8":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"docs":{}},"2":{"1":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0012449722275426163},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{},"❗":{"docs":{},"❗":{"docs":{},"️":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}},"2":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0020130850528434826},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"4":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"3":{"0":{"0":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"docs":{}},"6":{"5":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"docs":{},"d":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"docs":{},"e":{"2":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"docs":{}}},"5":{"2":{"4":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"docs":{}},"docs":{}},"9":{"5":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}},"docs":{}},"docs":{}}},"docs":{}}}},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"%":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"2":{"4":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"3":{"6":{"docs":{},"a":{"docs":{},";":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"docs":{}},"docs":{}}},"docs":{}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}},"r":{"docs":{},"u":{"docs":{},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"docs":{}},"3":{"docs":{},"c":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}},"8":{"docs":{},"d":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"1":{"9":{"5":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}},"v":{"docs":{},"a":{"docs":{},"r":{"docs":{},"_":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"v":{"docs":{},"a":{"docs":{},"r":{"docs":{},"_":{"docs":{},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}},"r":{"docs":{},"a":{"docs":{},"d":{"docs":{},"i":{"docs":{},"u":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}},"docs":{}},"6":{"0":{"0":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}},"docs":{}},"4":{"5":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"docs":{},"c":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}},"docs":{},"a":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}},"9":{"1":{"docs":{},"c":{"docs":{},";":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"docs":{}},"docs":{}},"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"docs":{}},"docs":{},"d":{"docs":{},"e":{"docs":{},"p":{"docs":{},"t":{"docs":{},"h":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}},"i":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"p":{"docs":{},"i":{"docs":{},"_":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"x":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"d":{"docs":{},"i":{"docs":{},"u":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}}},"2":{"1":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}},"3":{"7":{"docs":{},";":{"docs":{},"‍":{"docs":{},"♀":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"docs":{}},"5":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}},"6":{"7":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"4":{"docs":{},"a":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"4":{"docs":{},"a":{"docs":{},"f":{"docs":{},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}},"docs":{}}},"docs":{}}}}}}},"docs":{}},"docs":{}}},"docs":{}}}}}},"docs":{}},"8":{"3":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"docs":{}},"docs":{},"d":{"2":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755}}}},"docs":{}}},"docs":{}}},"docs":{}}},"n":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}},".":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},"[":{"docs":{},".":{"docs":{},".":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551}}},"{":{"docs":{},"i":{"docs":{},"d":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}},"t":{"docs":{},"m":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"b":{"docs":{},"u":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"a":{"docs":{},"r":{"docs":{},"n":{"docs":{},"s":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},"_":{"docs":{},"h":{"docs":{},"u":{"docs":{},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"b":{"docs":{},"a":{"docs":{},"b":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}}}}}}}}}},"c":{"docs":{},"b":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},"|":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"e":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"n":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"r":{"docs":{},"]":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},"q":{"docs":{},"n":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}}}},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},"[":{"docs":{},"h":{"docs":{},"u":{"docs":{},"l":{"docs":{},"l":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}}},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},"u":{"docs":{},"l":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{},"[":{"docs":{},"&":{"docs":{},"c":{"docs":{},"]":{"docs":{},")":{"docs":{},".":{"docs":{},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},"[":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}},"t":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"[":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}},"[":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"l":{"docs":{},"e":{"docs":{},"x":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579}}}}}}}}}}},"f":{"6":{"4":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}},"docs":{}},"docs":{}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}}}}}},"a":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}}}}},"=":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004111842105263158},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0024621878297572987},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.007098121085594989},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.008146639511201629},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0017418844022169437},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0029585798816568047},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}},"x":{"docs":{},"(":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835}}}}}}},"x":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"2":{"docs":{},"]":{"docs":{},")":{"docs":{},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"docs":{}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}},"c":{"docs":{},"!":{"docs":{},"[":{"2":{"docs":{},".":{"0":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"docs":{}}},"docs":{}}}}}},"o":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}},"r":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},")":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"f":{"6":{"4":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"docs":{}},"docs":{}},";":{"docs":{},"&":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}},"'":{"0":{"docs":{},"'":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"1":{"0":{"0":{"0":{"docs":{},"'":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"1":{"docs":{},"'":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"docs":{},"'":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"1":{"docs":{},"'":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}},"docs":{}},"1":{"0":{"0":{"docs":{},"'":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"1":{"docs":{},"'":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"docs":{},"'":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"1":{"docs":{},"'":{"docs":{},")":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}},"docs":{}},"docs":{},"'":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"2":{"docs":{},"p":{"docs":{},"i":{"docs":{},"'":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0013407393219689715},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"'":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},"'":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}}},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},".":{"docs":{},"p":{"docs":{},"n":{"docs":{},"g":{"docs":{},"'":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"'":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"q":{"docs":{},"n":{"docs":{},"s":{"docs":{},"'":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"'":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},"=":{"docs":{},"z":{"docs":{},"^":{"2":{"docs":{},"'":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"'":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"'":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}}}},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"f":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"'":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"t":{"docs":{},"e":{"docs":{},"s":{"docs":{},"'":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}},"u":{"docs":{},"b":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"'":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"h":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873}},".":{"docs":{},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"d":{"docs":{},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"d":{"docs":{},"_":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"'":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"o":{"docs":{},"m":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}}}}}}}}}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0024899444550852325}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011492051331162612}},"n":{"docs":{},"u":{"docs":{},"m":{"2":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"(":{"docs":{},"e":{"docs":{},"u":{"docs":{},"c":{"docs":{},"l":{"docs":{},"i":{"docs":{},"d":{"docs":{},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"(":{"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}}}}},"s":{"docs":{},"u":{"docs":{},"b":{"docs":{},"(":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"docs":{}},"docs":{}},"docs":{}}}}}}}}}}}}}}}},"docs":{}}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0013407393219689715}}},"[":{"docs":{},"#":{"docs":{},"]":{"docs":{},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0007101264024996449}}}}}},"_":{"docs":{},"_":{"docs":{},"m":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},"_":{"docs":{},"_":{"docs":{},"'":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}},"i":{"docs":{},"d":{"docs":{},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"'":{"docs":{},"]":{"docs":{},"]":{"docs":{},"]":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"n":{"docs":{},"u":{"docs":{},"m":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},"_":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},"'":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"s":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}}},"d":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},"'":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}}}}},"(":{"docs":{},"g":{"0":{"docs":{},")":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}},"docs":{}},"(":{"docs":{},"(":{"docs":{},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"1":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"docs":{}}}}}}},"\"":{"docs":{},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"u":{"docs":{},"l":{"docs":{},"u":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}}}}},"a":{"docs":{},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"\\":{"0":{"docs":{},"'":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}},"docs":{}},"a":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}},"b":{"docs":{},"i":{"docs":{},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"_":{"docs":{},"b":{"docs":{},"o":{"docs":{},"b":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"'":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}}}}}}}}}},"o":{"docs":{},"'":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"y":{"docs":{},"'":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"%":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"#":{"0":{"0":{"0":{"0":{"docs":{},"f":{"docs":{},"f":{"docs":{},"'":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}},"docs":{}},"docs":{},"f":{"docs":{},"f":{"0":{"0":{"docs":{},"'":{"docs":{},")":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"docs":{}},"docs":{}}}},"docs":{}},"docs":{}},".":{"docs":{},".":{"docs":{},"/":{"docs":{},".":{"docs":{},".":{"docs":{},"/":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},"/":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"'":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},")":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"+":{"docs":{},"+":{"docs":{},"'":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"*":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.021052631578947368},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703696609844858},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.015433652071800034},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0015942606616181746},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.003855278766310795},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.008188824662813102},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.010738255033557046},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.023558082859463852},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.02526315789473684},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.006008583690987125},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.015029118917903438},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.018092105263157895},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.006683081252198382},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.04033517966197983},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.03184199919387344},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.005681818181818182},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.009603340292275574},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.02308214528173795},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0125},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.009026128266033254},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.004204625087596356},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0033879164313946925}},"/":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.015438596491228071},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"*":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0022168480451430876},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}},"t":{"docs":{},"m":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"=":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0024671052631578946},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0026199113260781943}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"b":{"docs":{},"o":{"docs":{},"o":{"docs":{},"k":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"m":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"u":{"docs":{},"s":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0008896797153024911}}}}}}},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}},"h":{"docs":{},"e":{"docs":{},"a":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}}}}},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"b":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}}}}}}}}}},"q":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},".":{"docs":{},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"s":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},".":{"docs":{},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"(":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}}},"k":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}}}}},"o":{"docs":{},"o":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"*":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}},"t":{"docs":{},"m":{"docs":{},"p":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}}},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0006045949214026602}},")":{"docs":{},";":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"a":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"h":{"docs":{},"u":{"docs":{},"f":{"docs":{},"f":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},"_":{"docs":{},"o":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},"l":{"docs":{},"h":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"s":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},".":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"r":{"docs":{},"y":{"docs":{},"(":{"docs":{},"c":{"docs":{},")":{"docs":{},".":{"docs":{},"o":{"docs":{},"r":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"s":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}},"g":{"docs":{},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"o":{"docs":{},"b":{"docs":{},"a":{"docs":{},"b":{"docs":{},"i":{"docs":{},"l":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733}}},".":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"m":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},")":{"docs":{},".":{"docs":{},"u":{"docs":{},"n":{"docs":{},"w":{"docs":{},"r":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"f":{"docs":{},"c":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"f":{"docs":{},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{},"_":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}}}}}}}}}}}}}}},"b":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}},".":{"docs":{},"a":{"docs":{},"u":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}},"e":{"docs":{},"p":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"x":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}},"p":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.001136202243999432}},",":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"k":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"e":{"docs":{},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"_":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"+":{"1":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}},"3":{"docs":{},"]":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.010725914575751772},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.017935432443204464},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0074393108848864525},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.009489916963226572},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.005780346820809248},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0050335570469798654},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.008344923504867872},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.016194331983805668},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.007218212104386452},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.018277822908204712},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.014035087719298246},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.01201716738197425},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.015216982904377232},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.002435064935064935},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.004111842105263158},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.009497010200492437},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.019883539269990057},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.004635227730753728},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.005681818181818182},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0162839248434238},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.016293279022403257},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.030253623188405798},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.01330166270783848},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.008409250175192713},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.004517221908526256},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}},"+":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011492051331162612},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304}},"i":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}},"n":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"t":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"=":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}},"=":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002125680882157566},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0020759193357058124},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0026845637583892616},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.020451640391989774},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003800475059382423},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},")":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"y":{"docs":{},"^":{"2":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"docs":{}}}},".":{"0":{"1":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}},"docs":{}},"1":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}},"2":{"6":{"6":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"docs":{}},"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}},"3":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}},"4":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0027816411682892906}}},"5":{"docs":{},"f":{"docs":{},"]":{"docs":{},"\"":{"docs":{},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"(":{"docs":{},"s":{"docs":{},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"[":{"docs":{},"i":{"docs":{},"]":{"docs":{},")":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}}}}}}}}}}}}}}}},"*":{"docs":{},"a":{"docs":{},"c":{"docs":{},"c":{"docs":{},"*":{"docs":{},"d":{"docs":{},"t":{"docs":{},"*":{"docs":{},"d":{"docs":{},"t":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}}}}}}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002873012832790653},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.001644736842105263},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.006045949214026602},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0018050541516245488},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},".":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009299853859439352},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},".":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"t":{"docs":{},"h":{"docs":{},"i":{"docs":{},"s":{"docs":{},".":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{},".":{"docs":{},"s":{"docs":{},"l":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"(":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{},")":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}}}}}}}}}}},")":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"/":{"docs":{},"g":{"docs":{},"n":{"docs":{},"u":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{},"/":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{},"_":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},".":{"docs":{},"p":{"docs":{},"l":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},"s":{"docs":{},".":{"docs":{},"t":{"docs":{},"o":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}}}}}}}},":":{"docs":{},":":{"docs":{},">":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}},"d":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},"!":{"docs":{},"(":{"docs":{},"a":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}},"s":{"docs":{},"v":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0016280406052480367},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0018599707718878703}}}},"x":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}},"p":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"g":{"docs":{},"l":{"docs":{},"o":{"docs":{},"b":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"p":{"docs":{},"b":{"docs":{},"y":{"docs":{},"(":{"docs":{},"i":{"docs":{},"d":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},"s":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"l":{"docs":{},"_":{"docs":{},"s":{"docs":{},"y":{"docs":{},"n":{"docs":{},"t":{"docs":{},"a":{"docs":{},"x":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}},"o":{"docs":{},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"|":{"docs":{},"_":{"docs":{},"|":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"(":{"docs":{},"&":{"docs":{},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"i":{"docs":{},"|":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}}},"k":{"docs":{},"|":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"(":{"docs":{},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}}},"v":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"v":{"docs":{},"a":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"s":{"docs":{},"(":{"docs":{},"_":{"docs":{},".":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}}}}}}}},"{":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"r":{"docs":{},"o":{"docs":{},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}},"s":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}}}},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"(":{"docs":{},"n":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"t":{"docs":{},"r":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}}},"o":{"docs":{},"r":{"docs":{},"t":{"docs":{},"e":{"docs":{},"d":{"docs":{},"(":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"o":{"docs":{},"r":{"docs":{},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"m":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"d":{"docs":{},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{},"e":{"docs":{},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"m":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}},":":{"docs":{},":":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"o":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}},"s":{"docs":{},"v":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"a":{"docs":{},"k":{"docs":{},"e":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"_":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}},"f":{"docs":{},"l":{"docs":{},"a":{"docs":{},"t":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"i":{"docs":{},"l":{"docs":{},"l":{"docs":{},"(":{"docs":{},"n":{"docs":{},"e":{"docs":{},"w":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},"|":{"docs":{},"i":{"docs":{},"|":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}},"o":{"docs":{},"r":{"docs":{},"_":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{},"|":{"docs":{},"i":{"docs":{},"|":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}},"l":{"docs":{},"d":{"docs":{},"(":{"0":{"docs":{},".":{"0":{"docs":{},"_":{"docs":{},"f":{"6":{"4":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}},"docs":{}},"docs":{}}}},"docs":{}}},"docs":{}}}}}},"n":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}}},"=":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0011862396204033216},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"n":{"docs":{},"c":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154}}}}}}}}}}},"a":{"docs":{},"t":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}},"o":{"docs":{},"u":{"docs":{},"b":{"docs":{},"l":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}}}}},"p":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}},"l":{"docs":{},"o":{"docs":{},"n":{"docs":{},"g":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002437043054427295},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}},"i":{"docs":{},"m":{"docs":{},"i":{"docs":{},"t":{"docs":{},"(":{"docs":{},"n":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"a":{"docs":{},"l":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}}}}}},"+":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"*":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0026199113260781943},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}}}},"\"":{"docs":{},"\"":{"docs":{},"\"":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"z":{"docs":{},"i":{"docs":{},"p":{"docs":{},"(":{"docs":{},"e":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"g":{"docs":{},"y":{"docs":{},"_":{"docs":{},"r":{"docs":{},".":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"o":{"docs":{},"_":{"docs":{},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"(":{"docs":{},")":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}}}}},"/":{"docs":{},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{},"n":{"docs":{},"s":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},".":{"docs":{},"c":{"docs":{},"p":{"docs":{},"p":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}},"a":{"docs":{},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}}}}}},":":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0021068760773798123},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0018599707718878703},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.004306969459671104},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0026690391459074734},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0017587055926837848},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0014365064163953266},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0018453279651065259},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0006642752756742394},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.002843216896831844},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.003550632012498225},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.007859733978234583},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"=":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.002585711549511588},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003355141754739138},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0030556662681015014},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.00674373795761079},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.006167763157894737},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.006017418844022169}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"d":{"docs":{},"a":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"e":{"docs":{},"p":{"docs":{},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"i":{"docs":{},"r":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"e":{"docs":{},"l":{"docs":{},"s":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"s":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366}},"e":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"i":{"docs":{},"d":{"docs":{},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"f":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"]":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.005225653206650831}},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"p":{"docs":{},"y":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}}}}}}},"+":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0014107214832728737}}},"a":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}},"s":{"docs":{},"u":{"docs":{},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"e":{"docs":{},"d":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}}},"=":{"1":{"docs":{},":":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"(":{"docs":{},"b":{"docs":{},"i":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"i":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}}}},"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.025964912280701753},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0317946753495499},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.06777386344573058},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.04158363225720739},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.056382145653876274},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.04833926453143535},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.038053949903660886},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.042953020134228186},"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.004172461752433936},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.023320377568017768},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0070921985815602835},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.01020408163265306},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0012350761630300535},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.030463038180341188},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.01643835616438356},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.041403508771929824},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.039484978540772535},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.041330077024234455},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.011363636363636364},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.07935855263157894},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.03447062961660218},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.06561567959096719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.06590084643288996},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.023989898989898988},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.030897703549060542},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.03054989816700611},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.030797101449275364},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.052256532066508314},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.021660649819494584},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.008875739644970414},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.014716187806587245},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.028797289666854884},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.022245762711864406}},"=":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0035087719298245615},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0030645470216433632},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0020130850528434826},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.004251361764315132},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.003523884103367267},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.01571767497034401},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.008188824662813102},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.004697986577181208},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.007065217391304348},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.004592240696753761},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},"'":{"docs":{},"_":{"docs":{},"_":{"docs":{},"m":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},"_":{"docs":{},"_":{"docs":{},"'":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}},"=":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},">":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0013407393219689715},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0021808421405804393},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.004517071874584828},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.004698512137823023},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0038535645472061657},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0015029118917903438},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}},"&":{"4":{"docs":{},"+":{"1":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}}},"5":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.010638297872340425}}},"docs":{}}},"_":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0006703696609844858},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0018599707718878703},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"_":{"docs":{},"a":{"docs":{},"u":{"docs":{},"t":{"docs":{},"h":{"docs":{},"o":{"docs":{},"r":{"docs":{},"_":{"docs":{},"_":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}},"d":{"docs":{},"d":{"docs":{},"_":{"docs":{},"_":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}},"b":{"docs":{},"s":{"docs":{},"_":{"docs":{},"_":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"i":{"docs":{},"t":{"docs":{},"_":{"docs":{},"_":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"_":{"docs":{},"_":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}}}}}}}}},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"_":{"docs":{},"_":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"=":{"docs":{},"=":{"docs":{},"\"":{"docs":{},"_":{"docs":{},"_":{"docs":{},"m":{"docs":{},"a":{"docs":{},"i":{"docs":{},"n":{"docs":{},"_":{"docs":{},"_":{"docs":{},"\"":{"docs":{},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"_":{"docs":{},"_":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}},":":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"u":{"docs":{},"c":{"docs":{},"t":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}}}}},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{},"_":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"p":{"docs":{},"r":{"docs":{},"_":{"docs":{},"_":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958}}}}}}},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"_":{"docs":{},"_":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}},"a":{"docs":{},"t":{"docs":{},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"_":{"docs":{},"_":{"docs":{},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}}}}}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"s":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"n":{"docs":{},"g":{"docs":{},"(":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"m":{"docs":{},"u":{"docs":{},"l":{"docs":{},"d":{"docs":{},"c":{"3":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}}}}}}},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0005314202205393915},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.002414429768498793},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009299853859439352},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},".":{"docs":{},"w":{"docs":{},"e":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}}}},"}":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"p":{"docs":{},"o":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739}}}},"d":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"p":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}},"x":{"docs":{},"m":{"docs":{},"a":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},";":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}},"`":{"docs":{},"d":{"docs":{},"e":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"`":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"i":{"docs":{},"v":{"docs":{},"`":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}}}}}},"e":{"docs":{},"n":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"`":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"o":{"docs":{},"n":{"docs":{},"t":{"docs":{},"`":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}},"i":{"docs":{},"r":{"docs":{},"s":{"docs":{},"t":{"docs":{},"`":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}},"p":{"docs":{},"o":{"docs":{},"p":{"docs":{},"`":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}},"u":{"docs":{},"s":{"docs":{},"h":{"docs":{},"`":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{},"`":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"_":{"docs":{},"l":{"docs":{},"i":{"docs":{},"s":{"docs":{},"t":{"docs":{},"`":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"`":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0014035087719298245}}}}}},"e":{"docs":{},"c":{"docs":{},"o":{"docs":{},"n":{"docs":{},"d":{"docs":{},"`":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"t":{"docs":{},"o":{"docs":{},"p":{"docs":{},"`":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"`":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}},"b":{"docs":{},"`":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"m":{"docs":{},"o":{"docs":{},"d":{"docs":{},"`":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0014492753623188406}}}}},"a":{"docs":{},"r":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}},"a":{"docs":{},"n":{"docs":{},"d":{"docs":{},"`":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"p":{"docs":{},"r":{"docs":{},"i":{"docs":{},"l":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}}}},"n":{"docs":{},"o":{"docs":{},"t":{"docs":{},"`":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"u":{"docs":{},"m":{"docs":{},"b":{"docs":{},"e":{"docs":{},"r":{"docs":{},"_":{"docs":{},"o":{"docs":{},"f":{"docs":{},"_":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"n":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"`":{"docs":{},".":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}},"o":{"docs":{},"n":{"docs":{},"`":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}}},"i":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"v":{"docs":{},"e":{"docs":{},"_":{"docs":{},"c":{"docs":{},"o":{"docs":{},"o":{"docs":{},"l":{"docs":{},"e":{"docs":{},"y":{"docs":{},"_":{"docs":{},"t":{"docs":{},"u":{"docs":{},"k":{"docs":{},"e":{"docs":{},"y":{"docs":{},"`":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}}}}}}}}}}},"(":{"docs":{},"s":{"docs":{},"e":{"docs":{},"t":{"docs":{},"f":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"(":{"0":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}},"docs":{}}}},"}":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.05403508771929825},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.02499521164527868},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.024828048985069618},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.027500996412913512},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.04111198120595145},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.013938315539739028},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.02601156069364162},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.02919463087248322},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.008529650690495532},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0061995115536351685},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.008634868421052632},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.008793527963418923},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.014912654452492544},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.01713018943974204},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.006680584551148226},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.008514492753623188},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.026286619160728424},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.00350385423966363},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}},";":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.002807017543859649},"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0010534380386899062},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.002258535937292414},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0017793594306049821},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0024084778420038534},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0012782275244993609},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},")":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.00039856516540454366},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.001062840441078783},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789}}},")":{"docs":{},";":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"l":{"docs":{},"e":{"docs":{},"c":{"docs":{},"t":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.02023121387283237},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0050335570469798654},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"~":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"(":{"docs":{},")":{"docs":{"contents/stacks_and_queues/stacks_and_queues.html":{"ref":"contents/stacks_and_queues/stacks_and_queues.html","tf":0.0007017543859649122}}}}}}}}},"i":{"docs":{},"s":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{},"t":{"docs":{},"y":{"docs":{},"(":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408}}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"{":{"1":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}},"docs":{}}}}}}}}}},"n":{"docs":{},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{},"_":{"docs":{},"q":{"docs":{},"u":{"docs":{},"e":{"docs":{},"u":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}}}}}}}}}}}}},"=":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}}},"}":{"docs":{},"~":{"docs":{},"%":{"docs":{},"\"":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"a":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}},"$":{"1":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}},"2":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0011492051331162612},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0006711409395973154},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.002015316404675534},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0022169437846397467},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"c":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},")":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408}},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306}}},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}}}}}}}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},"d":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}}}},"+":{"docs":{},"+":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"n":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"o":{"docs":{},"d":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}},"u":{"docs":{},"m":{"docs":{},"o":{"docs":{},"f":{"docs":{},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},")":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}}},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},",":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}}}}}}}},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}},";":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}},"[":{"docs":{},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}}},"o":{"docs":{},"l":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"h":{"docs":{},"a":{"docs":{},"p":{"docs":{},"e":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},"s":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}},".":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{},"]":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}},"[":{"docs":{},"$":{"docs":{},"(":{"docs":{},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"e":{"docs":{},"m":{"docs":{},"p":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}},"[":{"0":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},"1":{"docs":{},"]":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}},"docs":{}}}}},"h":{"docs":{},"i":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0012449722275426163},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00548159749412686}}}},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551}},")":{"docs":{},":":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551}}}}}}},"m":{"docs":{},"p":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}}},"(":{"1":{"0":{"0":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"docs":{}},"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"docs":{}},"docs":{}},"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"docs":{}},"docs":{},"(":{"1":{"2":{"8":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"docs":{}},"docs":{}},"2":{"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"6":{"4":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"docs":{}},"docs":{}},"j":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"(":{"docs":{},"\"":{"docs":{},"\"":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"a":{"docs":{},"[":{"2":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}},"b":{"docs":{},"[":{"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}}}}}}}},"g":{"docs":{},"e":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}},"a":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.004193927193423922},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}}},"[":{"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"2":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}},"b":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0038584130179500084},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0018453279651065259}},":":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706}}}},",":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"]":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"2":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{}}},"f":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}},"g":{"docs":{},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}},"m":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0011746280344557558}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"t":{"docs":{},"c":{"docs":{},"h":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}},"e":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"p":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},"s":{"docs":{},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}},"e":{"docs":{},"r":{"docs":{},"c":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"r":{"docs":{},"\"":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}},"i":{"docs":{},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"+":{"docs":{},"+":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}},"e":{"docs":{},"s":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"a":{"docs":{},"t":{"docs":{},"e":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}},"o":{"docs":{},"s":{"docs":{},"i":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"x":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"y":{"docs":{},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}}}}}}},"u":{"docs":{},"n":{"docs":{},"m":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"i":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371}}}}}}}}},"w":{"docs":{},"o":{"docs":{},"m":{"docs":{},"a":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.001957713390759593}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}},"e":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}},")":{"docs":{},":":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"{":{"2":{"2":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}},"docs":{}},"docs":{},"g":{"docs":{},"i":{"docs":{},"r":{"docs":{},"l":{"docs":{},".":{"docs":{},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"p":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"y":{"docs":{},".":{"docs":{},"f":{"docs":{},"i":{"docs":{},"a":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},".":{"docs":{},"n":{"docs":{},"a":{"docs":{},"m":{"docs":{},"e":{"docs":{},"}":{"docs":{},"`":{"docs":{},")":{"docs":{},";":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"c":{"docs":{},"e":{"docs":{},"s":{"docs":{},".":{"docs":{},"m":{"docs":{},"a":{"docs":{},"p":{"docs":{},"(":{"docs":{},"p":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{},".":{"docs":{},"y":{"docs":{},"}":{"docs":{},")":{"docs":{},"`":{"docs":{},")":{"docs":{},")":{"docs":{},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}}}}}}}}}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}}}},"r":{"docs":{},"a":{"docs":{},"d":{"docs":{},"i":{"docs":{},"u":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},"s":{"docs":{},"=":{"1":{"docs":{},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}}},"docs":{}}}}}}}},"x":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},";":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"[":{"0":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"1":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"2":{"docs":{},"]":{"docs":{},",":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"docs":{},"$":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"y":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},")":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"[":{"docs":{},"$":{"docs":{},"i":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}},")":{"docs":{},"\"":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278}},"s":{"docs":{},".":{"docs":{},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{},"(":{"docs":{},"$":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"e":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0010869565217391304}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"k":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"q":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},")":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0026845637583892616},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0016304347826086956}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0029228112129666534},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0020134228187919465},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.005823783580687582},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0007246376811594203}},";":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"e":{"docs":{},"l":{"docs":{},"s":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}},"a":{"docs":{},"d":{"docs":{},"d":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}}}},"o":{"docs":{},"f":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"r":{"docs":{},"e":{"docs":{},"m":{"docs":{},"o":{"docs":{},"v":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}}},"t":{"docs":{},"o":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}},"\\":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"n":{"docs":{},"\"":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"a":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"^":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}}},"docs":{}}}}}},"e":{"docs":{},"q":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"\"":{"docs":{},"\"":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"{":{"docs":{},"o":{"docs":{},"}":{"docs":{},"(":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"^":{"2":{"docs":{},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"3":{"docs":{},")":{"docs":{},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"docs":{}},"h":{"docs":{},")":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}},",":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707}}}}},"\\":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},")":{"docs":{},",":{"docs":{"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577}}},".":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0014202528049992898}}}}}}}},"d":{"docs":{},"t":{"docs":{},"^":{"3":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}},"docs":{}}}}}}},"f":{"docs":{},"}":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}},"(":{"docs":{},"f":{"docs":{},")":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}},"*":{"docs":{},"g":{"docs":{},")":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}}},"g":{"docs":{},")":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}}},"^":{"docs":{},"{":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}}},"r":{"docs":{},"m":{"docs":{},"{":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"r":{"docs":{},"m":{"docs":{},"{":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},"}":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"b":{"docs":{},"b":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},"^":{"2":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}},")":{"docs":{},":":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}},"c":{"docs":{},"}":{"docs":{},")":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}},"p":{"docs":{},"}":{"docs":{},"(":{"docs":{},"a":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00423728813559322}}},"x":{"docs":{},"_":{"0":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"docs":{}}}}}}}},"f":{"docs":{},"{":{"0":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"1":{"0":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"2":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"3":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734}}}},"4":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}}}},"6":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"1":{"0":{"docs":{},"}":{"docs":{},"{":{"3":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"docs":{}}}},"docs":{}},"2":{"docs":{},"}":{"docs":{},"{":{"3":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"docs":{}}}},"docs":{}}}}}}},"r":{"docs":{},"}":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"a":{"docs":{},"}":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004142011834319527}},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"v":{"docs":{},"}":{"docs":{},"_":{"0":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"docs":{}}}}}}}}}}}},"_":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"r":{"docs":{},"o":{"docs":{},"t":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}}}}}}}}}}}}}}}},"v":{"docs":{},"_":{"0":{"docs":{},"}":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"docs":{}},"}":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.002366863905325444}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"_":{"0":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}},"docs":{}}}},"x":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}},"u":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}},")":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"docs":{}}}},"i":{"docs":{},"n":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564}},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"1":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{}}}}}}}}}},"\\":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.008097165991902834},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.04964539007092199},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.011158798283261802},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.005756578947368421},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0008521516829995739},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.022964509394572025},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00855106888361045},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.022485207100591716},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726}}},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"{":{"docs":{},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"}":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}}}}}}},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"}":{"docs":{},"{":{"docs":{},"c":{"docs":{},"c":{"docs":{},"c":{"docs":{},"c":{"docs":{},"c":{"docs":{},"c":{"docs":{},"c":{"docs":{},"|":{"docs":{},"c":{"docs":{},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}},"|":{"docs":{},"c":{"docs":{},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}},"|":{"docs":{},"c":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0028503562945368173}}}}},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{},"}":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.028368794326241134},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"c":{"docs":{},"u":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"}":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}},"b":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{},"}":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.002575107296137339},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.017954070981210855},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.009467455621301775}}}}}}}}}}}}}}},"i":{"docs":{},"g":{"docs":{},"c":{"docs":{},"u":{"docs":{},"p":{"docs":{},"_":{"docs":{},"{":{"docs":{},"i":{"docs":{},"=":{"1":{"docs":{},"}":{"docs":{},"^":{"3":{"docs":{},"f":{"docs":{},"_":{"docs":{},"i":{"docs":{},"(":{"docs":{},"p":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}},"4":{"docs":{},"f":{"docs":{},"_":{"docs":{},"i":{"docs":{},"(":{"docs":{},"p":{"docs":{},")":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}},"docs":{}}}},"docs":{}}}}}}}}}}},"e":{"docs":{},"n":{"docs":{},"d":{"docs":{},"{":{"docs":{},"a":{"docs":{},"l":{"docs":{},"i":{"docs":{},"g":{"docs":{},"n":{"docs":{},"}":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.004073319755600814},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001051156271899089}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003800475059382423}},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"]":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722}}}}}}}}}}}}}}},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{},"}":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.010638297872340425},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"\\":{"docs":{},"\\":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.01773049645390071}}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"c":{"docs":{},"u":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"}":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}},"b":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{},"}":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.008350730688935281},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.008284023668639054}},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"\\":{"docs":{},"\\":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"p":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.009603340292275574}}},",":{"docs":{},"\\":{"docs":{},"\\":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}}}}}}}},"l":{"docs":{},"l":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0035502958579881655}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}},"x":{"docs":{},"p":{"docs":{},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"[":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"{":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"y":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.0016939582156973462}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"{":{"docs":{},"i":{"docs":{},"=":{"0":{"docs":{},"}":{"docs":{},"^":{"docs":{},"{":{"docs":{},"n":{"docs":{},"}":{"docs":{},"w":{"docs":{},"_":{"docs":{},"i":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}}}}}}}}}},"docs":{}}},"n":{"docs":{},"=":{"0":{"docs":{},"}":{"docs":{},"^":{"9":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{},"{":{"docs":{},"\\":{"docs":{},"i":{"docs":{},"n":{"docs":{},"f":{"docs":{},"t":{"docs":{},"y":{"docs":{},"}":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}}}},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}}}}}},"docs":{},"a":{"docs":{},"}":{"docs":{},"^":{"docs":{},"{":{"docs":{},"b":{"docs":{},"}":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}}}}}}},"m":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608}}},"k":{"docs":{},"=":{"0":{"docs":{},"}":{"docs":{},"^":{"docs":{},"{":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"docs":{}}}},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"n":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}}}}},"i":{"docs":{},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002105263157894737},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"e":{"docs":{},"q":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.012145748987854251}}}}},"n":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407}},"(":{"0":{"docs":{},")":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"2":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"\\":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"g":{"docs":{},"a":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828}}}}}}}}}}},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0034334763948497852},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}},"_":{"docs":{},"x":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"y":{"docs":{},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}},"p":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"q":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"(":{"docs":{},"n":{"docs":{},",":{"docs":{},"a":{"docs":{},")":{"docs":{},"^":{"2":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}}}}}}}}}}},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"{":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407}},"g":{"docs":{},"_":{"docs":{},"x":{"docs":{},"^":{"2":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}},"docs":{}}}}},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"r":{"docs":{},"e":{"docs":{},"}":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},"^":{"2":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"docs":{}}}}}}}}}}}}},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"1":{"docs":{},"}":{"docs":{},"{":{"docs":{},"n":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"{":{"docs":{},"i":{"docs":{},"=":{"1":{"docs":{},"}":{"docs":{},"^":{"docs":{},"{":{"docs":{},"n":{"docs":{},"}":{"docs":{},"(":{"docs":{},"q":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}},"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}}}}},"p":{"docs":{},"i":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"u":{"docs":{},"_":{"1":{"docs":{},"^":{"2":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}},"docs":{}}},"docs":{}}}}}}}},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652}},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"}":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"(":{"docs":{},"c":{"docs":{},"_":{"docs":{},"i":{"docs":{},")":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453}}}}}}},"^":{"2":{"docs":{},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}}}}}}}}},"a":{"docs":{},"c":{"docs":{},"c":{"docs":{},"e":{"docs":{},"l":{"docs":{},"e":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"n":{"docs":{},"}":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}}}}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"}":{"docs":{},"_":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"c":{"docs":{},"i":{"docs":{},"r":{"docs":{},"c":{"docs":{},"l":{"docs":{},"e":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"=":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"i":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}},"s":{"docs":{},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"=":{"4":{"docs":{},"r":{"docs":{},"^":{"2":{"docs":{},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}}}},"docs":{}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"}":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"a":{"docs":{},"n":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"i":{"docs":{},"m":{"docs":{},"}":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"r":{"docs":{},"e":{"docs":{},"}":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"v":{"docs":{},"e":{"docs":{},"l":{"docs":{},"o":{"docs":{},"c":{"docs":{},"i":{"docs":{},"t":{"docs":{},"y":{"docs":{},"}":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}}}}}},"r":{"docs":{},"a":{"docs":{},"t":{"docs":{},"i":{"docs":{},"o":{"docs":{},"}":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}},"?":{"docs":{},"\"":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}},"w":{"docs":{},"i":{"docs":{},"d":{"docs":{},"t":{"docs":{},"h":{"docs":{},"}":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}},".":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}},"i":{"docs":{},"m":{"docs":{},"}":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}}}}}}},"f":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"e":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"e":{"docs":{},"r":{"docs":{},"}":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"}":{"docs":{},"~":{"docs":{},"\\":{"docs":{},"%":{"docs":{},"~":{"1":{"9":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}},"4":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"7":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"docs":{}}}}}}}}}},"c":{"docs":{},"u":{"docs":{},"r":{"docs":{},"r":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}}}}}}}},"p":{"docs":{},"i":{"docs":{},"v":{"docs":{},"o":{"docs":{},"t":{"docs":{},"_":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"}":{"docs":{},"_":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"}":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}}}}}}}}}}}}}}}}}},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"k":{"docs":{},"}":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}},"x":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"v":{"docs":{},"}":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.008344923504867872},"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.02127659574468085},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.005479452054794521},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0014035087719298245},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.003289473684210526},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.004142011834319527},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"docs":{},"l":{"docs":{},"e":{"docs":{},"n":{"docs":{},"g":{"docs":{},"t":{"docs":{},"h":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"docs":{}}}}}}}}}}}}}},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0025252525252525255},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0035502958579881655}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596}}},"}":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"(":{"1":{"docs":{},")":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"2":{"docs":{},"^":{"docs":{},"n":{"docs":{},")":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}},"3":{"docs":{},")":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"docs":{},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"3":{"docs":{},"n":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"docs":{}}}}},"docs":{}}}}}},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}}}}}}},"n":{"docs":{},")":{"docs":{},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}},"^":{"2":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"3":{"docs":{},")":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"docs":{}}}},".":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}}},"a":{"docs":{},"u":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}}}},"p":{"docs":{},"i":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0020876826722338203},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0026300958106331017},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"=":{"docs":{},"(":{"3":{"docs":{},",":{"1":{"docs":{},",":{"2":{"docs":{},",":{"4":{"docs":{},")":{"docs":{},")":{"docs":{"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.0010438413361169101}}}}},"docs":{}}},"docs":{}}},"docs":{}}},"docs":{}}},",":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"/":{"2":{"docs":{},")":{"docs":{},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},",":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828}}},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828}}}},"docs":{}}},"m":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0035087719298245615},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828}}},"s":{"docs":{},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}}}}}}}}}},"^":{"docs":{},"{":{"docs":{},"*":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}}}}}}}}}}}}}},"+":{"docs":{},"d":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}},"x":{"docs":{},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},".":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"\\":{"docs":{},"r":{"docs":{},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}},"_":{"docs":{},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"h":{"docs":{},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}}}}}}}}}}}}}}}},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"1":{"2":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"docs":{}},"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"{":{"1":{"8":{"docs":{},"}":{"docs":{},"{":{"1":{"1":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0009501187648456057}}}},"docs":{}},"docs":{}}}},"docs":{},"}":{"docs":{},"{":{"0":{"docs":{},".":{"7":{"8":{"5":{"3":{"docs":{},"}":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}},"1":{"docs":{},".":{"7":{"2":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}},"docs":{}}},"2":{"docs":{},"}":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"docs":{},"d":{"docs":{},"^":{"2":{"docs":{},"f":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"d":{"docs":{},"x":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{},"(":{"docs":{},"x":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}},"docs":{}}}}}}}}}}},"docs":{}}}}}}}},"h":{"docs":{},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"\\":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"g":{"docs":{},"a":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"g":{"docs":{},"a":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},"a":{"docs":{},"t":{"docs":{},"^":{"2":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"docs":{}}},"(":{"docs":{},"t":{"docs":{},")":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000568101121999716}}}}}}}}},"+":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}},"(":{"docs":{},"a":{"docs":{},"(":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}},"m":{"docs":{},"v":{"docs":{},"^":{"2":{"docs":{},"?":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}},"docs":{}}}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}},"\\":{"docs":{},"p":{"docs":{},"i":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{},"e":{"docs":{},"^":{"docs":{},"{":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}},"docs":{}}}}}}}}}}}},"3":{"docs":{},"}":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},"b":{"docs":{},"(":{"docs":{},"t":{"docs":{},")":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}}}}}}}}},".":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}}}}}},"6":{"docs":{},"}":{"docs":{},"b":{"docs":{},"(":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858}}}}},"t":{"docs":{},"^":{"3":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}},"docs":{}}}}}},"7":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"8":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},"9":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}},"docs":{},"n":{"docs":{},"}":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"_":{"3":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{},"{":{"docs":{},"v":{"docs":{},"+":{"1":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}}}}}},"(":{"2":{"docs":{},"^":{"3":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"docs":{}}},"docs":{}},"\\":{"docs":{},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"i":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}}}},"2":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00047505938242280285}},"d":{"docs":{},"^":{"2":{"docs":{},"x":{"docs":{},"(":{"docs":{},"t":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"d":{"docs":{},"t":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}},"docs":{}}}}}}}}}}},"docs":{}},"f":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"d":{"docs":{},"x":{"docs":{},"}":{"docs":{},"(":{"docs":{},"x":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}}}}}}}},"x":{"docs":{},"(":{"docs":{},"t":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"d":{"docs":{},"t":{"docs":{},"}":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}}}}}},"_":{"0":{"docs":{},"}":{"docs":{},"{":{"docs":{},"b":{"docs":{},"_":{"0":{"docs":{},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}}}}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}},"f":{"docs":{},"^":{"docs":{},"{":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},"}":{"docs":{},"(":{"docs":{},"a":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"n":{"docs":{},"!":{"docs":{},"}":{"docs":{},"(":{"docs":{},"x":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417}}}}}}}}}}}}}}}}}},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"x":{"docs":{},"}":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"y":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\\":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"d":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}}}}},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"d":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}}}}}}}}},"x":{"docs":{},"'":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"f":{"docs":{},"(":{"docs":{},"x":{"docs":{},"_":{"docs":{},"t":{"docs":{},")":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}}}}}},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},"_":{"docs":{},"{":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}},"n":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"y":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"{":{"docs":{},"n":{"docs":{},"}":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"_":{"docs":{},"{":{"docs":{},"n":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}},"+":{"1":{"docs":{},"}":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}},"docs":{}}}}},"docs":{}}}}},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{}}}},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"}":{"docs":{},"_":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"c":{"docs":{},"i":{"docs":{},"r":{"docs":{},"c":{"docs":{},"l":{"docs":{},"e":{"docs":{},"}":{"docs":{},"}":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"}":{"docs":{},"_":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"s":{"docs":{},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"r":{"docs":{},"e":{"docs":{},"}":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"c":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"t":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}}}}}}},"p":{"docs":{},"i":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}},"}":{"docs":{},"{":{"4":{"docs":{},"}":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},")":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}},"docs":{}}}},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147}},"a":{"docs":{},"l":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"h":{"docs":{},"i":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"h":{"docs":{},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"m":{"docs":{},"}":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"\\":{"docs":{},"n":{"docs":{},"a":{"docs":{},"b":{"docs":{},"l":{"docs":{},"a":{"docs":{},"^":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},"docs":{}}}}}}}}}}},"docs":{}}}},"docs":{}},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}},"docs":{}}}}}}},"v":{"docs":{},"e":{"docs":{},"c":{"docs":{},"{":{"docs":{},"p":{"docs":{},"_":{"1":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}},"docs":{}}}}}}},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{},"(":{"1":{"docs":{},"+":{"docs":{},"n":{"docs":{},"/":{"docs":{},"a":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{},"(":{"1":{"docs":{},"+":{"1":{"docs":{},"/":{"docs":{},"a":{"docs":{},")":{"docs":{},"}":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"docs":{}}},"docs":{}}}}}}}}}}}}}},"docs":{}},"_":{"docs":{},"e":{"docs":{},"(":{"docs":{},"n":{"docs":{},"+":{"1":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"l":{"docs":{},"o":{"docs":{},"g":{"docs":{},"_":{"docs":{},"e":{"docs":{},"(":{"2":{"docs":{},")":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}},"docs":{}}}}}}}}}}}},"docs":{}}}}}}}}},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"y":{"docs":{},"l":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"e":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"{":{"docs":{},"n":{"docs":{},"}":{"docs":{},"f":{"docs":{},"(":{"docs":{},"n":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"i":{"docs":{},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"y":{"docs":{},"l":{"docs":{},"e":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"u":{"docs":{},"m":{"docs":{},"_":{"docs":{},"{":{"docs":{},"n":{"docs":{},"}":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"p":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0024621878297572987}},"i":{"docs":{},"}":{"docs":{},"{":{"4":{"docs":{},"}":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122}}}},"docs":{}}}},"+":{"docs":{},"a":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}}},"docs":{}}}},"b":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}}},"docs":{}}}},"c":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}}},"docs":{}}}},"d":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{}}}}},"^":{"2":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"m":{"docs":{},"}":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}},"docs":{}}}},"docs":{}}},"x":{"docs":{},"^":{"2":{"docs":{},"+":{"docs":{},"y":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"i":{"docs":{},"g":{"docs":{},"m":{"docs":{},"a":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}},"docs":{}}}}}}}}},"docs":{}}}},"docs":{}}}}},"docs":{}},"(":{"docs":{},"t":{"docs":{},"+":{"docs":{},"\\":{"docs":{},"d":{"docs":{},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.00042607584149978694}}}}}}}}}}}},"c":{"docs":{},"_":{"0":{"docs":{},"}":{"docs":{},"{":{"docs":{},"b":{"docs":{},"_":{"0":{"docs":{},"}":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"docs":{}}}}}},"docs":{},"i":{"docs":{},"}":{"docs":{},"{":{"docs":{},"b":{"docs":{},"_":{"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{}}}},"b":{"docs":{},"(":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}}}}},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"docs":{}}}},"[":{"docs":{},"i":{"docs":{},"\\":{"docs":{},"h":{"docs":{},"a":{"docs":{},"t":{"docs":{},"{":{"docs":{},"h":{"docs":{},"}":{"docs":{},"_":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}},"i":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"h":{"docs":{},"a":{"docs":{},"t":{"docs":{},"{":{"docs":{},"h":{"docs":{},"}":{"docs":{},"_":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}},"\\":{"docs":{},"h":{"docs":{},"a":{"docs":{},"t":{"docs":{},"{":{"docs":{},"h":{"docs":{},"}":{"docs":{},"_":{"docs":{},"k":{"docs":{},"d":{"docs":{},"t":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"h":{"docs":{},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{},"}":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"e":{"docs":{},"^":{"docs":{},"{":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}}}}}}}}}}}}}}}},"r":{"docs":{},"d":{"docs":{},"t":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"\\":{"docs":{},"h":{"docs":{},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"e":{"docs":{},"^":{"docs":{},"{":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}},"docs":{},"\\":{"docs":{},"h":{"docs":{},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{},"}":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"e":{"docs":{},"^":{"docs":{},"{":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}},"d":{"docs":{},"t":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"h":{"docs":{},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{},"}":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{},"^":{"2":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}}}},"docs":{}}}},"docs":{}}},"h":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"l":{"docs":{},"a":{"docs":{},"m":{"docs":{},"b":{"docs":{},"d":{"docs":{},"a":{"docs":{},"}":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}}}}},"n":{"docs":{},"(":{"docs":{},"n":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"}":{"docs":{},"{":{"4":{"0":{"0":{"0":{"docs":{},"}":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}},"docs":{}},"docs":{}},"docs":{}},"docs":{}}}},"e":{"docs":{},"^":{"docs":{},"{":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"o":{"docs":{},"w":{"docs":{"contents/taylor_series_expansion/taylor_series_expansion.html":{"ref":"contents/taylor_series_expansion/taylor_series_expansion.html","tf":0.004048582995951417},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.001183431952662722},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},")":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}}}},".":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.001007658202337767},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003800475059382423},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}},".":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"a":{"docs":{},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147}},"e":{"docs":{},",":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0024067388688327317}}}}}}},"c":{"docs":{},"i":{"docs":{},"r":{"docs":{},"c":{"docs":{"contents/convolutions/convolutions.html":{"ref":"contents/convolutions/convolutions.html","tf":0.0044444444444444444}}}}},"o":{"docs":{"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.0007017543859649122},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407}},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"3":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"6":{"docs":{},"=":{"1":{"8":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}},"docs":{}}},"docs":{}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"2":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"6":{"docs":{},"+":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"3":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"5":{"docs":{},"=":{"2":{"7":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}},"docs":{}}},"docs":{}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"}":{"1":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"}":{"5":{"docs":{},"+":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"2":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"4":{"docs":{},"=":{"1":{"3":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}},"docs":{}}},"docs":{}}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}},"6":{"docs":{},"+":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"2":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"g":{"docs":{},"r":{"docs":{},"e":{"docs":{},"e":{"docs":{},"n":{"docs":{},"}":{"5":{"docs":{},"+":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"3":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"b":{"docs":{},"l":{"docs":{},"u":{"docs":{},"e":{"docs":{},"}":{"4":{"docs":{},"=":{"2":{"8":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}},"docs":{}},"docs":{}}},"docs":{}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}}}}},"docs":{},"{":{"1":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"c":{"docs":{},"o":{"docs":{},"l":{"docs":{},"o":{"docs":{},"r":{"docs":{},"{":{"docs":{},"r":{"docs":{},"e":{"docs":{},"d":{"docs":{},"}":{"docs":{},"{":{"4":{"docs":{},"}":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.0035460992907801418}}}},"docs":{}}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}},"s":{"docs":{},"(":{"0":{"docs":{},")":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"2":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}},"docs":{},"\\":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"g":{"docs":{},"a":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}},"t":{"docs":{},"h":{"docs":{},"e":{"docs":{},"t":{"docs":{},"a":{"docs":{},")":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0017751479289940828}}}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0005635919594213789},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.00350385423966363}}}}}},"i":{"docs":{},"n":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.001893939393939394},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}},"f":{"docs":{},"t":{"docs":{},"y":{"docs":{},"}":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},"^":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"i":{"docs":{},"n":{"docs":{},"f":{"docs":{},"t":{"docs":{},"y":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"f":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"x":{"docs":{},"i":{"docs":{},")":{"docs":{},"g":{"docs":{},"(":{"docs":{},"x":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}},"x":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}},"[":{"docs":{},"m":{"docs":{},"]":{"docs":{},"g":{"docs":{},"[":{"docs":{},"n":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}},"n":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}}}},"+":{"docs":{},"\\":{"docs":{},"i":{"docs":{},"n":{"docs":{},"f":{"docs":{},"t":{"docs":{},"y":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"^":{"docs":{},"\\":{"docs":{},"a":{"docs":{},"s":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}},"|":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{},")":{"docs":{},"|":{"docs":{},"^":{"2":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"t":{"docs":{},"_":{"docs":{},"{":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.001110494169905608},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"x":{"docs":{},"_":{"1":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{},"{":{"1":{"0":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}},"docs":{}},"docs":{}}}},"d":{"docs":{},"}":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}},"s":{"docs":{},"}":{"docs":{},"f":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"x":{"docs":{},"}":{"docs":{},")":{"docs":{},"d":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"x":{"docs":{},"}":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"d":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.001129305477131564},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},"a":{"docs":{},"^":{"docs":{},"b":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"p":{"docs":{},"u":{"docs":{},"t":{"docs":{},"{":{"docs":{},"o":{"docs":{},"u":{"docs":{},"t":{"docs":{},"}":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"{":{"docs":{},"h":{"docs":{},",":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}}}}}}}}}}},"x":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"d":{"docs":{},"\\":{"docs":{},"x":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}},"g":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"x":{"docs":{},"i":{"docs":{},")":{"docs":{},"d":{"docs":{},"\\":{"docs":{},"x":{"docs":{},"i":{"docs":{"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804}}}}}}}}}}}},")":{"docs":{},"d":{"docs":{},"x":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"}":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"h":{"docs":{},"l":{"docs":{},"i":{"docs":{},"n":{"docs":{},"e":{"docs":{"contents/convolutions/multiplication/multiplication.html":{"ref":"contents/convolutions/multiplication/multiplication.html","tf":0.024822695035460994}}}}}},"a":{"docs":{},"t":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.00510204081632653},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.006618531889290012}},"{":{"docs":{},"h":{"docs":{},"}":{"docs":{},"_":{"docs":{},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},")":{"docs":{},"d":{"docs":{},"t":{"docs":{},"}":{"docs":{},"{":{"docs":{},"\\":{"docs":{},"h":{"docs":{},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{},"}":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"]":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"u":{"docs":{},"}":{"docs":{},"_":{"docs":{},"k":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}},"b":{"docs":{},"a":{"docs":{},"r":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976}},"\\":{"docs":{},"o":{"docs":{},"m":{"docs":{},"e":{"docs":{},"g":{"docs":{},"a":{"docs":{},".":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}},"d":{"docs":{},"o":{"docs":{},"c":{"docs":{},"u":{"docs":{},"m":{"docs":{},"e":{"docs":{},"n":{"docs":{},"t":{"docs":{},"c":{"docs":{},"l":{"docs":{},"a":{"docs":{},"s":{"docs":{},"s":{"docs":{},"[":{"1":{"1":{"docs":{},"p":{"docs":{},"t":{"docs":{},"]":{"docs":{},"{":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"i":{"docs":{},"c":{"docs":{},"l":{"docs":{},"e":{"docs":{},"}":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}}}},"docs":{}},"docs":{}}}}}}}}}}}}},"t":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"d":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473}}}}},"e":{"docs":{},"l":{"docs":{},"t":{"docs":{},"a":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0017043033659991478},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.001401541695865452}},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"_":{"docs":{},"j":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}}},"i":{"docs":{},"s":{"docs":{},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"y":{"docs":{},"s":{"docs":{},"t":{"docs":{},"y":{"docs":{},"l":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},"e":{"docs":{},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}}}}}}},"u":{"docs":{},"s":{"docs":{},"e":{"docs":{},"p":{"docs":{},"a":{"docs":{},"c":{"docs":{},"k":{"docs":{},"a":{"docs":{},"g":{"docs":{},"e":{"docs":{},"{":{"docs":{},"g":{"docs":{},"n":{"docs":{},"u":{"docs":{},"p":{"docs":{},"l":{"docs":{},"o":{"docs":{},"t":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"}":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512}}}}}}}}}}}}}}}}}}}}}}}},"l":{"docs":{},"d":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/bitlogic/bitlogic.html":{"ref":"contents/bitlogic/bitlogic.html","tf":0.0013698630136986301}}}}},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}},"\\":{"docs":{},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"{":{"docs":{},"b":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"r":{"docs":{},"i":{"docs":{},"x":{"docs":{},"}":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}}}}}}}},"l":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"docs":{},"f":{"docs":{},"(":{"docs":{},"x":{"docs":{},"'":{"docs":{},")":{"docs":{},"}":{"docs":{},"{":{"docs":{},"f":{"docs":{},"(":{"docs":{},"x":{"docs":{},"_":{"docs":{},"t":{"docs":{},")":{"docs":{},"}":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}}}}}}}}}}}}}}}}}},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},"=":{"docs":{},"z":{"docs":{},"^":{"2":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}},"docs":{}}}}}}}}},"[":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.003800475059382423},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0012033694344163659}},"\\":{"docs":{},"h":{"docs":{},"a":{"docs":{},"t":{"docs":{},"{":{"docs":{},"u":{"docs":{},"}":{"docs":{},"_":{"docs":{},"r":{"docs":{},"\\":{"docs":{},"l":{"docs":{},"e":{"docs":{},"f":{"docs":{},"t":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"docs":{},"d":{"docs":{},"t":{"docs":{},"}":{"docs":{},"{":{"2":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"c":{"docs":{},"a":{"docs":{},"l":{"docs":{},"{":{"docs":{},"f":{"docs":{},"}":{"docs":{},"^":{"docs":{},"{":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}}}}}}}}}}},"b":{"docs":{},"e":{"docs":{},"g":{"docs":{},"i":{"docs":{},"n":{"docs":{},"{":{"docs":{},"a":{"docs":{},"r":{"docs":{},"r":{"docs":{},"a":{"docs":{},"y":{"docs":{},"}":{"docs":{},"{":{"docs":{},"@":{"docs":{},"{":{"docs":{},"}":{"docs":{},"c":{"docs":{},"c":{"docs":{},"c":{"docs":{},"|":{"docs":{},"c":{"docs":{},"@":{"docs":{},"{":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}},"|":{"docs":{},"c":{"docs":{},"@":{"docs":{},"{":{"docs":{},"}":{"docs":{},"}":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}}}}}}}}}}}}}}}}}}}}}}}}},"e":{"docs":{},"^":{"docs":{},"{":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}},"v":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}}}}}}}}}},"\\":{"docs":{},"{":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}},"h":{"docs":{},",":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"}":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},".":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}}}}}}}}}},"l":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},"\\":{"docs":{},"f":{"docs":{},"r":{"docs":{},"a":{"docs":{},"c":{"docs":{},"{":{"1":{"3":{"docs":{},"+":{"8":{"docs":{},"k":{"docs":{},"}":{"docs":{},"{":{"2":{"5":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}}},"docs":{}},"docs":{}}}}},"docs":{}}},"docs":{}},"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"y":{"docs":{},"e":{"docs":{},"a":{"docs":{},"r":{"docs":{},"}":{"docs":{},"}":{"docs":{},"{":{"1":{"0":{"0":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},",":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}}},"docs":{}},"docs":{}},"docs":{}}}}}}}}}}}}}},"k":{"docs":{},"}":{"docs":{},"{":{"4":{"docs":{},"}":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"i":{"docs":{},"g":{"docs":{},"h":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{},".":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}}},"docs":{}}}}}}}}}}}}}}}}}}},"q":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000700770847932726},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.011652542372881356}}}},"o":{"docs":{},"g":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},"_":{"2":{"docs":{},"(":{"1":{"docs":{},")":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}},"+":{"docs":{},"n":{"docs":{},")":{"docs":{},",":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"8":{"docs":{},")":{"docs":{},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},"docs":{}}},"docs":{},"e":{"docs":{},"(":{"1":{"docs":{},"+":{"docs":{},"e":{"docs":{},"^":{"docs":{},"v":{"docs":{},")":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"n":{"docs":{},")":{"docs":{},".":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}}},"docs":{}}}}}},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}},"\\":{"docs":{},"c":{"docs":{},"d":{"docs":{},"o":{"docs":{},"t":{"docs":{},"\\":{"docs":{},"r":{"docs":{},"f":{"docs":{},"l":{"docs":{},"o":{"docs":{},"o":{"docs":{},"r":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"m":{"docs":{},"b":{"docs":{},"d":{"docs":{},"a":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},"}":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}}}}}},"n":{"docs":{},"g":{"docs":{},"l":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0030084235860409147}}}}}},"v":{"docs":{},"e":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0036101083032490976}}}}}}},"o":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0017167381974248926}}}}},"m":{"docs":{},"e":{"docs":{},"g":{"docs":{},"a":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}},".":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"_":{"2":{"docs":{},"^":{"0":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}},"1":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},",":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}},"docs":{}}},"docs":{},"n":{"docs":{},"^":{"docs":{},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}},"(":{"1":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0016233766233766235}}}},"3":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}},"docs":{},"n":{"docs":{},")":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117}}}}},",":{"docs":{"contents/notation/notation.html":{"ref":"contents/notation/notation.html","tf":0.0008116883116883117},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}}}},"v":{"docs":{},"d":{"docs":{},"o":{"docs":{},"t":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}},"&":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}},"g":{"docs":{},"t":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}},"e":{"docs":{},"q":{"docs":{"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.00211864406779661}}}}},"%":{"3":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"~":{"3":{"0":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"1":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{}},"docs":{}}},"q":{"docs":{},"q":{"docs":{},"u":{"docs":{},"a":{"docs":{},"d":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.000350385423966363}}}}}},"u":{"docs":{},"a":{"docs":{},"d":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705}}}}}},";":{"docs":{},",":{"docs":{},"\\":{"docs":{},";":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.000791765637371338}}}}}},"a":{"docs":{},"p":{"docs":{},"p":{"docs":{},"r":{"docs":{},"o":{"docs":{},"x":{"docs":{"contents/approximate_counting/approximate_counting.html":{"ref":"contents/approximate_counting/approximate_counting.html","tf":0.002102312543798178}}}}}}}}},"]":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003355141754739138},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0013407393219689715},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413}}},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0003355704697986577},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}},")":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0016701461377870565}}}},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0020876826722338203}}}},"^":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.0009941769634995029},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0012091898428053204}},"s":{"docs":{},"e":{"docs":{},"l":{"docs":{},"f":{"docs":{},".":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204}}}}}}},"a":{"docs":{},".":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"^":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0016246953696181965}}},"\\":{"docs":{},"i":{"docs":{},"n":{"docs":{},"f":{"docs":{},"t":{"docs":{},"i":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719}}}}}}}}},"z":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/cryptography/cryptography.html":{"ref":"contents/cryptography/cryptography.html","tf":0.007306889352818371},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0011271839188427579},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.003787878787878788},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0011084718923198734},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.0035502958579881655}},"e":{"docs":{},"r":{"docs":{},"o":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0010065425264217413},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0009299853859439352},"contents/convolutions/1d/1d.html":{"ref":"contents/convolutions/1d/1d.html","tf":0.000555247084952804},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0007514559458951719},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0022169437846397467}},"?":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},":":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929}},"p":{"docs":{},")":{"docs":{},",":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}}}},"s":{"docs":{},"(":{"5":{"docs":{},",":{"5":{"docs":{},")":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},"docs":{}}},"docs":{},"k":{"docs":{},"e":{"docs":{},"r":{"docs":{},"n":{"docs":{},"e":{"docs":{},"l":{"docs":{},"_":{"docs":{},"s":{"docs":{},"i":{"docs":{},"z":{"docs":{},"e":{"docs":{},",":{"docs":{"contents/convolutions/2d/2d.html":{"ref":"contents/convolutions/2d/2d.html","tf":0.0008583690987124463}}}}}}}}}}}}}},"n":{"docs":{},",":{"2":{"docs":{},")":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}},"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}}}},"r":{"docs":{},"e":{"docs":{},"s":{"docs":{},")":{"docs":{},")":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683}}},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137}}}}}},"o":{"docs":{},"w":{"docs":{},"s":{"docs":{},")":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00031670625494853525}}}}}}},"c":{"docs":{},"e":{"docs":{},"i":{"docs":{},"l":{"docs":{},"(":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{},"(":{"docs":{},"b":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{},"s":{"docs":{},"[":{"1":{"docs":{},",":{"2":{"docs":{},"]":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},"docs":{}}},"docs":{}}}}}}}}}}}}}}}}}}},".":{"docs":{"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"ref":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","tf":0.002551020408163265}}}},".":{"docs":{"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000284050560999858},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"!":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}},")":{"docs":{},":":{"docs":{"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}}}}}}},"i":{"docs":{},"p":{"4":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}},"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},"w":{"docs":{},"i":{"docs":{},"t":{"docs":{},"h":{"3":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00037572797294758596},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}},"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139},"contents/verlet_integration/verlet_integration.html":{"ref":"contents/verlet_integration/verlet_integration.html","tf":0.000142025280499929},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}}}},"(":{"docs":{},"p":{"docs":{},"o":{"docs":{},"i":{"docs":{},"n":{"docs":{},"t":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0007034822370735139}}}}}}}}}}},")":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}},".":{"docs":{},"f":{"docs":{},"o":{"docs":{},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"c":{"docs":{},"h":{"docs":{},"(":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}}}}},",":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0006334125098970705},"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}},"p":{"docs":{},"r":{"docs":{},"e":{"docs":{},"f":{"docs":{},"e":{"docs":{},"r":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}}},"o":{"docs":{},"o":{"docs":{},"m":{"docs":{"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0008233841086867024}}}}},"[":{"0":{"docs":{},"]":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"6":{"4":{"docs":{},"]":{"docs":{},";":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}},"docs":{}},"docs":{},"i":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}},"]":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}},"s":{"docs":{},"t":{"docs":{},"a":{"docs":{},"r":{"docs":{},"t":{"docs":{},"_":{"docs":{},"i":{"docs":{},"n":{"docs":{},"d":{"docs":{},"e":{"docs":{},"x":{"docs":{},"+":{"docs":{},"k":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}}}}}}}}}},":":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}},"(":{"docs":{},"x":{"docs":{},",":{"docs":{},"y":{"docs":{},")":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"*":{"docs":{},"*":{"2":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}},"docs":{}}},"\\":{"docs":{},"i":{"docs":{},"n":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"b":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}}}}}}}}}}}},"^":{"2":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}},".":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"docs":{}},"_":{"1":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"2":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0013577732518669382}},")":{"docs":{},".":{"docs":{"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.0006788866259334691}}}},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}},"docs":{},"i":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"m":{"docs":{},"a":{"docs":{},"g":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0012626262626262627}}}}}},"r":{"docs":{},"e":{"docs":{},"a":{"docs":{},"l":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}},"n":{"docs":{},")":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0012526096033402922}}},"x":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"y":{"docs":{},",":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"z":{"docs":{},";":{"docs":{"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0004175365344467641}}}},"=":{"1":{"docs":{},".":{"docs":{"contents/affine_transformations/affine_transformations.html":{"ref":"contents/affine_transformations/affine_transformations.html","tf":0.000591715976331361}}}},"docs":{}}},"|":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00268411340379131},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0019267822736030828},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0016778523489932886},"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.0016907758782641368},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.0014069644741470278},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0008061265618702137},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.004592240696753761}},"c":{"docs":{},"h":{"docs":{},"i":{"docs":{},"l":{"docs":{},"d":{"docs":{},"|":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0007661367554108408}}}}}}}},">":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0005032712632108706},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0007971303308090873},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0014827995255041518},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0009633911368015414},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0013422818791946308},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0036555645816409425}}},"m":{"docs":{},"u":{"docs":{},"t":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479}}}},"|":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}},"|":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0015661707126076742},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.001445086705202312},"contents/box_muller/box_muller_rejection.html":{"ref":"contents/box_muller/box_muller_rejection.html","tf":0.002807017543859649},"contents/box_muller/box_muller.html":{"ref":"contents/box_muller/box_muller.html","tf":0.002036659877800407},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0014492753623188406}}},"r":{"docs":{},"o":{"docs":{},"u":{"docs":{},"n":{"docs":{},"d":{"docs":{},"|":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},"i":{"docs":{},"|":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0012335526315789473},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}}}},"j":{"docs":{},"|":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}},"\\":{"docs":{},"p":{"docs":{},"s":{"docs":{},"i":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"m":{"docs":{},"a":{"docs":{},"t":{"docs":{},"h":{"docs":{},"b":{"docs":{},"f":{"docs":{},"{":{"docs":{},"r":{"docs":{},"}":{"docs":{},",":{"docs":{},"t":{"docs":{},")":{"docs":{},"|":{"docs":{},"^":{"2":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/quantum_systems/quantum_systems.html":{"ref":"contents/quantum_systems/quantum_systems.html","tf":0.0006016847172081829}}},"docs":{}}}}}}}}}}}}}}}}}}}},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"i":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"r":{"docs":{},"e":{"docs":{},"}":{"docs":{},"(":{"docs":{},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},"^":{"docs":{},"t":{"docs":{},"|":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"|":{"docs":{},"\\":{"docs":{},"s":{"docs":{},"i":{"docs":{},"n":{"docs":{},"(":{"docs":{},"\\":{"docs":{},"p":{"docs":{},"i":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"i":{"docs":{},"m":{"docs":{},"e":{"docs":{},"s":{"docs":{},"\\":{"docs":{},"t":{"docs":{},"e":{"docs":{},"x":{"docs":{},"t":{"docs":{},"{":{"docs":{},"i":{"docs":{},"m":{"docs":{},"}":{"docs":{},"(":{"docs":{},"f":{"docs":{},"(":{"docs":{},"z":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{},"^":{"docs":{},"t":{"docs":{},"|":{"docs":{},",":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}},"a":{"docs":{},"c":{"docs":{},"c":{"docs":{},",":{"docs":{"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}}}}}},"z":{"docs":{},"|":{"docs":{"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314}}}},"y":{"docs":{},"|":{"docs":{"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00036231884057971015}}}}},"↩":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.000861903849837196},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455}}}},"↪":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0005746025665581306},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"⏫":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}},"⏹":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}},"▶":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0003830683777054204},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"◀":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"6":{"4":{"docs":{},"c":{"docs":{},";":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}}},"docs":{}},"docs":{}}},"docs":{}}}}}},"✖":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393}}}},"❎":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0002873012832790653},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}},"❗":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0015322735108216816},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.003249390739236393}},"❗":{"docs":{},"️":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00033551417547391375}}}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"9":{"1":{"docs":{},"b":{"docs":{},";":{"docs":{},"❗":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}}}}},"docs":{}},"docs":{}}},"docs":{}}}}}},"➕":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}},"➖":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0004788354721317755},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}},"➡":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0023941773606588777},"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.006498781478472786}}}},"⭐":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0000957670944263551}}}},"️":{"docs":{},"↪":{"docs":{},"️":{"docs":{"contents/tree_traversal/tree_traversal.html":{"ref":"contents/tree_traversal/tree_traversal.html","tf":0.0001915341888527102}}}},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"5":{"0":{"1":{"docs":{},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275}}}},"docs":{}},"3":{"docs":{},"c":{"docs":{},";":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"4":{"0":{"7":{"docs":{},";":{"docs":{},"⬆":{"docs":{},"️":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}}},"docs":{}},"docs":{}}},"docs":{}}}},"⏫":{"docs":{},"&":{"docs":{},"#":{"docs":{},"x":{"1":{"docs":{},"f":{"4":{"0":{"7":{"docs":{},";":{"docs":{},"⬆":{"docs":{},"️":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}}}},"docs":{}},"docs":{}},"docs":{}}},"docs":{}}}}}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.003019627579265224},"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0001328550551348479},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.0007830853563038371},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608},"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/graham_scan/graham_scan.html":{"ref":"contents/graham_scan/graham_scan.html","tf":0.0010067114093959733},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0020308692120227455},"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315},"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.001055223355610271},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00040306328093510683},"contents/domain_coloring/domain_coloring.html":{"ref":"contents/domain_coloring/domain_coloring.html","tf":0.0006313131313131314},"contents/barnsley/barnsley.html":{"ref":"contents/barnsley/barnsley.html","tf":0.0008350730688935282},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.0019002375296912114},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.001059322033898305}},")":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341}},";":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.0016122531237404273}}}},";":{"docs":{"contents/jarvis_march/jarvis_march.html":{"ref":"contents/jarvis_march/jarvis_march.html","tf":0.0004816955684007707},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.0005434782608695652},"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}}},"≠":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}},"⬅":{"docs":{},"️":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.0006710283509478275},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913}}}},"⬆":{"docs":{},"️":{"docs":{"contents/euclidean_algorithm/euclidean_algorithm.html":{"ref":"contents/euclidean_algorithm/euclidean_algorithm.html","tf":0.00016775708773695687}}}},"?":{"docs":{"contents/huffman_encoding/huffman_encoding.html":{"ref":"contents/huffman_encoding/huffman_encoding.html","tf":0.0002657101102696958},"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856},"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0002965599051008304},"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.00040617384240454913},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.00020153164046755341},"contents/computus/computus.html":{"ref":"contents/computus/computus.html","tf":0.00018115942028985507}},"p":{"docs":{},"e":{"docs":{},"r":{"docs":{},"s":{"docs":{},"o":{"docs":{},"n":{"docs":{"contents/stable_marriage_problem/stable_marriage_problem.html":{"ref":"contents/stable_marriage_problem/stable_marriage_problem.html","tf":0.00039154267815191856}}}}}}}},",":{"docs":{"contents/flood_fill/flood_fill.html":{"ref":"contents/flood_fill/flood_fill.html","tf":0.0005931198102016608}}}},",":{"docs":{"contents/data_compression/data_compression.html":{"ref":"contents/data_compression/data_compression.html","tf":0.0013908205841446453},"contents/plotting/plotting.html":{"ref":"contents/plotting/plotting.html","tf":0.0004116920543433512},"contents/split-operator_method/split-operator_method.html":{"ref":"contents/split-operator_method/split-operator_method.html","tf":0.004433696090286175},"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}},"r":{"docs":{},"e":{"docs":{},"t":{"docs":{},"u":{"docs":{},"r":{"docs":{},"n":{"docs":{"contents/cooley_tukey/cooley_tukey.html":{"ref":"contents/cooley_tukey/cooley_tukey.html","tf":0.00018786398647379298}}}}}}}},"d":{"docs":{},"i":{"docs":{},"v":{"docs":{},"i":{"docs":{},"s":{"docs":{},"o":{"docs":{},"r":{"docs":{},")":{"docs":{},")":{"docs":{},")":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.00041118421052631577}}}}}}}}}}}},"p":{"docs":{},"l":{"docs":{},"a":{"docs":{},"c":{"docs":{},"e":{"docs":{"contents/thomas_algorithm/thomas_algorithm.html":{"ref":"contents/thomas_algorithm/thomas_algorithm.html","tf":0.0008223684210526315}}}}}}},"(":{"docs":{},"s":{"docs":{},"q":{"docs":{},"r":{"docs":{},"t":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}},"x":{"docs":{},"_":{"docs":{},"n":{"docs":{},",":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.000564652738565782}}}}}}},"☝":{"docs":{},"️":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0012185215272136475}}}},"➗":{"docs":{"contents/monte_carlo_integration/monte_carlo_integration.html":{"ref":"contents/monte_carlo_integration/monte_carlo_integration.html","tf":0.0008123476848090983}}},"š":{"docs":{},"e":{"docs":{},"v":{"docs":{},"č":{"docs":{},"í":{"docs":{},"k":{"docs":{},"o":{"docs":{},"v":{"docs":{},"á":{"docs":{},",":{"docs":{"contents/IFS/IFS.html":{"ref":"contents/IFS/IFS.html","tf":0.00035174111853675694}}}}}}}}}}}},"—":{"docs":{"contents/gaussian_elimination/gaussian_elimination.html":{"ref":"contents/gaussian_elimination/gaussian_elimination.html","tf":0.00015835312747426763}}},"–":{"docs":{"contents/metropolis/metropolis.html":{"ref":"contents/metropolis/metropolis.html","tf":0.004517221908526256},"contents/probability_distributions/distributions.html":{"ref":"contents/probability_distributions/distributions.html","tf":0.0031779661016949155}}}},"length":30722},"corpusTokens":["!","!!","!!this.fiance;","!(*thi","!(a","!(idx","!(isnan(input_x)","!)","!=","!==","!counterclockwise(p,","!haskey(pairs,","!input[start..].is_empty()","!node.right)","!singular","!t","\"","\"!\"","\"\"","\"\"\"a","\"\"\"calcul","\"\"\"comput","\"\"\"contain","\"\"\"creat","\"\"\"determin","\"\"\"find","\"\"\"i","\"\"\"initi","\"\"\"pick","\"\"\"propos","\"\"\"return","\"\"\"set","\"\"\"the","\"\")","\"\"))","\"\",","\"\",:code","\"\";","\"\"}","\"#{@name.rjust(20)}:","\"#{a[i]}\\t#{servois_numbers[i]}\\t\\t#{easter_dates[i]}\"","\"#{node.id}","\"#{prefix}","\"#{temp.id}","\"$($_[0])`t$($_[1])\"","\"$1\")","\"$2\")","\"$2\\pi$\"])","\"$\\pi$\",","\"$a\"","\"$year`t$(calcul","\"%d","\"%d\",(21","\"%g\\n\"","\"%s\"","\"(\"","\"(bibbiti","\")","\")\";","\"),","\");","\"++\"","\",","\",error:","\",our","\".dat\")","\".dat\",\"w\")","\".join(p.nam","\"0\"","\"0\")","\"0\"),","\"0\",","\"0\":","\"0.1.11\"]","\"1\"","\"1\")","\"1\")))))","\"1\"),","\"1\",","\"1\":","\"19","\"2d","\"2d_sample_low_res.dat\"","\"8bit","\":\");","\"?\"))","\"[#]\\nmodulu","\"[#]\\nqueue","\"[#]\\nrecurs","\"[#]\\nstack","\"[#]\\nsubtract","\"[#]\\ntime","\"[#]\\nveloc","\"[#]`nmodulu","\"[#]`nsubtract","\"[#]~%modulu","\"[#]~%queue","\"[#]~%recurs","\"[#]~%stack","\"[#]~%subtract","\"[#]~%time","\"[#]~%veloc","\"[0.0","\"[1.0","\"[2.0","\"\\\":","\"\\n\"","\"\\n\")","\"\\n\".join(map(str,","\"\\n\".join(str(x)","\"\\ndecoding...\")","\"\\t\"","\"\\t\")","\"\\t\"))","\"\\t\\t\"","\"]\");","\"__main__\":","\"a","\"a\"","\"a11","\"a12","\"a13","\"a21","\"a22","\"a23","\"a31","\"a32","\"a33","\"absz\"","\"adaptive\"","\"affin","\"andgate\"","\"angle\"","\"anim","\"applic","\"approxim","\"april","\"b","\"b\"","\"b\",","\"barrier.\"","\"bbbbbbbb\"","\"beautiful.\"","\"better\"","\"bfssimple\"","\"bibbiti","\"bibbity_bobbity\"","\"bins\"","\"black\"","\"blend\"","\"blurred.\"","\"bottom\"","\"bucket","\"c\",","\"caesar","\"calcul","\"call","\"chao","\"check","\"check.png\"","\"check.png\".","\"check.tex\"","\"children","\"circl","\"coding...\")","\"coincidence\"","\"combin","\"complet","\"complex","\"container/heap\"","\"cos(x)\"","\"cosines\"","\"count","\"creat","\"current","\"cyclic\"","\"d\"]","\"data","\"decod","\"decoding:","\"delta","\"depth","\"determin","\"dfsinorder\"","\"dfspostorder\"","\"dfspreorder\"","\"difference:","\"dit","\"divid","\"doubl","\"echelon","\"encod","\"endod","\"error:\"","\"estim","\"euclidean","\"euclidmod\"","\"euclidsub\"","\"exampl","\"exp_fn\"","\"exp_fn_log\"","\"f\",","\"fact.\"","\"failed\"","\"fern","\"fill","\"fillsteps\"","\"find","\"finger","\"fmt\"","\"folder='../haskell'\"","\"frequenc","\"ftexample\"","\"ftgaussian\"","\"full","\"g\",","\"game\"","\"gaussian","\"gevis\"","\"gift\",","\"gnuplot","\"gnuplot_1d_sample\"","\"gnuplot_2d_sample\"","\"gnuplot_2d_sample_colorbar\"","\"gnuplot_exp_tex\"","\"gnuplot_histogram\"","\"gnuplot_scatterplot\"","\"gnuplot_sine_cosine_customtics\"","\"gnuplot_sine_cosine_label\"","\"gnuplot_sine_cosine_linetype\"","\"gnuplot_sine_cosine_log\"","\"gnuplot_sine_cosine_movekey\"","\"gnuplot_sine_cosine_movekey2\"","\"gnuplot_sine_cosine_nokey\"","\"gnuplot_sine_cosine_notics\"","\"gnuplot_sine_cosine_square\"","\"gnuplot_sine_cosine_title\"","\"gnuplot_sine_cosine_wave\"","\"gnuplot_sine_cosine_wave_range\"","\"gnuplot_sine_wave\"","\"gnuplot_test\"","\"grid","\"h\"]","\"ha","\"histogram","\"histograms\"","\"how","\"hsv\"),","\"hsv1\"","\"hsv2\"","\"hsv3\"","\"hsv4\"","\"hsv5\"","\"huffman_tree\"","\"if","\"im(z)\"","\"imaginarysplitop\"","\"integr","\"invalid","\"it'","\"languag","\"left\"","\"length:","\"levels\"","\"lonely\"","\"make","\"man\",","\"march","\"math\"","\"math/rand\"","\"meton","\"michael","\"mont","\"multipl","\"n","\"nandgate\"","\"norgate\"","\"not","\"notation)","\"notgate\"","\"on","\"orgate\"","\"origin","\"out.dat\"","\"out.tex\"","\"output00000.dat\"","\"output{}.dat\".format(str(i).rjust(5,","\"passed\"","\"passover\"","\"patching\"","\"percent","\"percentag","\"perform","\"period","\"phase","\"pivot\"","\"play","\"plot","\"probabl","\"pseudo","\"public","\"purple\"","\"queue","\"radix2\"","\"radix2positive\"","\"radix8\"","\"ramp","\"re","\"re(z)\"","\"real","\"realsplitop\"","\"recurs","\"reduc","\"rel","\"remov","\"result","\"return","\"rgb1\"","\"rgb2\"","\"right\"","\"rijndael\"","\"roll","\"rot13\"","\"rotat","\"round","\"sample_data.dat\"","\"sawtooth","\"scale\"","\"scatterplot_data.dat\"","\"semi","\"servoi","\"set","\"shade\"","\"shear\"","\"shift","\"sierpinski.dat\"","\"simpl","\"simplemontecarlo\"","\"sin(x)\"","\"sin(x)\",","\"sine","\"sine_cosine_plot.png\"","\"sines\"","\"sloshing\"","\"smeared\"","\"sobel","\"solut","\"sort\"","\"split_op_method\"","\"squar","\"squarecircle\"","\"stable\"","\"stack","\"stuff\"","\"synod","\"take","\"taylor","\"test\"","\"textbook\"","\"the","\"thi","\"time\"","\"top\"","\"trained\"","\"tree\"","\"triangl","\"unstable\")","\"utf8\"","\"utility.h\"","\"vx:\"","\"w\")","\"wait.","\"walker\",","\"what'","\"woman\",","\"world'","\"wrap","\"x","\"xorgate\"","\"y\")(uniform01,","\"year","\"year\\tservoi","\"year`tservoi","\"yes,","\"you","\"z2\"","\"{year}","\"{}\",","\"{}\\t{:","\"{}\\t{}\\t{}\",","\"{}\\t{}\\t{}\\n\".format","\"|\",","\"~%\")","\"~8a~18a~a~%\"","\"~a","\"~d~%\"","\"~f~c~f\"","\"~{~a~%~}\"","\"~{~f","#","#!/usr/bin/env","#'","#'*","#'+","#'format","#'make","#(*","#(+","#(0","#(1","#(4","#(7","#(appli","#(c/+","#(if","#(math/log","#(rand","#(str","#[derive(clone)]","#[derive(clone,","#[derive(debug)]","#[derive(debug,","#\\tab","#a","#c(0","#defin","#endif","#freq","#ifndef","#includ","#lang","#messag","#node","#simpl","#{i}\",","#{round}\"","#{self.lonely?","$","$((128","$((21","$((64","$(100","$(128","$(64","$(get","$(join((\"\",","$(join((a[2],","$(join((b[1],","$1","$2","$a","$a)","$a,","$a;","$a[1],","$a[2],","$b","$b)","$b):","$b,","$b;","$b[0],","$b[1],","$b[2],","$b];","$c","$c,","$c[0],","$c[1],","$child)","$child):","$child;","$children","$children;","$d","$d)","$e","$e)","$fianc","$groupsiz","$i","$i)","$i++)","$id,","$id;","$k","$k)","$m","$m)","$man","$man)","$man):","$man;","$match","$match)","$match):","$match;","$men","$men,","$men;","$n","$n)","$n;","$name;","$node","$node;","$numofchildren):","$numofrows,","$outputpoint","$outputpoints.add($point)","$p","$percenterror\")","$picount","$picount++","$piestim","$piestimate\"","$piestimate\")","$point","$positionx,","$positiony,","$prefer","$preference)","$preferences):","$preferences;","$q","$q)","$radiu","$radius=1)","$shapepoint","$shapepoints)","$shapepoints.count)]","$shapepoints[$(get","$solut","$stack","$stack[]","$temp","$temp[0])","$temp[1])","$thi","$tmp","$tree","$tree):","$unmarri","$woman","$woman)","$woman,","$women","$women):","$women);","$x","$x,","$x;","$x[$i","$x[$i]","$x[0],","$x[1],","$x[2],","$y","$y)","$y,","$y[$i]","$year","$year)\"","${22","${d","${girl.preferences.map(p","${guy.fiance.name}`);","${guy.preferences.map(p","${p.y})`));","%","%%","%))","%.1f,","%.1f][x]","%.1f][y]","%.1f][z]","%0.2f\\n\"","%1","%1)","%1))","%1)))]","%2)","%2))","%2)))]","%3","%d\",","%f%%\\n\",","%f\\n\",","%lf\\n\"","%n))","%s',","%s,","%s\\n\"","%s][x]","%s][y]","%s][z]","%t\\n\",","%}","&","🆔","🆕","🆕🌕🆕","🆕🌲🆕","🆕🌲⭐️","🆕🎰🆕","🆕⏩⏩","🆕⏹⏫❗️","🆕☝️🆕","🌀","🌀tree❗️","🌌","🌌🐕","🌕","🌲","🍆","🍇","🍉","🍥","🍥tree❗️","🍨","🍨🍆","🍨🐚🌲🍆","🍪🔤th","🍬⏹","🍭","🍭🐽","🍭binary_tree❗️","🍭tree❗️","🍼","🏁","🏃‍♀️","🏃‍♀️🐇🤡","🏢","🏢tree❗️","🏧","🏧a","🏧b","🐇","🐔","🐕","🐨","🐻","🐽","👌","💭","💯","💯samples❗️","📗","📥","📪","📫","🔁","🔂","🔐","🔘","🔡","🔡return❗❗️️","🔢","🔤","🔤%🔤🍪❗️","🔤🌀","🔤🍥","🔤🍭","🔤🏢","🔤🔤","🔤🥞","🔤run","🔤the","🔤tree","🔼","🖍🆕","🖍🆕var_a","🖍🆕var_b","🖍children","🖍id","🖍radiu","🖍var_a","🖍var_b","😀","🙅","🙌","🚮","🤜128","🤜64","🤜depth_count","🤜id","🤜pi_estim","🤜point_x","🤜radiu","🤡","🤷‍♀️","🥞","🥞tree❗️","🥧🕊💯","🦃","🧒","&&","&&&\\color{blue}6&5&4","&&&\\color{green}6&\\color{blue}5&4","&&&\\color{red}1&2&3","&&&\\color{red}1&\\color{green}2&3","&&&\\color{red}1&\\color{green}2&\\color{blue}3","&&&\\color{red}6&\\color{green}5&\\color{blue}4","&&1&2&3","&&1&\\color{green}2&\\color{blue}3&","&&6&\\color{red}5&\\color{green}4&","&0","&0.04","&0.16","&0.22","&0.24","&0.28","&0.5","&0.85","&1&2&\\color{blue}3&&","&4","&4&5&6","&6&5&\\color{red}4&&","&;&","&=","&=x(t)","&[complex])","&[f64])","&[f64],","&[point])","&[vec],","&\\time","&b,","&barnsley_hutchinson,","&barnsley_probabilities,","&builder,","&c,","&cb,","&codebook);","&count)|","&e","&encoder](char","&eqns)","&f64","&heap","&hull[hull.len()","&matrix)","&mut","&n);","&n.children","&n.children[..]","&node)","&node{id:","&operators)","&opr)","&opr));","&option","&par,","¶meters,","&point)","&point,","&result);","&self)","&self.codebook[&c]).join(\"\")","&self.data[row","&start);","&str)","&str,","&tmp","&tree,","&vec![2.0,","&vel,","&women[man","&x);","&x[0]);","&x[1]);","&x[2]);","'","'#0000ff',","'#00ff00')","'#00ff00',","'%","''","'''","'''iter","'''perform","'''random","''.join(decoded_message)","''.join(messag","'':","'(\"the","'(((node1","'(g0)')","')","'++'","',","',num2str(euclidmod(64","',num2str(euclidsub(128","'../../data/rand.dat'","'0'","'0')","'0'),","'0',","'0';","'1')","'1',","'1';","'100'),","'1000'),","'1001'),","'101'),","'110'),","'1100'),","'1101'),","'111')]","'2pi'","';","'[#]'","'\\0';","'__main__':","'a')","'a',","'a';","'april","'bibbity_bobbity'","'children","'children'","'data'","'dequeue'","'domain.png'","'enqueue'","'eqns'","'f(z)=z^2'","'front'","'i']]]","'id'","'list","'list))","'march","'modulu","'num","'num_child'","'num_rows'","'o'],","'pass","'pop'","'psetf',","'push'","'queue","'recurs","'red',","'rows'","'size'","'stack","'states'.","'subtract","'thi","'time","'top'","'vector","'veloc","'y'],","(","(!(o","(!))","(!empty($thi","(!equal(end_point,","(!girl.hasfiance)","(!heap","(!isa(current,","(!node.left","(!preferredmates.isempty())","(!prefers_partner(woman","(!queue_empty(&q))","(!queue_empty(q))","(!stack_empty(&stk))","(!stack_empty(stk))","(!tmp)","(!tree)","(!woman","(\"0\"","(\"bottom\"","(\"check","(\"output\"","(#560),","($a","($b","($d","($i","($man","($men","($numofrow","($point[0]","($point[1]","($prefer","($temp","($thi","($tree","($unmarried);","($woman","($women","(%","(%)","('#ff0000',","('_',","('i',","('o',","('t',","('y',","((","((!))","((!),","(($1","(((x+mu[1])^2)/(2*sigma^2)","((/","((1,","((10,10)","((128","((13","((1_f64","((2","((21","((22","((64","((:+","((>","((^","((a","((ab.getx()","((and","((avg","((b","((b.x","((d","((defin","((dft","((double)","((double)i","((fft","((format","((i","((i,","((j","((man,","((node","((par.x","((par.x[i]","((point(0,","((r1,","((ret","((stride","((tmp","((wrap","((x","((y+mu[2])^2)/(2*sigma^2)))","()","())","(),","();","(*","(*'","(*)","(*cb)[node.char]","(*dst)[len","(*dst)[len]","(*input","(*input);","(*it)","(*vel)","(+","(+)","(.*),","(.+)","(/","(/)","(/=p0)","(0","(0);","(0,","(0,0)","(0,0)).","(0..((n","(0..(size","(0..a.row","(0..iters)","(0..iters).into_iter().map(|_|","(0..n)","(0..n).step_by(strid","(0..num_child)","(0.0,","(0.4%).","(0.5","(0.5,","(1","(1+","(1,0.5),","(1...n).each","(1.0,","(1/2)","(100.0","(12","(128","(13","(15","(15,","(17","(19","(19a+m)~\\%~30","(2","(2*pi)","(2*sigma^2))","(2,","(2.0","(20","(2020..2030).to_a","(21","(21+d)~\\%~31,","(22","(2^2","(2^{10}).","(2b+4c+6d+n)~\\%~7.","(2d)","(3,","(32","(4","(4+k","(4000)","(5","(5,","(500,","(6,","(64","(7,","(9,","(:constructor","(:requir","(;","(;;)","(=","(>","(>).","([0.5,","([math]::pi))","([math]::pi))\"","([math]::pow($x,","(\\(px,","(\\(w,","(\\(x,y)","(\\cos(","(\\cos(2","(\\delta","(\\e","(\\k","(\\mathbf{r})","(\\mathbf{x})","(\\n","(\\psi_0);","(\\x","(^","(_,","(a","(a),","(a,","(a.i","(a.siz","(a/(a+1))^j","(a[(i,","(a[i","(a[i,","(a[i][col","(a[max_index,","(a[pivot","(a[pivot][col]","(a[pivot_i,","(a[r][col","(a[row,","(ab","(ab.gety()","(ab.magnitude()","(abs(sin(real_f(z(x,y))*pi)**thresh)","(actual","(ad)","(addition,","(albeit","(almost","(also","(and","(aold","(appli","(array","(array,","(assert","(assoc","(assum","(at","(atan","(auto","(auto&","(axis_num)","(b","(b),","(b.i","(b.x","(b[i]","(bachelors.nonempty)","(barely)","(becaus","(bf","(bfs)","(bi","(bin($1)):(1)","(bit","(blue,","(both","(bound","(boyfriend,","(but","(c","(c',","(c)","(c),","(c,","(c.data[cur_loc.x","(c.i","(c.x","(c/*","(c/complex","(c/exp","(c1,","(c_prime[i]","(candid","(canva","(case","(ccw(points[m","(chao","(char","(char)i;","(char,","(char?","(child","(children","(chin123)","(chosen","(cipher),","(clear)","(clojure.pprint/pprint","(clojure.set/map","(coder","(coeffici","(coerc","(col","(col+1):col","(comp","(compar","(complement","(complex","(complex::new(0.0_f64,","(computu","(computus)","(concat","(concaten","(concatmap","(cond","(const","(copi","(cough","(count","(count($tre","(counts[char]","(createtre","(cryptosystem),","(curpoint","(curr_point","(curr_row),","(current","(d","(d,","(d[i]","(data)","(date)","(dec","(decf","(decod","(def","(default","(defin","(defmacro","(defn","(defparamet","(defstruct","(defun","(defvar","(denot","(depend","(depthcount","(df","(dfs)","(dft","(dft)","(dft),","(dft,","(diagon","(display","(displayln","(div","(divf","(dot","(doubl","(double)i","(double)rand()","(double,","(dp","(drand()","(drop","(dt),","(dt^2)","(dx","(e","(e)","(easter","(either","(elemindex)","(elt","(end","(endpoint","(envis","(eq","(eql","(eqns[pivot][i]","(especi","(euclid","(euclid_mod","(euclid_mod*","(euclid_sub","(euclid_sub*","(even","(even?","(evol","(exclud","(exp","(export","(f(x_proposed)","(f(z)","(f*g)(x)","(f*g)[n]","(f64,","(f_val_ab","(factor","(fail)\");","(fft","(fft)","(fft).","(fftw_complex*)x,","(fftw_complex*)y,","(fifo),","(filter[i","(fingers),","(first","(flet","(float)","(float):","(float,","(floor","(fn","(follow.partn","(for","(format","(found","(fraction","(freq","(freq.empty())","(front","(front_pointer.get()","(func","(gaussian_valu","(gcd","(gcd)","(get","(gift)","(girl.prefers(guy))","(granted,","(grid[x][y]","(h)","(hash","(haskey(weights,","(heap","(heap.length","(heat)","(helper","(here","(here,","(homework","(hopefully)","(hue,","(hull[i]","(husband,","(hutchinson","(i","(i)","(i)'","(i)^*","(i,","(i..a.rows).rev()","(i.0","(i.e.","(i64,","(if","(ifss),","(ifss).","(in","(inbounds(canvas.shape,","(inbounds(size,","(inc","(incf","(index","(index)","(inner","(input_i","(input_x","(insert,","(instead","(int","(int)n];","(int,","(integer?","(intercal","(intercalate)","(intercalate,","(interest.partn","(interleav","(intermediat","(into","(invers","(inverse)","(is_leaf(tree))","(it","(it',","(items)","(iter","(j","(jspp)","(jspp),","(just","(k","(k)","(k,","(k..a.cols).rev()","(k_i)","(keep","(kernel_size,","(key","(kineticop","(kstep","(label","(lambda","(last","(leaf","(leav","(left","(left)","(left),","(leiosos):","(length","(length(a)","(length(filter)/2)","(length(n.children)","(let","(let'","(let*","(lifo),","(like","(list","(listarray","(littl","(loc[0]","(local","(lonelyfollows.count","(loop","(m","(m,","(m,_))","(m.fromlist","(make","(man,","(map","(map,","(map.entri","(map[c]","(mapcar","(mapv","(mat1.shape[0]","(mate","(math.abs((avg","(math.abs(a),","(math.pow(1","(math.random()","(math/ab","(math/pow","(matrix","(maximum","(mayb","(merg","(method","(middle),","(mod","(modulo","(mont","(more","(mostdesir","(mult","(multipl","(n","(n(v","(n)","(n),","(n.children)","(n.children.size())","(n.children_size)","(name","(nconc","(negative?","(new_x[k","(newline)","(next","(nlse):","(no","(node","(node)","(node.children.size())","(node.isleaf)","(node.left","(node.left)","(node.leftchild","(node.right","(node.right)","(node.rightchild","(node2","(nodeprioritylist.count","(normal","(normalized)","(note:","(np.abs(np.sin(np.pi","(np.pi","(np.sqrt(np.pi)","(null","(num","(num_row","(number","(numrow","(o","(odd","(odd?","(of","(old_val","(old_valu","(on","(on)","(one","(one:","(oper","(optional)","(or","(ord","(orthodox)","(out","(output","(p","(p)","(p.getx()","(p.i","(p.x","(p.x,","(p1","(p1:p2:ps)","(p2.0","(p2.1","(p2.i","(p2.x","(p2:ps)","(p2[0]","(p2[1]","(p3.0","(p3.1","(p3.i","(p3.x","(p3[0]","(p3[1]","(p[1],","(pa","(par.im_time)","(par.k","(par.timestep","(par.x","(par.x[i]","(partial","(partit","(partition)","(person","(pi","(pi_estim","(place","(po","(point","(point)o;","(point.i","(pointonhul","(pointonhull.equals(hull.get(0)))","(pop","(pop())","(popularli","(pos_x","(position,","(post","(potentially)","(potentialnextpointonhul","(pow((1","(pow(1","(print","(println","(priorityqueue.data.length","(priorityqueue.size()","(probabl","(product","(propos","(psetf","(ptr)","(push","(push())","(px","(q","(q.size()","(queue.count","(queue.length","(queue.size()","(queue_empty(q))","(quot","(r","(r,","(r,r)","(r1,","(r2,","(radix","(rand","(rand_max));","(random","(randomr","(rang","(re","(read,","(real","(rear","(receiver).","(recur","(red).","(red,","(reduc","(remov","(repeat","(repeatedli","(requir","(rest","(ret.size()","(return","(right","(rn,","(rnd","(roughli","(row","(row+1):row","(row,","(rowcount","(rstep","(s.size()","(s:p1:p2:ps)","(s:ss)","(scale","(second","(self.x,","(sender)","(servoi","(servois)","(set","(setf","(show","(show)","(show,","(shown","(similar","(size","(size)));","(size_t","(size_t)rand()","(so","(solar)","(sometim","(sort","(sort,","(sorton,","(split","(sqrt","(stack.count","(stack.length","(stack.size()","(stack_empty(stk))","(standard","(std::size_t","(std::uint32_t","(step","(stk","(stormer","(str","(strawberry)","(stride","(string","(string,","(struct","(such","(sum)","(svref","(t","(t)","(t,","(t1:t2:ts)","(t2,","(tabl","(tail","(take","(target","(target,","(tdma)","(temp","(the","(there","(thi","(this.mat","(thoma","(though","(time","(time,","(time:","(time:time,","(time_sv,","(time_vv,","(timestep","(timesv,","(timevv,","(to","(top","(top())","(top_pointer.get()","(tree","(tree,","(tree._children.count)","(tree.children.length)","(tree.siz","(twiddl","(u_1","(ubsan)","(uncurri","(unless","(unsign","(updat","(use","(usize,","(v","(v1","(v=2),","(val","(valu","(var","(variance)","(vec","(veloc","(verlet","(w,","(we","(wfc","(when","(where","(which","(with","(within","(without","(woman)","(woman.prefers(this))","(women!theone)","(x","(x'","(x',","(x*x","(x*x)","(x,","(x,y)","(x,y),","(x.0","(x.len()","(x.size()));","(x:xs)","(x:y:rest)","(x[i]","(x^2","(x_i)","(x_t","(xa,","(xb","(xb,","(xc","(xc,","(xold,","(xx,","(y","(y*y)","(y,","(yb","(yc","(year","(yes,","(yet","(z","(z)","(z[i]","(z_1","(zero:","(zero?","(zerop","(zip4)","({","(|\\psi(x)|^2)","(~",")","))","));",");","*","*)","*));","*)a,","**","**data;","**tmp","*.aux,","*.ep","*/","*/)","*=","*_","*a,","*array,","*b)","*children;","*codebook","*codebook,","*computus(int","*data;","*dequeue(struct","*dst","*element)","*first_point_it);","*group,","*huffman_tre","*hutchinson_op,","*in","*in,","*input));","*input;","*k;","*ke;","*lh","*lhs;","*man","*map.entry(c).or_insert(0)","*n","*neighbors)","*node","*node)","*node,","*nodeheap)","*opr,","*out","*out,","*par,","*partner;","*pe;","*points,","*points.iter().min().unwrap();","*prefers;","*probabilities,","*q)","*q,","*queue.front();","*ret","*rh","*rhs;","*self","*shape","*sooner*","*stack.top();","*stack_pop(struct","*stk)","*stk,","*str","*time","*time,","*tmp","*tmp;","*v;","*vel","*vel,","*wfc;","*woman","*x,","*x;","+","+))","++","++=","++i)","++input)","++it)","++row;","++str)","+1","+1,","+1.","+3].","+=","+y^2",",",",(sqrt",",divisor)))",",place",",return",",x_n,",".",".\"\"\"",".*",".*)",".+","..","...","...)}.","...this.data.slice(target)];","../gnuplot/plot_output.plt","..]","./barnsley.cpp",".01)",".1",".2",".266]",".3",".4",".5*acc*dt*dt",".5f]\".format(solution[i]))",".=",".average()",".code",".collect()",".collect();",".collect(collectors.tolist());",".collect::>();",".count!(a",".csv",".dat",".distinct()",".doubl",".equ",".exp()",".extern",".fill(new",".filter(|i|",".flatmap(bit",".fold(0.0_f64,",".for_each(|i|",".getasdouble();",".global",".groupby(identity)",".intel_syntax",".into_iter()",".iter()",".limit(ntrials)",".long",".map((temp,",".map(v",".map(|(&value,",".map(|_|",".map(|i|",".map(|k|",".mapvalues(_.length)",".map{",".next_index",".png",".rodata",".section",".select(n",".sorted(comparator.comparingdouble(point",".str",".string",".sum()",".sum::()",".take(n)",".take(n_trials)",".tex",".text",".tolist();",".tsv",".zip(energy_r.into_iter())","/","/)","/*","/**","//","///return","//add","//alway","//find","//found","//print","//shift","//system.out.println(\"us","//test","//tree.dfsrecursiveinorderbinary();","//utility_h","/=","0","0!","0\"","0'","0)","0)'.","0))","0)))","0))))","0));","0),","0).","0);","0)]","0+127","0,","0,0","0.","0.,","0..","0..((stride","0..(a.col","0..(n","0...n","0..64","0..len(w)","0..min(a.cols,","0..n","0..n_item","0..par.r","0..par.timestep","0..re","0..row","0..self.col","0..x.len()","0.0","0.0)","0.0));","0.0),","0.0);","0.0)]","0.0,","0.001","0.01","0.01)","0.01))","0.01);","0.01d0","0.025%","0.025\\%","0.037","0.04","0.04,","0.05,","0.053","0.07","0.07,","0.07]","0.07];","0.0:","0.0;","0.0]","0.0],","0.0];","0.0][x]","0.0]]","0.0_f64));","0.0_f64).powi(2);","0.0_f64);","0.0_f64,","0.0im","0.0}","0.0},","0.0};","0.0}};","0.1","0.1)","0.1,","0.13307711243511333","0.15","0.15,","0.16,","0.18541942067815853","0.1\\time","0.2","0.2(x+1)^2}","0.2,","0.22,","0.23","0.23648916187439406","0.23842162678327328","0.24,","0.25","0.25.","0.26","0.26,","0.26666668","0.27999628668153087","0.28,","0.3","0.30699091691896263","0.3548405553754319","0.35589625594005647","0.361307926046027","0.3692102429804389","0.4","0.4%","0.4%).","0.40610861857701597","0.42","0.42%","0.44","0.44),","0.44],","0.5","0.5)","0.5*(abs(f(z(x,y)))","0.5*(rand(shape_points)","0.5*acc","0.5*opr.v*par.dt)","0.5*par.k.^2*par.dt)","0.5*wfc_c.*ifft((par.k.^2)","0.5,","0.58),","0.587785252292473","0.5877852522924731","0.5877852522924732","0.5877852522924734","0.592m","0.5]),","0.5_f64","0.5d0","0.6075688534409027","0.618m","0.6338943724188091","0.6351126027850458","0.75)","0.75))","0.75.","0.75_f64.sqrt()},","0.7605752608745506","0.7796784902862803","0.789554555806735","0.7972009737623846","0.85","0.85,","0.8661873069668018","0.8666667","0.8686860241215444","0.9510565162951535","0.9510565162951536","0.],","0.}","0.},","0/1","0/1a","00","000","0000","00000000","00000000000010100000000","00000001","00000010","00000100","00000101","00001010","0001","00010000","00010100","001","0010","00100100000000000000000","0011","01","0100","01000000","01000010010111011110111000100101110.","0100101010110100","0101","01010000000000000000000","0110","0111","01110011110110011010110000111101100","01110011111010110000100100111110101","0111101,","01111110","01111111","0:","0:bnum","0:length(a)","0:n","0;","0]","0][x]","0_f64;","0aa","0d0","0d0)","0f,","0s","0u;","0x+0y+0z=1,","0x00ff00ff)","0x0f0f0f0f)","0x1","0x33333333)","0x55555555)","0}","0},","0};","0}};","0❗️","0❗️❗️","1","1!","1\"","1\"));","1🤛","1'","1's.","1)","1)(rng());","1))","1)))","1)))))","1)),","1)).rev()","1));","1)*pi*i*k/n)","1)*pi/(xmax)),","1),","1).","1)..a.col","1)..a.row","1).rev()","1):","1);","1)]","1)}","1)}{2a}.","1+1/a","1,","1,0.5","1,000","1,000,","1,000,000","1,000,000\"","1,000,000)","1,000,000.","1,1","1,1)","1,1).","1.","1.,","1..","1...numchildren","1..=((n","1..a.row","1..n","1..size","1.0","1.0)","1.0)(rng());","1.0))","1.0),","1.0);","1.0+0.0im","1.0+0.0im;","1.0+2.44929e","1.0,","1.0.","1.00","1.00)","1.00001","1.001001","1.0]","1.0]*[","1.0]*[1.0","1.0],","1.0]])","1.0_f64);","1.0f,","1.0f\\n\",","1.0im","1.0im]","1.1\\time","1.2","1.2246467991473532e","1.22465e","1.273","1.5333333","1.6","1.60),","1.6],","1.71","1.83697e","1.85","1.9","1.9m","1.]).reshape(3,","1.],","1.barnsley,","1.box,","1.bucket","1.canny,","1.cooley,","1.graham,","1.jarvis,","1.metropolis,nichola","1.sanderson,","1.step","1.upto(a.s","1.venerabilis,","1.wikipedia:","1.williams,","1/(n(v","1/(n(v+1,","1/0","1/4000","1/6,","1/a)**v","10","10)","10))","10)))","10):","10)?","10,","10,000","10,000\"","10,000,","10,000,000","10,000.","10,11),","10.","10.,","10.0","10.0),","10.0,","10.0/512","10.0/512,","10.0],","10.25","100","100%","100)","100))","100))))","100).floor();","100).toint","100*abs(math.pi","100,","100.","100.0","1000","1000,","10000","10000000","10000000❗️","10000001","10000010","10001011","1001","1001.001","100;","100_000","100}%\");","101","1010.01","1023","1023,","1023?","1024","1040","10:","10;","10]","10]],","10^{","10^{110}.","10^{16}","10^{16},","10^{19}","10^{38}","10^{41}","10^{50}","10^{76}","10^{76}.","10_000,","10cm","10cm,","10d","10d0","10e^{","10s,","10},","10}^{10}","10}};","10❗","10❗🍪❗️","10❗️❗️","11","11));","11),","11.0","110","1101:","1105199103","1110","1110010101,","1111","11111111","11aa","11z","11},","11~\\%~30","12","12🤛","12)","12))","12));","12),","12,","12,000,","12.0","123","123,","123\\times456=56088,","126","127","127.","128","128*77)","128/192","12]","12]#","12],","12ab","12ba","12cm,","12},","13","13,","13.","130,000","130,000,","13aab","13bba","13tba","14","14));","14),","14,","14.0","14.0,","14.0}};","14},","14}{11}","15","15));","15),","15);","15,","15.0","15.0,","15.0},","1536","15;","15},","16","16)","16+1.0im","16+1.0im;","16.5.","16:9)","16]","16]#","16],","16im","16im;","17","17,","17,000).","1777,","18","180","1800","1800's.","1800,","1805","1813.","1816.","1876.5.servois,","18\\\\","18]=[4+1,","19","19)","19))","19.","19.347","1900.","1953.2.wikipedia:","1958","1958.2.wikipedia:","1965","1965.","1967.3.jampour,","1970.6.wikipedia:","1972.","1973","1973.","1977","1978","1978.3.flajolet,","1981.11.wikipedia:","1985.4.bhayani,","1986.","1994.","1994.6.sanderson,","1999.2.dictionary.com","19;","19a","19th","19th.","1:","1:(col","1:1","1:2","1:2:(color($1,$2))","1:3","1:axis_num","1:col","1:digit","1:half","1:i","1:kernel_s","1:length(a)","1:length(a)/2","1:length(a)]","1:length(bit_indices)","1:length(density)","1:length(energy_k)","1:length(indices)","1:length(opr.wfc)","1:length(other_points)","1:length(probabilities)","1:length(x)]","1:length(y)","1:logn","1:n","1:num_child","1:par.timestep","1:row","1:size","1:size(histogram)[1]","1:size(histogram)[2]","1:size(input_pts)[1]","1;","1=","1\\right).","1\\time","1]","1])","1]);","1]*a[i])","1],","1];","1]^2","1_f64","1_f64)","1_f64,","1aa","1d","1e","1i","1j","1j)","1s","1s.","1st","1st,","1}","1}&","1})","1},","1};","1}\\left(","1}\\left[\\hat{u}_k(dt)","1}}","1}}{2}","1}}{b_i","1❗️","1❗️❗️","2","2\"","2(x","2)","2))","2)))","2)));","2)),","2));","2),","2).","2).downto(0)","2).downto(0).each","2):","2);","2)];","2**32","2*sqrt(","2*xmax/res,","2,","2,0):","2,1],","2.","2.,","2.0","2.0)","2.0),","2.0);","2.0,","2.0_f64","2.0_f64)","2.0_f64).exp(),","2.0j","2.4492935982947064e","2.64m","2.7+","2.81m","2.]).reshape(3,","20","20%","20.0","20.0/512","200,000","2000","2000,","2001.10.wikipedia:","2004.","2004.4.unknown,","2004.7.wikipedia:","2008.4.wegert,","2010.4.wikipedia:","2011.9.gareth","2012.5.poelke,","2012.9.wikipedia:","2014.2.wikipedia:","2015.","2015.2.morris,","2016.","2017","2017.7.wikipedia:","2018","2019","2019.","2019.10.hutchinson,","2019.12.wolfram:","2019.2.mandelbrot,","2019.3.pethick,","2019.3.saupe,","2019.5.saupe,","2019.8.gneiting,","2020","2020,","2020.","2020..2030)","2020..2030:","2020..=2030;","2020.2.schloss,","2020.2.torbert,","2020.3.bien,","2020.5.gundersen,","2020;","2021","2021.","2021.3.wikipedia:","2021.4.wikipedia:","2021.5.hastings,","2021.7.wikipedia:","2021.8.rosenthal,","2021;","2022.","2022.10.wikipedia:","2022.11.wikipedia:","2022.2.wikipedia:","2022.3.wikipedia:","2022.4.wikipedia:","2022.5.crypto","2022.6.wikipedia:","2022.7.wikipedia:","2022.8.wikipedia:","2022.9.wikipedia:","2030","2030]","2031):","2039.","2099,","20\\time","21","21.46\\%","21.47\\%","2147483647","21st","21st).","21st,","21st.","22","22+d+e>31","22+d+e\\leq31","22nd","23","24","24]","25","25%","25)","25))","25).floor();","25).toint","250","2500","2500.","255","255),","255,","255.","256","256,","25;","25th","26","26.712","26th","27","27.5","273.308","28","28)","28).","29","29)","29.5","29th","2:","2:2]","2:n","2;","2\\ln(r_0)}\\left(\\frac{u_1}{\\sqrt{r_0}}\\right)","2\\ln(r_0)}\\left(\\frac{u_2}{\\sqrt{r_0}}\\right)","2\\ln(r_0)}{r_0}}","2\\ln(r_0)}{r_0}}.","2\\ln(u)}.","2\\ln(u_1)}","2\\pi","2\\pi,","2]","2],","2];","2]^2","2^(j","2^0","2^1","2^2","2^3","2^4","2^5","2^6","2^7","2^8","2^9","2^n","2^v","2^{","2^{0}.","2^{10}","2^{126}","2^{130},","2^{255}","2^{3}","2_u128.pow(i","2ab","2b+4c,","2ba","2d","2d,","2d0","2dup","2half","2i,","2im*pi*n*k/n)","2im*pi*n/n)","2pi","2pi*i*(k+n/2)/n=","2pi*i*k/n)","2s","2v(t)\\delta","2x","2x(t)","2y","2z","2},","2❗️","3","3\"","3)","3))","3))))","3);","3+127=130,","3+2","3,","3,3)","3.","3.,","3.0","3.0)","3.0,","3.0]","3.0];","3.0}","3.0},","3.0};","3.14159","3.14159)","3.14159,","3.141592653589793","3.14159265358979323846","3.14159265358979323846264338327950288419716;","3.14159265358979323846264338;","3.36","3.40","3.67394e","3.84","3.}","30","30)","30))","300","301","30;","30th","31","31)","31)))))","31).to_","31).to_string();","31).tostring()","31).tostring();","31);","31:","31}\"","32","32.","32]","32],","35","35\"","354","35},","36","36,","365","365).","365.","365.2425","365.25","3700x","385.819","3:","3;","3\\\\","3\\time","3]","3aab","3bba","3blue1brown:","3d","3d,","3e^{","3jane","3n","3rd","3s","3tba","3x","3x3","3y","3z","3}","3❗️","4","4\"","4(x+4)^2}","4)","4))","4),","4).floor();","4).toint","4);","4*r12]","4*r8]","4*rax]","4*rdi]","4,","4,000","4,000.","4,],","4.","4.,","4.0","4.0,","40","400","400,","4000","4000*v.","4000,","4000.","4000:","4000th","4096","4096.625","4096^2","42","4200","4288","4290772992","4294967295","433.644","45","456","48","480","483,200.0","499,813.2","4;","4\\\\","4\\pi","4d!","4r^2","4s,","4th","4u;","4y","4z","4}","4},","5","5\"","5)","5))","5));","5),","5);","5)^2}.","5+1","5,","5,2),","5.","5.,","5.0","5.0,","5.0:","5.0][y]","5.25","5.272859","5.51091e","5.56","5.79","5.]).reshape(3,","50","50%","500)","500,000","500,000\"","500,000,","500x500","50\\%","50\\time","50_000","50_000))","50_000):","511!","511,","512","512,","512.","512/2","5128","5184","52","52\\times7=364,","56","56088.","58%","58.","5:00am","5;","5\\%","5][y]","5_000,","5d0","5x5","5},","6","6\"","6)","6))","6),","6,","6,15),","6.0","6.0)","6.0,","6.0]","6.0];","6.0][z]","6.0}","6.0};","6.12323e","6.28318530718","6.}","622:","63","64","64*81)","64,","640,","65535","67","67🤛","67)","67))","67,","6:9","6;","6]","6],","6][z]","6},","7","7)","7))","7)))","7));","7),","7+1","7,","7.0","7.0,","71)","754","77","77🤛","77)","77))","77))\"","77)))","77)).","77));","77))]","77);","78.54\\%,","7;","7]","7},","8","8)","8));","8),","8*r13],","8*rax]","8*rcx]","8*rcx],","8*rdx]","8+2","8,","8,000","8,000.0","8.","8...","8.0","8.25","80","800","81","81🤛","81)","81))","81))\"","81)))","81))))","81)).","81));","81))]","81);","84","8\\\\","8]","8],","8]=[5,8]","8cm","8},","8}};","9","9)","9))","9));","9),","9).to_","9);","9,","9,958.0","9.0","9.0,","9.000","9.125","9.125,","917","917:","96","961,600.0","97","970","9856","999,466.0","9:","9\\text{","9th.","9}\"","9}\".fmt","9}';","9},","9}`;",":",":+","::",":=",":]",":].copy()",":a",":child",":children",":code",":code)",":data",":depend",":direct",":els",":id,",":if",":messag",":message))",":name",":output",":partner",":supersede)",";",";;",";;;;",";;els",";add",";extract",";of",";remov",";to","=","=&4+1","=&5","=1:length(bit_indices)","==","=='__main__':","===","=>",">",">\",",">());",">)",">=",">>",">>=",">back",">back;",">back]",">capac",">capacity)",">capacity;",">children",">children,",">children;",">children[]",">children[i]);",">choosematch();",">codes)",">codes[(unsign",">codes[0]);",">count",">count)",">count;",">data",">data);",">data,",">data[",">data[0]));",">data[0]);",">data[0],",">data[0];",">data[heap",">data[index]);",">data[index],",">data[left]",">data[parent_index]",">data[parent_index],",">data[q",">data[right]",">data[stk",">data[target]);",">decoder.get();",">dk",">dt",">dx",">encoder;",">float",">frequenc",">frequency),",">frequency;",">front",">front)",">front,",">front];",">getchildren()",">getchildren()))",">getchildren()[0]);",">getchildren()[1]);",">getid()",">getmatch());",">getname(),",">getpreferences()));",">id",">id);",">id,",">id;",">im_tim",">index++;",">index]];",">issingle())",">k",">k[i]",">ke",">ke[i]",">key);",">key,",">left",">left);",">left,",">length",">length)",">length++]",">length]);",">lhs.get(),",">lhs.get();",">match",">match;",">name;",">next",">next);",">next;",">next_index",">next_index++]",">next_index]",">partner",">partner)",">partner;",">pe",">pe[i]",">prefer",">preferences))",">preferences);",">preferences;",">prefers,",">prefers[man",">propose();",">re",">receiveproposal($this);",">rhs.get(),",">rhs.get();",">right",">right);",">right,",">right;",">second;",">setmatch($preference);",">setmatch($this);",">setpreferences($preferences);",">singl",">size",">str);",">str[builder",">string",">suitor",">suitors))",">suitors[]",">timestep",">top",">top++]",">top];",">unmatch();",">v",">v[i]",">v[i]);",">value);",">value;",">value]",">wfc",">wfc[i]",">x",">xmax",">y",">y)","?","?,","?person","@","@(","@($(get","@(0.0,","@(0.5,","@(1.0,","@(a,","@(k,v)","@[0.0,","@[1.0,","@[4.0,","@[7.0,","@amara","@amaras,@peanutbutterwarrior","@children","@choic","@id","@inbound","@index(global,","@kernel","@leio","@name","@ntindl","@ntindle,","@ntindle,@shadowmitia","@ntindle,@shadowmitia,@amaras,@peanutbutterwarrior","@overrid","@param","@partner","@partner.name}\"","@partner.nil?","@partner.partn","@partner.sett","@pref","@prefs.index(partner.id)","@prefs.siz","@prefs[@choices]","@properti","@return","@shadowmitia","@shadowmitia,@peanutbutterwarrior","@test","@testset","@time","[","[\"\",","[\"a\",","[\"e\",","[$a","[$tree];","[%.1f]\".format(a[1],","[%.1f]\".format(b[0],","[%.1f]\\n\",","[%.1f]\\n\".format(0f,","[%s,","[%s]%s',","[&","[&]","[&freq](char","[&ret,","['[#]","['b',","['t',","[('b',","[((r,","[(>","[(a,","[(b,","[(char,","[(eq?","[(i","[(int,","[(k","[(k,","[(m","[(or","[(p","[(t1,","[(x,y)","[...\"abcde\"].map(nam","[...\"fghij\"].map(nam","[...]","[...array(children).keys()].map(()","[...bitstring])","[...iterable].sort((a,","[...iterable];","[...points].sort((a,","[...str].map(c","[...str];","[...this.data.slice(0,","[.8666]","[0","[0,","[0,0,1]","[0,0],","[0.,","[0.0,","[0.01,","[0.0],","[0.2,","[0.23,","[0.26,","[0.5,","[0.85,","[0:10]","[0:1]","[0:]","[0]","[1","[1,","[1,2]","[1,n]","[1.0+0.0im","[1.0,","[1.0]],","[1.533]","[10].","[11].","[11][12]..","[1]","[1],","[1].","[1]:","[1~0~","[1~2~1]","[2","[2,","[2.","[2.0],","[2020","[2]","[2],","[2].","[2][3].","[3,","[3.0]\"","[3.0]\")","[3.0]\");","[3]","[3],","[3].","[4,","[4.0,","[4]","[4].","[4][5].","[5.0]\"","[5.0]\")","[5.0]\");","[5]","[5].","[64","[6],","[6].","[6][7][8].","[7,","[7.0,","[7.0]\"","[7.0]\")","[7.0]\");","[7]","[7],","[7].","[8]","[8].","[9].","[9][10],","[;;","[[","[[((r2,","[[0.0,","[[1.0,","[[['_',","[[noreturn]]","[[w","[\\![1,6]\\!]","[\\![2,12]\\!].","[]","[](auto","[](const","[])","[]*node","[]*node{n}","[];","[][]float64)","[][]float64{","[]f32","[]f32)","[]f32,","[]float64","[]float64)","[]float64{0.,","[]float64{1.,","[]float64{4.,","[]float64{7.,","[]point","[]point)","[]point{{","[]rune)","[a","[a[1],","[a]","[a])]","[array[i],","[array[j],","[b[0],","[b]))","[b])]","[bit","[bit]","[bit])","[c](auto","[charact","[code","[codebook]","[complex","[complex(x[i])","[complex.cor","[constant","[double]","[double])","[double],","[ecx","[els","[first,","[float(i)","[float(i)/200","[float])","[hull[i],","[hull[m],","[hull_point]","[i","[import:1","[int]","[it',","[it,","[l,","[l])","[left","[left,","[left]","[len","[letter","[lf][lf][lf]","[lf][lf][lf][lf]","[lf][space][lf][lf]","[lf][space][space][lf]","[lf][space][space][tab][lf]","[lf][space][space][tab][space][lf]","[lf][tab][space][tab][lf]","[lf][tab][tab][tab][space][lf]","[loc","[location]","[m","[math]::abs($a)","[math]::abs($b)","[math]::abs($piestim","[math]::floor($k","[math]::floor($year","[math]::floor((13","[math]::pow($radius,","[math]::pow($y,","[math]::sqrt(0.75)),","[middl","[n","[n:m],","[nan,","[new","[new_freq](auto","[node]","[node])","[node]?","[operators]","[p0]","[p]","[particle]","[person(name)","[point(0.0,","[point]","[point_on_hull]","[pos(2,1.5),","[pv","[r10","[r10]","[r10],","[r11","[r12","[r12]","[r12],","[r13","[r13]","[r14","[r14]","[r14],","[r15","[r15]","[r15],","[r8","[r8]","[r9","[r9]","[r9],","[r]","[rand(),","[random(),","[ratio","[rax","[rax]","[rax],","[rbx","[rbx],","[rcx","[rcx]","[rdi","[rdi]","[rdx","[rdx]","[rdx],","[rsi","[rsp","[rsp],","[s","[s,","[show","[sigma","[space][lf][space]","[space][lf][tab]","[space][space][space][lf]","[space][space][space][tab][lf]","[st]","[stack","[start,","[string]","[switch]$servois)","[t]","[tab][lf][space][tab]","[tab][lf][tab][tab]","[tab][space][space][tab]","[tab][space][tab][tab]","[tab][tab][space]","[tab][tab][tab]","[top](it","[tree","[tree]","[tree];","[tree_left,","[value][next]","[vx","[vx]","[x","[x]","[{:?}]\",","\\","\\\"\"","\\%","\\%30","\\%~30","\\%~31","\\&","\\;,\\;","\\\\","\\approx","\\begin{align}","\\begin{array}{ccccccc|c}","\\begin{array}{ccccc|c}","\\begin{array}{ccccc}","\\begin{array}{ccc|c}","\\begin{array}{ccc}","\\begin{array}{cc}","\\begin{array}{c}","\\begin{bmatrix}","\\begin{document}","\\begin{matrix}","\\bigcup_{i=1}^3f_i(p)","\\bigcup_{i=1}^4f_i(p),","\\cdot","\\circ","\\co","\\color{blue}3\\times\\color{blue}6=18","\\color{green}2\\times\\color{green}6+\\color{blue}3\\times\\color{blue}5=27","\\color{red}1\\times\\color{red}5+\\color{green}2\\times\\color{green}4=13","\\color{red}1\\times\\color{red}6+\\color{green}2\\times\\color{green}5+\\color{blue}3\\times\\color{blue}4=28","\\color{red}{1}\\times\\color{red}{4}","\\cos(0)","\\cos(2","\\cos(\\omega","\\cos(\\theta)","\\ddot","\\delta","\\delta,","\\delta_j","\\displaystyl","\\displaystyle\\frac","\\documentclass[11pt]{article}","\\dot","\\ell","\\ell.","\\ell\\tim","\\end{align}","\\end{align},","\\end{array}","\\end{array}\\right]","\\end{bmatrix}","\\end{bmatrix},\\\\","\\end{bmatrix}.","\\end{bmatrix}\\\\","\\end{bmatrix}p","\\end{document}","\\end{matrix}","\\end{matrix}.","\\end{matrix}\\\\","\\exp\\left[","\\exp\\left[\\frac{","\\exp\\left[{\\displaystyle\\frac{","\\frac","\\frac12","\\frac{","\\frac{18}{11}","\\frac{1}{(2^3","\\frac{1}{0.7853}","\\frac{1}{1.72","\\frac{1}{2\\pi\\sigma^2}e^{","\\frac{1}{2}","\\frac{1}{2}(a(t)","\\frac{1}{2}.","\\frac{1}{2}\\frac{d^2f(a)}{dx^2}(x","\\frac{1}{2}\\hbar","\\frac{1}{2}\\hbar\\omega,","\\frac{1}{2}\\left(r","\\frac{1}{2}\\omega","\\frac{1}{2}a(t)\\delta","\\frac{1}{2}a(t+\\delta","\\frac{1}{2}at^2","\\frac{1}{2}mv^2?","\\frac{1}{3}","\\frac{1}{3}.","\\frac{1}{3}\\tim","\\frac{1}{3}b(t)\\delta","\\frac{1}{6}b(t)","\\frac{1}{6}bt^3","\\frac{1}{7","\\frac{1}{8}.","\\frac{1}{9}.","\\frac{1}{\\sqrt{\\pi}}","\\frac{1}{n_3","\\frac{1}{n_{v+1}","\\frac{1}{n}","\\frac{2","\\frac{[i\\hat{h}_r,","\\frac{\\displaystyl","\\frac{\\displaystyle\\sum_{n}f(n)}{\\displaystyle\\sum_{n}","\\frac{\\hbar^2}{2m}","\\frac{\\hbar^2}{2m}\\nabla^2","\\frac{\\hbar}{2}","\\frac{\\log(1+n/a)}{\\log(1+1/a)}.","\\frac{\\log_e(n+1)}{\\log_e(2)}","\\frac{\\parti","\\frac{\\partial\\phi(\\mathbf{r},t)}{\\parti","\\frac{\\pi","\\frac{\\pi}{4}","\\frac{\\pi}{4}).","\\frac{\\text{area}_{\\text{circle}}}{\\text{area}_{\\text{square}}}","\\frac{\\text{count","\\frac{\\vec{p_1","\\frac{a_{n","\\frac{a_{n+1}}{2},","\\frac{a}{2}","\\frac{b(t)","\\frac{b}{2}","\\frac{c_0}{b_0}","\\frac{c_i}{b_i","\\frac{c}{2}","\\frac{d^2x(t)}{dt^2}","\\frac{d_0}{b_0}","\\frac{d_i","\\frac{df(a)}{dx}(x","\\frac{dx(t)}{dt}","\\frac{e^{","\\frac{f(\\mathbf{x})}{\\displaystyle\\int_d","\\frac{f(\\mathbf{x})}{\\int_d","\\frac{f(n)}{\\displaystyle\\sum_{n}","\\frac{f(x')}{f(x_t)}\\right).","\\frac{f(x)}{\\int_{","\\frac{f^{(n)}(a)}{n!}(x","\\frac{h}{\\lambda}","\\frac{i(\\hat{h}_r","\\frac{i\\hat{h}_kdt}{\\hbar}},","\\frac{i\\hat{h}_kdt}{\\hbar}}e^{","\\frac{i\\hat{h}_rdt}{2\\hbar}}","\\frac{i\\hat{h}_rdt}{2\\hbar}}e^{","\\frac{i\\hat{h}_rdt}{\\hbar}},","\\frac{i\\hat{h}_rdt}{\\hbar}}e^{","\\frac{i\\hat{h}dt}{\\hbar}}\\right]\\psi(\\mathbf{r},t)","\\frac{n(n","\\frac{n}{4000}","\\frac{p","\\frac{p+a}{2}","\\frac{p+b}{2}","\\frac{p+c}{2}","\\frac{p+d}{2}","\\frac{p^2}{2m}","\\frac{pi}{4}","\\frac{r^2}{2}},","\\frac{x(t+\\delta","\\frac{x^2+y^2}{2\\sigma^2}},","\\geq","\\gt","\\hat","\\hat{h}_k","\\hat{h}_k)dt}{\\hbar}}\\right]\\psi(\\mathbf{r},t)","\\hat{h}_r","\\hat{u}_k","\\hat{u}_r","\\hbar","\\hbar\\omega.","\\hline","\\in","\\in\\left\\{h,t\\right\\},","\\infty}","\\infty}^{+\\infty}\\psi^\\ast\\psi","\\infty}^{+\\infty}|\\psi(\\mathbf{r},t)|^2","\\infty}^{\\infty}","\\infty}^{\\infty}f(\\xi)g(x","\\infty}^{\\infty}f(x","\\infty}^{\\infty}f[m]g[n","\\infty}^{\\infty}f[n","\\input{out}","\\int_a^b","\\int_d","\\int_{","\\int_{d}","\\int_{s}f(\\mathbf{x})d\\mathbf{x}","\\int_{x_1}","\\int_{x_{10}}","\\lambda","\\lambda}","\\langl","\\ldot","\\left(","\\left(\\begin{bmatrix}","\\left(\\frac{f(x')}{f(x_t)},","\\left(\\lfloor","\\left(f(z)=z^2\\right),","\\left[","\\left[\\begin{array}{@{}ccc|c@{}}","\\left[\\begin{array}{@{}cc|c@{}}","\\left[\\hat{u}_r\\left(\\frac{dt}{2}\\right)","\\left[\\hat{u}_r\\left(\\frac{dt}{2}\\right)\\mathcal{f}^{","\\left[e^{","\\left[v(\\mathbf{r})","\\left\\lfloor\\frac{13+8k}{25}\\right\\rfloor.","\\left\\lfloor\\frac{\\text{year}}{100}\\right\\rfloor,","\\left\\lfloor\\frac{k}{4}\\right\\rfloor.","\\left\\{","\\left\\{h,t\\right\\}","\\left\\{h,t\\right\\}.","\\leq","\\lfloor","\\lfloor\\cdot\\rfloor","\\log","\\log_2(1)","\\log_2(1+n),","\\log_2(8),","\\log_e(1+e^v).","\\log_e(1+n).","\\lvert","\\mathbb{c}),","\\mathbb{c}.","\\mathbb{p}(a","\\mathbb{p}(x_0","\\mathbb{r}):","\\mathbb{r}^2","\\mathbb{r}^2)","\\mathbb{r}^n","\\mathbf{","\\mathbf{0}","\\mathbf{10}","\\mathbf{1}","\\mathbf{2}","\\mathbf{3}","\\mathbf{4}","\\mathbf{6}","\\mathbf{\\frac{10}{3}}","\\mathbf{\\frac{2}{3}}","\\mathbf{a}","\\mathbf{a}\\mathbf{v}_0","\\mathbf{a}\\mathbf{v}_0.","\\mathbf{a}_{\\text{rot}}","\\mathbf{r}","\\mathbf{v_0}","\\mathbf{v}","\\mathbf{v},","\\mathbf{v}_0","\\mathbf{x}","\\mathbf{x},","\\mathbf{x}.","\\mathcal{f}","\\mathcal{f}(f)","\\mathcal{f}(f*g)","\\mathcal{f}(g)","\\mathcal{f}\\left(","\\mathcal{f}^{","\\mathcal{o}(\\delta","\\mathcal{o}(dt^3)","\\mathcal{o}(n","\\mathcal{o}(n\\log(n)),","\\mathcal{o}(n\\log(n)).","\\mathcal{o}(n^2)","\\mathcal{o}(n^3).","\\mathcal{o}(nh)","\\mathcal{o}(nh),","\\mathrm{size}\\times\\mathrm{size}","\\min","\\min\\left(1,","\\mu","\\mu)^2}.","\\mu,","\\mu.","\\n\"","\\nabla","\\nabla^2","\\neq","\\omega","\\omega(1)","\\omega(3)","\\omega(n)","\\omega,","\\omega.","\\omega_2^0","\\omega_2^1","\\omega_2^1,","\\omega_n^k","\\otim","\\phi","\\phi(\\mathbf{r},t)","\\phi,","\\pi","\\pi,","\\pi/2),","\\pi/2,","\\pi/2.","\\pi=(3,1,2,4))","\\pm","\\psi","\\psi(\\mathbf{r},t","\\psi(\\mathbf{r},t)","\\psi(\\mathbf{r},t),","\\psi(\\mathbf{r},t)^{*}\\psi(\\mathbf{r},t)","\\psi(\\mathbf{r},t)}{\\parti","\\psi(\\mathbf{r},t+dt)","\\psi(\\mathcal{r},","\\psi(x)","\\psi(x).","\\psi(x)\\rangl","\\psi_i","\\qquad","\\quad","\\rangl","\\rangle,","\\rfloor","\\rfloor.","\\right)","\\right),","\\right).","\\right)\\right)","\\right.","\\right]","\\right].","\\right]\\psi(\\mathbf{r},t)","\\right]\\psi(\\mathbf{r},t).","\\right]}","\\rightarrow","\\rvert","\\sigma","\\sigma(n,a)^2","\\sigma,","\\sigma_p","\\sigma_q","\\sigma_x","\\sigma_y.","\\sim","\\simeq","\\sin","\\sin(","\\sin(0)","\\sin(2","\\sin(\\omega","\\sin(\\theta)","\\sqrt{","\\sqrt{\\frac{","\\sqrt{\\frac{1}{n}\\sum_{i=1}^{n}(q_i","\\sqrt{\\pi}.","\\sqrt{\\text{re}(z)^2","\\sqrt{g_x^2","\\sqrt{u_1^2","\\sum_i","\\sum_n","\\sum_{i=0}^{n}w_i\\tim","\\sum_{k=0}^{n","\\sum_{m","\\sum_{n=0}^9","\\sum_{n=0}^{\\infty}","\\sum_{n=0}^{n","\\sum_{n=a}^{b}","\\tau","\\textbf{k}","\\textbf{v}","\\textbf{x},","\\text{","\\text{acceleration}","\\text{area}_{\\text{circle}}","\\text{area}_{\\text{circle}}.","\\text{area}_{\\text{circle}}=\\pi","\\text{area}_{\\text{square}}","\\text{area}_{\\text{square}}=4r^2.","\\text{area}_{\\text{square}}\\times\\text{ratio}","\\text{atan}\\left(\\frac{\\text{im}(z)}{\\text{re}(z)}\\right)","\\text{current_row}","\\text{easter}","\\text{if","\\text{im}(z)^2}","\\text{length}","\\text{length}(c_i)","\\text{length}^2.","\\text{pivot_row},","\\text{pivot}_{\\text{col}})","\\text{ratio}","\\text{ratio}?\"","\\text{velocity}","\\text{width}","\\text{width}.","\\text{year}~\\%~19,","\\text{year}~\\%~4,","\\text{year}~\\%~7,","\\tfrac{length}{2}","\\theta","\\theta(1).","\\theta(2^n),","\\theta(3),","\\theta(\\frac{3n}{2}","\\theta(\\log(n))","\\theta(n).","\\theta(n^2)","\\theta(n^3),","\\theta)","\\theta,","\\theta.","\\theta}","\\time","\\usepackage{gnuplottex}","\\vdot","\\xi","\\xi)","\\xi))dx","\\xi)d\\xi","\\xi)g(\\xi)d\\xi","\\xi}","]","])","]),","],","].","];","^","^\\infti","^^","^a.","^self.","_","_)","_),","_,","_.weight))","_________________________________________________________________________","__abs__(self)","__add__(self,","__author__","__construct(int","__init__(self)","__init__(self):","__init__(self,","__len__(self)","__muldc3","__muldc3,","__name__","__name__==\"__main__\":","__repr__","__rmatmul__(self,","__rmul__(self,","__str__","__str__(self)","__str__(self):","__tostring():","_children","_dt,","_dt;","_i","_po","_res,","_res;","_timesteps,","_timesteps;","_xmax,","_xmax;","_}","`((0","`(setf","`and`","`april","`b`","`children`","`dequeue`","`div`","`enqueue`","`first`","`front`","`iterative_cooley_tukey`","`march","`mod`","`not`","`number_of_partners`.","`on`","`person`","`pop`","`preference_list`","`push`","`second`","`size`","`top`","a%b","a%b,b","a'","a',","a'_i","a(\\text{curr_row},","a(\\text{pivot}_{\\text{row}},","a(t)\\delta","a(t+\\delta","a)","a)(ab","a)(negative?","a))","a)))","a)))))","a));","a))]))","a),","a).partial_cmp(&polar_angle(&start,","a).powf(v)","a):","a);","a)]","a)^2","a)^n","a*((1","a*((1+1/a)^v","a,","a.","a.ab","a.abs();","a.absolutevalu","a.add(b.mul(new","a.col","a.each_index","a.equals(b);","a.getx(),","a.gety());","a.len();","a.length","a.length;","a.map","a.prefer","a.rows)","a.rows];","a.shape[0]):","a.shape[1]","a.shape[1])):","a.shape[1]:","a.siz","a.weight","a.x","a.x)","a.x))","a.x)*(c.i","a.x);","a.y)","a.y));","a.y)*(c.x","a.y);","a:","a;","a=$(ab","a=1","a=30","a=30,","a==b","a=abs(a);","a=b","a>10","a>b:","a@(xa,","a[(a.row","a[(i","a[(i,","a[(k,","a[(row,","a[0],","a[0].length","a[0].length;","a[1])","a[1],","a[2*i+1])","a[2*i]","a[2*i])","a[2]","a[2],","a[3],","a[3][4]","a[col]","a[col];","a[end])","a[i","a[i,","a[i,col]","a[i,col]*a[row,j]","a[i,col]/a[row,col]","a[i,j]","a[i]","a[i])","a[i]))","a[i][col]","a[i][i];","a[i][j]","a[i][j];","a[indices[i]]","a[max_i,","a[max_index,","a[p]","a[p],","a[p][c]","a[pivot]","a[pivot];","a[pivot_i,","a[pivot_row,","a[r+1:]","a[r,","a[r:]","a[r]","a[r],","a[r][c]","a[r][j]","a[r][r]","a[row","a[row,","a[row,col]","a[row,i]","a[row,j]*fract","a[row][col];","a[row][i]","a[row][j];","a[rowa]","a[rowa];","a[rowb]","a[rowb];","a\\left(\\left(1+\\frac{1}{a}\\right)^v","a]","a])","a^*_i","a_0","a_0,","a_1","a_2","a_i","a_n","a_{n}","aa","aab","ab","aba","abbbbab","abbbbab.","abbcccdddd","abbcccdddd.","abbrevi","abc","abil","abilities)","about,","about.","about:","abov","above,","above.","above:","above;","above?","aboveground","abruptli","abs($a);","abs($b);","abs()","abs(a","abs(a)","abs(a);","abs(a:a)","abs(a:b)","abs(b)","abs(b);","abs(in1)","abs(in2)","abs(p","abs(p)","abs(pi_estim","abs(sin(imaginary_f(z(x,y))*pi))**thresh)","abs)","abs,","abs.","abs2.(opr.wfc)","absolut","absolutes.","abstract","abstractions.","abysmal!","abz","academ","acc","acc*dt","acc*dt*dt","acc*dt;","acc,","acc:","acc::float64,","acceler","accelerating,","acceleration!","acceleration,","accept","acceptable,","access","access_image(img::array{float64},","accord","accordingly.","accordingly;","account","account.","accru","accum","accumul","accur","accuraci","accurate:","achiev","acknowledg","acm","acm,","act","action","action,","action.","actions:","activ","actual","ad","ad:\"","ad:\")","ad:\");","ad:\",","ad:\\n\"","ad:\\n\");","ad:~%\"","adapt","add","add(nod","addchild($child);","addchild(tre","addit","addition,","additionally,","addlast:","addpattern","address","addresses.","addsd","adequ","adjust","admittedly,","advanc","advantag","advantage.","adventur","advic","ae","aes.","affect","affin","affine;","after,","after.","afterwards,","ag","again","again,","again.","again...","again:","age,","agnostic,","agnostic.\"","ago,","agree;","ahead","ahem","aim","al","al,","al.,","algorithm","algorithm!","algorithm)","algorithm).","algorithm,","algorithm.","algorithm:","algorithm;","algorithm?","algorithms,","algorithms.","algorithms:","alia","alias","aliases,","alic","alice'","alice,","align","all!","all((man.has_partn","all,","all.","all;","alloc","allow","allowed\"","allud","along","along!","alphabet","alphabet,","alphabets:","alreadi","already.","also,","also.","alter","altern","although","altogeth","altogether!","altogether,","alway","always)","always,","amara","amaz","ambigu","ambiguous.","ambiti","american","amin","amount","an","analag","analog","analogu","analogy.","analysis,","analyt","analytically.","analyz","ancient","angl","angle\"","angle\")","angle(endpoint,","angle(point","angle(self,","angle(x,y)","angle.","angular","anim","animation,","animation.","animation:","animations,","animations.","annal","anomaly:","anoth","another,","another.","ans(rows);","ans;","answer","answer,","answer_grid","answer_grid[1:3,","any.","anymore.","anyon","anyth","anything,","anything.","anyway","anyway,","anyway.","anyway?","anywher","aold,","api","api,","api.","appar","apparent.","apparently,","appeal.","appear","appears,","append","append()","append(*n,","append(code,","append(code[:len(code)","append(cur.children,","append(hullpoints,","append(queue,","appendix.","appli","applic","applications,","applications.","applies,","appliquées.6.standish,","apply.","approach","appropri","appropriate.","appropriately,","appropriately.","approx","approx(y,","approx(z,","approxim","approximate.\\n\");","approximate_count","approximatecount","approximatecount(nitems,","approximation\"","approximation).","approximation,","april","april.","april}&","arbitrari","arbitrarili","arbitrary.","arc","arcan","archiv","archive!","archive,","archive.","archive.org/","archive:","archivists/algorithm","are...\")","are:","are:\"","are:\")","are:\");","are:\\n\");","are;","area","area,","area.","areas.","aren't","argmax(abs.(a[row:end,col]))","args)","args]","argu","arguabl","argument","aris","arises!","arithmet","arithmetic)","arithmetic,","arithmetic.","around","around\"","arr","arr)","arr[#arr","arrang","array","array(n)","array(n).fill(null);","array(node))","array)","array,","array.","array.length","array.new(size){|i|","array;","array?","array[i]","array[i];","array[i]];","array[j]","array[j];","array[j]]","array[rand()","array[string]):","array_pop($stack)))","array_shift($stack)))","array_shift($thi","arraylist","arraylist();","arraylist<>();","arraylist<>(mates);","arrays.","arrays.stream(a).foreach(x","art","art.","articles,","arxiv,","arxiv.org","as,","as:","ascens","ascertain","ascii","ascii_lowercas","ascii_lowercase[:num_pairs]]","ascii_uppercase,","ascii_uppercase[:num_pairs]]","aside,","ask","ask,","asm","aspect","aspect=\"equal\"","aspect=\"equal\")","assert(count","assert(test_grid","assess","assign","associ","assum","assumpt","assumption:","astound","astrolog","astronom","asymmetr","asymmetric.","at(zeros(n,","at.","at:","atan(item.i","atan2","atan2(","atan2(p.i","atan2(point[1]","atan2(y,x)","atan2(y1","atom","atoms,","attack","attempt","attend","attent","attention.","attr_read","attr_writ","attract","attractor","attractor,","attractor.","attractor;","attractors,","attractors.","attractors:","attribut","audienc","audience'","augment","author","author.","author:","auto","auto&","automat","auxiliari","avail","available.","averag","average!","avg","avoid","avoided,","aw","away","awful,","ax","ax=axes,","axes.","axes.get_xticklines():","axes.get_yticklines():","axes.imshow(","axes.set_title(\"$f(x)=z^2$\")","axes.set_xlabel(\"$re(z)$\")","axes.set_ylabel(\"$im(z)$\")","axi","axis,","axis.","axis:","axis_num","axis_num^2","a{b};","a}{2}\\\\","b","b!","b'_i","b'_i=1","b)","b)(euclid","b))","b))(euclid","b)))","b))))","b)).unwrap());","b))]","b).","b):","b);","b)]","b){","b,","b,a","b.","b.ab","b.abs();","b.absolutevalu","b.getx(),","b.gety()","b.gety());","b.prefer","b.weight),","b.x","b.x);","b.y));","b.y,","b.y;","b.zero?","b:","b::int64)","b::point,","b::uint64)","b::vector{float64},","b;","b=$(ab","b=0","b=abs(b);","b@(xb,","b[0]","b[0],","b[0];","b[1]","b[1],","b[1]}","b[2]","b[2],","b[3],","b[i]","b]","b^*_i","b_0","b_0:","b_1","b_i","b_n","ba","bab","bacccdba.","bachelor","bachelor,","bachelors.dequeue.propose()","bachelors.enqueue(this)","bachelors.push(girl.fiance);","bachelors.shift();","bachelors[","bachelors[bachelors_s","bachelors_size]","back","back,","back.","back_substitution(&a);","back_substitution(a)","back_substitution(a):","back_substitution(a:","back_substitution(a::array{float64,2})","back_substitution(const","background","backquot","backsubs(const","backsubs(equations);","backsubstitut","backsubstitution(a","backsubstitution(a)","backsubstitution(double[][]","backtrack","backward","backwards,","bad","bad,","baffl","bag","baker","balanc","ball","bamboozl","banking.","bar","bar.","barn","barnsley","barnsley_hutchinson","barnsley_hutchinson,","barnsley_prob","barnsley_probabilities)","barycent","barycenter.","base","base(name)","base,","basement","bases,","bases.","bash","basi","basic","basically,","basics:","bat","bba","bc","bc)","bc.getx())","bc.gety()))","bc.magnitude()));","be","be,","be.","be:","be;","beauti","beautiful,","beautifulli","becam","becker","becom","becomes!","beda","bede,","befor","before!","before).","before,","before.","before:","before;","before?","began","begin","begin(freq),","begin(initial),","begin,","behave,","behavior","behavior.","behaviors:","behind","behind.","beholder,","being,","believ","bell","bellow","belong","below","below)!","below),","below):","below,","below.","below:","belt.","benchmark","benchmarks,","benchmarktools,","beneath","benefit","benoit,","best","best.","better","better!","better.","better:","between","between,","bewildering.","beyond","beyond:","bf","bfs(root);","bfs(tree)","bfs.","bfs:\"","bfs:\")","bfs:\");","bfs:'","bfs:\\n\");","bfs:~%\")","bfs_queue","bfs_queue(&root);","bfs_queue(n)","bfs_queue(n:","bfs_queue(n::node)","bfs_queue(nod","bfs_queue(node)","bfs_queue(node):","bfs_queue(root)","bfs_queue(root);","bfs_queue(struct","bfs_queue(tree)","bfs_queue:","bfs_queue_end_push","bfs_queue_end_push:","bfs_queue_loop","bfs_queue_loop:","bfs_queue_push_child","bfs_queue_push_child:","bfs_queue_return","bfs_queue_return:","bfsqueue()","bfsqueue(n","bfsqueue(node:","bi@","bias","bibbity_bobb","bibbity_bobbity:","bibliographi","big","big)","bigger","biggest","biggr","billion","bin","bin(x)","bin,","bin.","bin[1]","bin[2]","bin_id(x)","bin_width","bin_width)","bin_width/2,","binari","binary!🔤","binary🔤❗️","binary,","binary:","binary_root","binary_tre","bind","bins=bins,","bioinformatics.","biologi","birthday","bisect","bisect(tre","bit","bit,","bit.","bit.\"","bit...","bit:","bit?","bit_indic","bit_indices[i]","bit_indices[i][end","bit_reverse(x)","bit_reverse(x);","bit_reverse(x,","bit_reverse(x:","bit_reverse:","bit_reverse_entries:","bit_reverse_idxs(math.log2(n));","bit_reverse_return","bitlogic,","bitlogic.","bitlogic:","bitmask","bitreverse(a::array)","bitreverse(x)","bits)","bits),","bits).","bits,","bits.","bits.push_back(b);","bits;","bits?","bitshift","bitstr","bitstr_len,","bitstr_len]","bitstr_siz","bitstr_size,","bitstring(indices[i]))","bitstring)","bitstring);","bitstring,","bitstring.","bitstring::string)","bitstring;","bitstring?","bitstring_build","bitstring_builder*","bitstrings:","black","blank","blanketli","blend","blissfulli","block","blog","blowfish","blowfish:","blue","blue),","bluntly,","blur","blur\"","blurrier","bnum","bnum)","boast","bob","bob'","bobbity\"","bobbity\")","bobbity\");","bobbity\",","bobbity\";","bobbity)\")","bobbity)\";","boca","bodi","body.","boggl","boil","boltzmann","boltzmann,","book","book\");","book,","book.","books,","bool","bool)","bool,","boolean","border","boring,","born","bose","both","both!","both,","bottom","bottom,","bottom.","bottom.\"","bottom.\"\"\"","bottom;","bounc","bound","boundari","boundaries.","boundaries:","boundary.","bounds,","bounds[1,1]","bounds[1,1])","bounds[1,1])/dx),","bounds[2,1]","bounds[2,1])","bounds[2,1])/dx))","box","box,","box.","box::new(left),","box::new(right),","box—mul","boyfriend","bra","braket","branch","branch(left,","branch(left:","branch(node1,","branch(node_ptr","branch)","branch))","branch);","branch.","branch.freq","branch.left","branch.right","branch:","branches.","branch}","breadth","break","break;","breath","brevity,","brief","briefli","bright","bright,","brilliant!","bring","britain","britain?","broader","broadli","brogli","brought","brows","browser","btree","bucket","build","build_codebook(empty(),","build_codebook(leaf(char,","build_codebook(left,","build_codebook(node(left,","build_codebook(right,","build_codebook(tree)","build_huffman_tree(message)","build_huffman_tree(message):","builder","builder,","buildtre","buildtree(messag","buildtree(message)","built","built.","bulk","bunch","busi","butterfli","butterflies,","butterflies.","butterfly\"","butterfly(x)","butterfly(z[start_index:start_index","butterfly:","button:","by,","bypass","byte","b|","b}{2}\\\\","c","c#","c'","c'_0","c'_i","c'_{i","c)","c))","c)),","c))]","c),","c);","c++","c++,","c++14,","c,","c.","c.clone()","c.data[cur_loc.x","c.data[p.x","c.dup","c.gety()","c.max_i","c.max_x","c.max_x)","c.prefer","c/","c/*","c/+)","c/c++,","c/exp","c/stringifi","c1)","c1),","c:","c::point)","c::vector{float64},","c;","c==b","c?","c@(xc,","c[0]","c[0],","c[1],","c[2],","c[i","c[i]","c[j]","c]","c]))","c^*_i","c_0","c_1","c_i","c_i'","c_in","c_in,","c_n","c_prime","c_prime[0]","c_prime[1]","c_prime[i","c_prime[i]","c_{n","cabs,","caesar","caeser","cairo","calcul","calculate,","calculate_energy(&par,","calculate_energy(par,","calculate_energy(par:","calculate_energy(param","calculate_energy(struct","calculateenergi","calculation,","calculation.","calculation:","calculations.\"","calculator,","calculu","calendar","calendar,","calendar.","calendars.","calendrier,","call","calle","calloc","calloc((q","calloc(0,","calloc(1,","calloc(4,","calloc,","cambridg","camp\"","campbel","can!","can't","can.","can:","candid","candidate,","canni","canva","canvas[cur_loc]","canvas[current_loc]","canvas[current_location]","canvas[loc]","canvas[location]","canvas[neighbor]","canvas[neighbour]","canvas[p]","canvas[possible_neighbor]","canvas[x]","canvas_size[1]","canvas_size[2]","capabl","capac","capacity,","capacity;","capcaiti","capit","care","carefulli","carlo","carlo\"","carlo([int]$n)","carlo,","carlo.","carlo.core)","carray","carri","cartesian","cartesian_box_muller!(input_pts,","cartesian_box_muller(input_pts,","cartesian_kernel!(cpu(),","cartesian_kernel!(cudadevice(),","cartesian_kernel!(input_pts,","cartesianindex","cartesianindex(","cartesianindex(0,","cartesianindex(1,","cartesianindex(1,1)","cartesianindex(ceil(int,","cartesianindex{","cartesianindic","case","case!","case),","case,","case.","case:","case;","cases!","cases,","cases.","cast","catch","categori","categories:","categorized.","caus","caveat","caveats.","cb","cb,","cb[char]","cbar","cbar.set_ticklabels([\"$0.0$\",","cbar.set_ticks([0.0,","cbbbc!","cblabel","cbrang","cbtic","ccw","ccw(a,","ccw(a::point,","ccw(const","ccw(gift[j],","ccw(p1,","ccw(point","ccw(struct","cdq","ceasar","ceil(int,","ceil(int,(bounds[2,2]","celebr","cell","cell)","cell_index","cell_index(keys(n),","cell_index(keys(parent),","cell_index(values(n),","cell_index(values(parent),","center","center),","center)^2","center)^2)","center+1)**2","center+1)**2)/(2*sigma**2))","center,","center.","central","centuri","centuries,","centuries.","century.","certain","certainli","certainly,","certainti","certainty.","cexp","cexp(","cexp()","cexp,","cf","chain","challeng","chan'","chanc","chang","change,","change.","channel","chao","chaos_game(","chaos_game(10000,","chaos_game(10_000,","chaos_game(initial_loc","chaos_game(iters:","chaos_game(n,","chaos_game(n::int,","chaos_game(point(0,","chaos_game(struct","chaosgam","chaosgame($n,","chaosgame(10000,","chaosgame(int","chapman","chapter","chapter,","chapter.","chapter:","chapters,","chapters.","char","char)","char)*str]","char)c];","char)tre","char*","char**","char,","charact","character","character,","character.","characters,","characters:","charcount","charged,","charli","chars.reduce((counts,","chart","cheatsheet","check","check,","check.tex","check1","check1);","check2","check2);","check:","chemistry.","child","child'","child)","child))","child)))","child)))))","child,","child.","children","children'","children)","children))","children)):","children,","children.","children:","children::vector{node}","children;","children_count","children_count❗️","children_count❗️❗️","children_s","children_size,","children_size;","childrencount)","childrencount);","children|value|children_s","children❗️","child};","child❗️","chinmaya","chip","chk1","chk1);","chk2","chk2);","choic","choice(shape_points))","choice(shape_points))]","choice,","choice.","choice;","choices(hutchinson_op,","choices,","choices:","choices[currenttopchoiceindex++];","choos","choose(const","choose(inputpoints));","choose,","choose.","choosematch():","choosemate()","choosetreebranch(bit)","choosetreebranch(bit:","chore.","chose","chosen","chosen,","chosen:","choseth","christendom.","christian","christoph","chunk","chunks,","chunks.","church","church'","ciccotosto","cipher","cipher\"","cipher,","cipher:","circl","circle\"","circle(1.0);","circle(doubl","circle,","circle.","circle.c","circle:","circle?","circles?","circle}}{\\text{tot","circuit","circuits:","cl","claim","clang++","clarification.)","clarity),","clarity:","class","class.","classic","classifi","classvariablenames:","claud","clean","clean,","cleaner","cleaner,","cleanest","cleanli","cleanup:","clear","clear,","clear.","clear:","clearli","clearly,","clergi","click","climate,","clobber","clockwis","clockwise)","clockwise,","clockwise?","clockwise?\"\"\"","clojur","clone)]","close","close(outfile)","close?","closed,","closer","closest","clutter,","cm,","cmath","cmovnz","cmp","cmp(&self,","cmp_points(const","cmp_points);","cn","cn)","cn))","cnt","coast","coastlin","coconut","coconut.","code","code!","code)","code)))))","code);","code)]","code+'0')","code+'1')","code,","code.","code.append(0));","code.append(1));","code.deletecharat(code.length()","code.tostring());","code/","code:","code::string,","code='')","code]","codearr","codearr)","codebase.","codeblock","codebook","codebook'","codebook(it","codebook)","codebook);","codebook*","codebook,","codebook.","codebook.decode(&encoded);","codebook.encode(input);","codebook.entryset())","codebook.getorelse(c,","codebook.insert(value,","codebook.put(node.letter,","codebook.put(symbol,","codebook/tre","codebook:","codebook::codebook(it","codebook::decode(it","codebook::encode(it","codebook::node::~node()","codebook;","codebook[0][0]","codebook[c]).join(\"\"),","codebook[i]","codebook[n.key]=\"0\"","codebook])","codebook_free(struct","codebook_ptr","codebook_recurse!(branch.left,","codebook_recurse!(branch.right,","codebook_recurse!(branch::branch,","codebook_recurse!(leaf::leaf,","codebook_recurse!(n,","codebook_recurse(const","codebook_recurse(tre","codebook_recurse(tree,","codebook_s","codebook_size,","codebook_size]","codebookrecurse(c,","codebookrecurse(left,","codebookrecurse(nod","codebookrecurse(node.left,","codebookrecurse(node.right,","codebookrecurse(node:","codebookrecurse(right,","codebookrecurse(root,","codebookreverse()","coder","coder))","coder]","codes(begin(s),","codes(codes),","codes,","codes.decode(begin(string),","codes;","codes[256];","codes[i]);","codeword","codeword.","codewords.","coding.","coeffici","coefficients.","coefficients.\"\"\"","coin","col","col):","col);","col,","col]","col]))","col];","colinear","collabor","collaps","collect","collect(2020:2030)","collect:","collections.shuffle(preferredmates);","collinear","collinear.","colloqui","color","color(f_val,","color(x,y)","color.","colorbar","colored,","colored.","coloring,","coloring:","colors,","coloss","cols)","cols);","cols,","cols:","cols]","column","column)","column)))","column,","column.","columns,","columns.","combin","come","comfort","comisd","comma","command","command,","command.","command:","commands:","comment","comments.","common","common,","common.","commonli","commun","communicating.","communication,","community,","community.","commut","compar","comparable.","compareto(nod","comparison","compatriot","compel","compil","compiler,","complain","complet","complete,","complete.","completed.","completeness.","complex","complex(0,","complex(math.random(),","complex)","complex::new(1.0_f64,","complex::new(par.k[i],","complexity.","complic","complicated).","complicated.","complicated:","compon","component,","component.","components,","components.","compos","composit","comprehens","comprehension,","compress","compression!","compression,","compression.","comput","computation","computation,","computation.","computation:","computations,","compute_sobel(signal)","compute_sobel(signal):","computer,","computer.","computer?","computers.","computers?","computers?\"","computing.","computu","computus([int]$year,","computus(int","computus(y)","computus(y,","computus(year","computus(year,","computus(year:","computus(year;","computus,","computus.(a)","computus.(a;","conc","concat","concat(&result,","concat(char**","concat_char(char**","concat_char(result,","concaten","concatenation,","concatmap","concav","concept","concept,","conceptu","concern","concerns,","concession,","conclud","conclus","conclusion,","concret","condens","condit","condition\"","conditionals,","conditions,","conditions.","conditions:","condon","configur","configuration,","configuration:","confin","confus","confusing.","conglomer","conj(wfc_r)","conjug","conjugate.","connect","consecut","consequ","consequences:","consid","consider","consider:","consist","console.log(","console.log(\"[#]\\nqueu","console.log(\"[#]\\nrecurs","console.log(\"[#]\\nstack","console.log(\"[0.0","console.log(\"[1.0","console.log(\"[2.0","console.log(\"\\ngirls\");","console.log(\"\\npairings\");","console.log(\"cooley","console.log(\"guys\");","console.log(\"ha","console.log(\"it","console.log(\"th","console.log('[#]\\nmodulu","console.log('[#]\\nsubtract","console.log();","console.log(`${girl.name}:","console.log(`${guy.name}:","console.log(`${stormer.time}`);","console.log(`${stormer.vel}`);","console.log(`${time}`);","console.log(`${velocity.time}`);","console.log(`${velocity.vel}`);","console.log(`(${p.x},","console.log(`[#]\\ntim","console.log(`[#]\\nveloc","console.log(decoded);","console.log(encoded.string);","console.log(euclidmod(64","console.log(euclidsub(128","console.log(numberqueue.dequeue());","console.log(numberqueue.front());","console.log(numberqueue.size());","console.log(numberstack.pop());","console.log(numberstack.size());","console.log(numberstack.top());","console.log(tree.id);","console.println(","console.write(choice.name);","console.write(queue.peek().id","console.write(stack.peek().id","console.write(tree.id","console.writeline(\"[#]\\nmodulu","console.writeline(\"[#]\\nqueu","console.writeline(\"[#]\\nrecurs","console.writeline(\"[#]\\nstack","console.writeline(\"[#]\\nsubtract","console.writeline(\"galeshapleyalgorithm\");","console.writeline();","console.writeline(check);","console.writeline(check2);","console.writeline(man.nam","console.writeline(woman.nam","const","const&","const*","const;","constant","constant(a::array{float64})","constant(a::uint64,","constant,","constantli","constants!","constants,","constants.","constexpr","constitu","constrain","constrained,","constraint","constrict","constrictions.","construct","constructed.","construction,","constructor(name)","consult","consum","consume(","contact","contact.","contain","containers.map(k,v);","contains?","contend","content","context","context.","context?","contextlib","contin","continu","continue,","continue.","continue;","continues.","continuing,","continuing:","contour","contour.","contours.","contractive.","contractivity,","contradiction.","contrast","contribut","contribute,","contributors.md","contributors.md.","contributors.md:","control,","control.monad.st","convent","converg","convers","conversation,","convert","convert(int,ceil(log2(length(a))))","convert(int,ceil(log2(length(x))))","convex","convex,","convexhul","convexhull.foreach(p","convexhull;","convexhull[0]);","convinc","convolut","convoluted!","convolution!","convolution\"","convolution,","convolution.","convolution1d","convolution:","convolutions,","convolutions.","convolutions:","convolutions?","convolv","convolve_cyclic(signal,","convolve_cyclic(signal::array{t,","convolve_fft(signal1,","convolve_fft(signal1::array{t},","convolve_fft(x,","convolve_linear(signal,","convolve_linear(signal::array{t,","convolve_linear(x,","convolvecyclic(double[]","convolvelinear(double[]","convolvelinear(x,","cool","cool.","cooler","cooley","cooley_tukey","cooley_tukey(&x);","cooley_tukey(&x.iter().skip(1).step_by(2).cloned().collect::>());","cooley_tukey(begin(recursive),","cooley_tukey(doubl","cooley_tukey(it","cooley_tukey(x)","cooley_tukey(x):","cooley_tukey(x);","cooley_tukey(x.filter((_,","cooley_tukey(x:","cooley_tukey(x[1:2:n])","cooley_tukey(x[2:2:n])","cooley_tukey:","cooley_tukey_end","cooley_tukey_end:","cooley_tukey_loop","cooley_tukey_loop:","cooley_tukey_mov","cooley_tukey_mov_data","cooley_tukey_mov_data:","cooley_tukey_moved:","cooley_tukey_return","cooley_tukey_return:","cooley_tukey_split","cooley_tukey_split:","cooley_tukey_spliting:","coord","coordin","coordinate,","coordinates)","coordinates,","coordinates.","coordinates[0];","coordinates[1];","coordinates[2];","coords)","copi","copy(c)","copy(d)","copy(men)","copy(women)","copy)]","copy,","copyright.","core","corner","corner:","cornerston","correct","correct,","correct.","correct;","correctly.","correl","correlation,","correspond","cos(theta)","cos(x)","cosin","cosine,","cost","costli","costly.","cough)","couldn't","count","count($x));","count(&self)","count(0ull)","count)","count))))))","count,","count.","count:","count;","countdown(n","counted,","counted.","counter","counter!","counter(message)","counter,","counter.","counter_clockwise(&hull[hull.len()","counter_clockwise(a:","counter_clockwise(hull[","counter_clockwise(p,","counter_clockwise(p1","counter_clockwise(p1,","counterclockwise\"","counterclockwise(p1,","counting!","counting\"","counting,","counting:","counts,","counts.","counts:","counts;","counts[(unsign","counts[256]","counts[char]","counts[i];","counts_size,","counts_size]","counts_size],","count❗️","coupl","cours","course!).","course)","course,","cover","covered.","cpow(par.k[i],","cpow(par.x[i]","cpp","cprime","cprime[0]","cprime[i","cprime[i]","cpu","cpu,","cpu.","cr.","crack","craft.","crate","crazi","crazy,","creat","create.","create_btree()","create_btree();","create_circle(image_resolution,","create_codebook(huffman_tree)","create_codebook(n::node)","create_gaussian_kernel(kernel_size)","create_gaussian_kernel(kernel_size):","create_grid(n,","create_group(struct","create_rand_dist(4096^2,[0,1])","create_rand_dist(4096^2,[0,1],","create_rand_dist(n,","create_sobel_operators()","create_sobel_operators():","create_tre","create_tree()","create_tree();","create_tree(2,","create_tree(3,","create_tree(3,2)","create_tree(int","create_tree(levels,","create_tree(node(),","create_tree(node,","create_tree(num_row","create_tree(num_row:","create_tree(num_row::int64,","create_tree(num_rows,","create_tree(phrase)","create_tree(phrase::string)","create_tree:","create_tree_children","create_tree_children:","create_tree_leaf","create_tree_leaf:","create_tree_return","create_tree_return:","createallchildren(nod","createbitstring(str","createbranch","createbranch(nod","createcodebook(mayberoot:","createcodebook(tree)","createcodebook(tree);","created.","createdictionary(nod","createdictionary(node.leftchild,","createdictionary(node.rightchild,","createdictionary(root,","createleaf(char","createsawtooth(int","createtre","createtree()","createtree(2,","createtree(3,","createtree(numrow,","createtree(numrows:","createtree(originaltext)","createtree(phrase:","createtree(row","createtree(rows,","createtree(str)","createtree(str);","creation","creation.","creativ","cri","criterion","crop","cross","crosses.","crucial","crunching.","cryptograph","cryptographi","cryptography\"","cryptography,","cryptography.","cryptography:","crystal","cuarray)","cube","cube!","cube\"","cube,","cube:","cuda","cuda.@sync.","cuda.@tim","cudakernel","cumulprob","cur","cur.char","cur.children...)","cur.id","cur.id)","cur.left","cur.right","cur_loc","cur_loc,","cur_loc.y]","cur_point","curpoint","curpoint;","curr_point","curr_point)","curr_product","curr_product)","current","current)","current))","current.left","current.right","current.value);","current;","current_loc","current_loc,","current_location,","current_nod","current_node.children:","currently,","currentnod","currenttopchoic","currenttopchoiceindex","curv","curve.","custom","cut","cutoff","cutoff)","cutoff::int64)","cvtsi2sdq","cvttsd2si","cvx","cvx))","cvx)]","cycl","cycle)","cycle,","cyclic","cypher.","c|","c}{2}\\\\","d","d')","d'_0","d'_0.","d'_i","d'_i.","d'_n.","d'_{i","d)","d))","d),","d):","d+e","d+e+22\\text{","d+e.","d,","d,31))","d.clone()","d.count","d.dup","d.length","d:","d::vector{float64},","d=28","d=28,","d=29","d[0]","d[0]].join(\"\\t\")","d[1])","d[1]),","d[1]].join(\"\\t\")","d[2])","d[2]),","d[2]].join(\"\\t\")","d[3])","d[3]),","d[i","d[i+1]","d[i]","d[j","d[j]","d\\mathbf{r}","d\\mathbf{x}","d\\mathbf{x}.","d\\xi","d^*_i","d_0","d_1","d_glibcxx_debug","d_i","d_in","d_in:","d_n","d_{n","damage.","dangerous!","dart","dash","dashtyp","data","data'","data)))","data);","data,","data.","data.array","data.array.carray","data.complex","data.funct","data.list","data.map","data.ratio","data.to_vec(),","data:","data;","data[index]","data[target]","datafil","dataset","datasets.","datastructur","datastructures,","data{std::move(decoder),","date","date.","dates.","david","day","day!","day,","day.","days),","days,","days.","de","dead","deal","death","debat","debug","dec","decad","decay","decent","decid","decim","decis","decod","decode(&self,","decode(bitstring,","decode(const","decode(enc,","decode(encoded,","decode(encoded.string,","decode(encoded:","decode(huffman_tree,","decode(huffman_tree::node,","decode(it","decode(messag","decode,","decode:","decode_dfs(&self,","decode_don","decode_done:","decode_loop","decode_loop:","decode_loop_char","decode_loop_char:","decode_loop_char_branch","decode_loop_char_branch:","decode_recurse(const","decode_recurse(input","decode_recurse(input,","decode_singl","decode_single(it,","decoded()","decoded)","decoded);","decoded:","decoded_messag","decoded_message)","decoded_message.append(inverse_dict[key])","decoded_message:","decoder)","decoder))","decoder;","decoder]","decoding.","decreas","decrement","decrypt","decrypt,","decrypting.","deduc","deem","deep.\"","deep.\"\"\"","deeper","deepli","def","default","default:","defaultparamet","defin","defined.","definit","definition)","definition,","definition:","definitions,","definitions:","definitions;","degre","degrees,","del","delambre)","delete!(mentowomen,","delimitedfil","delimitedfiles,","delta","delv","demand.","demonstr","denomin","denominator)","denominator,","denot","densiti","densities.","density\"","density,","density.iter().sum::()","density:","density=true)","density[j],","density[j].real,","density[opr.size];","dep","depend","dependence,","depict","depth","depth,","depth_count","depthcount,","dequ","deque()","deque([node])","deque.new","dequeu","dequeue!(nodes)","dequeue!(q)","dequeue!(weights)[1]","dequeue(&mut","dequeue(&q);","dequeue()","dequeue():","dequeue();","dequeue(self)","dequeue(struct","dequeue:","dequeue_return","dequeue_return:","derefer","deriv","derivatives.","derivatives:","descend","describ","describe,","descript","descriptions,","descriptor","deserv","design","desir","desire,","desired.","desktop","destroy","destroy_tree(root);","destroy_tree(root_binary);","destruct","destructively\"","detail","detail:","details,","details.","detect","detection,","detector.","determin","determinist","dev","develop","developed.","development.","deviat","deviates,","deviation,","deviations.","devic","devis","devot","df","dfs(&self,","dfs.","dfs:\"","dfs:\")","dfs:\");","dfs:'","dfs:\\n\");","dfs:~%\")","dfs_recurs","dfs_recursive(&root);","dfs_recursive(...)","dfs_recursive(child)","dfs_recursive(child);","dfs_recursive(n)","dfs_recursive(n:","dfs_recursive(n::node)","dfs_recursive(nod","dfs_recursive(node(value,","dfs_recursive(node)","dfs_recursive(node):","dfs_recursive(root)","dfs_recursive(root);","dfs_recursive(struct","dfs_recursive(tree)","dfs_recursive:","dfs_recursive_bt_return","dfs_recursive_bt_return:","dfs_recursive_bt_size0","dfs_recursive_bt_size0:","dfs_recursive_bt_size1","dfs_recursive_bt_size1:","dfs_recursive_bt_size2","dfs_recursive_bt_size2:","dfs_recursive_children","dfs_recursive_children:","dfs_recursive_inorder_btre","dfs_recursive_inorder_btree(&root_binary);","dfs_recursive_inorder_btree(binary_tree)","dfs_recursive_inorder_btree(children[0])","dfs_recursive_inorder_btree(children[1])","dfs_recursive_inorder_btree(children{1})","dfs_recursive_inorder_btree(children{2})","dfs_recursive_inorder_btree(left);","dfs_recursive_inorder_btree(n)","dfs_recursive_inorder_btree(n.children[0]);","dfs_recursive_inorder_btree(n.children[1])","dfs_recursive_inorder_btree(n.children[1]);","dfs_recursive_inorder_btree(n.children[2])","dfs_recursive_inorder_btree(n:","dfs_recursive_inorder_btree(n::node)","dfs_recursive_inorder_btree(nod","dfs_recursive_inorder_btree(node(value,","dfs_recursive_inorder_btree(node)","dfs_recursive_inorder_btree(node):","dfs_recursive_inorder_btree(node.children[0])","dfs_recursive_inorder_btree(node.children[1])","dfs_recursive_inorder_btree(right);","dfs_recursive_inorder_btree(root_binary)","dfs_recursive_inorder_btree(root_binary);","dfs_recursive_inorder_btree(rootb)","dfs_recursive_inorder_btree(struct","dfs_recursive_inorder_btree:","dfs_recursive_po_children","dfs_recursive_po_children:","dfs_recursive_po_return","dfs_recursive_po_return:","dfs_recursive_postord","dfs_recursive_postorder(&root);","dfs_recursive_postorder(child)","dfs_recursive_postorder(child);","dfs_recursive_postorder(n)","dfs_recursive_postorder(n:","dfs_recursive_postorder(n::node)","dfs_recursive_postorder(nod","dfs_recursive_postorder(node(value,","dfs_recursive_postorder(node)","dfs_recursive_postorder(node):","dfs_recursive_postorder(root)","dfs_recursive_postorder(root);","dfs_recursive_postorder(struct","dfs_recursive_postorder(tree)","dfs_recursive_postorder:","dfs_recursive_return","dfs_recursive_return:","dfs_stack","dfs_stack(&root);","dfs_stack(...)","dfs_stack(n)","dfs_stack(n:","dfs_stack(n::node)","dfs_stack(nod","dfs_stack(node)","dfs_stack(node):","dfs_stack(root)","dfs_stack(root);","dfs_stack(struct","dfs_stack(tree)","dfs_stack:","dfs_stack_end_push","dfs_stack_end_push:","dfs_stack_loop","dfs_stack_loop:","dfs_stack_push_child","dfs_stack_push_child:","dfs_stack_return","dfs_stack_return:","dfsinord","dfsinorder(root_binary);","dfsinorder(tree)","dfsinorder(tree.children[0]);","dfsinorder(tree.children[1]);","dfsinorderbinarytree.","dfsinorderbinarytree:","dfsiterative(root);","dfsiterative(tree)","dfspostord","dfspostorder(root);","dfspostorder(tree)","dfspreorder(root);","dfspreorder(tree)","dfsqueue(tre","dfsrecurs","dfsrecursive()","dfsrecursive(c);","dfsrecursive(child)","dfsrecursive(n","dfsrecursive(n);","dfsrecursive(nod","dfsrecursive(node:","dfsrecursive(this);","dfsrecursive(tre","dfsrecursive.","dfsrecursiveinorderbinari","dfsrecursiveinorderbinary()","dfsrecursiveinorderbinary()!\");","dfsrecursiveinorderbinary(nod","dfsrecursiveinorderbinary(node.children.get(0));","dfsrecursiveinorderbinary(node.children.get(1));","dfsrecursiveinorderbinary(node:","dfsrecursiveinorderbinary(this);","dfsrecursiveinorderbinary(this.root);","dfsrecursiveinorderbinary(tre","dfsrecursiveinorderbinary(tree._children[0]);","dfsrecursiveinorderbinary(tree._children[1]);","dfsrecursiveinorderbtree(n","dfsrecursiveinorderbtree(n.children[0])","dfsrecursiveinorderbtree(n.children[1])","dfsrecursivepostorder()","dfsrecursivepostorder(c);","dfsrecursivepostorder(child)","dfsrecursivepostorder(n","dfsrecursivepostorder(n);","dfsrecursivepostorder(nod","dfsrecursivepostorder(node:","dfsrecursivepostorder(this);","dfsrecursivepostorder(tre","dfsrecursivepostorder)].","dfsrecursivepostorder.","dfsstack","dfsstack()","dfsstack(n","dfsstack(node:","dfsstack(tre","dfsstack.","dft","dft(&x);","dft(doubl","dft(iter","dft(x)","dft(x):","dft(x);","dft(x:","dft.","dft:","dft:\"","dft_end_i","dft_end_i:","dft_end_j","dft_end_j:","dft_loop_i","dft_loop_i:","dft_loop_j","dft_loop_j:","dftmat","diagon","diagonalization,","diagram","diagram,","diagram:","diagrams.","dial","dice","dice),","dice,","dice.","dict","dict((v,","dict([(v,","dict(codebook)","dict(map(m","dict(map(w","dict)","dict);","dict::dict{char,string})","dict;","dict[leaf.key]","dict[node.key]","dictat","dictionari","dictionary();","dictionary)","dictionary);","dictionary,","dictionary.","dictionary;","dictionary[character];","dict{char,string}()","dict{string,string}","dict{string,string}()","dict{string,vector{string}}","didn't","die","dietmar","diff","differ","differences:","different?","differenti","differently,","difficult","diffrint","diffus","diffv","diffv))))","dig","digit","digit.","digits:end]","dil","dil,","dilut","dimens","dimension","dimension)","dimension,","dimension.","dimension:","dimensional;","dimensionality,","dimensions!\")","dimensions,","dimensions.","direct","direction,","direction.","directions,","directions.","directli","directly,","directori","directory.","dirti","disappears.","disciplin","discontinu","discord","discov","discoveri","discrep","discret","discrete,","discuss","discuss.","discussion,","discussion.","disect","disguise.","display","display,","dissimilar","dist(0,","distanc","distance.","distil","distinct","distinct.","distinctli","distinguish","distract","distracting,","distribut","distribution(0.0,","distribution(rng);","distribution(s)","distribution)","distribution,","distribution.","distribution:","distribution?","distributions),","distributions,","distributions.","div","div(bnum,2)","div(n,","div(n,2)","div(par.timesteps,","dive","diverg","divergence,","divf","divid","divis","division),","divisor","divisor\"","divisor)","divisor.","divsd","divsor","dk","dk,","dk:","dk::float64","dk;","dmrg,","do","do!","do,","do.","do?","docker","document","document,","documentation,","documents,","does!","doesn't","domain","domain,","domain.","domain;","domains\"","domains:","don't","don't.","donald","done","done,","done.","door","doors,","dot","doubl","double)","double):","double,","double.random(in:","double[3];","double[]","double[][]","double[length];","double[outputsize];","double[rows];","double[size];","double]","doublearray","doublearray):","doublearray,","doublearrayof(0.0,","doublearrayof(1.0,","doublearrayof(4.0,","doublearrayof(7.0,","doubli","doubt","down","down\"","down,","down.","down.\"","downto","downwards.","dp","drama","dramat","drand()","drand();","drand()};","drastic","draw","drawback","drawn","drawn.","drop","dst","dst,","dst;","dst_len","dt","dt)","dt))","dt)))","dt),","dt):","dt,","dt:","dt::float64","dt::float64)","dt::float64,","dt;","dt^2","dt^3,","dtor","dtype=complex)","dtype=float)","duct","due","dumb","dump","dup","duplic","duplicate(build","duplicate(const","duplicate(get_code(codebook,","duplicates.","dure","during,","dwell","dword","dx","dx)","dx))","dx),","dx);","dx,","dx:","dx::float64","dx;","dx_1\\dot","dx_{10}.","dx}","dynam","dynamic_cast(cur))","dynamic_cast(current_node))","d}{2}\\\\","e","e(\\mathbf{x})","e(\\mathbf{x})/t\\right],","e(\\mathbf{x})}{t}","e(x_1,","e(x_1,...,x_{10})","e(x_1,\\dot","e)","e))","e)))","e),","e).to_","e);","e,","e.","e.g","e.g.:","e=","e=6","e=6,","e^(","e^(n*k*2*pi*(1/len)*(","e^v","e^{","e^{2","e^{255}","e^{2\\pi","each","each.","earli","earlier,","earth","earth'","earth,","earth.","earthfail","easi","easier","easiest","easili","east","east,","easter","easter\"","easter\"))","easter)","easter)))","easter,","easter.","easter:","easter?","easter_d","easterd","eastern","easy:","eavesdropp","eavesdropper.","eax","eax,","ecc","echelon","echelon)","echo","ecx","ecx,","edg","edge!).","edge)","edge.","edi","edi,","edit","educ","edx","edx,","effect","effect,","effect.","effici","efficient.","effort","eigenst","eigenvalu","einstein","either.","either:","elabor","electromagnetism,","electron","elegantli","elem","element","element'","element)","element);","element,","element.","element:","element;","elementari","elements,","elements.","elemindex","elems)","elems,","elias,","elif","elimin","elimination\")","elimination,","elimination.","elimination:","elimination:\")","elimination:\");","elimination:\\n\");","ellipsoid","ellipt","elm","else).","else,","else:","elseif","elsevier,","em,","emb","embed","emojicod","empir","empti","empty()","empty,","empty:","enc)","enc,","enclos","encod","encode(\"bibb","encode(\"bibbity_bobbity\")","encode(&self,","encode()","encode(codebook,","encode(codebook::dict{char,","encode(const","encode(it","encode(messag","encode(originaltext,","encode(phrase:","encode(str)","encode:","encode_calculate_length","encode_calculate_length:","encode_calculate_new_bit_offset","encode_calculate_new_bit_offset:","encode_don","encode_done:","encode_messag","encode_message:","encode_message_bit","encode_message_bits:","encode_message_bits_qword","encode_message_bits_qword:","encode_message_bits_try_overflow","encode_message_bits_try_overflow:","encoded)","encoded);","encoded.tree);","encoded:","encoded_messag","encoded_message)","encoded_message):","encoded_message:","encoded_str","encoded_string(codebook","encoded_string(std::str","encoder;","encoder_rec(&decoder,","encoder_rec(b","encoder_t","encoder_t&","encoder_t();","encoding.","encoding:","encodingresult","encodingresult(str","encompass","encount","encourag","encrypt","encryption:","end","end(code),","end(encoder))","end(encoder),","end(freq))","end(freq),","end(initial),","end(iterative));","end(recursive));","end(ret),","end(s)))","end(s)),","end(string));","end)","end).","end,","end.","end='","end='')","end_point","end_point;","endfunct","endif","endmethod","endpoint","endpoint)","endpoint)):","endpoint):","endpoint.equal(hullpoint)","endpoint.equal(hullpoints[0])","endpoint:","endpoint;","endpoints)","endpoints;","endpoints[1]","endpoints[1])","endpoints[1],","endpoints[1]]","endpoints[2]","endwhil","energi","energy)","energy,","energy.","energy_fin","energy_final*par.dx","energy_k","energy_k,","energy_k[i]","energy_r","energy_r).r","energy_r[i]","energy_r[i])","enforc","engag","engin","engineering,","engineering.","enjoy","enjoy.","enlighten","enough","enqueu","enqueue!(nodes,","enqueue!(q,","enqueue!(q,neighbor)","enqueue(&mut","enqueue(&q,","enqueue(const","enqueue(data:","enqueue(self,","enqueue(struct","enqueue(t","enqueue(value)","enqueue:","enqueue_append","enqueue_append:","enqueued,","enqueued:","ensur","enter","entir","entirely,","entirely:","entireti","entri","entry.","enum","enumerate(encoded_message):","enumerate(trees)","ep,","epslatex","epslatex.","eq","eq(&self,","eq)","eqns.size(),","eqns.size();","eqns[0].size();","eqns[i]);","equal","equal,","equals(object","equals(point","equat","equation!","equation,","equation.","equation:","equations,","equations.","equations:","equations;","equations?","equations{","equilater","equilibrium","equinox","equival","era","era!","err(why)","error","error🔤❗️","error(\"postord","error)))","error,","error.","error:","error_fmt:","errors!","escap","esi","esi,","especi","essence,","essenti","essentially,","establish","estaim","estim","estimate)))","estimate))))","estimate_fmt:","et","etc).","etc.","etc.),","etc.).","euclid","euclid%","euclid'","euclid($a,","euclid()","euclid)","euclid_mod","euclid_mod()","euclid_mod(0,","euclid_mod(128","euclid_mod(64","euclid_mod(a","euclid_mod(a,","euclid_mod(a:","euclid_mod(a::int64,","euclid_mod(b,","euclid_mod(in1,","euclid_mod(int","euclid_mod:","euclid_mod_fmt","euclid_mod_fmt:","euclid_rem(64","euclid_rem(mut","euclid_sub","euclid_sub()","euclid_sub(0,","euclid_sub(128","euclid_sub(64","euclid_sub(a","euclid_sub(a,","euclid_sub(a:","euclid_sub(a::int64,","euclid_sub(in1,","euclid_sub(int","euclid_sub(mut","euclid_sub(x","euclid_sub(x,","euclid_sub,","euclid_sub:","euclid_sub_fmt","euclid_sub_fmt:","euclidean","euclideanalgo","euclideanalgorithm","euclideanalgorithm();","euclideanalgorithm.c","euclideanalgorithm.euclidmod(64","euclideanalgorithm.euclidsub(128","euclidian","euclidmod","euclidmod(64*67,","euclidmod(a,","euclidmod(a,b)","euclidmod(a:","euclidmod(int","euclidmod:","euclidsub","euclidsub(128*12,","euclidsub(a,","euclidsub(a,b)","euclidsub(a:","euclidsub(int","euclidsub:","euler'","ev","evalst","evalu","evaluate,","even","even[k]","evenli","evens)","event","events,","events.","eventu","eventually,","everybodi","everyon","everyone'","everyone.","everyth","everything,","everywher","everywhere,","evid","evil","evil.","evol","evolution.","evolv","evolves,","exact","exact,","exactli","exactly,","exactly.","exampl","example,","example.","example:","examplequeue()","examplequeue();","examples!","examples,","examplestack()","examplestack();","except","exception(\"not","excit","exclud","exclus","exclusive\"","execut","exist","exist,","exist.","existed,","exists!","exists,","exists.","exit","exit_success;","exp","exp(","exp(x)","exp,","exp.(","expand","expans","expansion,","expansion.","expect","expect,","expect.","expect:","expectation.","expected,","expens","expensive.","experi","experiment","experiment,","experiment.","experiment?","experimentalist","experiments,","experiments.","experiments.core)","experiments:","explain","explain,","explain.","explain:","explan","explanation,","explanation.","explicit","explicitli","explicitly:","exploit","explor","exploration,","expon","exponent,","exponenti","exponential(value,","exponential(value::int64,","exponential.","exponentially.","exponentials,","exponentials.","export","expres","express","expressions.","extend","extens","extent","extent=(","extern","extra","extraordinari","ey","eye.","e}\"","e}\".fmt","e}';","e}`;","f","f'({self.x},","f'leaf({self.char},","f'node({str(self.left)},","f'{self.name}:","f(2)=1.","f(3)=2.","f(\\mathbf{x})","f(\\mathbf{x}).","f(\\mathbf{x})d\\mathbf{x}.","f(\\mathbf{x})d\\mathbf{x}},","f(\\mathbf{x})d\\mathbf{x}}.","f(\\xi)","f(a)","f(centers,","f(cpu(),","f(cudadevice(),","f(n)","f(n),","f(n).","f(n)}","f(n)}.","f(x')","f(x(t+\\delta","f(x)","f(x)).item())","f(x),","f(x).","f(x)},","f(x,","f(x_t),","f(x_t).","f(z)","f(z)!","f(z).","f(z):","f(z)=z^2.","f)","f*g=c","f,","f.","f.write(\"{0}\\t{1}\\n\".format(*point))","f.write(\"{0}\\t{1}\\n\".format(p.x,","f1)","f1+f2)","f2))","f64","f64)","f64))","f64)).exp()","f64)).exp();","f64).log2()","f64).sqrt()).collect()","f64).sqrt();","f64);","f64,","f64;","f:","f=f,","f[n]","f^{(n)}(x)","f_1","f_1(p)","f_1,","f_2","f_2(p)","f_2,","f_3","f_3(p)","f_3,","f_4","f_4(p)","f_4,","f_val","f_val_ab","fabs(a[pivot","fabs(eqns[pivot][i]))","fabs_const:","face","facet","fact","fact,","factor","factor,","factor[1:half])","factor[1:half],","factorial.)","factors)))","factors.","fail","failure_count","failure_count))","failures')","fair,","fairli","fall","fals","false)","false):","false):6}\".fmt","false);","false;","false})","familiar","famou","fan","fano","fano,","fantast","faq","far","far.","fashion","fashion,","fashion.","fast","fast!","fast,","fast.","fast?","faster","faster,","fastest","favor","favored.","favorit","feasibl","featur","feature!","features,","features;","februari","fed","feebl","feel","female,","fern","fern\"","fern,","fern.","fern:","festival.","few","few.","few:","fewer","fft","fft'","fft(&mut","fft(&x);","fft()","fft(doubl","fft(opr.wfc)","fft(wfc_k,","fft(wfc_r)","fft(x)","fft(x:","fft)","fft))))))","fft,","fft.","fft.core","fft.process(x.as_mut_slice(),","fft:\"","fft;","fft_output","fftplanner::new(false);","fftplanner::new(inverse);","ffts.","fftw","fftw)","fftw3","fftw_backward","fftw_backward,","fftw_complex","fftw_destroy_plan(p);","fftw_estimate);","fftw_execute(p);","fftw_forward),","fftw_forward,","fftw_plan","fftw_plan_dft_1d((int)n,","fftw_plan_dft_1d(static_cast(x.size()),","fi","fi)","fianc","fiance.recieveproposal(this);","fiance:","field","field,","fields:","fig,","fig.colorbar(","fig.savefig(\"domain.png\")","fight","figur","file","file),","file,","file.","file.flush()","file.gp","file::create(&path)","file_0000.dat,","file_0001.dat,","file_0002.dat,","filenam","files,","files;","fill","fill\"","fill,","fill.","fill?","fillstep","filter","filter$(in_circle$(?,","filter$(x","filter)","filter,","filter,\"","filter.","filter.length);","filter.shape[0]),","filter.shape[1]),","filter:","filter::array{t,","filter?","filter[i","filter_array):","filter_array,","filters\"","filters,","filters.","filters:","final","final_bitstr","final_canvas).all()","final_canvas,","final_str","finally,","find","find;","find_neighbors(","find_neighbors(c,","find_neighbors(canvas,","find_neighbors(grid,","find_neighbors(struct","find_neighbours(canvas,","findfirst(m","findstablemarriages(list","findstablemarriages(women,","findstablematches(men:","fine","fine.","finger","finger.","fingerprint","fingers?","fingertips,","finish.","finished;","finit","finite:","first","first)","first,","first.","first;","first[i]);","first[k","first[k];","first_point_it","firsti","firstly,","firxt","fit","fix","fl,","flags,","flajolet","flatmap","flavor.","fld(13","fld(k,","fld(year,","fledgl","flexibl","fli","flip","flip(children)","flip.","float","float)","float):","float,","float.","float64","float64(point.x","float64)","float:","floats,","flonum","flood","floor","floor(abs(f(z(x,y)))))","floor(x/bin_width)","flowchart","fluctuat","fluid","fluids,","flush","fmap","fmt.print(\"[\")","fmt.printf(\"%9.4f","fmt.printf(\"%d","fmt.printf(\"[%f]\\n\",","fmt.printf(\"i","fmt.printf(\"x=%f","fmt.println(\"[#]\\nmodulu","fmt.println(\"[#]\\nsubtract","fmt.println(\"[#]\\ntim","fmt.println(\"[#]\\nveloc","fmt.println(\"[0.0","fmt.println(\"[1.0","fmt.println(\"[2.0","fmt.println(\"\\nencoded:\",","fmt.println(\"]\")","fmt.println(\"codebook:\")","fmt.println(\"decoded:\",","fmt.println(\"gauss","fmt.println(\"gaussian","fmt.println(\"ha","fmt.println(\"origin","fmt.println(\"solut","fmt.println(\"th","fmt.println(\"thi","fmt.println()","fmt.println(check1)","fmt.println(check2)","fmt.println(string(r),","fmt.println(time)","fmt.println(vel)","fmt:","fmt_tree","fmt_tree:","fn","focu","focus","follow","follow;","following,","following:","followit","follows)","follows,","follows:","food","footbal","for(","for)),","for.","forc","foreach","foreach($year","forego","forest","forev","forg","forgotten","form","form\"","form,","form.","form:","formal","formalism.","formally):","formally,","format","format!(\"april","format!(\"march","format!(\"output{}.dat\",","format!(\"{:18}\",","format!(\"{:?}\",","format!(\"{}\\t{}\\n\",","format,","former,","formerli","formula","formula,","formula:","formulas,","formulations.","forth","fortran","fortran,","fortunately,","forward","forward,","forward.","forward_dict","forward_dict[char]","found","found,","foundat","four","four:","fourier","fprintf(\"not","fprintf(\"perc","fprintf(\"th","fprintf('%u","fprintf('\\n')","fprintf('\\nbf","fprintf('\\ndf","frac","fractal","fractals,","fraction","fraction,","fraction;","fractions).","framework,","frederick","free","free!","free(heap","free(q","free(q.data);","free(stk.data);","free(tree);","free,","free.","free_group(men,","free_group(struct","free_group(women,","free_queu","free_queue(q);","free_queue(struct","free_queue:","free_stack","free_stack(stk);","free_stack(struct","free_stack:","free_tre","free_tree:","free_tree_free_array","free_tree_free_array:","free_tree_free_kid","free_tree_free_kid:","free_tree_return","free_tree_return:","freefal","freeli","freq","freq,","freq.emplace_back(1,","freqmap","freqmap[char]","freqmap[char].freq++","freqmap[char];","frequenc","frequencies,","frequencies.most_common()","frequency)","frequency,","frequency.","frequency;","frequency]","frequency_array(message)","frequency_array(str)","frequencymap","frequencymap.entryset())","frequent","friday","friend","friendlier,","from(input:","from,","from.","fromintegr","front","front(&self)","front()","front():","front();","front(self)","front,","front_point","front_pointer.reset();","front_pointer:","front_pointer;","frontel","fst","full","full,","full_linear_output","fulli","fulllinearoutput","fun","fun.","func","func(a,","function","function'","function(a,","function(canvas)","function):","function,","function.","function:","function?","functions,","functions.","functions.6.lundmark,","functions:","functions;","functions?","fundament","funky,","furious","further","further,","fuss!","futur","future!","future,","future.","fuzzier","f}{\\partial","g","g'","g''","g'')","g')","g()","g():","g(\\xi),","g(r)","g(x)","g(x,y)","g,","g.","g=g):","g[n]","g_i","g_x","g_y^2}","g_{\\text{total}}","gale","galeshapley(men,","galeshapley(men::preferences,","galeshapleyalgorithm","galeshapleyalgorithm.c","galeshapleyalgorithm.rungaleshapleyalgorithm(women,","gambler!","game","game\"","game).","game,","games,","games.","gammison","gases,","gate","gate,","gate:","gates,","gathro","gathros,","gauss","gauss'","gauss,","gauss.","gauss_jordan(&mut","gauss_jordan(a:","gauss_jordan(doubl","gauss_jordan_elimination!(a)","gauss_jordan_elimination!(a::array{float64,2})","gauss_jordan_elimination(a)","gauss_jordan_elimination(a):","gausseast","gaussian","gaussian,","gaussian.","gaussian;","gaussian?","gaussian_elimination!(a)","gaussian_elimination!(a::array{float64,2})","gaussian_elimination(&mut","gaussian_elimination((doubl","gaussian_elimination(a)","gaussian_elimination(a):","gaussian_elimination(a:","gaussian_elimination(doubl","gaussian_valu","gaussianelimin","gaussianelimination(a","gaussianelimination(a)","gaussianelimination(a);","gaussianelimination(double[][]","gaussianelimination(std::vector","gaussians.","gaussjordan","gaussjordan(a","gaussjordan(a)","gaussjordan(a);","gaussjordan(double[][]","gaussjordan(std::vector","gave","gcd","gcd_minus(128","gcd_minus(a,","gcd_mod(64","gcd_mod(a,","gdwarf","gem","gender","gener","general,","general.","generate_codebook","generate_codebook(*huffman_tree);","generate_codebook(const","generate_codebook:","generate_codebook_branch","generate_codebook_branch:","generate_codebook_recurs","generate_codebook_recurse:","generate_codebook_recurse_don","generate_codebook_recurse_done:","generate_tre","generate_tree(2,","generate_tree(3,","generate_tree(const","generate_tree(input);","generate_tree(int","generate_tree:","generate_tree_branch","generate_tree_branches:","generate_tree_count_char","generate_tree_count_chars:","generate_tree_don","generate_tree_done:","generate_tree_leav","generate_tree_leaves:","generate_tree_leaves_count","generate_tree_leaves_counters:","generate_tree_leaves_setup","generate_tree_leaves_setup:","generate_tree_one_leaf","generate_tree_one_leaf:","generate_tree_ret","generate_tree_ret:","generatecodebook(root","generatecodebook(root)","generation:","generators.","genet","genius.\"","genpreferences(mannames::vector{string},","genpreferences(mnames,","genuin","geometr","geometri","geometry.","georg","get","get,","get;","get_code(codebook,","get_code(const","get_queu","get_queue(size_t","get_queue(sizeof(struct","get_queue:","get_stack","get_stack();","get_stack(size_t","get_stack(sizeof(struct","get_stack:","getchildren():","getclass().getname()","getfrequ","gethashcode()","getid():","getmatch():","getmate()","getname():","getnexttopchoice();","getpreferences():","getpreferredmates()","getter\"","getter.\"","getx()","gety()","giallouraki","gif","gift","gift\"","gift)","gift))","gift)))))","gift.","gift.add(new","gift.get(0);","gift.len()","gift.remove(start)","gift.size());","gift.stream()","gift.sublist(1,","gift:","gift[0]","gift[j]","giftwrap","giftwrap)","gimp,","girl","girl.prefer","girlfriend,","girls)","girls);","git","gitbook","github","github)","give","given","given_id","given_radiu","given_radius❗️","givennodes)","givennodes.tolist();","glanc","glance,","global","global_random_device;","global_rng(global_random_device());","global_rng);","glory!","gnuplot","gnuplot,","gnuplot.","go","go!","go,","go.","goal","goal,","gobbledygook","goe","going.","gone","good","good!","good,","googl","gotta","gotten","gpu","gpu,","gpus)","gradient","gradient,","gradient.","gradient:","graham","graham_scan!(points)","graham_scan!(points::vector{point})","graham_scan(gift):","graham_scan(mut","graham_scan(points);","graham_scan(std::vector&","graham_scan(struct","graham_scan(test_gift)","grahamscan","grahamscan(list","grahamscan(point","grahamscan(points)","grahamscan(points);","grain","grant","graph","graphic","graphics.","graviti","gray,","great","great!","great,","great.","greater","greatest","greatli","greec","greek","green","green,","gregorian","grew,","grey","greyscal","grid","grid,","grid.","grid;","grid[1:2,:]","grid[2,:]","grid[3,:]","grid[neighbor_x][neighbor_y]","grid[x][y]","grid_ext","grid_extents)","grid_extents,","grid_extents/2","gridlin","gridlines(f_val,","gridlines(x,y)","gridlines(x,y))","gridlines.","grid{","groceri","ground","group","group.","groups,","grover'","grow","grown","grows.","grumpili","gt","gtx","guarante","guess","guid","guide,","guide.","guidelin","guston","gustorn","guy","guy.engageto(girl);","guy.prefer","guy.preferences)","guys)","gx","gy","gy.^2)","g|\\psi(\\mathbf{r},t)|^2","h","h(p)","h(z)","h.len()","h.pop().(*node)","h.pop().(*node),","h_r","hack:","hacki","hai","hairs.","half","half)","half,","half.","half:","halfway","hall/crc","hamiltonian","hamiltonian.","hamiltonians.","hamzaoui,","hana","hand","hand,","hand.","handi","handl","hands,","hans,","happen","happen!","happens).","happens,","happens:","happili","hard","hardwar","hardware,","hardware...","hardware;","harm","harmon","harsh","has_cuda_gpu()","has_partner(self):","hasfiance()","hash","hashmap","hashmap)","hashmap,","hashmap::new();","hashmap<>(),","hashmap<>();","hashmap};","haskel","haskell,","hast","hausdorff","have","have,","have.","haven't","head","header","heap","heap'","heap)","heap*","heap,","heap.init(h)","heap.pop(h).(*node)","heap.push(h,","heap_data,","heap_data]","heap_free(&heap);","heap_free(struct","heap_len,","heap_len]","heap_len],","heap_pop","heap_pop(&heap);","heap_pop(struct","heap_push","heap_push(&heap,","heap_push(struct","heap_push:","heap_push_don","heap_push_sift_up:","heap_size,","hear","heard,","heart","heart\"","heart,","heart.","heartili","heat","heavili","height,","height.","heights,","heisenberg","held","help","helper","helper::make_decoder(first,","helper::make_encoder(*decoder);","helps.","henc","hence,","henrik,","here","here'","here,","here.","here:","here;","here?","hermitian","hero","heroic","hesit","hexagons?","hidden","hide","high","high!","high,","high.","higher","higher)","higher,","highest","highlight","highlighted,","himself","himself!","hire","histep","histogram","histogram[bin]","histogram[i,j])^2","histograms\"","histor","histori","history,","hit","hitch...","hobbi","hobbies:","hoist","hold","hold.","holiday","home.","honest","honest,","honestly,","honkit","hood","hop","hope","hopefulli","hopefully,","horizont","horribl","host","hot","hotli","hour","hous","housdorff","how?","however,","hs","hsl","hsv","hsv,","hsv2rgb(angle(real_f(z(x,y)),","html","https://discord.gg/pb976sy.","https://discord.gg/pr2e9s6","https://github.com/alanforr/complex","https://github.com/algorithm","https://www.algorithm","https://www.twitch.tv/leioslab","https://www.youtube.com/user/leioso","hue","huffman","huffman,","huffman.","huffman::encoded_string(to_be_encoded);","huffman_decode(codebook,","huffman_encode(codebook,","huffman_tre","huffman_tree,","huffman_tree:","huffmancod","huffmancoding();","huffmancoding.c","huffmancoding.decode(result);","huffmancoding.encode(\"bibb","huffmancoding.nod","huffmanencod","huffmantre","huffmantree(\"bibbity_bobbity\");","huffmantree(str","huffmantree,","huffmantree.createtree();","huffmantree.decode(encoded));","huffmantree.encode();","huffmantree::branch","huffmantree::from(input);","huffmantree::leaf","huge","hull","hull)","hull))","hull,","hull.","hull.add(0,","hull.add(pointonhull);","hull.append(point)","hull.append(point_on_hull)","hull.append(pt)","hull.get(i);","hull.get(m));","hull.length;","hull.set(i,","hull.set(m,","hull.size();","hull.slice(0,","hull.sort(comparator.comparingdouble(point","hull.sublist(0,","hull.unshift(pivot);","hull:","hull;","hull[","hull[0]","hull[1])","hull[1],","hull[i","hull[i],","hull[i]];","hull[m]]","hull_point","hull_points,","hull_points;","hull_points[0]));","hull_points[15];","hullpoint","hullpoint)","hullpoints[len(hullpoints)","human","hundr","hundred:","hungarian","hunter'","husband,","hut","hutchinson","hutchinson)","hutchinson_op","hutchinson_op,","hutchinson_op[0];","hyper","hypothet","h}{2","i'll","i'm","i)","i))","i))))","i)))))","i))))))","i))));","i);","i)]","i)];","i*dx","i*siz","i+(length(filter)/2)","i++;","i+1):","i,","i.","i.1).norm()","i.e.,","i32","i32,","i32queu","i32queue.dequeue().unwrap());","i32queue.enqueue(4);","i32queue.enqueue(5);","i32queue.enqueue(6);","i32queue.front().unwrap());","i32queue.size());","i32stack.pop().unwrap());","i32stack.push(4);","i32stack.push(5);","i32stack.push(6);","i32stack.size());","i32stack.top().unwrap());","i32stack:","i64","i64)","i64);","i64,","i;","i=0:18446744073709551615","i\\hat{h}_k]dt^2}{2}}\\right]\\psi(\\mathbf{r},t)","i\\hbar","i\\sin(\\theta))","i]","i];","iceberg","icompar","icon","id","id)","id);","id,","id:","id::int64","id;","idea","idea,","idea.","idea:","ideal","ideal,","ideal.","ideally,","ident","identif","identifi","idft","idft)","idiv","idx","idx)","ieee","ieee,","if","if($servois)","if(($d","if(22","if(a","if(isapprox(y,","if(isapprox(z,","if(mod1(i","if(n","if(points.empty())","if_tru","if_true:","iffalse:","ifft","ifft(np.multiply(fft(signal1),fft(signal2)))","ifft(opr.wfc)","iftrue:","ignor","ignored.","ilist","ill","im","im)","im*0.5*opr.v*par.dt)","im*0.5*par.k.^2*par.dt)","im;","im_tim","im_time,","im_time:","im_time::bool","im_time;","im_val","im_val::bool)","imag","imag(f(z))","image),","image,","image.","image:","image_resolution)","image_resolution))","images!","images,","images.","images/graph","images:","images?","imagin","imaginari","imaginary_f(z(x,y))),","imaginary_f(z)","imagine!","imaging,","immedi","impact","impl","implement","implement,","implement.","implementation,","implementations,","implementations.","implemented.","impli","implicit","implies:","implode(',',","import","importantly,","imposs","impossible,","impress","impressive!","improperly,","improv","improvise.","imput","imtim","imul","in!","in(number)","in,","in.","in2:","in:","in_array($preference,","in_circl","in_circle()","in_circle(doubl","in_circle(float","in_circle(p","in_circle(pos_x,","in_circle(x,","in_circle(x:","in_circle(x_pos::float64,","in_circle:","in_n,","inbetween","inbounds(canvas.shape,","inbounds(canvas_shape,","inbounds(canvas_size,","inbounds(cartesianindex","inbounds(size(canvas),","inbounds(struct","inbuilt","inc","incap","inches,","incircl","incircle($x,","incircle()","incircle(a.x,","incircle(doubl","incircle(r","incircle(x,","incircle(x:","incircle(xpos,","incircle_array","inclined).","inclined,","includ","include,","included\"","inclus","incomplete!","incomprehens","inconsistent.","incorpor","increas","increases,","increases.","incred","incredibly,","increment","increment(doubl","increment(int","increment(v,","increment(v:","indeed.","independ","index","index'","index(&self,","index)","index))))))","index).","index,","index.","index:","index;","index_mut(&mut","indexerror:","indexmut","indexmut};","indic","indices)","indices.","indices.\"","indices[i]","indici","individu","individually.","industri","industry,","ineffici","inefficient,","infin","infinit","infinitesim","inform","information,","information.","information:","ingenu","inher","inhibit","iniit","init","init(par,","init(par:","init(par::param,","init(value:","init_operators(struct","init_params(struct","initi","initial;","initial_canva","initial_canvas.copy()","initial_loc","initial_location,","initial_location.x,","initial_location.y,","initial_location[1],","initialize(@id","initialize(id,","initialized;","initially,","inlin","inner","inner,","innov","inord","inplac","input","input\"),","input)","input,","input.","input.chars().fold(hashmap::new(),","input.chars().map(|c|","input.chars().next();","input:","input;","input_i","input_pt","input_pts[1]","input_pts[1]^2","input_pts[2]","input_pts[2]^2","input_pts[i,","input_pts[tid,","input_pts[tid,1]","input_x","inputpoint","inputpoints)","inputpoints);","inputs.","insecur","insert","insid","instal","instanc","instanceof","instancevariablenames:","instead","instead,","instead.","instead?","institut","instruct","int","int(log2(n))","int)","int):","int)time(null));","int,","int32,","int64}()","int:","int]","int_queue.enqueue(4)","int_queue.enqueue(5)","int_queue.enqueue(9)","int_queue:","int_stack.push(4)","int_stack.push(5)","int_stack.push(9)","int_stack:","integ","integer,","integer.","integer.compare(this.id,","integer>>euclidmod:","integer>>euclidsub:","integers\"","integers.","integr","integral,","integrals:","integrate,","integration!","integration.","integration.\"","integration:","integration:'","integration:~%\")","integrators.","intend","intens","intense.","intent(in)","intent(inout)","interact","interact,","interactions.","intercal","intercept","interest","interest'","interest.choices.indexof(thi","interested!","interested,","interesting?","interestingly,","interfac","interface{}","interface{})","interior","interleav","intermedi","intern","interpret","interpret.","interpretation!","interpretation,","intersect","interv","intervals,","intial","into:","intqueu","intqueue.dequeue();","intqueue.enqueue(4);","intqueue.enqueue(5);","intqueue.enqueue(9);","intqueue.front();","intqueue;","intrins","intro","introduc","introduct","introductori","intstack","intstack.pop();","intstack.push(4);","intstack.push(5);","intstack.push(9);","intstack.top();","intstack;","intuit","intuitive,","intuitive.","intuitively,","invalidargumentexception('not","invent","invers","inverse)","inverse:","inverse_dict","inverse_dict:","inverse_dict['']","inverse_dict[key]","invert","investig","inviscid","involv","inward,","io","ioutputlin","ioutputline[]","iqueu","is!","is)","is).","is,","is.","is...","is:","is:\"","is:\")","is:\");","is:\\n\");","is:\\n%lf\\n\"","is:\\n%lf\\n[#]\\nveloc","is:`);","is:~%\")","is;","is_gaussian(input_pts;","is_leaf(const","isa(huffman_tree,","isa(input_pts,","isa(n,","isfree(candidate,","isfree(m,","isfree(person,","isinme(point","isiz","isize;","isleaf","isleftof(pointonhull,","isleftof(vector","islonely()","ismainmodule:","isn't","isnan(input_y))","isosampl","isosamples\"","issingle():","isstable(men::preferences,","issu","issue!","issue,","issue.","istack","it!","it'","it).","it,","it.","it:","it?","item","item,","item.","item.x","item.x)","item.y)","item:","items,","items.","items;","items?","iter","iterate.","iteration,","iteration.","iterations!","iterations\"","iterations,","iterative_cooley_tukey(&x);","iterative_cooley_tukey(begin(iterative),","iterative_cooley_tukey(doubl","iterative_cooley_tukey(it","iterative_cooley_tukey(x)","iterative_cooley_tukey(x):","iterative_cooley_tukey(x);","itertools::itertools;","itertools;","ith","itself","itself!","itself,","itself.","itz","iz","i{1};","j","j)","j)))))","j),","j)]","j)];","j*dx","j*stride","j+1):","j,","j;","j]","j]))","j]).","j]);","j];","ja","jame","james,","jan","januari","jar","jarvi","jarvis_cross(hull[i","jarvis_cross(point1::pos,","jarvis_cross(pos(0,0),","jarvis_march(const","jarvis_march(gift):","jarvis_march(gift:","jarvis_march(point","jarvis_march(points)","jarvis_march(points);","jarvis_march(points,","jarvis_march(points::vector{pos})","jarvis_march(test_gift)","jarvismarch","jarvismarch();","jarvismarch(arraylist","jarvismarch(gift);","jarvismarch(point","jarvismarch(points)","jarvismarch(points);","jarvismarch.c","jarvismarch.run(points);","java","java,","java.io.filewriter;","java.io.ioexception;","java.lang.math;","java.util.*;","java.util.arraylist;","java.util.arrays;","java.util.collections;","java.util.comparator;","java.util.linkedlist;","java.util.list;","java.util.queue;","java.util.random","java.util.random;","java.util.stack;","java.util.stream.collectors;","java.util.stream.doublestream;","javascript","javascript,","javascript/typescript","jbe","je","jean","jeffrey","jerk","jess","jewish","jge","jie","jimmi","jl","jle","jmp","jne","jnz","job","johann","john","john,","join","joke","jordan","jordan\")","jordan:\")","jordan:\");","joseph","journal","journey","journey.","joy","jr.","jsonserializ","jsonserialize():","jstor,","julia","julia'","julia,","julia;","julian","juliu","jz","k","k)","k))","k)]","k)].abs();","k)];","k,","k.","k.,","k.push(((i","k.push((i","k.push_back((static_cast(i)","k.reserve(res);","k:","k::vector{complex{float64}}","k::vector{float64}","k;","k[i]","ke,","ke.push(complex::new(","ke.reserve(size);","ke:","keep","kelley,","kept","kerckhoffs'","kernel","kernel!","kernel!(input_pts,","kernel,","kernel.","kernel:","kernel[i,j]","kernel_function(x,","kernel_s","kernel_size)","kernel_size))","kernel_size*0.5","kernelabstract","kernelabstractions.jl,","ket","key","key(key)","key)","key,","key.","key::char","key;","key=(p","key=(point","key=lambda","keys(men)","keys.","keyword","keywords,","kid","kill","kind","kinda","kinemat","kinet","kinetic","kineticop","kmax","knew","knob","know","know!","know,","know.","know:","knowledg","knowledge,","knowledge.","knowledge;","known","known:","konrad,","konstantin","kotlin","kotlin.math.absolutevalu","ks","ks)","kstep","kthxbye","l","l(c(w))","l)","l,","l.","l:a","l:b","l:c","l]","l_1","l_2","lab","label","label,","label=\"phas","label_0","label_0:","label_1","label_1:","label_2","label_2:","labels,","labels.","laboratories,","labview","lack","lagrangian","lambert","land","landscap","lang","lang:\"julia\"](code/julia/conv.jl)","lang=\"jl\"","langevin","languag","language'","language,","language.","languages,","languages.","laplacian,","larg","larger","largest","last","last)","last);","last,","last.","last;","last;)","lasty))))))","lasty]","later","later):","later,","later.","latest","latex","latex.","latter","law","lay","layer","lc","lea","lead","lead,","leader","leadit","leads'","leads)","leads,","leads;","leads_end","leads_end,","leaf","leaf(*t))","leaf(_,","leaf(c,","leaf(char,","leaf(char:","leaf(i,","leaf(int","leaf(symbol,","leaf(t,","leaf(weight,","leaf)","leaf.","leaf;","leap","learn","learning!","learning,","learning.","leastcommongend","leav","lecture.","lectures,","lefmost","left","left,","left.","left.count()","left.decode_dfs(&input[1..],","left.dfs(code.clone()","left.freq","left.weight","left:","left::union{leaf,","left;","left?","left_most_point(point","left_most_point(points)","left_most_point(struct","leftchild","leftchild,","leftchild.weight","leftchild;","leftmost","leftmost.x","leftmostpoint(point","leftmostpoint(points)","leftov","legend","legend,","legend.","lein","len","len()","len(a)","len(a[0])","len(children):","len(codebook)","len(d)","len(d_in)","len(encoded_message)","len(filter_array))","len(filter_array)),","len(gift)","len(message)","len(n)","len(n.children)","len(node.children)","len(old)","len(queue)","len(self)","len(self.__list)","len(stack)","len(trees)","len(x)","len(x))","len(y)","len)","len))))","len)]","lend","length","length(bachelors)","length(children)","length(filter)","length(filter)):i","length(points)","length(q)","length(s)","length(x)","length(x))","length(y)","length)","length)))","length,","length.","length;","length]","less","less(i,","lesson","lest","let","let'","letter","letter))","letter,","letter;","letters:","level","level.","levels:","leverag","lh","lhs(std::move(lhs)),","lhs,","lhs.frequenc","lhs.i","lhs;","librari","library.","licens","license.","license.md).","license.md;","licensing:","lie","life","life.","lift","liftarray","liftarray2","liikt","like","like,","like.","like:","likelihood","limit","limits.","line","line),","line,","line.","line:","linear","linear\"","linear(a::array{float64})","linear)","linear,","linearalgebra","linearli","linecolor","lines,","lines.","linger","link","linkedlist","linkedlist();","links:","lisp","list","list\"\"\"","list($b,","list()","list())","list(),","list();","list(a,","list(b,","list(c,","list(follows);","list(men).shuffle(random);","list(metropolis_iterate(x0,","list(set(gift))","list(women).shuffle(random);","list(x,","list(y,","list,","list.","list:","list;","list[man]","list[t]","list[woman]","listarray","listarray)","listarray,","listextens","listextensions.c","liter","literatur","literature,","littl","little,","live","livecod","liverpool","livestream:","load","loc","loc)","loc,","loc::cartesianindex,","loc[1]","loc[1]},","loc[1]}};","local","localdictionary)","localdictionary);","localdictionary.add(node.key[0],","locat","location!","location):","location,","location.","location.x","log","log(input_pts[1]))","log(input_pts[tid,1]))","log(r_0)","log2","log_2(n)","logarithm","logarithm\"","logarithm):","logarithm,","logarithm.","logarithmic(a::array{float64},","logarithmic(a[length(a)/2+1:end],","logic","logic.","logn","logscal","logscale,","lolatomroflsinnlos,","lolcod","lone","lonely!'","lonely.","lonely?","lonelyfollow","lonelyfollow.proposetonext();","lonelyfollows)","long","long)","long,","longer","longer.","look","loop","loop)","loop,","loop.","loop:","loops,","loops.","lose","lossless","lost","lot","lot.","love","loves.","loves:","low","low_index","lower","lower.","lowest","lowest.","lt","lua","luckily,","ludwig","lunar","ly","m","m\"","m'","m)","m))","m++;","m,","m.","m.!)","m.assoc","m.empti","m.fromlist","m.fromlistwith","m.getkey());","m.getpreferredmates());","m.getvalue()));","m.getvalue());","m.insert","m.propose(women)","m.receiveoptions(women);","m.tolist","m;","m?","m]","m]g[m]","m_pi","machin","machine,","machine.","machines,","machines.","made","made.","mag","magic","magic,","magic.","magic:","magnitud","magnitude!","magnitude()","magnitude,","magnitude.","magnitude:","magnitude_shading(f_val)","magnitude_shading(f_val):","magnitude_shading(x,y)","magnitude_shading(x,y),","mahdi","mahesh","mailman","main","main()","main():","main(args:","main(string[]","main:","mainli","major","mak","make","make([]float64,","make([]point,","make([]rune,","make(codebook)","make(map[rune]*node)","make_codebook(self)","make_decoder(it","make_encoder(nod","make_person_list(size_t","makeoper","makepair","makeparamet","makequeue(iterable)","makequeue(nodes);","male,","malloc","malloc(4","malloc(length","malloc(sizeof(doubl","malloc(sizeof(double)","malloc,","man","man(\"a\"),","man(\"b\"),","man(\"c\"),","man(\"d\"),","man(\"e\")","man(name:","man(str","man):","man*):","man.choic","man.choices)","man.has_partner:","man.prefer","man.propose_to_next()","man;","manag","mani","manipul","mannames))","mantissa","mantissa.","manual","manually.","map","map$(","map$(forward_dict[]))","map$(location.__add__))","map$(p","map$(pow$(?,","map$(recursive_fill$(canvas,","map$(t","map$(weight)","map,","map[c]","map[char,","map[rune]str","mapm_","maps,","march","march,","march.","march}&","margin","mariu","mark","markdown","market","markov","marri","marriag","marriages\"\"\"","married,","marsaglia","mask","mask:","mass","massiv","master","mat","mat,","mat.xi","mat.xx","mat.xz","mat.yi","mat.yx","mat.yz","mat.zi","mat.zx","mat.zz","mat1.shape[1]","mat2):","mat2.shape[0],","mat2.shape[1])","mat:","match","mate","mate)","mate,","mate.","mate.m","mate;","materi","material;","mates)","math","math,","math.","math.ab","math.abs(a)","math.abs(a);","math.abs(a[pivot][col]))","math.abs(b)","math.abs(b))","math.abs(b);","math.abs(piestim","math.abs(radius);","math.abs(row[c]);","math.acos(","math.atan2(a.i","math.atan2(float64(point.i","math.atan2(p.i","math.const","math.fft","math.floor(math.random()","math.floor(n","math.funct","math.max(0,","math.max(signal.length,","math.pi","math.pi)","math.pi);","math.pow(point.x,","math.pow(point.y,","math.pow(y,","math.rang","math.sqrt","math.sqrt(math.pow(x,","math/ceil","math/pi","mathemat","mathematical.","mathematician","mathematics,","mathematics.","mathjax.hub.queue([\"typeset\",mathjax.hub]);","mathématiqu","matlab","matlab,","matmul(struct","matmult","matplotlib.cm","matplotlib.color","matplotlib.colors.hsv_to_rgb(hsv)","matplotlib.pyplot","matric","matrices.","matrices:","matrix","matrix!","matrix)","matrix,","matrix.","matrix:\"","matrix:\")","matrix::new(","matrix;","matrix_mul(self,","matrixmultiplication(double[][]","matter","matter.","matters!","matthew","max","max(1,","max(len(signal),","max_i","max_index","max_row","max_valu","max_x,","max_y;","maximum","maximumbi","maximumby)","maxval","mayb","maybegetacharact","mayberoot.foreach(c","mayberoot.getorelse(leaf('?',","mayberoot:","mayl","mazzuca","mazzuca.","mcmc,","me,","me.","mean","mean,","mean.","mean?","mean_valu","mean_value)","meaning","meaningful.","means,","meant","meanwhile,","measur","measurement,","mechan","mechanics!","mechanics,","mechanics.","media,","mediev","member","members.","memcpi","memcpy(dst,","memcpy(points,","memcpy(tmp","memcpy(tmp,","memcpy(tmp_point","memcpy(wfc_k,","memcpy(wfc_r,","memcpy,","memori","memory,","memset","memset(y,","memset,","men","men)","men)):","men);","men,","men.foreach(m","men.select(&:lonely?)","men.to[queue]","men/women","men:","men:')","men[bachelor]","men[husband]","mention","mentioned,","mentowomen","mentowomen)]","mentowomen,","mentowomen::pairs,","mentowomen[bachelor]","merg","mervin","mess","messag","message)","message):","message,","message,:cod","message.","message:","message:',","messeng","messenger'","messenger).","messenger;","messi","met","meter","method","method!","method'","method),","method,","method.","method.\"","method:","methodolog","methods\"","methods,","methods.","meton","metric","metric.","metropoli","metropolis\"","metropolis_iterate()","metropolis_iterate(x0,","metropolis_step(x)","metropolis_step(x,","michael","mid","mid)","mid))","middl","middle)))","midpoint","migrat","millennia","millennia.","million","min(1,","min(gift)","min(gift,","min(location)","min(p)","min(true_values))","mind","mind,","mind:","mine.","minesweep","minim","minimum","minimum(tuple(loc))","minimumbi","minimumby)","minu","minut","mirror","mislead","mismatch","misrepresent","miss","missed,","missed.","mit","mix","mix,","mix:","mkay","mktabl","mname","mod","mod(15","mod(19","mod(2","mod(4","mod(a,","mod(a,b);","mod(a:","mod(int","mod(year,","mod1(x,","mod_check","mod_check:","mod_loop","mod_loop:","mode","model","models)","moder","modern","modif","modifi","modulo","modulo(a,b)","modulu","modulus.\"","molecules,","moment","moment,","momentum","momentum,","momentum.","monday","mont","monte_carlo(10000000);","monte_carlo(samples)","montecarlo","montecarlo();","montecarlo(1000);","montecarlo(100000)","montecarlo.c","montecarlo.run(10000000);","montecarlointegr","montecarlopi","montecarlopi(100_000);","month","month)","month,","month.","months),","months,","months:","moon","moon'","moon).","moon,","moon.","more","more,","more.","moreover,","morri","morris'","morsel","most,","mostdesir","mostli","mother","mother'","motion","motiv","mov","movap","move","move,","movement","movements.","moves.","movi","movq","movsd","movup","msg","msg)","msg_data,","msg_data]","msg_len,","msvc","mu","mu)","mu,","mu;","mu[1],","mu[2]]","much","much,","much.","muller","mulsd","mult","multidimension","multidimensional,","multimedia","multipl","multipli","multiplication,","multiplication.","multiplication:","multiplications.","multiply,","mut","mutabl","my::queu","my::stack","myself","mystifying,","n","n'","n(doubl","n(v,","n(v,a),","n(v:","n)","n))","n),","n).exp()));","n):","n);","n+1","n,","n.","n.children","n.children)","n.children_s","n.count()))","n.id)","n.id);","n.value),","n.value);","n/2","n:","n::int64)","n;","n=1","n=1.","n=100)","n=100,","n=100:","n=2","n=2,","n=3,","n=4","n=7","n=7,","n[i]","n[i],","n[i].freq","n[j]","n[j],","n[j].freq","n\\time","n];","n^{\\text{th}}","n_2}","n_item","n_items:","n_items_float","n_items_float)","n_sampl","n_trial","n_trials:","n_v","n_v.","n_v:","n_{v+1}","n_{v}}","na","naiv","name","name\"","name)","name):","name,","name:","name;","namedtupl","namedtuple(\"point\",","namedtuple('testresults',","namely,","namely:","names,","namespac","nan","nan,","nan]","nand","nanosecond","natur","naïv","ndrange=size(input_pts)[1])","ne","near","nearbi","nearest","nearli","neat","neat?","necessari","necessarili","necessary!","necessary,","necessary.","need","need,","need.","needed,","needed.","needed?","neg","negative,","negative.","negoti","neighbor","neighbor,","neighbor.","neighbor_i","neighbor_x","neighbors);","neighbors,","neighbors.","neighbors.append(possible_neighbor)","neighbors.push_back(possible_neighbor);","neighbors:","neighbors;","neighbors[4];","neighbour","nest","never","nevertheless,","new","new(","new()","new(10.0,","new(node)","new(nodeheap)","new(par:","new(rows:","new(vector{node}(),","new(x:","new(xmax:","new(zeros(res),","new.","new:","new_c","new_c[0]","new_c[i]","new_d","new_d[0]","new_d[i+1]","new_d[i]","new_freq","new_nod","new_node;","new_tre","new_tree)","new_val","new_val)","new_val):","new_val:","new_val;","new_valu","new_value)","new_value))","new_value):","new_value);","new_value;","new_weight","new_x","new_x[k","newchildren","newchildren.","newdata","newdata.","newer","newlin","newline,","newlonelyfollow","newlonelyfollows.add(follow);","newlonelyfollows;","newnod","newnode)","newnode.char","newnode.freq","newton'","newtonian","next","next!","next((i","next,","next.","next...","next:","next;","next_choice(self):","next_index;","next_nod","next_nodes;","next_po","next_pos;","nextpo","nice","nice,","nicol","night","nil","nil)","nil))","nim","nitems)","nmsd","no.","nobodi","nocontour","node","node!.","node'","node(0,","node(1,","node(10,","node(11,","node(12,","node(2,","node(3,","node(4,","node(5,","node(6,","node(7,","node(8,","node(9,","node(const","node(freq),","node(id::int64)","node(int","node(key.tostring(),","node(leaf(b,","node(left","node(leftchild.key","node(lh","node(node(leaf(o,","node(node(leaf(y,","node(num_row)","node(num_rows,","node(rowcount);","node(str","node(tree_left,","node(value:","node)","node))","node)))","node))))","node));","node):","node*));","node*)dequeue(&q);","node*)malloc(num_children","node*)stack_pop(&stk);","node,","node.","node.children!","node.children![0])","node.children![1])","node.children)","node.children.append(child)","node.children.each{","node.children.s","node.children:","node.children?.append(child)","node.children?.count","node.children[0]","node.children[1]","node.createbranch(leftchild,","node.createleaf(n.key,","node.data","node.left","node.new(levels,","node.right","node.right;","node1","node1,","node1.weight","node10","node11","node11,","node12","node12});","node1[2]","node2","node2,","node2.weight)","node2[1]","node2[2]","node3","node3,","node3});","node4","node4});","node5","node5,","node6","node6});","node7","node7,","node8","node8});","node9","node9});","node:","node>>bf","node>>children","node>>children:","node>>data","node>>data:","node>>dfsinorderbinarytre","node>>dfsrecurs","node>>dfsrecursivepostord","node>>dfsstack","node[])","node_ptr","node_queu","node_stack","node_stack(end)","node_stack{end};","nodeheap","nodeheap)","nodeprioritylist","nodeprioritylist()","nodeprioritylist(list","nodeprioritylist(nodes);","nodeprioritylist.","nodeprioritylist.add(parentnode);","nodeprioritylist.pop();","nodes)","nodes,","nodes.","nodes.count;","nodes:","node{std::move(vec),","nois","noise.","nokey","nominally,","non","noncommerci","none","none)","none:","nonlinear","nonzero","noon","noprefix","nor:","norm","norm2","normal","normalize!(histogram)","normalize(kernel)","normalize:","normalize=false):","normalize=true)","north","north,","northeast,","northwest","not,","not.","not.\"\"\"","not:","not_bt","not_bt:","notabl","notat","notation","notation\",","notation)","notation),","notation,","notation.","notches)","note","note,","note:","notebook","noth","notic","notifi","now","now)","now,","now.","nowaday","nowadays,","np","np.abs(f_val)","np.abs(np.sin(np.pi","np.abs(opr.wfc)","np.angle(f_val))","np.arange(","np.arange(xmin","np.arange(xmin,","np.argmax(abs(a[pivot_row:,","np.array([","np.array([*output_gen$[:10000]])","np.array([10.,","np.array([[2,","np.array([self.x,","np.array):","np.average((height","np.concatenate((np.arange(0,","np.conj(wfc_r)","np.dot([[","np.dot([[1.0],","np.empty(res,","np.exp(","np.fft.fft(opr.wfc)","np.fft.fft(wfc_r)","np.fft.ifft((par.k","np.fft.ifft(opr.wfc)","np.floor(f_val_abs))","np.fromfunction(kernel_function,","np.histogram(x_dat,","np.imag(f_val)))","np.linalg.norm(kernel)","np.linalg.norm(x)","np.linalg.norm(y)","np.linspace(","np.mean(true_valu","np.meshgrid(coords,","np.moveaxis((hue,","np.pi)","np.pi),","np.pi,","np.pi])","np.power(gy,","np.random.choice([x_proposed,","np.random.uniform(","np.random.uniform(xmin,","np.real(f_val)))","np.real(fft_output))","np.savetxt(\"fft.dat\",","np.savetxt(\"out.dat\",","np.sqrt(0.1*kernel_size)","np.sqrt(b))).sum()","np.sqrt(nmsd)","np.sqrt(np.power(gx,","np.zeros((5,","np.zeros((image_resolution,","np.zeros((kernel_size,","np.zeros(a.shape[0]).t","np.zeros(output_size)","npair","npm","nrmsd","null","null)","null);","null,","null;","nullptr)","num","num1","num2","num2,","num_child","num_child)","num_child))","num_child):","num_child);","num_child,","num_child:","num_child::int64)","num_children)","num_children;","num_childs)","num_childs.times{children.push","num_childs:","num_hull_point","num_initial_point","num_op)","num_pair","num_points)","num_row","num_row,","num_row};","num_step","num_steps))","num_steps):","num_steps.","number","number\"","number\":","number'","number):","number,","number.","number;","number\\teaster\"","number\\teaster\")","number\\teaster\");","number\\teaster\\n\")","number\\teaster\\n\");","number_of_partn","number_of_partners)","number_of_partners),","number_of_partners,","number`teaster\"","numberqueu","numberqueue.enqueue(4);","numberqueue.enqueue(5);","numberqueue.enqueue(9);","numbers!","numbers,","numbers.","numbers:","numbers?\"","numberstack","numberstack.push(4);","numberstack.push(5);","numberstack.push(9);","numchild","numchildren)","numchildren:","numcor","numcores)","numelem","numelems)","numer","numerically.","numoutputpoints,","numpi","numrow","numrows,","numthread","numthreads)","nvidia","ny,","n}","o","o(1)","o(1).","o(3)","o(\\log","o(b),","o(log(n))?","o(n)","o(n)!","o(n),","o(n).","o(n^2)","o(n^2).","o(n^3)","o(n^3),","o)","o,","o.","o.frequency));","o3","obj","obj)","object","object,","object.","object.entries(charcounts).map(([key,","objects)","objects.","obnoxi","observ","observation.","observed.","observed;","obsolet","obtain","obviou","obvious","obvious!","obvious.","obvious:","obviously,","ocaml","occur","occur.","occurr","occurred.","occurs.","odd","odd[k];","odds)","odds)))","of","of!","of\"","of:","off!","off,","off.","offend","offer","offici","offset","offset,","offset]","offsets,","ofs(\"sierpinski.dat\");","oic","ok","ok(good)","ok,","okay.","old","old[0","old[l","old_point","old_point.x,","old_point.y,","old_val","old_val)","old_val,","old_val:","old_valu","old_value)","old_value))","old_value):","old_value,","old_value:","oldb","oldb.","older","omega","on","on,","on.","on:","onc","once,","once.","one,","one.","one...","one:","one:p)]","one;","one?","ones.","ongo","onlin","online,","onpropose(partner)","onto","op","op&","op@(oper","opaque,","open","open(\"output\"","open(\"output.dat\",","open(\"sierpinski.dat\",","open(filename,","oper","operation,","operation.","operation:","operations,","operations.","operator!=(const","operator!=(vector","operator&","operator*(const","operator*(doubl","operator*(point","operator*(std::array","operator+(point","operator+(std::array","operator,","operator.","operator:","operator==(const","operator==(vector","operators(len(par.x))","operators(length(par.x))","operators(param","operators(res)","operators)","operators,","operators.","operators:","operators::new(&par,","operators;","opn","oppos","opposit","opr","opr)","opr);","opr.k","opr.ke[j];","opr.pe[j];","opr.r","opr.size,","opr.v","opr.v[i]","opr.v[j].re)","opr.v[j].real)","opr.wfc","opr.wfc,","opr.wfc.clone();","opr.wfc.iter().map(|x|","opr.wfc[j]","opr:","opr::operators)","ops))","opt","optim","optimal,","optimally.","option","option,","option>","option[man]","option[node]","option[node]):","op}","orbit\"","orbits\"","ord","order","order🔤❗️","order).\"","order,","order.\"","ordering,","ordinari","organ","origin","origin,","origin.","origin.x);","origin.y,","origin;","origin=\"lower\"","origin=\"lower\",","original:","originalstr","originaltext","originaltext)","os","oscil","oscillations.","oscillator,","other","other)","other):","other,","other.","other.count()","other.count().cmp(&self.count())","other.count().partial_cmp(&self.count())","other.i","other.id);","other.weight;","other.x,","other.y)","other:","other_point","other_points[i]","others,","others.","otherwis","otherwise,","otherwise.\"\"\"","ourselves.","out","out!","out(number)","out)","out).unwrap();","out);","out,","out.","out.pdf.","out.push_back(std::make_pair(l","out.tex","out.write(\"\\n\")","out.write(output_string)","out:","out;","out[i,","out_n)","out_size)","out_size,","outcom","outcome,","outcome.","outcome:","outcomes.","outdo","outer","outfil","outfile.write(line)","outfile:","outlin","outline,","outpoint","output","output,","output.","output:","output_gen","output_point","output_points)","output_points[i,:]","output_pt","output_pts,","output_pts[tid,1]","output_pts[tid,2]","output_s","output_size)","output_size):","output_str","outputpoint","outputpoints(numoutputpoints);","outputpoints)","outputpoints;","outputs","outputs.","outputsize)","outright","outsid","outsider,","outta","over","over\"","over,","overal","overall,","overcompl","overflow","overjoy","overkill.","overlap","overrid","overwhelm","own,","own.","ownership","p","p(\\mathbf{r},","p(\\mathbf{x})","p(\\mathbf{x}),","p(h)","p(n)","p(n),","p(n).","p(t)","p(x)","p(x)\"","p(x),","p(x).","p(x)dx","p(x)dx,","p(x)dx.","p)","p))))","p):","p);","p)]","p+k","p,","p.","p.first","p.first;","p.getx()","p.gety()","p.i","p.key","p.name).join()}`)","p.plan_fft(x.len());","p.x","p.x,","p.y)","p.y))","p.y)))","p.y));","p.y),","p.y+1),","p.y]","p.y}","p.y},","p0","p0@(x,","p1","p1))","p1)))","p1)))))","p1.0)","p1.1)","p1.x)","p1.y)","p1.y)*(p2.x","p1.y)*(p3.x","p1.y);","p1[0])","p1[1])","p1^2","p2","p2\"","p2)","p2,","p2:","p2^2","p3","p3)","p3):","p3:","p:","p;","p=[a,","p=np","p[0]))","p]","p_1","p_2,","p_2}}{\\vec{p_3","p_3","p_4,","p_4}}","pa","packag","package.\")","package:","pad","page","page,","pages.","pain","paint","pair","pair:","paired,","pairs(map)","pairs)","pairs,","pairs.","palett","panic!(\"couldn't","panic!(\"unexpect","paper","paper,","paper.","par","par,","par.dt","par.dt)","par.dx","par.dx;","par.im_tim","par.im_time:","par.k[i].powi(2)).exp(),","par.res);","par.res;","par.res];","parallel","parallel,","param","param()","param(5.0,","param(xmax::float64,","param)","param,","param:","paramet","parameter","parameters,","parameters.\"\"\"","parameters::new(5.0,","params(doubl","params:","parent","parent_cel","parent_cell{1};","parent_index","parent_index;","parentnod","parse(int,","part","part,","parti","partial","partial_cmp(&self,","partialeq","partialeq,","partialord","partialord};","particl","particle'","particle.","particles\">","particles,","particles.","particular","particular,","particular.","particularli","parties.","partner","partner(self):","partner(self,","partner.nil?","partner.partn","partners.","partners[choice].onpropose(self)","parts.","parts:","parts;","paschal","pass","pass,","pass_count","passes,","past","path","path.display();","path::new(&path_name);","path_nam","patholog","pattern","pattern.","patterns,","paul","paus","pay","pb","pdf","pdflatex","pe,","pe.push(complex::new((","pe.push(complex::new(0.0_f64,","pe.reserve(size);","pe:","peak","peculiar","peek(weights)[2]","peopl","people.","per","percent","percent_error","percenterror","percival,","perfect","perfectli","perform","performance,","performed,","period","periodic,","permut","person","person'","person(name));","person(str","person)","person):","person,","person.","person._partner)","person.c","person.candidates.append(self)","person.generate(4,","person.new(","person:","person{false,","perspective,","perspective;","peter","phase","phase.","phases,","phd","phd,","phd.","phenomen","phenomenon.","philipp","php","php_eol","php_eol);","php_eol;","phrase","phrase)","phrase.flatmap(c","phrase::string)","physic","physical,","physically.","physicist","physicist.","physics,","physics.","physics?","pi","pi\"","pi)","pi))","pi))]","pi).abs()","pi);","pi,","pi/10.0),","pi/xmax,","pi:","pi;","pi_estim","pi_estimate)/math.pi","pi_estimate);","pi_estimate=monte_carlo(n)","pick","pick_preferred(self):","picount","pictori","pictur","piec","piece.","pieces.","piestim","piestimation);","piet","pinch.","pink","pivot","pivot)","pivot)));","pivot));","pivot);","pivot,","pivot.","pivot_angle)","pivot_col","pivot_col]","pivot_col]))","pivot_i","pivot_i]","pivot_row","pivots.","pixar","pixel","pixel.","pk","place","place.","planar","planb)","planck'","plane","plane,","plane.","planes.","planner","planner.plan_fft(n);","plate.","platform","play","pleas","please.","pleasur","plenti","plethora","plot","plot,","plot.","plot:","plot;","plot_output.plt","plots,","plots.","plotted,","plotted:","plotter","plotter.","plotting,","plotting.","plotting:","plt","plt.subplots(1,","plu","pluck","plug","plugin","pm","pm3d","png","pngcairo","po","point","point\"\"\"","point&","point(","point(*p))","point(*t))","point(0,","point(0,14),","point(0.5,","point(1,","point(1.0,","point(15,","point(2,","point(2,8)","point(5,","point(5,7),","point(6,","point(7,","point(9,","point(9,9),","point(b.getx()","point(c.getx()","point(doubl","point(double.max_value,","point(double[]","point(p.x","point(p.x+1,","point(p.x,","point(random(),","point(random.uniform(0,","point(rng.nextdouble(),","point(self.x","point(x,","point(x1,","point(x=0,","point)","point))","point)))","point))))","point));","point),","point):","point*","point*)","point,","point.","point.i","point.matrix_mul(operation);","point.x","point.x,","point.y))","point.y).as_str();","point.z","point.z,","point1.x,","point1.y)","point2","point2.i","point2.x,","point2.y)","point2::pos,","point2d","point3","point3.i","point3::new(","point3::new(0.0,","point3::new(0.20,","point3::new(0.23,","point3::new(0.26,","point3::new(0.85,","point3::pos)","point3d","point:","point;","point[0]","point[]","point[])","point[]:","point[n];","point_array","point_array))","point_i","point_on_hul","point_x","point_y🤛","pointer","pointonhul","pointonhull,","points\"\"\"","points)","points)))","points*","points*)))))","points,","points.","points.add(new","points.aggregate((leftmost,","points.begin()","points.end(),","points.is_empty()","points.reduce((leftmost,","points.retain(|a|","points.size())","points.slice(1).sort((a,","points.sort_unstable_by(|a,","points:","points[0]","points[0],","points[0];","points[1:]","points[1:m]","points[1])","points[1].x))","points[1].y,","points[1]];","points[2..points.len()].iter()","points[2]","points[4]","points[]","points[a].i","points[i+1]","points[i]","points[i])","points[i],","points[i];","points[j]","points[j];","points[m]","points[m]);","points[m],","points[randrange(points.size())];","pointtyp","pointvector","pointvector&","point{x:","point❗️","poison:","polar","polar_angle(&start,","polar_angle(ref,","polar_angle(reference:","polar_angle(start,","polar_angle(struct","polar_angles_sort(point","polar_angles_sort(points,","polar_angles_sort(struct","polar_box_muller!(input_pts,","polar_box_muller(input_pts,","polar_muller_noreplacement!(input_pts,","polar_muller_noreplacement!)","polar_muller_replacement!(input_pts,","polarangle(a,","polarangle(b,","polarangle(point","polarangle(point,","polarangle(ref,","polthier,","polynomi","poor","poor,","pop","pop!(s)","pop(&mut","pop()","pop():","pop();","pop(self)","pop.","pope).","pope;","popular","pore","portal","portion","portraits,","pos(1,","pos(2,","pos(3,","pos(point2.x","pos(point3.x","pos)","pos*2","pos,","pos,acc,","pos:","pos;","pos_i","pos_in","pos_x,","pos_y,","pose","posist","posit","position),","position,","position.","position.'''","positions)","positions,","positions.","positive,","possibilities,","possibl","possible,","possible.","possible_neighbor","possible_neighbor)","possible_neighbor):","possible_neighbor,","possible_neighbors)","possible_neighbors:","possible_neighbors{","possible_neighbour","post","postord","postorder\\n')","posts,","potenti","potential","potential,","potential.","potential.\"\"\"","potentialnextpointonhul","potentialnextpointonhull,","potentialnextpointonhull.","potentialnextpointonhull;","pow($positionx,","pow($positiony,","power","powerful,","powershel","pr","practic","practice,","practice.","practice:","pre","precis","precise)","precise.","precisely.","precision)","precision.","predecessor","predefin","predict","predict?","pref","pref))","pref):bachelors)","prefer","prefer,","preference;","preference_list;","preferences.indexof(man)","preferences:","preferred\"\"\"","preferredm","preferredmates)","preferredmates.remove(0);","preferredmates;","prefers(man:","prefers(men,","prefers(other)","prefers(prefs,","prefers(women,","prefix","prefix,","preform","prefs)","prefs[person])","premis","present","preserv","press,","presum","pretend","pretti","prev","prev_po","prev_pos,","prevalent.","prevent","previou","prevpo","prevpos,","prevpos:","primari","primarili","prime","principl","principle,","print","print!(\"thi","print!(\"{}","print(","print(\"\",","print(\"[#]","print(\"[#]\\nmodulu","print(\"[#]\\nqueu","print(\"[#]\\nrecurs","print(\"[#]\\nstack","print(\"[#]\\nsubtract","print(\"[#]\\ntim","print(\"[#]\\nveloc","print(\"\\(stormer.time)\")","print(\"\\(stormer.vel)\")","print(\"\\(velverlet.time)\")","print(\"\\(velverlet.vel)\")","print(\"\\(verlettime)\")","print(\"back","print(\"energi","print(\"gauss","print(\"gaussian","print(\"ha","print(\"not","print(\"original\")","print(\"output","print(\"th","print(\"year\\tservoi","print(\"{:.10f}\".format(time))","print(\"{:.10f}\".format(vel))","print('.',","print('[#]\\nmodulu","print('[#]\\nsubtract","print('\\n')","print('codebook:","print('codebook:',","print('decod","print('encod","print('f',","print('huffman","print('invalid","print('message:","print('message:',","print('prefer","print('th","print()","print(a,","print(a[2],","print(all(abs([y[i]","print(b[1],","print(back_substitution(a),","print(current_node.value,","print(euclid_mod(64","print(euclid_sub(128","print(euclidmod(a:","print(euclidsub(a:","print(f\"test","print(f\"us","print(f\"{'num_steps':>10s}","print(f\"{num_steps:10d}","print(f\"{year}\\t{computus(year,","print(f'{man.name}","print(first(q).id,","print(int_queue.dequeue())","print(int_queue.front())","print(int_stack.pop())","print(int_stack.top())","print(len(int_queue))","print(len(int_stack))","print(man)","print(n.id,","print(node.data)","print(node.data,","print(node.value,","print(point)","print(soln)","print(table.unpack(solution))","print(temp.value,","print(testresults(pass_count,","print(top(s).id,","print(value,","print(woman)","print).","print,","print:","print_codebook","print_int","print_messag","print_newlin","print_newline;","printcodebook()","printevolut","printf","printf(\"%d","printf(\"%lf\\n\",","printf(\"[#]\\nmodulu","printf(\"[#]\\nqueu","printf(\"[#]\\nrecurs","printf(\"[#]\\nstack","printf(\"[#]\\nsubtract","printf(\"[#]\\ntim","printf(\"[#]\\nveloc","printf(\"\\n\");","printf(\"codebook:\\n\");","printf(\"gaussian","printf(\"points:\\n\");","printf(\"th","printf(\"thi","printf(\"year\\tservoi","printf('","printf('%","printf('%s\\'","printf('[#]'.php_eol.'modulu","printf('[#]'.php_eol.'subtract","printf('ha","printf('th","printf,","printf.printf","printi","println","println!(","println!(\"[#]\\nmodulu","println!(\"[#]\\nqueu","println!(\"[#]\\nrecurs","println!(\"[#]\\nstack","println!(\"[#]\\nsubtract","println!(\"[#]\\ntim","println!(\"[#]\\nveloc","println!(\"[{:>19}]\",","println!(\"[{:?}","println!(\"ha","println!(\"solution:","println!(\"th","println!(\"year\\tservoi","println!(\"{:#?}\",","println!(\"{:?}\",","println!(\"{}\",","println!();","println(","println(\"$(a[i])\\t$(servois_numbers[i])\\t\\t$(easter_dates[i])\")","println(\"$(time)\")","println(\"$(vel)\")","println(\"$verlettime\")","println(\"${stormerverlet.time}\")","println(\"${stormerverlet.vel}\")","println(\"${velocityverlet.time}\")","println(\"${velocityverlet.vel}\")","println(\"[#]\\nmodulu","println(\"[#]\\nqueu","println(\"[#]\\nrecurs","println(\"[#]\\nstack","println(\"[#]\\nsubtract","println(\"[#]\\ntim","println(\"[#]\\nveloc","println(\"[$i]\")","println(\"[%","println(\"[%.1f,","println(\"[0.0","println(\"[1.0","println(\"[2.0","println(\"a","println(\"b","println(\"cannot","println(\"codebook","println(\"decod","println(\"encod","println(\"energi","println(\"estim","println(\"ha","println(\"it","println(\"matrix","println(\"not","println(\"origin","println(\"output","println(\"perc","println(\"recurs","println(\"solution:\")","println(\"system:\")","println(\"th","println(\"year\\tservoi","println()","println(a)","println(a[1])","println(a[2])","println(a[3])","println(a[i])","println(b)","println(euclid_mod(64","println(euclid_sub(128","println(euclidmod(64","println(euclidsub(128","println(hull)","println(img[index])","println(isstable(men,","println(length(a))","println(mentowomen)","println(soln)","println(value)","println,","printm","printmatrix(a","printmatrix(a)","printmatrix(const","printmatrixrow(row","printmatrixrow(row)","printmatrixrow(x)","printv","prioriti","priorityqueu","priorityqueue()","priorityqueue.add(new","priorityqueue.dequeue();","priorityqueue.enqueue({","priorityqueue.remove();","priorityqueue<>(comparator.comparingint(o","priorityqueue[node]()(ordering.by(","priorityqueue{node,","priorityqueue}","privat","private,","private:","probabilites.","probabilities)","probabilities):","probabilities);","probabilities.iter().enumerate()","probabilities:","probability)","probability,","probability.","probabl","problem","problem!","problem,","problem.","problem:","problem;","problems.","proc","proce","procedur","procedure,","process","process,","process.","process.stdout.write(current.id","process.stdout.write(tree.id","process:","processing),","processing.","processor","processor,","produc","product","product)","product,","product.","produkt","profession","professor","profound","program","program,","program.","program.c","programm","programmer,","programmers,","programmers.","programming,","progress","progress,","progress.","prohibit","project","project!","project.","project.clj","projects.","prolif","promis","promot","proof","proper,","properli","properti","properties.","property.","proport","propos","proposal,","proposal_index","proposals(number_of_partners);","propose()","propose():","propose(partners)","propose_to_next(self):","proposetonext()","prospect","prospect!","protect","provabl","provid","ps","pseudo","pseudocod","pt","pt)","pt):","pt,","pt.x,","pt.y};","pt;","ptr","ptr,","ptr[r12]","pub","public","public.","public:","publication,","publication.","publish","pull","pure","purpl","purple,","purpos","purpose.","purposes,","purposes.","purposes;","pursu","push","push!(bit_indices,","push!(hull,","push!(neighbors,","push!(ret.children,","push!(s,","push!(s,neighbor)","push(&mut","push(const","push(data:","push(self,","push(t","push(x","push/pop","push:","put","put,","put:","putstrln","puzzl","pv","pxor","py)","pythagorean","python","python,","python3","q","q)","q))","q),","q)~\\%~30","q)~\\%~7.","q,","q.","q.back","q.capac","q.data","q.empty():","q.front","q.front();","q.get()","q.pop();","q.push(loc);","q.push(neighbor);","q.put(neighbor)","q.put(p)","q;","q_i","qsort(points,","quadrant","quadratur","qualifi","qualiti","quantifi","quantiti","quantity,","quantity:","quantum","quarter","qubit","qubits!","qubits,","qubits.","queri","question","question!","question,","question.","question:","questions:","queu","queue","queue\");","queue🔤❗️","queue()","queue();","queue(generic[t]):","queue)","queue))","queue)))","queue,","queue.","queue.add(c);","queue.add(this.root);","queue.append(child)","queue.append(location)","queue.append(neighbour)","queue.count","queue.dequeue();","queue.empty?","queue.enqueue(c);","queue.enqueue(this);","queue.extend(¤t.children);","queue.extend(node.children)","queue.len()","queue.poll();","queue.pop().expect(\"th","queue.pop().unwrap();","queue.pop();","queue.pop(0)","queue.pop_front()","queue.popleft()","queue.push","queue.push(&n);","queue.push(...current.children);","queue.push(huffmantree::branch","queue.push_back(n);","queue.remove(at:","queue.shift","queue.shift();","queue:","queue::new();","queue;","queue<>();","queue[0]","queue[1:]","queue[int]","queue[man]()","queue\\n')","queue_array,","queue_back,","queue_cap,","queue_empty(struct","queue_fill!(canvas,","queue_fill!(grid,","queue_fill$(?,","queue_fill(","queue_fill(canvas,","queue_fill(struct","queue_fill(test_grid,","queue_front,","queue_res","queue_resize(q);","queue_resize(struct","queue_resize:","queue_size,","queue_test_func","queue_test_func):","queued,","queues,","queues.","queues.\"","queuetest","queue{","queue{cartesianindex}()","queue{node}()","queue❗️","quick","quickli","quickly,","quickly.","quiet","quit","quot","qword","qword]","r","r\"(bibbiti","r(\\cos(\\theta)","r(x,y)","r(x,y)*exp(theta(x,y)*sqrt(","r)","r)))","r++","r,","r.","r1","r10,","r10b,","r11","r11,","r11]","r12","r12,","r12:","r12]","r12d","r12d,","r13","r13,","r13:","r13]","r13d","r13d,","r14","r14,","r14]","r14d","r14d,","r15","r15,","r15]","r15],","r15d,","r2","r8","r8,","r8d,","r9","r9,","r9b","r9d,","r::vector{complex{float64}}","r;","r=\\sqrt{","r?","r\\cos(\\theta)","r\\sin(\\theta)","r\\sin(\\theta).","r]","r])","r^2.","r^2}{(2r)^2}","r_0","r_0)","r_0.","racket","racket/bas","racket/local)","racket/math)","radial","radians\"","radic","radiu","radius🤛","radius)","radius))","radius)))","radius),","radius):","radius.","radius:","radius=1)","rais","ran","rand","rand()","rand()*2","rand()]","rand(128)","rand(2,","rand,","rand::*;","rand::prelude::*;","rand::random();","rand::random::()","rand::thread_rng();","rand;","rand_max:","rand_max;","randengine(std::random_device{}());","randengine;","random","random()","random())","random();","random()]","random)","random),","random,","random.","random.new(42)","random.uniform(0,","random?","random_element(struct","random_pref_list","random_pref_list()};","randomgen","randomize()","randomli","randomr","random❗️","random❗️❗️","randrange(std::size_t","randx","randx:","randy:","rang","range\");","range(0,","range(1,","range(1,101)]","range(2020,","range(64):","range(64)][j])","range(a.shape[0]","range(a.shape[0]):","range(image_resolution):","range(len(density)):","range(max(0,","range(min(a.shape[0],","range(n","range(n):","range(num_child)))","range(num_child):","range(num_steps):","range(output_size):","range(output_size[0]):","range(output_size[1]):","range(par.timesteps):","range(pivot_i","range(pivot_row","range(row):","range(strid","range,","range.","rank","raouf,","rapidly,","rare","ratio","ratios.","raton,","rax","rax,","rax:","rax:rdx","rax]","ray","rbp","rbp,","rbx","rbx,","rcx","rcx,","rdi","rdi,","rdx","rdx,","re","re^{i","reach","read","readabl","reader","reader!).","reader'","reader.","readers,","readi","readili","reading!","readme.md","readonli","ready,","real","real(16),","real(8)","real(8),","real(energy_k[i]","real(f(z))","real,","real.","real_f(z)","realist","reality.","realiz","realized.","realli","realloc","realloc(*dst,","realloc(heap","realloc(stk","really,","realpart","realpart)","reappear","rear_point","rear_pointer.reset();","rear_pointer:","rear_pointer;","reason","reason,","reason.","reasons,","reasons.","reasons:","rec","receiv","receiveoptions(list","receiveproposal(person","receiver,","receiver.","recent","recieveproposal(man","reciproc","reckon","recogn","recommend","reconstruct","recreat","recurs","recurse(node,","recurse(node.left,","recurse(node.right,","recurse(tree,","recursion!","recursion,","recursion.","recursive.","recursive\\n')","recursive_fill!(canvas,","recursive_fill!(grid,","recursive_fill$(?,","recursive_fill(","recursive_fill(canvas,","recursive_fill(grid,","recursive_fill(struct","recursive_fill(test_grid,","recursive_test_func","recursive_test_func):","recursively,","red","red,","red.","redefin","reduc","redund","ref","ref))","ref.","ref.x))","ref.y),","ref[0])","ref[1],","refer","reference,","reference.x)","reference.y).atan2(point.x","reflection,","regard","regardless","regardless,","region","region,","regist","register,","register.","registers,","registers:","regular","regularli","regularly,","reinhold,","reiniti","reinterpret_cast(x.data());","reinterpret_cast(y.data());","reject","rel","relat","relax!\"","released.","relev","reli","remain","remaind","remainingprefer","remark","rememb","reminder,","remov","removefirst.","render","renorm","renorm_factor","reorder","rep","repeat","repel","repercussions,","repl","replac","replaced,","replacement:","replacement?","repli","replic","replot","report","repositori","repository:","repres","represent","representations:","represents,","request","request,","request.","requir","require(\"complex.js\");","required.","requires.","res)","res));","res);","res,","res/2:","res:","res::int64","res::int64,","res;","res])","research","research,","research.","research;","resembl","reshap","resiz","resolut","resolution\"","resolution)","resolution,","resolv","resourc","respect","respectively.","respectively:","rest","rest.","restor","restrict","result","result!","result)","result))","result);","result,","result.dictionary)","result.join(\"\");","result.push(node.key);","result.push(value);","result:","result:\"","result:\")","result:\");","result:'","result:')","result:'),","result:'.php_eol.'%s',","result:\\n\"","result:\\n\",","result:\\n\";","result:\\n$(check1)\")","result:\\n$(check2)\")","result:\\n$result\"","result:\\n%d\\n\"","result:\\n%d\\n\",","result:\\n{}\",","result:`n$(mod","result:`n$(sub","result:~%\")","result;","result=$(euclid_mod","result=$(euclid_sub","result[i","result[i]","results!","results,","results.","ret","ret(number_of_partners);","ret);","ret,","ret.pop_back();","ret.push_back(p.second);","ret;","ret=$1","ret_cross","ret_cross*ret_cross","retain","retriev","return","return(at(rand(n,2))","return(rand(n,2)","return:","return;","reus","revers","reversal,","reverse(bit_indices[i])","reversecodebook","reversecodebook.put(m.getvalue(),","reversedo:","revert","review","revis","revised.","revolut","revolutionari","revolutionary,","revolv","rgb","rgb.","rh","rhs(std::move(rhs))","rhs)","rhs.frequency;","rhs.x,","rhs.y};","rhs:","rhs;","rhs[0].i","rhs[0].x","rhs[0].z","rhs[1].i","rhs[1].x","rhs[1].z","rhs[2].i","rhs[2].x","rhs[2].z","rich","rid","right","right!","right)","right))","right));","right),","right,","right.","right.count(),","right.decode_dfs(&input[1..],","right.dfs(code.clone()","right.freq","right.frequency,","right.weight,","right:","right::union{leaf,","right;","right?","right]","rightchild","rightchild)","rightchild);","rightchild.key,","rightchild.weight,","rightchild;","rigor","rigorous,","rijndael","rip","rly,","rly?","rm","rn)","rnd","rng","rng()","rng)","rng.gen(),","rng.gen()};","rng.gen::();","rng.gen_range(0.0_f64,","rng.nextdouble());","robert","robust","robust.","roll","roll\"","roll.","roman","rome.","ronald","room,","root","root\")","root)","root))","root,","root.left","root.right","root;","root_bin","root_binari","rootb","rootbinari","rootbinary)","rosenthal,","rot","rot13,","rot13:","rotat","rotate\"","rotation\"","rotation,","rotation.","rotation:","rotations,","rotations.","rough","roughli","round","rounded.","rounding)","row","row\"","row'","row)","row)))))","row++;","row,","row.","row:","row;","row?","row[c]","row[j]","rowa,","rowb)","rowcount","rowcount,","rows'","rows)","rows,","rows.","rows:","rows};","rsa","rsa:","rsi","rsi,","rsi]","rsp","rsp,","rstep","rubi","rule","rule,","run","run!","run(int","run(list","run,","run.","rune","rungaleshapleyalgorithm(list","runtim","runtime,","runtime.","runtime:","ruse),","rust","rustfft::fftplanner;","rustfft::num_complex::complex;","rustfft;","rustl","ryzen","s","s\"","s\"${(21","s\"april","s\"march","s)","s)))","s.","s.pop();","s.push(loc);","s.push(neighbor);","s.top();","s:check_1","s:check_2","s:euclid_mod(64","s:euclid_mod(a,","s:euclid_sub(128","s:euclid_sub(a,","s[0],","s[1]]","s[2:]:","s_i","s_x","s_x*a","s_y*a.","sacrif","saem","safe","said,","salt.","same","same)","same,","same.","sampl","sampled,","samples)","samples.\")","samples.\");","samples.🔤❗️","samples❗️","sampling)","sampling,","sampling.","sampling?","sanderson","saniti","sar","satisfi","satisfied.","satur","saturation,","save","save_encod","savor","saw","sawtooth","say","say,","saying,","says:","scala","scala.collection.mutable._","scala.collection.mutable.{map,","scalarmapp","scalarmappable(matplotlib.colors.normalize(0.0,","scale","scale,","scale.","scale:","scale;","scale?\"","scales,","scaling\"","scaling,","scan","scanl","scanl1","scanlin","scanr","scatter","scenario","schacher","scheme","scheme,","scheme.","schemes,","schemes.","schloss","schloss.","scholars,","schonhag","school","school,","school.","schrödinger","scienc","science,","science.","scientif","scientific,","scientist","scientist.","scipy.fft","scon","scope","scope.","score(@partner)","score(partner)","scrambl","scratch","scratch:","screen,","screen;","script","script,","script.gp","script.gp)","script:","scripts,","sea","search","search,","search.","search.\"","second","second)","second,","secondly,","secondnumb","seconds.","secret","secret.","secretli","section","section,","section.","section:","section;","sections!","sections,","sections.","sections;","sector","security.","see","see,","seed","seem","seemingli","seen","segment","segment.","segments,","segments.","select","select_array(","select_array(hutchinson_op,","select_array(hutchinson_op:","select_array(struct","self","self)","self,","self.","self.__list.append(element)","self.__list.pop()","self.__list.pop(0)","self.__list:","self.__list[","self.__list[0]","self._partn","self._partner._partn","self._partner:","self.candid","self.candidates.clear()","self.candidates:","self.children","self.col","self.count()","self.data","self.data.swap(a","self.data[row","self.decode_dfs(&input[start..],","self.dfs(string::from(\"\"),","self.dk","self.dt","self.dx","self.dx)","self.generate(size,","self.has_partn","self.has_partner()","self.i","self.im_tim","self.k","self.list.front()","self.list.last()","self.list.len()","self.list.pop()","self.list.pop_front()","self.list.push(item);","self.list.push_back(item);","self.lonely?","self.nam","self.next_choic","self.partial_cmp(other).unwrap()","self.partn","self.partner:","self.pref_index","self.prefer","self.preference)}'","self.preference:","self.preference[self.pref_index]","self.r","self.timestep","self.tree.decode(input)","self.v","self.valu","self.wfc","self.x","self.x)","self.x.partial_cmp(&other.x)","self.xmax","self.y)","self.y,","self.y.partial_cmp(&other.y)","self.z;","self::new(x,","send","sender","sender,","sens","sense!\"","sense,","sense.","sensitive;","sent","separ","seq","seq[float]","seq[float]):","sequenc","sequenti","seri","series,","seriou","serv","server","server:","servoi","servois\"","servois\",","servois'","servois)","servois)`t`t$(calcul","servois,","servois:","servois=false)","servois=false):","servois=true)","servois=true)}\\t\\t{computus(year)}\")","servois_numb","servoisnumb","servoisnumbers,","set","set\");","set,","set.","set;","setmatch(person","setmate(mostdesired);","setmate(person","setpreferences($preferences);","setpreferences(array","setter\"","setter.\"","settl","setup","sever","shade","shadows\"","shake","shall","shame.","shane,","shannon","shannon,","shape","shape,","shape.","shape?","shape?:","shape_point","shape_points)","shape_points):","shapepoint","shapepoints)","shapes)","shapes.","shapes:","shapes[rng.gen_range(0..shapes.len())];","shapley","share","sharealik","sharp","sharpli","shear","shearing)","shearing,","sheep","sheep,","sheep.","sheer","shell)","shi","shift","shl","shor'","short","short)","short,","shortcut:","shorter","should!","shouldn't","show","show:","showcas","shown","shownod","showpoint","shr","shudipto","shuffl","shuffle($preferences);","shuffle(girls);","shuffle(guys);","shuffle(iterable)","shuffle(man.preference)","shuffle(mannames)),","shuffle(size_t","shuffle(thi","shuffle(woman.preference)","shuffle(womannames)),","side","side,","side.","sierpinski","sierpinski.dat,","sift","sigma","sigma,","sign","signal","signal,","signal,\"","signal.","signal2):","signal2::array{t})","signal;","signal?","signal[k,","signals,","signals.","signifi","signific","significantli","significantly,","signing,","silly,","similar","similar)","similar).","similar,","similarity,","similarli","similarly,","simpl","simple,","simple.","simple:","simple_linear_output","simplelinearoutput","simpler","simpler,","simpler:","simplest","simpli","simplicity,","simplicity.","simplifi","simply:","simul","simulation,","simulation.","simulator,","simulators.","simultan","sin(theta)","sin(x)","sine","singl","singles.each","singles.empty?","singular","singular!\")","singular\");","singular,","singular.\")","singular.\");","singular.\\n\");","sinusoid","sit","site.","site:","situat","situation.","situation?","six","sixes,","size","size(&self)","size()","size():","size();","size(a,1)","size(a,2)","size(signal)","size(sx))","size(sy))","size)","size))","size).","size).to_a.shuffle(random:","size);","size,","size.","size:","size::int64)","size;","size[0]","size[1])","size];","size_t","size_t(0));","sizeof(codebook","sizeof(double));","sizeof(q","sizeof(stk","sizeof(struct","sizeof(tree)","sizeof(wfc_k));","sizeof(wfc_r));","sizeof(y));","skew","skill","skip","slice","slide","slight","slightli","slip","sliver","slope","slow","slow,","slower","slowest","slowest.","slowli","slowly,","small","small,","smaller","smallest","smallr","smalltask","smith,","smooth","smoothli","snapshot","snd","snd)","snippet","snippet,","snow","snprintf(out,","so!","so)","so),","so,","so.","so:","sobel","softwar","sol","sol;","sol[col]","sol[i]","sol[j]","sol[pivot_i]","solar","solid","soln","soln);","soln.join(\"\\t\")","soln:","soln[a.row","soln[i]","soln[j]","soln[j]*a[i,j]","solut","solution\");","solution,","solution.","solution.indices)","solution:","solution:\"","solution:\"\"\"","solution:\")","solution:%s',","solution:')","solution:\\n\");","solution;","solution?","solution[0]","solution[i","solution[i]","solution[j]","solution_grid","solution_grid);","solution_grid,","solution_grid[:3,]","solution_grid{","solutions.","solv","solvabl","solve,","solve;","solved.","solver","solver...","solvers.","some('0')","some('1')","some(approximate_count(n_items,","some(c)","some(current)","some(otherman)","some(this)","somehow","someon","someone,","someth","something).","something,","something...","sometim","sometimes,","somewhat","somewher","soon","soon!","soon,","sophist","sort","sort!(points,","sort(points[2:end],","sort)","sort.","sort.slice(points,","sort_by_bit_reverse(first,","sort_by_bit_reverse(it","sorted(gift,","sortedpt","sorting,","sorton","sorts.","soul","sourc","south,","southeast,","southwest,","space","space\"","space,","space.","space:","spacer","spaces,","spaces;","sparingly.","spatial","spawn","speaking,","special","specialty,","specif","specifi","specifically,","specifically:","specified,","specified.","specifiers,","spectral","sped","speed","speed,","spend","spent","spheric","spice","spin","split","split_op!(par,","split_op!(par::param,","split_op(&par,","split_op(par,","split_op(par:","split_op(param","split_op(struct","split_op.jl","splitop","splot","spot,","spread","spring","spring,","spring.","springer","springer,","spruce","spy?","sqrt","sqrt(","sqrt()","sqrt(0.1*kernel_size)","sqrt(0.75))","sqrt(0.75)),","sqrt(0.75)],","sqrt(n)","sqrt(n))","sqrt(renorm_factor)","sqrt(rms/n)","sqrt(x*x","sqrt.(gx.^2","squar","square\"","square).","square,","square.","square?","squares.","squares?","squares_array","srand((unsign","srand,","src)","src);","src,","src_len","ss","st","st)))","stabl","stable.","stable_marriage($men,","stable_marriage(array","stable_marriage(men,","stable_match(leadit","stablemarriag","stablemarriage(guys,","stablemarriage.findstablematches(a,","stablemarriage.man(\"adam\")","stablemarriage.man(\"bart\")","stablemarriage.man(\"colm\")","stablemarriage.woman(\"xena\")","stablemarriage.woman(\"yeva\")","stablemarriage.woman(\"zara\")","stablemarriageexampl","stablemarriageproblem","stablematch","stack","stack\");","stack🔤❗️","stack()","stack();","stack(generic[t]):","stack)","stack))","stack)))","stack))))","stack,","stack.","stack.\"","stack.\"\"\"","stack...)","stack.append(child)","stack.count","stack.empty?","stack.extend(¤t.children);","stack.extend(find_neighbours(canvas,","stack.extend(node.children)","stack.pop","stack.pop()","stack.pop();","stack.poplast()!","stack.push","stack.push(&n);","stack.push(...current.children);","stack.push(c);","stack.push(this);","stack.push(this.root);","stack:","stack::new();","stack;","stack<>();","stack[0]","stack[1:]","stack[int]","stack\\n')","stack_array,","stack_cap,","stack_empty(struct","stack_fill!(canvas,","stack_fill!(grid,","stack_fill$(?,","stack_fill(","stack_fill(canvas,","stack_fill(struct","stack_fill(test_grid,","stack_pop","stack_pop(&stk);","stack_pop(struct","stack_pop:","stack_pop_el","stack_pop_element:","stack_pop_return","stack_pop_return:","stack_push","stack_push(&stk,","stack_push(struct","stack_push:","stack_push_append","stack_push_append:","stack_size,","stack_test_func","stack_test_func):","stack_top,","stacks,","stacktest","stack{cartesianindex}()","stack{node}()","stack❗️","stage","stage,","stand","standalon","standard","standard,","standard.","standard:","star","start","start,","start.","start.angle(point)))","start:","start_index","start_loc","start_loc,","start_loc{1,","starting,","starting_loc","starting_location,","starts.","state","state,","state.","statement","statements,","statements:","states,","states.","static","static::dfsrecursive($child);","static::dfsrecursiveinorderbinary($tre","static::dfsrecursivepostorder($child);","static_cast(current_loc[0]);","static_cast(current_loc[1]);","static_cast(grid.size())};","static_cast(grid[0].size()),","static_cast(loc[0]);","static_cast(loc[1]);","static_cast(neighbor[0]);","static_cast(neighbor[1]);","static_cast(possible_neighbor[0]);","static_cast(possible_neighbor[1]);","statist","statistics,","statistics.","stay","stay.","std.math","std.math;","std.stdio","std.stdio;","std::abs(a);","std::abs(b);","std::array","std::array&","std::array;","std::back_inserter(ret));","std::back_inserter(ret),","std::begin;","std::cerr","std::cmp::min;","std::cmp::ordering;","std::cmp::{ord,","std::collections::vecdeque;","std::collections::{binaryheap,","std::complex(0.0,","std::complex;","std::copy(begin(code),","std::cout","std::default_random_engin","std::default_random_engine&","std::end;","std::exchange(b,","std::f64::consts::pi;","std::find_if(","std::find_if(begin(encoder),","std::find_if(begin(ret),","std::for_each(first,","std::fs::file;","std::fs::write(\"./out.dat\",","std::fs::write(\"./sierpinski.dat\",","std::generate(","std::generate_n(std::back_inserter(ret),","std::generate_n(std::back_inserter(vec),","std::invalid_argument(","std::invalid_argument(\"attempt","std::io::write;","std::iota(begin(ret),","std::iter::from_fn(||","std::make_pair(it,","std::make_pair(last,","std::make_shared(","std::make_shared>(element);","std::make_unique(l);","std::make_unique(std::move(lhs),","std::make_unique>(element);","std::min_element(points.begin(),","std::move(bits)));","std::move(encoder)});","std::move(new_node);","std::move(ret.back());","std::move(rhs));","std::move(top_point","std::move(top_pointer);","std::mt19937","std::ofstream","std::ops::{index,","std::optional,","std::ostream&","std::pair","std::path::path;","std::queue","std::queue{};","std::random_devic","std::shared_ptr","std::shared_ptr>","std::shuffle(begin(ret),","std::size_t","std::size_t;","std::sort(begin(freq),","std::sqrt(0.75)},","std::stack","std::stack{};","std::string","std::swap(eqns[pivot],","std::swap(points[i],","std::swap;","std::to_string((21","std::to_string(22","std::to_string(d","std::transform(","std::uint32_t(log2(static_cast(size))));","std::uniform_int_distribution(0,","std::uniform_real_distribution(0.0,","std::unique_ptr>","std::vector","std::vector&","std::vector(),","std::vector();","std::vector(a.size(),","std::vector(opr.size,","std::vector(points.begin(),","std::vector(s","std::vector;","std::vector>","std::vector>&","std::vector>();","std::vector>;","std::vector{};","std=c++17","stem","stem,","stem.","step","step,","step.","step:","step?","steps)","steps.","steps:","stereotyp","stick","sticky.","still","still,","stk","stk)","stk.capac","stk.data","stk.top","stk;","stolen?","stop","storag","storage.","store","stori","storm,","stormer","stormer_fmt","stormer_fmt:","stormer_verlet","stormer_verlet(&time,","stormer_verlet(5,","stormer_verlet(5.0,","stormer_verlet(doubl","stormer_verlet(mut","stormer_verlet(pos,","stormer_verlet(pos::float64,","stormer_verlet:","stormer_verlet_loop","stormer_verlet_loop:","stormer_verlet_return","stormer_verlet_return:","stormerverlet","stormerverlet(5,","stormerverlet(5.,","stormerverlet(5.0,","stormerverlet(_pos:","stormerverlet(pos,","stormerverlet(pos:","stormerverlet(pos_in,","story.","storytel","str","str((21","str(0)))","str(22","str(codebook))","str(d","str(self.__list)","str(tree))","str)","str:","str:gmatch(\".\")","str[257];","straddl","straight","straightforward","straightforward,","straightforward.","straightforward:","straightforwardli","strang","strassen","strategi","strategy,","strategy:","strategy?","strcat(*dst,","stream","streaming.","strengthen","strformat","strictli","stride","stride)","stride):","string","string\"","string(0)))","string(22","string(bit_indices[i][end","string(char)","string(code)","string(code,","string(codes.encode(begin(s),","string(cur.char)","string(current.key)","string(d","string(density[j])","string(huffman_tree.key)","string(i)","string(lpad(string(i","string(mod(21","string(par.x[j])","string(real(opr.v[j]))","string)","string):","string,","string.","string:","string::from(\"\");","string::new();","string;","string]","string]()","string]):","stringbuild","stringbuilder());","stringbuilder();","stringtoencode)","stringtoencode;","string},","strip","strive","strlen(*dst);","strlen(src);","strong","stronger","struct","structur","structure,","structure.","structure?","structures,","strung","student","students).","studi","studio","stuff,","stun","stupid!","style","style:","style=\"width:100%\"/>","style=\"width:80%\"/>","style=\"width:80%\">","sub","sub(","sub*","subclass:","subdivis","subdivision),","subject","subjective.","submission,","submissions;","submit","subroutin","subrow","subsd","subsect","subsections:","subsequ","subset","subsitution\")","substitut","substitute,","substitution\"","substitution,","substitution.","substitution:","subtract","subtraction\"","subtraction,","subtraction:","success","such","such,","such.","suddenli","suffic","suggest","suit","suitabl","suitor","suitor)","suitors.add(suitor);","suitors.contains(mostdesired))","sum","sum'","sum(density)","sum(energy_k","sum(histogram)","sum(squares_array)","sum)","sum.","sum.sqrt();","sum:","sum_matrix_dimensions(mat1,","sum_matrix_dimensions(signal,","summar","summary,","summat","summer","summer,","summer.","sun","sun,","sunday","sunni","super","super(name);","supercomput","superfluid","superimpos","supersed","support","support.","suppos","supposedli","suppress","suppress(indexerror):","sure","sure,","sure.","surface,","surpris","surprising.","surprisingli","surprisingly,","surround","survey","suspect","swap","swap(&heap","swap(first[b],","swap(i,","swap(struct","swap_rows(&mut","swap_rows(a,","swap_rows(doubl","swaprow","swaprow(a,","swaprow(double[][]","swift","switch","sx","sx))","sx,","sy","sy))","sy,","symmetr","symmetric,","symmetrical,","sync","synchron","synchronized,","synod","syntax,","system","system!","system\"","system\")","system\");","system'","system,","system,\"","system,\")","system,\");","system,%s',","system,\\n\");","system.","system.collections.arraylist","system.collections.generic;","system.collections;","system.console.writeline(\"jarvismarch\");","system.console.writeline(\"run","system.console.writeline($\"th","system.console.writeline($\"{entry.key}","system.console.writeline($\"{point.x},","system.console.writeline($\"{result.bitstring}","system.console.writeline(originalstring);","system.err.println(\"not","system.err.println(\"th","system.io;","system.linq;","system.out.format(\"[%.1f,","system.out.format(\"ha","system.out.format(\"th","system.out.print(node.id","system.out.print(queue.peek().id","system.out.print(stack.peek().id","system.out.printf(\"%","system.out.printf(\"perc","system.out.println(\"[\"","system.out.println(\"[#]\\nmodulu","system.out.println(\"[#]\\nqueu","system.out.println(\"[#]\\nrecurs","system.out.println(\"[#]\\nstack","system.out.println(\"[#]\\nsubtract","system.out.println(\"[#]\\ntim","system.out.println(\"[#]\\nveloc","system.out.println(\"\\ngauss","system.out.println(\"\\nsolutions:\");","system.out.println(\"cod","system.out.println(\"decod","system.out.println(\"encod","system.out.println(\"estim","system.out.println(\"gaussian","system.out.println(\"gift:\");","system.out.println(\"wrapping:\");","system.out.println();","system.out.println(arrays.tostring(backsubstitution(a)));","system.out.println(arrays.tostring(x)));","system.out.println(euclidmod(64","system.out.println(euclidsub(128","system.out.println(intqueue.dequeue());","system.out.println(intqueue.front());","system.out.println(intqueue.size());","system.out.println(intstack.pop());","system.out.println(intstack.size());","system.out.println(intstack.top());","system.out.println(m","system.out.println(m.getkey()","system.out.println(stormerverlet.time);","system.out.println(stormerverlet.vel);","system.out.println(velocityverlet.time);","system.out.println(velocityverlet.vel);","system.out.println(verlettime);","system.out.println(w","system.random","system:","system;","systems!","systems,","systems.","systems:","systems;","t","t\".","t&","t)","t))","t)),","t));","t))\\delta","t),","t):","t)\\delta","t)}{2\\delta","t+dt)","t,","t.","t0","t0)","t1","t1)","t2","t2)","t2,","t:","t;","t^2","t^2)","t^2),","t^2).","t^3","t^3).","t^3.","t^3}{3","t^4)","t^4),","tab","tabl","table\"","table,","table.remove(freq)","table.remove(freq),","table.sort(arr,","table:","tackl","tactic","tag.","tail","tak","take","taken","takes.","takewhil","talk","tape","target","target),","target;","task","task.","tasks:","tastes.","taught","taylor","tba","tdma,","teach","teacher","technic","techniqu","techniques,","techniques.","technolog","technology,","tediou","tell","temp","temp)","temp))","temp)))))","temp);","temp._children)","temp.children","temp.children!","temp.children)","temp.children.each{","temp:","temp;","temp[b]","temp[i]","temp[k","temp[k]","temp_","temp_children","temp_nod","temp_node,","temp_node.weight)","temp_po","temp_pos,","temp_pos;","temp_str","temp_string))","temp_vector","temperatur","temperature)","templat","template(par.x[j],","temporari","temporarili","temppo","temppos:","temppos;","tempt","temp❗️","tend","tent","term","term,","term.","termin","terminal,","terminator:\"","terminolog","terms)","terms))))","terms.","ternari","terribl","territory!","ters","test","test\"","test()","test():","test_approximate_count(n_trials:","test_gift","test_grid","test_grid(grid,","test_grid(initial_canvas,","test_metropolis_iter","test_metropolis_iterate(num_steps,","testing,","testresult","tests\"","tests,","testtre","tex","tex,","text","text!","text,","text.","text:","textbook","textbook.","tfollow","thank","that!","that'","that,","that.","that:","that?","them),","them,","them.","theme","theme,","theme:","themes,","themselv","themselves.","then,","then.","theon","theorem","theorem,","theori","theorist","theory,","theory.","there!","there'","there,","there.","thereafter.","therebi","therefor","therefore,","theta","theta(x,y)","thin)","thing","thing,","thing:","things!","things,","things.","things:","think","think!","thinking,","thinner","third","third,","this)","this,","this.","this.bitstr","this.children","this.createallchildren(this.root,","this.data","this.data.findindex(x","this.data.push(value);","this.data.shift();","this.dfsrecursive(this.root);","this.dfsrecursivepostorder(this.root);","this.dictionari","this.frequ","this.i","this.id","this.key","this.left","this.leftchild","this.lett","this.list","this.list.add(element);","this.list.get(0);","this.list.get(this.size()","this.list.length;","this.list.pop();","this.list.push(data);","this.list.remove(0);","this.list.remove(this.size()","this.list.shift();","this.list.size();","this.list[0];","this.list[this.list.length","this.mat","this.mate.m","this.nam","this.nod","this.nodes.binarysearch(newnode);","this.nodes.sort();","this.preferences.indexof(other)","this.radiu","this.right","this.rightchild","this.root","this.size();","this.stringtoencod","this.tim","this.tre","this.vel","this.weight","this.x","this.x)","this.y;","this.z","this:","this;","this?","this_fft","this_fft.process(new_x.as_mut_slice(),","thm","thoma","thomas(","thomas(&a,","thomas(a","thomas(a,","thomas(a:","thomas(a::vector{float64},","thomas(doubl","thomas_algorithm($a,","thomas_algorithm(a,","thomas_algorithm(x,","thomasalgorithm(a,","thomasalgorithm(double[]","those","though","though,","though.","thought","thought,","thought.","thought:","thousand","thread","thread_loc","thread_rng();","threads,","threads.","three","thresh","threshold","threshold)","threshold):","threshold.","threshold:","through","throughout","throw","thrown","thu","thumb","thumb,","thus,","tic","tick","tick.set_visible(false)","tics,","tid","tilmann","tilt","time","time!","time)","time)))","time);","time,","time.","time:","time;","time_sv);","time_v","time_v);","time_vv);","timeless","times,","times.","timestep","timestep!","timestep,","timestep.","timestep:","timesteps,","timesteps.","timesteps:","timesteps::int64","timesteps::int64,","timesteps;","timesv","timev","timeveloc","timevv","tip","titl","title,","title.","titles,","tittl","tlead","tmp","tmp(n);","tmp))","tmp.children)","tmp.x);","tmp.y);","tmp1[9],","tmp2[9];","tmp;","tmp[n];","tmp_point","tmp_points[0]","tmp_points[i]","tmp_points[i];","tmp_points[m]","tmp_points[m];","tmp_points[siz","tmp_points[size];","to.","to:","to_","to_be_encod","to_choic","today","today.","today?\"","togeth","together!","together,","together.","together.)","together:","told","told,","toler","tomorrow","too!","too,","took","tool","tool!","toolchain","tools,","top","top(&self)","top()","top().","top():","top();","top(self)","top)","top,","top.","top;","top_point","top_pointer:","top_pointer;","topair","topchoice,","topel","topic","topic,","topic:","topics.","tosortedlist","toss","toss,","tostring()","total","total.","touch","tour","toward","tpref","track","tradit","traditionally,","train","trait","traj","traj)","trajectori","transcrib","transcript","transform","transform!","transform\"","transform,","transform.","transform.\"","transform;","transform?","transform_matrix","transform_matrix*x","transformation,","transformation.","transformations,","transformations:","transforms!","transforms,","transforms.","transit","translat","translation,","translation.","transpos","transpose)","trap","trap,","trap.","travel","travers","traversal🔤️❗️","traversal,","traversal:","traverse(node.left,","traverse(node.right,","traverse(root,","traverse(treenod","treat","treat!","tree","tree!\"","tree!\")","tree!\");","tree!');","tree!';","tree\"","tree\")","tree'","tree')","tree($numofrows);","tree(2,","tree(3,","tree(int","tree)","tree))","tree)))))","tree));","tree))]","tree);","tree*","tree*));","tree**","tree,","tree.","tree.\"","tree.\"\"\"","tree.\"))))","tree.\\n\"","tree.\\n\");","tree._children)","tree.bfsqueue();","tree.c","tree.children.foreach(dfspostorder);","tree.children.foreach(dfspreorder);","tree.dequeue()","tree.dfsrecursive();","tree.dfsrecursiveinorderbinary();","tree.dfsrecursivepostorder();","tree.dfsstack();","tree.headopt","tree.java","tree.make_codebook();","tree:","tree:\"","tree:\")","tree:\");","tree:'","tree:',","tree:\\n\");","tree:~%\")","tree;","tree?","tree[1]","tree\\n')","tree_children,","tree_count,","tree_count]","tree_count],","tree_free(struct","tree_free(tre","tree_left","tree_left,","tree_left,weight_left","tree_left]","tree_left],","tree_num_children,","tree_right","tree_right)","tree_right,","tree_right,weight_right","tree_right]","tree_right],","tree_siz","tree_size,","tree_traversal.c","tree_value,","tree_value]","tree_value],","treenod","treenode(int","treenode(left.frequ","treenode(m.getkey(),","treenode(str","trees\");","trees.insert(index,","trees.pop()","trees.popleft()","trees:","trees[0]","treetravers","treetraversal::dfsqueue($node);","treetraversal::dfsrecursive($node);","treetraversal::dfsrecursiveinorderbinary($node);","treetraversal::dfsrecursivepostorder($node);","treetraversal::dfsstack($node);","tree}","trend","tri","trial","trials\"","triangl","triangle,","triangle.","triangle:","triangular","triangular,","triangular.","trick","trick!","trick.","tricki","tricky)","tricky.","tridiagon","trigger","trigonometr","trillion","trit","trivial","trivial!","trope","troubl","trouble.","true","true)","true):14}","true);","true,","true:","true;","true_valu","true_values)**2","truli","truncat","trust","truth","truth!","try:","ts","ts)","tself","tself)","tuesday","tug","tukey","tukey,","tune","tupl","tuple!(\"x\",","tuple(*(mat","tuple(create_tree(num_row","tuples,","turbul","turn","turn.","turn_counter_clockwise(p1:","twice","twice,","twice.concat(twice.map(x","twiddl","twist","twitch","twitch.","two","two.","two:","two_pass_huffman(\"b\")","two_pass_huffman(\"bbbbbbbb\")","two_pass_huffman(\"bibb","two_pass_huffman(phrase::string)","two_pi","two_pi:","type","types,","types.","typescript","typesetting,","typevar(\"t\")","typevar,","typic","t}","t}.","u","u32);","u64)","u64,","u_1","u_1/\\sqrt{r_0}","u_2","u_2),","u_2.","u_2/\\sqrt{r_0}.","u_2^2}.","ui","uklidmod","uklidsup","ultim","ultimately,","unaccept","unawar","unbound","uncertain","uncertainti","unchang","unclear,","unclear.","uncom","uncommon","under","undergo","underlying_","underlying_;","underneath","underneath.","underpinnings,","understand","understand,","understand.","understandable.","understood!","undocu","undoubtedli","unfair","unfeas","unfeasible.","unfortun","unfortunately,","uniform","uniform,","uniform.","uniform01))","uniform?","uniformli","union","union{leaf,","uniqu","unit","unititialized,","unitless","units,","units.","unity,","univers","universe.","unknowns,","unless","unlik","unlikely,","unlin","unlucky).","unmatch():","unnecessari","unnecessary.","unpack","unphysical,","unport","unreachable()","unreachable();","unrel","unsatisfying!","unscrambl","unset","unsettl","unsign","unsurprisingly,","until","untrain","unusu","unword","unwrap","up","up\"","up,","up,\"","up.","updat","updated.","updating!","upon","upper","upto","upward","url","us","us,","usa,","usabl","use)","use:","used,","used.","used;","used}}","useful","useful)","useful.","useless.","user","using,","using.","using:","usiz","usize)","usize))","usize)]","usize)];","usize,","usual","utility.h","utility_h","utter","v","v\"","v'","v',","v(\\mathbf{r})","v(\\mathbf{r},t)","v(n)","v(t)","v(t),","v(t)\\delta","v(t+\\delta","v(t+\\frac{1}{2}\\delta","v)","v))","v,","v.","v.iter().zip(y.iter()).all(|i|","v.push(complex::new(","v.reserve(size);","v.x","v.y;","v0","v0)","v1","v2","v3","v:","v::vector{complex{float64}}","v;","v=1.","v=255.","v=\\frac{\\delta","v[i]","v[i].re).exp()));","v[i].re).exp(),","v]","v_0t","v_offset).powi(2),","v_offset:","vagu","vague,","vague.","val","valid","valu","value\"","value(v)","value)","value),","value).","value,","value.","value.weight);","value:","value;","values).","values,","values.","values:","values?","value|children_s","vanish.","var","var_a","var_b","vari","variabl","variable,","variable.","variables,","variant","variat","varies.","varieti","variou","vcat(x_odd","vec","vec![","vec![0.0,","vec![0.01,","vec![0.0;","vec![1.0,","vec![4.0,","vec![7.0,","vec![],","vec![complex::new(0.0_f64,","vec![n];","vec![start,","vec)","vec)]","vec,","vec1","vec1.x*vec2.i","vec1.y*vec2.x","vec2","vec3","vec3&","vec3{initial_location[0],","vec3{};","vec::from(x);","vec::new(),","vec::new();","vec::with_capacity(64);","vec::with_capacity(par.res);","vec::with_capacity(res);","vec;","vec>","vec>,","vecdequ","vecdeque::new(),","vecdeque::new();","vector","vector'","vector(","vector(0,","vector(15,","vector(2,","vector(5,","vector(6,","vector(7,","vector(9,","vector(int","vector,","vector.","vector.'''","vector_complex","vector_r","vectors,","vectors.","vector{float64}(","vector{float64}(vcat(0:512/2","vector{float64}(vcat(0:res/2","vector{pos}()","vel","vel)","vel))))","vel);","vel*dt","vel:","vel:vel)","vel;","vel_sv)","vel_sv);","vel_vv)","vel_vv);","veloc","velocity!","velocity,","velocity_fmt","velocity_fmt:","velocity_verlet","velocity_verlet(&time,","velocity_verlet(5,","velocity_verlet(5.0,","velocity_verlet(doubl","velocity_verlet(mut","velocity_verlet(pos,","velocity_verlet(pos::float64,","velocity_verlet:","velocity_verlet_loop","velocity_verlet_loop:","velocity_verlet_return","velocity_verlet_return:","velocityverlet","velocityverlet(5,","velocityverlet(5.,","velocityverlet(5.0,","velocityverlet(_pos:","velocityverlet(pos,","velocityverlet(pos:","velocityverlet(pos_in,","velsv","velsv)","velverlet","velvv","velvv)","veri","verifi","verlet","verlet(&time,","verlet(5,","verlet(5.,","verlet(5.0,","verlet(_pos:","verlet(doubl","verlet(mut","verlet(pos,","verlet(pos:","verlet(pos::float64,","verlet(pos_in,","verlet:","verlet_fmt","verlet_fmt:","verlet_integr","verlet_loop","verlet_loop:","verlet_return","verlet_return:","verlettim","verletvalu","verletvalues(doubl","verletvalues(time,","verletvalues(v","versa.","version","versions.","vertic","vetting.","via","vice","vicinity,","video","video,","view","villain","viml","viren","virtual","visibl","visible.","visit","visit.","visual","visualization,","visualizations,","voffset)","voffset).^2","voffset,","voffset:","voffset::float64,","void","vortex","vortic","vs","vx","vx)","vx)))","vx)]","vx:\"","v}","w","w)","w))","w,","w.","w.fiance.getorelse(stablemarriage.man(\"nobody\")).name))","w.getmate()));","w.getpreferredmates());","w.name","w.receiveoptions(men);","w0","w:","w;","w_i","wai,","wait","wait(cartesian_box_muller!(input_pts,","wait(polar_box_muller!(input_pts,","walk","walk\"","walk,","walk.","walker","walker'","walker,","wall","wander","wanderin","wanna","want","want!","want,","want.","wants,","war","warm","warm.","warn","warp","warp.","was:","wash","wasn't","wast","watch","wave","wave\"","wave\",","wave,","wave.","wave;","waveform,","wavefunct","wavefunction,","wavefunction.","wavefunctions,","wavefunctions.","wavelength.","wavevector","wavevectors,","wavey","wavey,","way","way!","way,","way.","way:","way;","ways,","ways.","wcast","wconvers","wdoubl","we'll","we'r","we'v","website:","wednesday","week","week,","weekli","weight","weight(leaf(char,","weight(left)","weight(new_tree))","weight(node(left,","weight(right)","weight(tree())","weight)","weight,","weight:","weight::int64","weight;","weight?","weight])","weight_left","weight_right","weights[temp_string]","weinstein","weird","weird.","well","well\"\"\"","well),","well,","well.","well...","west","west,","west.","western","wextra","wfc","wfc'","wfc)","wfc.push(complex::new(","wfc.reserve(size);","wfc0","wfc0)","wfc:","wfc::vector{complex{float64}}","wfc_c","wfc_c(opr.size);","wfc_c.*opr.v","wfc_c[i]","wfc_c[i].scale(0.5_f64);","wfc_c[opr.size];","wfc_k","wfc_k(opr.wfc);","wfc_k)","wfc_k,","wfc_k[i]","wfc_k[opr.size];","wfc_offset).powi(2))","wfc_offset:","wfc_r","wfc_r(opr.wfc);","wfc_r[i].conj();","wfc_r[i];","wfc_r[opr.size];","wfcconj","wfcoffset)","wfcoffset).^2/2)","wfcoffset,","wfcoffset:","wfcoffset::float64)","wformat=2","what'","what,","whatev","wheel","whenev","where'","where,","wherea","wherev","whether","whichev","while(*next_point_it","while(b","while(length(nodes)","while(length(q)","while(length(s)","while(length(weights)","while,","while:","whilefalse:","whiletrue:","white","white,","whitespac","whole","whose","why)","why),","why,","wide","wide.","wider","wider.","widescreen","width","wife","wife)","wifi","wiki","wikipedia)","wild","wild:","will","win","wind","winding.","wise","wish","wish!","with.","with:","with_new_bit(bits,","with_new_bit(std::move(bits),","with_new_bit(std::vector","within","within.","without","wname","wnames)","wnon","wnull","wobbl","wold","woman","woman(\"f\"),","woman(\"g\"),","woman(\"h\"),","woman(\"i\"),","woman(\"j\"),","woman(name:","woman(str","woman.choic","woman.choices)","woman.fi","woman.pick_preferred()","woman.prefer","woman;","woman?.partner.name);","womannames))","womannames::vector{string})","women","women)","women):","women,","women.","women.size()","women/men.","women:","women:')","women::preferences)","women::preferences,","womentoman::pairs)","womentoman[candidate])","womentomen","womentomen)","womentomen[candidate]","womentomen[candidate])","won't","wonder","word","word.","words,","work","work!","work,","work.","work:","worked.","works,","works.","world","world\"","world,","world.","world;","worlds,","worri","worry!","worse!","worse,","worse.","worst","worst,","worth","worthwhil","would'v","wouldn't","woverload","wpedant","wrap","wrap.","write","write(*,","write(*,'(a)')","write(*,*)","write(outfile,","write,","write:","writedlm(\"sierpinski.dat\",","writefil","writeln!(file,","writeln(\"[#]\\nmodulu","writeln(\"[#]\\nsubtract","writeln(\"estim","writeln(\"perc","writeln;","writing,","written","written.","wrong","wrong;","wshadow","wsign","wunus","x","x'","x(t","x(t)","x(t),","x(t)}{\\delta","x(t+","x(t+\\delta","x(t\\pm","x)","x))","x);","x*x","x*x+y*i","x,","x,i","x,y;","x.","x.(*node);","x.1).re);","x.append(random())","x.len();","x.len()];","x.length","x.length);","x.length;","x.map((_,","x.norm().powi(2)).collect();","x.prefer","x.push(complex::new(real,","x.push(xmax","x.reduce((a,","x.reserve(res);","x.to_vec();","x.weight","x/ytic","x0","x0)","x0):","x1","x2","x64","x:","x::float64","x::vector{float64}","x;","x=0.","x[0]","x[0]))","x[0]);","x[1]","x[1]))","x[1]);","x[2]","x[2]))","x[2]);","x[64],","x[b]","x[c]","x[half+i]*factor[i]","x[i","x[i+1])","x[i]","x[i];","x[indexes[i]]);","x[j]","x[k","x[k]","x[n]","x[n];","x[r]","x\\sigma","x],","x^2","x^2+y^2","x^2}","x^2},","x^2}.","x^2}}{\\displaystyle\\int_{","x_0","x_0'''","x_0.","x_2,","x_dat","x_dat)","x_even","x_i","x_i,","x_i.","x_k","x_n","x_new","x_odd","x_pos^2","x_posit","x_propos","x_t","x_{10})}{t}\\right]\\","x_{i+1}","x_{t+1}","xa)","xadisten","xam4lor","xlabel","xmax","xmax)","xmax),","xmax);","xmax+xmax/res:2*xmax/res:xmax),","xmax,","xmax:","xmax::float64","xmax;","xmin,","xmm0","xmm0,","xmm1","xmm1,","xmm2","xmm2,","xmm3","xmm3,","xmm4","xmm4,","xmm5","xmm5,","xmm6","xmm6,","xmm7","xmm7,","xmmword","xold","xor","xorp","xpo","xrang","xrange[","xs","xs)","xs)**2)).sum(axis=0)","xtic","xvalue,","xvalue;","xx","xx,","xy","xy,","xy_array","xy_array.^2;","xz,","x|","x}","x}{\\delta","y","y\")","y(x.size(),","y)","y)))","y):","y)=","y*i","y*y)","y,","y.","y.as_mut_slice());","y.into_iter().map(|i|","y.iter()","y.length","y.prefer","y1)","y:","y::float64","y;","y=%f\\n\",","y=0):","y=x","y=x.","y[0]","y[64],","y[half+i]","y[i","y[i]","y[k]","y[n];","y[size];","y\\sigma","y^2","y_1,","y_2,","y_i,","y_n,","y_pos::float64)","y_pos^2","y_posit","ya","ya)","yb)","yc)","year","year!","year\"","year'","year,","year.","year:","years)","years,","years.","years.for_each(|year|","yes.","yet.","yield","ylabel","york","york,","you!","you'd","you'r","you,","younger,","yourself","youtub","youtube,","ypo","ypos)","yr","yrang","yrange[","ys","ytic","yvalue)","yvalue;","yx","yx,","yy","yy)","yy,","yz,","z","z(x,y)","z)","z).foreach(","z**2","z,","z.","z.prefer","z:","z;","z=1.","z[0]","z[64];","z[i","z[i]","z[start_index+k","z\\in\\mathbb{r}","z^2","z^2,","z^2.","z_1","z_1,","z_2","z_2).","z_2,","z_i","z_imag","z_n),","z_real","z_real,","zero","zero!","zero):","zero.","zero:","zero:p),","zero?","zeros(5,5)","zeros(ceil(int,(bounds[1,2]","zeros(kernel_size,","zeros(n,","zeros(n,2)","zeros(res))","zeros(res),","zeros(rows)","zeros.","zip","zip(point,","zip4","zipwith","zipwith3","zoom","zx,","zy,","zz;","{","{\"\"","{\",","{%","{'nrmsd':10s}\")","{0,","{0.0,","{0.5,","{1,","{1.0,","{15,","{2,","{2.0,","{22","{3,","{4.0,","{5,","{5.0,","{6,","{7,","{7.0,","{9,","{:.3f}\".format(percent_error))","{:.3f}\".format(pi_estimate))","{:.3}%\",","{:?}","{:?}\",","{:?}][x]","{:messag","{bool","{c[1]","{computus(year,","{d","{d[1]","{drand(),","{entry.value}\");","{k","{k,","{lhs.x","{loc[0]","{loc[0],","{man.partner.name}')","{math.abs(piestim","{next_nodes{:},","{node1,","{node10,","{node1[1],","{node2,","{node5,","{node6,","{node_stack{:}","{nrmsd:5.1%}\")","{null,","{number}","{n};","{p.x","{p.x,","{piestimate}\");","{point.y}\");","{q},","{result.bitstring.length}\");","{samples:_}","{self.n})'","{self.y})'","{str(self.right)})'","{t","{wfc","{x0:5.2f}\")","{{","{{0.0,","{{3.0,","{{}});","{}","{}\",","{});","{}:","{};","|","|>","|\\psi(\\mathbf{r},t)|^2","|\\sin(\\pi\\times\\text{re}(f(z)))^t|\\times|\\sin(\\pi\\times\\text{im}(f(z)))^t|,","|acc,","|child|","|i|","|j|","|mut","|m|","|round|","|y|","|z|","||","}","})","}));","}).collect()","});","},","}.","};","~=","~a\"","~isempty(child)","~isempty(children{1})","~isempty(node_queue)","~isempty(node_stack)","~queue()","~stack()","~}~%\"","ševčíková,","–","—","↩️","↪️","≠","⏫","⏹","▶️","◀️","◀️🙌","☝️","✖️","❎","❗️","❗️🤛❗️","❗️❗️","➕","➖","➗","➡️","⬅️","⬆️","⭐️","️🔁","️🔼🐇⬆️","️↪️","️⏫🐇⬆️"],"pipeline":["stopWordFilter","stemmer"]},"store":{"./":{"url":"./","title":"Algorithm Archive","keywords":"","body":"The Arcane Algorithm Archive\nThe Arcane Algorithm Archive is a collaborative effort to create a guide for all important algorithms in all languages.\nThis goal is obviously too ambitious for a book of any size, but it is a great project to learn from and work on and will hopefully become an incredible resource for programmers in the future.\nTo change the language, please use the UI at the top of the site:\n\n \n\n\nHere are some essential links:\n\nBook / website: https://www.algorithm-archive.org/\nGitHub repository: https://github.com/algorithm-archivists/algorithm-archive\nYouTube channel (LeiosOS): https://www.youtube.com/user/LeiosOS\nTwitch livestream: https://www.twitch.tv/leioslabs\nDiscord server: https://discord.gg/Pr2E9S6\n\nNote that this project is essentially a book about algorithms collaboratively written by an online community.\nFortunately, there are a lot of algorithms out there, which means that there is a lot of content material available.\nUnfortunately, this means that we will probably never cover every algorithm ever created and instead need to focus on what the community sees as useful and necessary.\nThat said, we'll still cover a few algorithms for fun that have very little, if any practical purpose.\nIf you would like to contribute, feel free to go to any chapter with code associated with it and implement that algorithm in your favorite language, and then submit the code via pull request.\nYou can find help and instructions regarding the contribution process in our How to Contribute wiki entry.\nHopefully, this project will grow and allow individuals to learn about and try their hand at implementing different algorithms for fun and (potentially) useful projects.\nIf nothing else, it will be an enjoyable adventure for our community.\nThanks for reading and let me know if there's anything wrong or if you want to see something implemented in the future!\n\nLicense\nThe code examples for this project are licensed under the MIT license (found in LICENSE.md).\nAll text content is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License with attribution specified at the end of every chapter.\nAll graphics are licensed under the license stated at the end of every chapter.\nIf no attribution is specified, please attribute James Schloss.\n\n"},"contents/introduction/introduction.html":{"url":"contents/introduction/introduction.html","title":"Introduction","keywords":"","body":"Introduction\nPeople learn differently, there's no doubt about that. I for one, have never been able to follow a lecture. No matter how interesting the subject might be, the teacher or professor either moves too slowly or too quickly, and in both cases I lose the motivation to study and learn outside of class. Looking back at all my past lectures, this is a bit of a shame. I genuinely love learning! In fact, nowadays there's nothing I enjoy more than poring through the ArXiv, looking for the latest and greatest algorithms in physics and computer science. Sure, I cannot understand them all, but sometimes it's nice to be completely overwhelmed and chip away at problems one piece at a time. In the end, modern research is a conglomeration of fun little (or big) puzzles to solve; however, I find that many papers are too harsh for most people to tackle without a significant background in computer science or physics. For this reason, they are ignored by the public. We live in an era where nearly the entire sum of human knowledge is available at our fingertips, and yet people are blissfully unaware of the unique ideas and challenges that are pushing our understanding forward.\nI guess that is the point of this work. Throughout the past few years, I have been collecting small morsels of knowledge that are hard to express in any meaningful way through blog posts, YouTube, or twitch streaming. YouTube, for example, is a great place to introduce the general idea of an algorithm; however, I personally find it a poor choice to show a worked example. Twitch is great to show everything, but spending 5 hours programming up an algorithm for the first time is generally not everyone's idea of fun. Blog posts work well for this type of material; however, they lack a comprehensive nature that I tend to enjoy. So what's left? Well, I suppose that would be a book, which is an incredibly exciting prospect!\nSee, when I was younger, maybe around Jr. High School age, I really wanted to become an author. I spent as much free time as I could manage writing fantastical stories about heroes and villains creating their own worlds and redefining reality. It was (and still is) an enjoyable hobby of mine. In many ways, my love of storytelling is echoed in my love of science and mathematics. In my mind, every discovery is its own story -- an adventure just waiting to be understood! It seems incredible to me that I now have the chance to combine my two favorite hobbies: writing and learning.\nNow, to be clear, I am not a master computer scientist. In fact, my degree is in physics and at the time of writing, I am in a PhD program studying quantum systems; however, I really, really love learning algorithms. About a year or two ago, I started a Twitch stream focused on computational physics. Almost every day, I would get up at 5:00AM and livecode something I had never coded before. It was incredibly fun and through working with the community, we learned a lot. In addition, I found my programming abilities improving significantly, and I learned to see the power in a community of hobby programmers.\nThis text is a natural extension of that idea -- a community effort to learn as much as possible about as many algorithms as we can. Because of this, I feel like I should be as honest as possible about the nature of this book. As mentioned, I am not classically trained in computer science, so for the most part, I will be learning right along with you, the reader. My hope is to advance my own understanding of computer science while also providing a comprehensive guide for those wishing to improve their own understanding as well.\nFor this reason, I hesitate to call this a work a \"textbook\" and would prefer to think of it as a lab notebook of sorts. It will be an archive filled with cool ideas in computer science and physics that I hope will be interesting in their own right. My hope is that this book perfectly straddles the line between comprehensiveness and pleasure and will be an enjoyable read for anyone at any stage on their hobby programming journey.\nKeeping with the community theme, this book is freely available on GitHub and GitHub pages. Please feel free to read / browse the content available there. If you have any questions / comments / concerns, please let me know. This book is a community project and will only work if there is a community that works on it!\nAs a final note before beginning the bulk text, I would like for this book to be \"language agnostic.\" This basically means that I would like to use pseudocode in the main text, but provide source code in any language you could want in the appendix. Though this may seem a little counter-intuitive, I think it offers the greatest flexibility for myself as the author and for the community to develop their own code in any way they please. In fact, if you feel inclined, please feel free to implement your own version of any algorithm mentioned in this text. If you submit it and it passes all my ahem rigorous tests, then I can throw it at the end of each chapter with attribution to you!\nSo I guess that's all for now. Because this book is freely available online, I may be heavily modifying the content as we delve deeper into the archive of arcane algorithms.\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/how_to_contribute/how_to_contribute.html":{"url":"contents/how_to_contribute/how_to_contribute.html","title":"How To Contribute","keywords":"","body":"How to Contribute to the Algorithm Archive\nThe Algorithm Archive is an effort to learn about and teach algorithms as a community.\nAs such, it requires a certain level of trust between community members.\nFor specific details on how to contribute, please consult the How to Contribute guide.\nIf you are having trouble with git and version control, please also check out this video series with more details.\nIn addition, we also have an FAQ and a code style guide, which is currently being written for all languages submitted to the Algorithm Archive so far.\nCurrently, we are not accepting chapter submissions; however, we will allow for this in the near future.\nFor now, here are the basics for submitting code to the Algorithm Archive:\n\nStyle: We are developing a code style guide for all the languages in the Algorithm Archive. For the most part, follow standard style guidelines associated with your language of choice. Your code should be readable and understandable to anyone -- especially those who are new to the language. In addition, remember that your code will be displayed in this book, so try to keep to around 80 columns, try to remove any visual clutter, and keep variable names clean and understandable.\nLicensing: All the code from this project will be under the MIT license found in LICENSE.md; however, the text will be under a Creative Commons Attribution-NonCommercial 4.0 International License.\nCONTRIBUTORS.md: After contributing code, please echo your name to the end of CONTRIBUTORS.md with echo \"- name\" >> CONTRIBUTORS.md.\nBuilding the Algorithm Archive: Before every submission, you should build the Algorithm Archive on your own machine. To do this, install Node and use npm install and then npm run serve in the main directory (where README.md is). This will provide a local URL to go to to view the archive in your browser of choice. Use this server to make sure your version of the Algorithm Archive works cleanly for the chapter you are updating!\n\nTo submit code, go to the code/ directory of whatever chapter you want and add another directory for your language of choice.\nYou can also help out by reviewing code, if you have the ability to review a language (and want to be asked to do so), please add yourself to the Code Reviewers list\nWe use two GitBook plugins to allow users to flip between languages on different algorithms.\nOne is the theme-api, and the other is the include-codeblock api.\nWe need the following statements in the markdown file for these to work together:\n{% method %}\n{% sample lang=\"jl\" %}\n[import:1-17, lang:\"julia\"](code/julia/conv.jl)\n{% endmethod %}\n\nFor this example, we are starting the theme-api method and importing lines 1-17 from a sample Julia snippet from the code directory.\nNote that to standardize the language capitalization schemes, we ask that each language's sample lang is the file extension for their code, cpp for C++, hs for Haskell, etc.\nThis keeps the title in the theme-api consistent across different languages.\nAlso note that depending on the algorithm, there might be in-text code snippets that also need to be written.\nI'll update this page as the project grows.\nIf you would like to be a part of the ongoing discussion, please feel free to join our discord server: https://discord.gg/pb976sY.\nThanks for all the support and considering contributing to the Algorithm Archive!\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/code_reviews/code_reviewers.html":{"url":"contents/code_reviews/code_reviewers.html","title":"Code Reviewers","keywords":"","body":"Code Reviewers\nIf you are comfortable reviewing a language, please add yourself to the table below:\n\n\n\nLanguage\nReviewers\n\n\n\n\nasm-x64\n\n\n\nbash\n\n\n\nc\n@amaras\n\n\nc#\n\n\n\nclojure\n\n\n\ncoconut\n@amaras\n\n\nc++\n@ShadowMitia\n\n\ncrystal\n\n\n\nD\n\n\n\ndart\n\n\n\nelm\n\n\n\nemojicode\n\n\n\nfactor\n\n\n\nfortran\n@leios\n\n\ngnuplot\n@leios\n\n\ngo\n\n\n\nhaskell\n\n\n\njava\n\n\n\njavascript\n@ntindle,@ShadowMitia\n\n\njulia\n@leios\n\n\nkotlin\n\n\n\nlabview\n\n\n\nlolcode\n\n\n\nlisp\n\n\n\nlua\n\n\n\nmatlab\n\n\n\nnim\n\n\n\nocaml\n@ShadowMitia\n\n\nphp\n\n\n\npiet\n\n\n\npowershell\n\n\n\npython\n@ntindle,@ShadowMitia,@amaras,@PeanutbutterWarrior\n\n\nr\n\n\n\nracket\n\n\n\nruby\n\n\n\nrust\n@ShadowMitia,@PeanutbutterWarrior\n\n\nscala\n\n\n\nscheme\n\n\n\nscratch\n@leios\n\n\nsmalltask\n\n\n\nswift\n\n\n\ntypescript\n@ntindle\n\n\nv\n\n\n\nviml\n\n\n\nwhitespace\n\n\n\n\nIf you are comfortable reviewing a toolchain change, please add yourself to the list below:\n\n\n\nFeature\nReviewers\n\n\n\n\nDev Container\n@ntindle, @ShadowMitia\n\n\nDocker\n@ntindle, @ShadowMitia\n\n\nGithub Actions\n@ntindle\n\n\nHonkit\n\n\n\nScons\n@amaras,@PeanutbutterWarrior\n\n\nChapters\n@leios\n\n\n\n"},"contents/data_structures/data_structures.html":{"url":"contents/data_structures/data_structures.html","title":"Data Structures","keywords":"","body":"Data Structures\nThis is a book about algorithms.\nThe fundamental building blocks of algorithms are data structures, and thus as more algorithms are added to the Archive, more data structures will be added to this section.\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/stacks_and_queues/stacks_and_queues.html":{"url":"contents/stacks_and_queues/stacks_and_queues.html","title":"Stacks and Queues","keywords":"","body":"Stacks and Queues\nStacks and Queues are two sides of the same coin in computer science. They are both simple data structures that hold multiple elements, but allow you to use a single element at a time. The biggest difference between the two structures is the order in which you can access the elements in the data structure.\nIn stacks, data follows Last In, First Out (LIFO), which basically means that whichever element you put in last will be the first element you take out. It acts exactly like a stack in real life. If you put a book on a stack of other books, the first book you will look at when sifting through the stack will be the book you just put on the stack.\nIn Queues, data follows First In, First Out (FIFO), which means that whichever element you put in first will be the first element you take out. Imagine a queue of people. It would be unfair if the first person in line for groceries were not the first person to receive attention once the attendant finally shows up.\nFor the most part, though, queues and stacks are treated the same way. There must be a way to:\n\nlook at the first element (top())\nto remove the first element (pop())\nto push elements onto the data structure (push())\n\nThe notation for this depends on the language you are using. Queues, for example, will often use dequeue() instead of pop() and front() instead of top(). You will see the language-specific details in the source code under the algorithms in this book, so for now it's simply important to know what stacks and queues are and how to access elements held within them.\nExample Code\nHere is a simple implementation of a stack:\ninterface IStack {\n /**\n * `pop` removes last element from the stack and returns the same\n */\n pop(): T;\n /**\n * `push` adds element to last of the stack and returns the size\n */\n push(data: T): number;\n /**\n * `size` return size or length of the stack\n */\n size(): number;\n /**\n * `top` returns last element of the stack\n */\n top(): T;\n}\n\nclass Stack implements IStack {\n private readonly list: Array = [];\n\n public push(data: T) {\n return this.list.push(data);\n }\n\n public pop() {\n return this.list.pop();\n }\n\n public size() {\n return this.list.length;\n }\n\n public top() {\n return this.list[this.list.length - 1];\n }\n}\n\nfunction exampleStack() {\n const numberStack = new Stack();\n\n numberStack.push(4);\n numberStack.push(5);\n numberStack.push(9);\n\n console.log(numberStack.pop());\n console.log(numberStack.size());\n console.log(numberStack.top());\n}\n\nexampleStack();\n\nimport java.util.List;\nimport java.util.ArrayList;\n\n\npublic class StackTest {\n\n public static void main(String[] args) {\n IStack intStack = new Stack<>();\n\n intStack.push(4);\n intStack.push(5);\n intStack.push(9);\n\n System.out.println(intStack.pop());\n System.out.println(intStack.size());\n System.out.println(intStack.top());\n }\n\n}\n\n\ninterface IStack {\n /*\n * 'pop' removed the last element from the stack and returns it\n */\n T pop();\n\n /*\n * 'push' adds an element to at the end of the stack and returns the new size\n */\n int push(T element);\n\n /*\n * 'size' returns the length of the stack\n */\n int size();\n\n /*\n * 'top' returns the first element of the stack\n */\n T top();\n}\n\n\nclass Stack implements IStack {\n\n private List list;\n\n public Stack() {\n this.list = new ArrayList<>();\n }\n\n public T pop() {\n return this.list.remove(this.size() - 1);\n }\n\n public int push(T element) {\n this.list.add(element);\n return this.size();\n }\n\n public int size() {\n return this.list.size();\n }\n\n public T top() {\n return this.list.get(this.size() - 1);\n }\n\n}\n\n#include\n#include\n#include\n\nnamespace my {\n /**\n * implementation using linked list\n * [value][next] -> [value][next] -> ... -> [value][next]\n * (top Node) (intermediat Nodes)\n * left most Node represents top element of stack\n */\n template\n struct Node {\n /**\n * next: will store right Node address\n */\n T value;\n std::unique_ptr> next;\n Node(const T& V) : value(V) { }\n };\n\n template\n class stack {\n private:\n /**\n * top_pointer: points to left most node\n * count: keeps track of current number of elements present in stack\n */\n std::unique_ptr> top_pointer;\n size_t count;\n public:\n stack() : count(0ULL) { }\n\n void push(const T& element) {\n auto new_node = std::make_unique>(element);\n new_node->next = std::move(top_pointer);\n top_pointer = std::move(new_node);\n count = count + 1;\n }\n\n void pop() {\n if (count > 0) {\n top_pointer = std::move(top_pointer->next);\n count = count - 1;\n }\n }\n\n T& top() {\n assert(count > 0 and \"calling top() on an empty stack\");\n return top_pointer->value;\n }\n // returning mutable reference can very be usefull if someone wants to modify top element\n\n T const& top() const {\n assert(count > 0 and \"calling top() on an empty stack\");\n return top_pointer->value;\n }\n\n size_t size() const { return count; }\n\n bool empty() const { return count == 0; }\n\n ~stack() {\n while (top_pointer.get() != nullptr) {\n top_pointer = std::move(top_pointer->next);\n }\n }\n };\n}\n\nint main() {\n my::stack intStack;\n\n intStack.push(4);\n intStack.push(5);\n intStack.push(9);\n\n int topElement = intStack.top();\n intStack.pop();\n std::cout \nstruct Stack {\n list: Vec\n}\n\nimpl Stack {\n fn new() -> Self {\n Stack {\n list: Vec::new(),\n }\n }\n\n // Note that this returns a reference to the value\n // This is in contrast to pop which gives ownership of the value\n fn top(&self) -> Option {\n self.list.last()\n }\n\n fn pop(&mut self) -> Option {\n self.list.pop()\n }\n\n fn push(&mut self, item: T) {\n self.list.push(item);\n }\n\n fn size(&self) -> usize {\n self.list.len()\n }\n}\n\nfn main() {\n let mut i32stack: Stack = Stack::new();\n\n i32stack.push(4);\n i32stack.push(5);\n i32stack.push(6);\n\n println!(\"{:?}\", i32stack.pop().unwrap()); // 6\n println!(\"{:?}\", i32stack.size()); // 2\n println!(\"{:?}\", i32stack.top().unwrap()); // 5\n}\n\n#!/usr/bin/env python3\n\n__author__ = \"Michael Ciccotosto-Camp\"\n\nfrom typing import TypeVar, Generic\n\n\nT = TypeVar(\"T\")\n\n\nclass Stack(Generic[T]):\n def __init__(self) -> None:\n self.__list: list[T] = []\n\n def pop(self) -> T:\n return self.__list.pop()\n\n def push(self, element: T) -> int:\n self.__list.append(element)\n return len(self)\n\n def top(self) -> T:\n return self.__list[-1]\n\n def __len__(self) -> int:\n return len(self.__list)\n\n def __str__(self) -> str:\n return str(self.__list)\n\n\ndef main() -> None:\n int_stack: Stack[int] = Stack()\n\n int_stack.push(4)\n int_stack.push(5)\n int_stack.push(9)\n\n print(int_stack.pop())\n print(len(int_stack))\n print(int_stack.top())\n\n\nif __name__ == \"__main__\":\n main()\n\n\n\nHere is a simple implementation of a queue:\ninterface IQueue {\n /**\n * `dequeue` removes first element from the queue and returns the same\n */\n dequeue(): T;\n /**\n * `enqueue` adds element to last of the queue and returns the size\n */\n enqueue(data: T): number;\n /**\n * `size` return size or length of the queue\n */\n size(): number;\n /**\n * `front` returns first element of the queue\n */\n front(): T;\n}\n\nclass Queue implements IQueue {\n private readonly list: Array = [];\n\n public enqueue(data: T) {\n return this.list.push(data);\n }\n\n public dequeue() {\n return this.list.shift();\n }\n\n public size() {\n return this.list.length;\n }\n\n public front() {\n return this.list[0];\n }\n}\n\nfunction exampleQueue() {\n const numberQueue = new Queue();\n\n numberQueue.enqueue(4);\n numberQueue.enqueue(5);\n numberQueue.enqueue(9);\n\n console.log(numberQueue.dequeue());\n console.log(numberQueue.size());\n console.log(numberQueue.front());\n}\n\nexampleQueue();\n\nimport java.util.List;\nimport java.util.ArrayList;\n\npublic class QueueTest {\n\n public static void main(String[] args) {\n IQueue intQueue = new Queue<>();\n\n intQueue.enqueue(4);\n intQueue.enqueue(5);\n intQueue.enqueue(9);\n\n System.out.println(intQueue.dequeue());\n System.out.println(intQueue.size());\n System.out.println(intQueue.front());\n }\n\n}\n\n\ninterface IQueue {\n\n /*\n * 'dequeue' removes the first element from the queue and returns it\n */\n T dequeue();\n\n /*\n * 'enqueue' adds an element at the end of the queue and returns the new size\n */\n int enqueue(T element);\n\n\n /*\n * 'size' returns the size of the queue\n */\n int size();\n\n /*\n * 'front' returns the first element of the queue without removing it\n */\n T front();\n}\n\n\nclass Queue implements IQueue {\n\n private List list;\n\n public Queue() {\n this.list = new ArrayList<>();\n }\n\n public T dequeue() {\n return this.list.remove(0);\n }\n\n public int enqueue(T element) {\n this.list.add(element);\n return this.size();\n }\n\n public int size() {\n return this.list.size();\n }\n\n public T front() {\n return this.list.get(0);\n }\n\n}\n\n#include\n#include\n#include\n\nnamespace my {\n /**\n * implementation using linked list\n * [value][next] -> [value][next] -> ... -> [value][next]\n * (front Node) (intermediat Nodes) (rear Node)\n */\n template\n struct Node {\n /**\n * next: will store right Node address\n */\n T value;\n std::shared_ptr> next;\n Node(const T& V) : value(V) { }\n };\n\n template\n class queue {\n private:\n /**\n * front_pointer: points to left most node\n * count: keeps track of current number of elements present in queue\n * rear_pointer: points to most recent Node added into the queue, which is right most Node\n */\n std::shared_ptr> front_pointer;\n std::shared_ptr> rear_pointer;\n size_t count;\n public:\n queue() : count(0ULL) { }\n\n void enqueue(const T& element) {\n auto new_node = std::make_shared>(element);\n if (count > 0) {\n rear_pointer->next = new_node;\n rear_pointer = new_node;\n } else {\n rear_pointer = front_pointer = new_node;\n }\n count = count + 1;\n }\n\n void dequeue() {\n if (count > 1) {\n front_pointer = front_pointer->next;\n count = count - 1;\n } else if (count == 1) {\n front_pointer.reset();\n rear_pointer.reset();\n count = count - 1;\n }\n }\n\n T& front() {\n assert(count > 0 && \"calling front on an empty queue\");\n return front_pointer->value;\n }\n\n T const& front() const {\n assert(count > 0 && \"calling front on an empty queue\");\n return front_pointer->value;\n }\n\n size_t size() const { return count; }\n\n bool empty() const { return count == 0; }\n\n ~queue() {\n while (front_pointer.get() != nullptr) {\n front_pointer = front_pointer->next;\n }\n }\n };\n}\n\nint main() {\n my::queue intQueue;\n intQueue.enqueue(4);\n intQueue.enqueue(5);\n intQueue.enqueue(9);\n\n int frontElement = intQueue.front();\n intQueue.dequeue();\n std::cout \nuse std::collections::VecDeque;\n\nstruct Queue {\n list: VecDeque\n}\n\nimpl Queue {\n fn new() -> Self {\n Queue{\n list: VecDeque::new(),\n }\n }\n\n // Note that this returns a reference to the value\n // This is in contrast to dequeue which gives ownership of the value\n fn front(&self) -> Option {\n self.list.front()\n }\n\n fn dequeue(&mut self) -> Option {\n self.list.pop_front()\n }\n\n fn enqueue(&mut self, item: T) {\n self.list.push_back(item);\n }\n\n fn size(&self) -> usize {\n self.list.len()\n }\n}\n\nfn main() {\n let mut i32queue = Queue::new();\n\n i32queue.enqueue(4);\n i32queue.enqueue(5);\n i32queue.enqueue(6);\n\n println!(\"{:?}\", i32queue.dequeue().unwrap()); // 4\n println!(\"{:?}\", i32queue.size()); // 2\n println!(\"{:?}\", i32queue.front().unwrap()); // 5\n}\n\n#!/usr/bin/env python3\n\n__author__ = \"Michael Ciccotosto-Camp\"\n\nfrom typing import TypeVar, Generic\n\n\nT = TypeVar(\"T\")\n\n\nclass Queue(Generic[T]):\n def __init__(self) -> None:\n self.__list: list[T] = list()\n\n def dequeue(self) -> T:\n return self.__list.pop(0)\n\n def enqueue(self, element: T) -> int:\n self.__list.append(element)\n return len(self)\n\n def front(self) -> T:\n return self.__list[0]\n\n def __len__(self) -> int:\n return len(self.__list)\n\n def __str__(self) -> str:\n return str(self.__list)\n\n\ndef main() -> None:\n int_queue: Queue[int] = Queue()\n\n int_queue.enqueue(4)\n int_queue.enqueue(5)\n int_queue.enqueue(9)\n\n print(int_queue.dequeue())\n print(len(int_queue))\n print(int_queue.front())\n\n\nif __name__ == \"__main__\":\n main()\n\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/mathematical_background/mathematical_background.html":{"url":"contents/mathematical_background/mathematical_background.html","title":"Mathematical Background","keywords":"","body":"Mathematical Background\nNo matter who you ask, programming requires at least a little math.\nThat said, for most programmers, it doesn't require too much.\nFor the most part, depending on your specialty, you will probably not see too much calculus or differential equations.\nHonestly, you could probably get away with what you learned in high school.\nHowever, this is a book about algorithms, and algorithms sometimes require a deeper understanding of mathematics.\nThis section attempts to provide the mathematical foundations that you will need to understand certain algorithms.\nAs we add new algorithms and need new mathematical tools, we will add them to this section.\nA notable exception to this rule will be in the case of classes of algorithms that require domain-specific knowledge, like quantum simulations or bioinformatics.\nIn those cases, we will place the mathematical methods in more relevant sections.\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/tree_traversal/tree_traversal.html":{"url":"contents/tree_traversal/tree_traversal.html","title":"Tree Traversal","keywords":"","body":"Tree Traversal\nTrees are naturally recursive data structures, and because of this, we cannot access their elements like we might access the elements of a vector or array. Instead, we need to use more interesting methods to work through each element. This is often called Tree Traversal, and there are many different ways to do this. For now, we will restrict the discussion to two common and related methods of tree traversal: Depth-First and Breadth-First Search. Note that trees vary greatly in shape and size depending on how they are used; however, they are composed primarily of nodes that house other, children nodes, like so:\nstruct Node\n children::Vector{Node}\n ID::Int64\n Node(ID::Int64) = new(Vector{Node}(), ID)\nend\n\nstruct node {\n std::vector children;\n size_t value;\n};\n\npublic class Tree\n{\n public int Id { get; private set; }\n private List _children = new List();\n\nstruct node {\n struct node *children;\n size_t children_size;\n int id;\n};\n\nprivate class Node implements Comparable {\n public ArrayList children;\n public int id;\n\n public Node(int id) {\n this.children = new ArrayList();\n this.id = id;\n }\n\n @Override\n public int compareTo(Node other) {\n // Need to implement Comparable and override this\n // method because of the method BFSQueue() which uses Queues\n // and must know how to check if two nodes are the same or not\n return Integer.compare(this.id, other.id);\n }\n}\n\nfunction createTree(rows, children) {\n if (rows === 0) {\n return { id: rows, children: [] };\n }\n\n return {\n id: rows,\n children: [...Array(children).keys()].map(() => createTree(rows - 1, children))\n };\n}\n\nAs a note, a node struct is not necessary in javascript, so this is an example of how a tree might be constructed.\nclass Node:\n def __init__(self):\n self.data = None\n self.children = []\n\n\n \nstruct Node {\n children: Vec,\n value: u64,\n}\n\ndata Tree a = Node\n { node :: a,\n forest :: [Tree a]\n }\n\nclass Node {\n var value: Int\n var children: [Node]?\n\n init(value: Int, children: [Node]) {\n self.value = value\n self.children = children\n }\n}\n\nclass Tree implements JsonSerializable\n{\n private $id;\n private $children = [];\n\n public function __construct(int $id, array $children = [])\n {\n $this->id = $id;\n $this->children = $children;\n }\n\n public function getId(): int\n {\n return $this->id;\n }\n\n public function getChildren(): array\n {\n return $this->children;\n }\n\n public function addChild(Tree $child): void\n {\n $this->children[] = $child;\n }\n\n public function jsonSerialize(): array\n {\n return [\n 'id' => $this->id,\n 'children' => $this->children,\n ];\n }\n}\n\nclass Node \n property id, children \n def initialize(@id : Int32, @children : Array(Node))\n end \nend\n\nObject subclass: #Node\n instanceVariableNames: 'children data'\n classVariableNames: ''\n package: ''\n\nNode>>children\n \"Children getter.\"\n ^ children\n\nNode>>children: newChildren\n \"Children setter.\"\n children := newChildren.\n\nNode>>data\n \"Data getter\"\n ^ data\n\nNode>>data: newData\n \"Data setter\"\n data := newData.\n\ntype node struct {\n id int\n children []*node\n}\n\n.equ tree_children, 0\n.equ tree_num_children, 8\n.equ tree_value, 12\n.equ tree_size, 16\n\n🦃 ⏹ 🍇\n 🔘 ⏫\n\n(defstruct node data children)\n\nnode = @(k,v) containers.Map(k,v);\n\ndata Node(value: int, children: Node[])\n\n\n\nBecause of this, the most straightforward way to traverse the tree might be recursive. This naturally leads us to the Depth-First Search (DFS) method:\nfunction DFS_recursive(n::Node)\n # Here we are doing something...\n print(n.ID, \" \")\n\n for child in n.children\n DFS_recursive(child)\n end\nend\n\n// Simple recursive scheme for DFS\nvoid dfs_recursive(node const& n) {\n // Here we are doing something...\n std::cout \nprivate void DFSRecursive(Tree tree) {\n Console.Write(tree.Id + \" \");\n\n foreach (var c in tree._children)\n DFSRecursive(c);\n}\n\npublic void DFSRecursive()\n{\n DFSRecursive(this);\n\n}\n\nvoid dfs_recursive(struct node n) {\n printf(\"%d \", n.id);\n\n if (n.children) {\n for (size_t i = 0; i \nprivate void dfsRecursive(Node node) {\n System.out.print(node.id + \" \");\n\n for (Node n : node.children) {\n dfsRecursive(n);\n }\n}\n\nfunction dfsPreorder(tree) {\n if (!tree) {\n return;\n }\n\n process.stdout.write(tree.id + \" \");\n tree.children.forEach(dfsPreorder);\n}\n\ndef dfs_recursive(node):\n if node.data != None:\n print(node.data, end=' ')\n\n for child in node.children:\n dfs_recursive(child)\n\n\n \nfn dfs_recursive(n: &Node) {\n print!(\"{} \", n.value);\n\n for child in &n.children {\n dfs_recursive(child);\n }\n}\n\ndfs :: Tree a -> [a]\ndfs (Node x ts) = x : concatMap dfs ts\n\nfunc dfsRecursive(node: Node) {\n print(node.value, terminator:\" \")\n\n for child in node.children! {\n dfsRecursive(node: child)\n }\n}\n\npublic static function DFSRecursive(Tree $tree): void\n{\n echo $tree->getId() . ' ';\n foreach ($tree->getChildren() as $child) {\n static::DFSRecursive($child);\n }\n}\n\ndef dfs_recursive(node) \n print \"#{node.id} \"\n node.children.each{ |child| dfs_recursive child } \nend\n\nNode>>dfsRecursive\n \"Recursive depth first search.\"\n Transcript show: data; cr.\n children collect: [ :child | child dfsRecursive ]\n\nNode>>dfsRecursivePostOrder\n\nfunc dfsRecursive(n *node) {\n fmt.Printf(\"%d \", n.id)\n for _, child := range n.children {\n dfsRecursive(child)\n }\n}\n\n# rdi - children ptr\n# rsi - value|children_size\ndfs_recursive:\n push r12\n push r13\n mov r12, rdi\n mov r13, rsi\n mov rdi, OFFSET fmt_tree # Handle the current node\n shr rsi, 32 # The tree value is in the upper 32 bits\n xor rax, rax\n call printf\n mov r13d, r13d # Zero out the top 32 bits\n add r13, r12 # Pointer pointing after the last element of the children array\ndfs_recursive_children:\n cmp r12, r13 # If we reached the end, return\n je dfs_recursive_return\n mov rdi, QWORD PTR [r12]\n mov rsi, QWORD PTR [r12 + 8]\n call dfs_recursive\n add r12, tree_size\n jmp dfs_recursive_children\ndfs_recursive_return:\n pop r13\n pop r12\n ret\n\n 🌌🐕 depth_count children_count❗️\n🍉\n\n❗️ 🆔 ➡️ 🔢 🍇\n ↩️ id\n🍉\n\n❗️ 🧒 ➡️ 🍨🐚🌲🍆 🍇\n\n(defun dfs-recursive (node)\n \"A depth first approach for printing out all values in a tree.\"\n (when (node-data node)\n (format t \"~a \" (node-data node)))\n (loop for child in (node-children node) do\n (dfs-recursive child)))\n\nfunction DFS_recursive(n)\n\n cell_index = @(a, b) a{b};\n ID = cell_index(keys(n), 1);\n\n fprintf('%u ', ID);\n\n children = cell_index(values(n), 1);\n for i = children\n child = i{1};\n if ~isempty(child)\n DFS_recursive(child);\n end\n end\nend\n\ndef dfs_recursive(Node(value, children)):\n \"\"\"A depth first approach for printing out all values in a tree.\"\"\"\n print(value, end=' ')\n for child in children:\n dfs_recursive(child)\n\n\n\nAt least to me, this makes a lot of sense. We fight recursion with recursion! First, we first output the node we are on and then we call DFS_recursive(...) on each of its children nodes. This method of tree traversal does what its name implies: it goes to the depths of the tree first before going through the rest of the branches. In this case, the ordering looks like:\n\n \n\n\nNote that the in the code above, we are missing a crucial step: checking to see if the node we are using actually exists! Because we are using a vector to store all the nodes, we will be careful not to run into a case where we call DFS_recursive(...) on a node that has yet to be initialized; however, depending on the language we are using, we might need to be careful of this to avoid recursion errors!\nNow, in this case the first element searched through is still the root of the tree. This type of tree traversal is known as pre-order DFS. We perform an action (output the ID) before searching through the children. If we shift the function around and place the data output at the end of the function, we can modify the order in which we search through the tree to be post-order and look something like this:\nfunction DFS_recursive_postorder(n::Node)\n\n for child in n.children\n DFS_recursive_postorder(child)\n end\n\n # Here we are doing something...\n print(n.ID, \" \")\nend\n\nvoid dfs_recursive_postorder(node const& n) {\n for (auto const& child : n.children) {\n dfs_recursive_postorder(child);\n }\n std::cout \nprivate void DFSRecursivePostorder(Tree tree)\n{\n foreach (var c in tree._children)\n DFSRecursivePostorder(c);\n\n Console.Write(tree.Id + \" \");\n}\n\npublic void DFSRecursivePostorder()\n{\n DFSRecursivePostorder(this);\n\nvoid dfs_recursive_postorder(struct node n) {\n for (size_t i = 0; i \nprivate void dfsRecursivePostOrder(Node node) {\n for (Node n : node.children) {\n dfsRecursivePostOrder(n);\n }\n\n // Here we are doing something ...\n System.out.print(node.id + \" \");\n}\n\nfunction dfsPostorder(tree) {\n if (!tree) {\n return;\n }\n\n tree.children.forEach(dfsPostorder);\n process.stdout.write(tree.id + \" \");\n}\n\ndef dfs_recursive_postorder(node):\n for child in node.children:\n dfs_recursive_postorder(child)\n\n if node.data != None:\n print(node.data, end=' ')\n\n\n \nfn dfs_recursive_postorder(n: &Node) {\n for child in &n.children {\n dfs_recursive_postorder(child);\n }\n\n print!(\"{} \", n.value);\n}\n\ndfsPostOrder :: Tree a -> [a]\ndfsPostOrder (Node x ts) = concatMap dfsPostOrder ts ++ [x]\n\nfunc dfsRecursivePostOrder(node: Node) {\n for child in node.children! {\n dfsRecursivePostOrder(node: child)\n }\n\n print(node.value, terminator:\" \")\n}\n\npublic static function DFSRecursivePostorder(Tree $tree): void\n{\n foreach ($tree->getChildren() as $child) {\n static::DFSRecursivePostorder($child);\n }\n echo $tree->getId() . ' ';\n}\n\ndef dfs_recursive_postorder(node) \n node.children.each{ |child| dfs_recursive_postorder child }\n print \"#{node.id} \"\nend\n\n children collect: [ :child | (child dfsRecursivePostOrder)].\n Transcript show: data; cr.\n\nNode>>dfsInOrderBinaryTree\n \"Recursive depth first search on a binary tree in order.\"\n children size > 2 ifTrue: [\n\nfunc dfsRecursivePostorder(n *node) {\n for _, child := range n.children {\n dfsRecursivePostorder(child)\n }\n fmt.Printf(\"%d \", n.id)\n}\n\n# rdi - children ptr\n# rsi - value|children_size\ndfs_recursive_postorder:\n push r12\n push r13\n push r14\n mov r12, rdi\n mov r13, rsi\n mov r14, rsi\n mov r13d, r13d # Zero out the top 32 bits\n add r13, r12 # Pointer pointing after the last element of the children array\ndfs_recursive_po_children:\n cmp r12, r13 # If we reached the end, return\n je dfs_recursive_po_return\n mov rdi, QWORD PTR [r12]\n mov rsi, QWORD PTR [r12 + 8]\n call dfs_recursive_postorder\n add r12, tree_size\n jmp dfs_recursive_po_children\ndfs_recursive_po_return:\n mov rdi, OFFSET fmt_tree # Handle the current node\n mov rsi, r14\n shr rsi, 32 # The tree value is in the upper 32 bits\n xor rax, rax\n call printf\n pop r14\n pop r13\n pop r12\n ret\n\n🍉\n\n📗 Depth-First Search Recursive pre-order 📗\n❗️ 🌀 🍇\n 😀 🔡 id 10❗️❗️\n\n 🔂 child children 🍇\n 🌀 child❗️\n\n(defun dfs-recursive-postorder (node)\n \"A depth first approach for printing out all values in a tree starting from the bottom.\"\n (loop for child in (node-children node) do\n (dfs-recursive-postorder child))\n (when (node-data node)\n (format t \"~a \" (node-data node))))\n\nfunction DFS_recursive_postorder(n)\n\n cell_index = @(a, b) a{b};\n\n children = cell_index(values(n), 1);\n for i = children\n child = i{1};\n if ~isempty(child)\n DFS_recursive_postorder(child);\n end\n end\n\n ID = cell_index(keys(n), 1);\n fprintf('%u ', ID);\n\nend\n\ndef dfs_recursive_postorder(Node(value, children)):\n \"\"\"A depth first approach for printing out all values in a tree starting from the bottom.\"\"\"\n for child in children:\n dfs_recursive_postorder(child)\n print(value, end=' ')\n\n\n\n \n\n\nIn this case, the first node visited is at the bottom of the tree and moves up the tree branch by branch. In addition to these two types, binary trees have an in-order traversal scheme that looks something like this:\n# This assumes only 2 children, but accounts for other possibilities\nfunction DFS_recursive_inorder_btree(n::Node)\n\n if (length(n.children) == 2)\n DFS_recursive_inorder_btree(n.children[1])\n print(n.ID, \" \")\n DFS_recursive_inorder_btree(n.children[2])\n elseif (length(n.children) == 1)\n DFS_recursive_inorder_btree(n.children[1])\n print(n.ID, \" \")\n elseif (length(n.children) == 0)\n print(n.ID, \" \")\n else\n println(\"Not a binary tree!\")\n end\nend\n\nvoid dfs_recursive_inorder_btree(node const& n) {\n switch (n.children.size()) {\n case 2:\n dfs_recursive_inorder_btree(n.children[0]);\n std::cout \n\nprivate void DFSRecursiveInorderBinary(Tree tree)\n{\n switch (tree._children.Count)\n {\n case 2:\n DFSRecursiveInorderBinary(tree._children[0]);\n Console.Write(tree.Id + \" \");\n DFSRecursiveInorderBinary(tree._children[1]);\n break;\n case 1:\n DFSRecursiveInorderBinary(tree._children[0]);\n Console.Write(tree.Id + \" \");\n break;\n case 0:\n Console.Write(tree.Id + \" \");\n break;\n default:\n throw new Exception(\"Not binary tree!\");\n }\n}\n\npublic void DFSRecursiveInorderBinary()\n{\n DFSRecursiveInorderBinary(this);\n\nvoid dfs_recursive_inorder_btree(struct node n) {\n switch (n.children_size) {\n case 2:\n dfs_recursive_inorder_btree(n.children[0]);\n printf(\"%d \", n.id);\n dfs_recursive_inorder_btree(n.children[1]);\n break;\n case 1:\n dfs_recursive_inorder_btree(n.children[0]);\n printf(\"%d \", n.id);\n break;\n case 0:\n printf(\"%d \", n.id);\n break;\n default:\n printf(\"This is not a binary tree.\\n\");\n break;\n }\n}\n\nprivate void dfsRecursiveInOrderBinary(Node node) {\n switch (node.children.size()) {\n case 2:\n dfsRecursiveInOrderBinary(node.children.get(0));\n System.out.print(node.id + \" \");\n dfsRecursiveInOrderBinary(node.children.get(1));\n break;\n case 1:\n dfsRecursiveInOrderBinary(node.children.get(0));\n System.out.print(node.id + \" \");\n break;\n case 0:\n System.out.print(node.id + \" \");\n break;\n default:\n System.err.println(\"Not a binary tree at dfsRecursiveInOrderBinary()!\");\n }\n}\n\nfunction dfsInorder(tree) {\n if (!tree) {\n return;\n }\n\n switch (tree.children.length) {\n case 2:\n dfsInorder(tree.children[0]);\n console.log(tree.id);\n dfsInorder(tree.children[1]);\n break;\n case 1:\n dfsInorder(tree.children[0]);\n console.log(tree.id);\n break;\n case 0:\n console.log(tree.id);\n break;\n default:\n throw new Error(\"Postorder traversal is only valid for binary trees\");\n }\n}\n\ndef dfs_recursive_inorder_btree(node):\n if len(node.children) == 2:\n dfs_recursive_inorder_btree(node.children[0])\n print(node.data, end=' ')\n dfs_recursive_inorder_btree(node.children[1])\n elif len(node.children) == 1:\n dfs_recursive_inorder_btree(node.children[0])\n print(node.data, end=' ')\n elif len(node.children) == 0:\n print(node.data, end=' ')\n else:\n print(\"Not a binary tree!\")\n\n\n \nfn dfs_recursive_inorder_btree(n: &Node) {\n match &n.children[..] {\n [left, right] => {\n dfs_recursive_inorder_btree(left);\n print!(\"{} \", n.value);\n dfs_recursive_inorder_btree(right);\n }\n [left] => {\n dfs_recursive_inorder_btree(left);\n print!(\"{} \", n.value);\n }\n [] => print!(\"{} \", n.value),\n _ => print!(\"This is not a binary tree. \"),\n }\n}\n\ndfsInOrder :: Tree a -> [a] -- For binary trees only\ndfsInOrder (Node x []) = [x]\ndfsInOrder (Node x [l]) = dfsInOrder l ++ [x] -- Single branch assumed to be left\ndfsInOrder (Node x [l, r]) = dfsInOrder l ++ [x] ++ dfsInOrder r\ndfsInOrder _ = error \"Not a binary tree\"\n\nfunc dfsRecursiveInOrderBinary(node: Node) {\n if node.children?.count == 2 {\n dfsRecursiveInOrderBinary(node: node.children![0])\n print(node.value, terminator:\" \")\n dfsRecursiveInOrderBinary(node: node.children![1])\n } else if node.children?.count == 1 {\n dfsRecursiveInOrderBinary(node: node.children![0])\n print(node.value, terminator:\" \")\n } else if node.children?.count == 0 {\n print(node.value, terminator:\" \")\n } else {\n print(\"Not a binary tree!\")\n }\n}\n\npublic static function DFSRecursiveInorderBinary(Tree $tree): void\n{\n switch (count($tree->getChildren())) {\n case 2:\n static::DFSRecursiveInorderBinary($tree->getChildren()[0]);\n echo $tree->getId() . ' ';\n static::DFSRecursiveInorderBinary($tree->getChildren()[1]);\n break;\n case 1:\n static::DFSRecursiveInorderBinary($tree->getChildren()[0]);\n echo $tree->getId() . ' ';\n break;\n case 0:\n echo $tree->getId() . ' ';\n break;\n default:\n throw new InvalidArgumentException('Not a binary tree!');\n break;\n }\n}\n\ndef dfs_recursive_inorder_btree(node) \n case node.children.size\n when 2\n dfs_recursive_inorder_btree node.children[0]\n print \"#{node.id} \"\n dfs_recursive_inorder_btree node.children[1] \n when 1 \n dfs_recursive_inorder_btree node.children[0]\n print \"#{node.id} \"\n when 0 \n print \"#{node.id} \"\n else \n print \"Not a binary tree!\"\n end \nend\n\n ^self.\n ].\n children size = 2 ifTrue: [\n (children at: 1) dfsInOrderBinaryTree: value.\n ].\n Transcript show: data; cr.\n children size >= 1 ifTrue: [\n (children at: 0) dfsInOrderBinaryTree: value.\n ].\n ^self.\n\nNode>>dfsStack\n \"Depth-first search with a stack.\"\n | stack top |\n\nfunc dfsRecursiveInorderBtree(n *node) {\n switch len(n.children) {\n case 2:\n dfsRecursiveInorderBtree(n.children[0])\n fmt.Printf(\"%d \", n.id)\n dfsRecursiveInorderBtree(n.children[1])\n case 1:\n dfsRecursiveInorderBtree(n.children[0])\n fmt.Printf(\"%d \", n.id)\n case 0:\n fmt.Printf(\"%d \", n.id)\n default:\n fmt.Println(\"This is not a binary tree\")\n }\n}\n\n# rdi - children ptr\n# rsi - value|children_size\ndfs_recursive_inorder_btree:\n push r12\n push r13\n mov r12, rdi\n mov r13, rsi\n mov rax, rsi\n mov eax, eax\n cmp rax, 0 # Check what type of tree it is.\n je dfs_recursive_bt_size0\n cmp rax, 16\n je dfs_recursive_bt_size1\n cmp rax, 32\n je dfs_recursive_bt_size2\n mov rdi, OFFSET not_bt # If the tree is not binary then print a warning\n xor rax, rax\n call printf\n jmp dfs_recursive_bt_return\ndfs_recursive_bt_size0:\n mov rdi, OFFSET fmt_tree # If the node is a leaf then print its id\n shr rsi, 32\n xor rax, rax\n call printf\n jmp dfs_recursive_bt_return\ndfs_recursive_bt_size1:\n mov rdi, QWORD PTR [r12] # If the node has 1 child then call the function and print the id\n mov rsi, QWORD PTR [r12 + 8]\n call dfs_recursive_inorder_btree\n mov rdi, OFFSET fmt_tree\n mov rsi, r13\n shr rsi, 32\n xor rax, rax\n call printf\n jmp dfs_recursive_bt_return\ndfs_recursive_bt_size2:\n mov rdi, QWORD PTR [r12] # Same as above just print id inbetween the calls\n mov rsi, QWORD PTR [r12 + 8]\n call dfs_recursive_inorder_btree\n mov rdi, OFFSET fmt_tree\n mov rsi, r13\n shr rsi, 32\n xor rax, rax\n call printf\n mov rdi, QWORD PTR [r12 + 16]\n mov rsi, QWORD PTR [r12 + 24]\n call dfs_recursive_inorder_btree\ndfs_recursive_bt_return:\n pop r13\n pop r12\n ret\n\n🍉\n\n📗 Depth-First Search Recursive post-order 📗\n❗️ 🍥 🍇\n 🔂 child children 🍇\n 🍥 child❗️\n 🍉\n\n 😀 🔡 id 10❗️❗️\n🍉\n\n📗\n Depth-First Search Recursive Inorder Binary\n This assumes only 2 children.\n📗\n❗️ 🍭 ➡️ 🍬⏹ 🍇\n ↪️ 🐔 children❗️ ▶️ 2 🍇\n ↩️ 🆕⏹⏫❗️\n\n(defun dfs-recursive-inorder-btree (node)\n \"A depth first search approach for printing all values in a binary tree.\"\n (case (length (node-children node))\n (2\n (dfs-recursive-inorder-btree (first (node-children node)))\n (format t \"~a \" (node-data node))\n (dfs-recursive-inorder-btree (second (node-children node))))\n (1\n (dfs-recursive-inorder-btree (first (node-children node)))\n (format t \"~a \" (node-data node)))\n (0\n (format t \"~a \" (node-data node)))\n (t\n (print \"Invalid binary tree.\"))))\n\nfunction DFS_recursive_inorder_btree(n)\n\n cell_index = @(a, b) a{b};\n ID = cell_index(keys(n), 1);\n children = cell_index(values(n), 1);\n\n if length(children) == 2\n DFS_recursive_inorder_btree(children{1})\n fprintf('%u ', ID)\n DFS_recursive_inorder_btree(children{2})\n elseif length(children) == 1\n if ~isempty(children{1})\n DFS_recursive_inorder_btree(children{1})\n end\n fprintf('%u ', ID)\n else\n fprintf(\"Not a binary tree!\")\n end\nend\n\ndef dfs_recursive_inorder_btree(Node(value, children)):\n \"\"\"A depth first search approach for printing all values in a binary tree.\"\"\"\n case len(children):\n match 2:\n dfs_recursive_inorder_btree(children[0])\n print(value, end=' ')\n dfs_recursive_inorder_btree(children[1])\n match 1:\n dfs_recursive_inorder_btree(children[0])\n print(value, end=' ')\n match 0:\n print(value, end=' ')\n else:\n print('Invalid binary tree')\n\n\n\n\n \n\n\nThe order here seems to be some mix of the other 2 methods and works through the binary tree from left to right.\nNow, at this point, it might seem that the only way to search through a recursive data structure is with recursion, but this is not necessarily the case! Rather surprisingly, we can perform a DFS non-recursively by using a stack, which are data structures that hold multiple elements, but only allow you to interact with the very last element you put in. The idea here is simple:\n\nPut the root node in the stack\nTake it out and put in its children\nPop the top of the stack and put its children in\nRepeat 3 until the stack is empty\n\nIn code, it looks like this:\nfunction DFS_stack(n::Node)\n s = Stack{Node}()\n push!(s, n)\n\n while(length(s) > 0)\n print(top(s).ID, \" \")\n temp = pop!(s)\n for child in temp.children\n push!(s, child)\n end\n end\nend\n\nvoid dfs_stack(node const& n) {\n // this stack holds pointers into n's `children` vector,\n // or its children's `children` vector.\n std::stack stack;\n stack.push(&n);\n\n while (stack.size() > 0) {\n auto const& temp = *stack.top();\n stack.pop();\n std::cout \n}\n\npublic void DFSStack()\n{\n var stack = new Stack();\n stack.Push(this);\n\n while (stack.Count != 0)\n {\n Console.Write(stack.Peek().Id + \" \");\n var temp = stack.Pop();\n\n foreach (var c in temp._children)\n stack.Push(c);\n\nvoid dfs_stack(struct node n) {\n struct stack stk = get_stack(sizeof(struct node*));\n stack_push(&stk, &n);\n struct node *tmp;\n\n while (!stack_empty(&stk)) {\n tmp = (struct node*)stack_pop(&stk);\n if (!tmp) {\n break;\n }\n\n printf(\"%d \", tmp->id);\n for (size_t i = 0; i children_size; ++i) {\n stack_push(&stk, &tmp->children[i]);\n }\n }\n\n free_stack(stk);\n}\n\npublic void dfsStack() {\n Stack stack = new Stack();\n stack.push(this.root);\n\n Node tmp;\n\n while (stack.size() != 0) {\n System.out.print(stack.peek().id + \" \");\n tmp = stack.pop();\n\n for (Node c : tmp.children) {\n stack.push(c);\n }\n }\n}\n\nfunction dfsIterative(tree) {\n const stack = [tree];\n while (stack.length > 0) {\n const current = stack.pop();\n process.stdout.write(current.id + \" \");\n stack.push(...current.children);\n }\n}\n\ndef dfs_stack(node):\n stack = [node]\n while stack:\n node = stack.pop()\n stack.extend(node.children)\n print(node.data, end=' ')\n\n\n \nfn dfs_stack(n: &Node) {\n let mut stack = vec![n];\n\n while let Some(current) = stack.pop() {\n print!(\"{} \", current.value);\n stack.extend(¤t.children);\n }\n}\n\ndfsStack :: Tree a -> [a]\ndfsStack t = go [t]\n where\n go [] = []\n go ((Node x ts) : stack) = x : go (ts ++ stack)\n\nfunc dfsStack(node: Node) {\n var stack = [node]\n var temp: Node\n\n while stack.count > 0 {\n temp = stack.popLast()!\n print(temp.value, terminator:\" \")\n\n for child in temp.children! {\n stack.append(child)\n }\n }\n}\n\npublic static function DFSStack(Tree $tree): void\n{\n $stack = [$tree];\n $temp = null;\n\n while (null !== ($temp = array_pop($stack))) {\n echo $temp->getId() . ' ';\n foreach ($temp->getChildren() as $child) {\n $stack[] = $child;\n }\n }\n}\n\ndef dfs_stack(node) \n stack = [node] \n\n until stack.empty? \n temp = stack.pop \n print \"#{temp.id} \"\n temp.children.each{ |child| stack.push child } \n end \nend\n\nNode>>dfsStack\n \"Depth-first search with a stack.\"\n | stack top |\n stack := Stack new.\n stack push: self.\n [stack size > 0] whileTrue: [\n top := stack pop.\n Transcript show: (top data); cr.\n top children reverseDo: [ :child |\n stack push: child.\n ].\n ].\n\nfunc dfsStack(n *node) {\n stack := []*node{n}\n\n for len(stack) > 0 {\n cur := stack[0]\n stack = stack[1:]\n fmt.Printf(\"%d \", cur.id)\n stack = append(cur.children, stack...)\n }\n}\n\n# rdi - children ptr\n# rsi - value|children_size\ndfs_stack:\n push r12\n push r13\n push r14\n sub rsp, 16 # Create stack\n mov r12, rsp\n push rsi # Save node to use as pointer\n push rdi\n mov rdi, r12\n call get_stack # Init stack\n mov rdi, r12\n mov rsi, rsp\n call stack_push # Push node\n mov rdi, r12 # Pop stack\n call stack_pop\ndfs_stack_loop:\n test rax, rax # Test if stack is empty\n jz dfs_stack_return\n mov r13, rax\n mov rdi, OFFSET fmt_tree # Print id\n mov esi, DWORD PTR [r13 + 12]\n xor rax, rax\n call printf\n mov eax, DWORD PTR [r13 + 8] # Get start and end of array\n mov r13, QWORD PTR [r13]\n lea r14, [r13 + rax]\ndfs_stack_push_child:\n cmp r13, r14 # Check if the pointers are the same\n je dfs_stack_end_push\n mov rdi, r12 # Push node into the stack\n mov rsi, r13\n call stack_push\n add r13, tree_size\n jmp dfs_stack_push_child\ndfs_stack_end_push:\n mov rdi, r12 # Pop stack\n call stack_pop\n jmp dfs_stack_loop\ndfs_stack_return:\n mov rdi, r12 # Free stack\n call free_stack\n add rsp, 32\n pop r14\n pop r13\n pop r12\n ret\n\n\n ↪️ 🐔 children❗️ ▶️ 0 🍇\n 🍭🐽 children 0❗️❗️\n 😀 🔡 id 10❗️❗️\n 🍭🐽 children 1❗️❗️\n 🍉\n 🙅 🍇\n 😀 🔡 id 10❗️❗️\n 🍉\n ↩️ 🤷‍♀️\n🍉\n\n📗 Depth-First Search Stack 📗\n❗️ 🥞 🍇\n 🍨 🐕 🍆 ➡️ stack\n\n(defun dfs-stack (node)\n \"A depth first approach for printing out all values in a tree using a stack.\"\n (loop\n with stack = (list node)\n with temp = nil\n while (> (length stack) 0) do\n (format t \"~a \" (node-data (first stack)))\n (setf temp (pop stack))\n (loop for child in (node-children temp) do\n (push child stack))))\n\nfunction DFS_stack(n)\n\n cell_index = @(a, b) a{b};\n node_stack = {n};\n\n while ~isempty(node_stack)\n\n parent = node_stack{end};\n node_stack(end) = [];\n\n ID = cell_index(keys(parent), 1);\n fprintf('%u ', ID);\n\n children = cell_index(values(parent), 1);\n\n for i = flip(children)\n child = i{1};\n if ~isempty(child)\n node_stack = {node_stack{:} child};\n end\n end\n end\nend\n\ndef dfs_stack(node is Node):\n \"\"\"A depth first approach for printing out all values in a tree using a stack.\"\"\"\n stack = [node]\n while stack:\n current_node = stack.pop()\n print(current_node.value, end=' ')\n for child in current_node.children:\n stack.append(child)\n\n\n\nAll this said, there are a few details about DFS that might not be ideal, depending on the situation. For example, if we use DFS on an incredibly long tree, we will spend a lot of time going further and further down a single branch without searching the rest of the data structure. In addition, it is not the natural way humans would order a tree if asked to number all the nodes from top to bottom. I would argue a more natural traversal order would look something like this:\n\n \n\n\nAnd this is exactly what Breadth-First Search (BFS) does! On top of that, it can be implemented in the same way as the DFS_stack(...) function above, simply by swapping the stack for a queue, which is similar to a stack, except that it only allows you to interact with the very first element instead of the last. In code, this looks something like:\nfunction BFS_queue(n::Node)\n q = Queue{Node}()\n enqueue!(q, n)\n\n while(length(q) > 0)\n print(first(q).ID, \" \")\n temp = dequeue!(q)\n for child in temp.children\n enqueue!(q, child)\n end\n end\nend\n\nvoid bfs_queue(node const& n) {\n std::queue queue;\n queue.push(&n);\n\n while (queue.size() > 0) {\n auto const& temp = *queue.front();\n queue.pop();\n\n std::cout \n}\n\npublic void BFSQueue()\n{\n var queue = new Queue();\n queue.Enqueue(this);\n\n while (queue.Count != 0)\n {\n Console.Write(queue.Peek().Id + \" \");\n var temp = queue.Dequeue();\n\n foreach (var c in temp._children)\n queue.Enqueue(c);\n\nvoid bfs_queue(struct node n) {\n struct queue q = get_queue(sizeof(struct node*));\n enqueue(&q, &n);\n struct node *tmp;\n\n while (!queue_empty(&q)) {\n tmp = (struct node*)dequeue(&q);\n if (!tmp) {\n break;\n }\n\n printf(\"%d \", tmp->id);\n for (size_t i = 0; i children_size; ++i) {\n enqueue(&q, &tmp->children[i]);\n }\n }\n\n free_queue(q);\n}\n\npublic void bfsQueue() {\n Queue queue = new LinkedList();\n queue.add(this.root);\n\n while (queue.size() != 0) {\n System.out.print(queue.peek().id + \" \");\n Node temp = queue.poll(); // return null if the queue is empty\n\n if (temp != null) {\n for (Node c : temp.children) {\n queue.add(c);\n }\n }\n }\n}\n\nfunction bfs(tree) {\n const queue = [tree];\n while (queue.length > 0) {\n const current = queue.shift();\n process.stdout.write(current.id + \" \");\n queue.push(...current.children);\n }\n}\n\ndef bfs_queue(node):\n queue = [node]\n while queue:\n node = queue.pop(0)\n queue.extend(node.children)\n print(node.data)\n\n\n \nfn bfs_queue(n: &Node) {\n let mut queue = VecDeque::new();\n queue.push_back(n);\n\n while let Some(current) = queue.pop_front() {\n print!(\"{} \", current.value);\n queue.extend(¤t.children);\n }\n}\n\nbfs :: Tree a -> [a]\nbfs (Node x ts) = x : go ts\n where\n go [] = []\n go ts = map node ts ++ go (concatMap forest ts)\n\nfunc bfsQueue(node: Node) {\n var queue = [node]\n var temp: Node\n\n while queue.count > 0 {\n temp = queue.remove(at: 0)\n print(temp.value, terminator:\" \")\n\n for child in temp.children! {\n queue.append(child)\n }\n }\n}\n\npublic static function DFSQueue(Tree $tree): void\n{\n $stack = [$tree];\n $temp = null;\n\n while (null !== ($temp = array_shift($stack))) {\n echo $temp->getId() . ' ';\n foreach ($temp->getChildren() as $child) {\n $stack[] = $child;\n }\n }\n}\n\ndef bfs_queue(node) \n queue = Deque.new [node]\n\n until queue.empty? \n temp = queue.shift\n print \"#{temp.id} \"\n temp.children.each{ |child| queue.push child }\n end \nend\n\nNode>>bfs\n \"A breadth-first tree search using queues.\"\n | queue current |\n queue := LinkedList with: self.\n [ queue size > 0 ] whileTrue: [\n current := queue first.\n queue removeFirst.\n Transcript show: (current data); cr.\n current children collect: [ :child |\n queue addLast: child\n ].\n ].\n\nfunc bfsQueue(n *node) {\n queue := []*node{n}\n\n for len(queue) > 0 {\n cur := queue[0]\n queue = queue[1:]\n fmt.Printf(\"%d \", cur.id)\n queue = append(queue, cur.children...)\n }\n}\n\n# rdi - children ptr\n# rsi - value|children_size\nbfs_queue:\n push r12\n push r13\n push r14\n sub rsp, 20 # Create queue\n mov r12, rsp\n push rsi # Save node to use as pointer\n push rdi\n mov rdi, r12\n call get_queue # Init queue\n mov rdi, r12\n mov rsi, rsp\n call enqueue # enqueue node\n mov eax, DWORD PTR [r12 + 8]\n mov edi, DWORD PTR [r12 + 12]\nbfs_queue_loop:\n cmp eax, edi\n je bfs_queue_return\n mov rdi, r12 # dequeue\n call dequeue\n test rax, rax # Test if queue is empty\n jz bfs_queue_return\n mov r13, rax\n mov rdi, OFFSET fmt_tree # Print id\n mov esi, DWORD PTR [r13 + 12]\n xor rax, rax\n call printf\n mov eax, DWORD PTR [r13 + 8] # Get start and end of array\n mov r13, QWORD PTR [r13]\n lea r14, [r13 + rax]\nbfs_queue_push_child:\n cmp r13, r14 # Check if the pointers are the same\n je bfs_queue_end_push\n mov rdi, r12 # enqueue node\n mov rsi, r13\n call enqueue\n add r13, tree_size\n jmp bfs_queue_push_child\nbfs_queue_end_push:\n mov eax, DWORD PTR [r12 + 8]\n mov edi, DWORD PTR [r12 + 12]\n jmp bfs_queue_loop\nbfs_queue_return:\n mov rdi, r12 # Free queue\n call free_queue\n add rsp, 36\n pop r14\n pop r13\n pop r12\n ret\n\n 🐽 stack 🐔 stack❗️ ➖ 1❗️ ➡️ temp\n 🐨 stack 🐔 stack❗️ ➖ 1❗️\n\n 😀 🔡 🆔 temp❗️ 10❗️❗️\n\n 🧒 temp❗️ ➡️ temp_children\n 🔂 child temp_children 🍇\n 🐻 stack child❗️\n 🍉\n 🍉\n🍉\n\n📗 Breadth-First Search Queue 📗\n❗️ 🏢 🍇\n 🍨 🐕 🍆 ➡️ queue\n\n(defun bfs-queue (node)\n \"A breadth first search approach for printing out all values in a tree.\"\n (loop\n with queue = (list node)\n with temp = nil\n while (> (length queue) 0) do\n (format t \"~a \" (node-data (first queue)))\n (setf temp (pop queue))\n ;; If the queue is empty, the queue should be filled with the children nodes.\n (if (eql queue nil)\n (setf queue (node-children temp))\n (nconc queue (node-children temp)))))\n\nfunction BFS_queue(n)\n\n cell_index = @(a, b) a{b};\n node_queue = {n};\n\n while ~isempty(node_queue)\n next_nodes = {};\n for parent_cell = node_queue\n parent = parent_cell{1};\n ID = cell_index(keys(parent), 1);\n fprintf('%u ', ID);\n children = cell_index(values(parent), 1);\n for i = children\n child = i{1};\n if ~isempty(child)\n next_nodes = {next_nodes{:}, child};\n end\n end\n end\n node_queue = next_nodes;\n end\nend\n\ndef bfs_queue(node is Node):\n \"\"\"A breadth first search approach for printing out all values in a tree.\"\"\"\n queue = deque([node])\n while queue:\n current_node = queue.popleft()\n print(current_node.value, end=' ')\n for child in current_node.children:\n queue.append(child)\n\n\n\nVideo Explanation\nHere is a video describing tree traversal:\n\n\n\n\nExample Code\nusing DataStructures, Printf\n\nstruct Node\n children::Vector{Node}\n ID::Int64\n Node(ID::Int64) = new(Vector{Node}(), ID)\nend\n\nfunction DFS_recursive(n::Node)\n # Here we are doing something...\n print(n.ID, \" \")\n\n for child in n.children\n DFS_recursive(child)\n end\nend\n\nfunction DFS_recursive_postorder(n::Node)\n\n for child in n.children\n DFS_recursive_postorder(child)\n end\n\n # Here we are doing something...\n print(n.ID, \" \")\nend\n\n# This assumes only 2 children, but accounts for other possibilities\nfunction DFS_recursive_inorder_btree(n::Node)\n\n if (length(n.children) == 2)\n DFS_recursive_inorder_btree(n.children[1])\n print(n.ID, \" \")\n DFS_recursive_inorder_btree(n.children[2])\n elseif (length(n.children) == 1)\n DFS_recursive_inorder_btree(n.children[1])\n print(n.ID, \" \")\n elseif (length(n.children) == 0)\n print(n.ID, \" \")\n else\n println(\"Not a binary tree!\")\n end\nend\n\nfunction DFS_stack(n::Node)\n s = Stack{Node}()\n push!(s, n)\n\n while(length(s) > 0)\n print(top(s).ID, \" \")\n temp = pop!(s)\n for child in temp.children\n push!(s, child)\n end\n end\nend\n\nfunction BFS_queue(n::Node)\n q = Queue{Node}()\n enqueue!(q, n)\n\n while(length(q) > 0)\n print(first(q).ID, \" \")\n temp = dequeue!(q)\n for child in temp.children\n enqueue!(q, child)\n end\n end\nend\n\n# function to create a simple, balanced tree\nfunction create_tree(num_row::Int64, num_child::Int64)\n ret = Node(num_row)\n if (num_row == 0)\n return ret\n end\n\n for i = 1:num_child\n child = create_tree(num_row - 1, num_child)\n push!(ret.children, child)\n end\n\n return ret\nend\n\nfunction main()\n root = create_tree(2, 3)\n\n println(\"[#]\\nRecursive DFS:\")\n DFS_recursive(root);\n println()\n\n println(\"[#]\\nRecursive Postorder DFS:\")\n DFS_recursive_postorder(root);\n println()\n\n println(\"[#]\\nStack-based DFS:\")\n DFS_stack(root);\n println()\n\n println(\"[#]\\nQueue-based BFS:\")\n BFS_queue(root);\n println()\n\n root_binary = create_tree(3,2)\n println(\"[#]\\nRecursive Inorder DFS for Binary Tree:\")\n DFS_recursive_inorder_btree(root_binary)\n println()\nend\n\nmain()\n\n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing std::size_t;\n\nstruct node {\n std::vector children;\n size_t value;\n};\n\n// Simple recursive scheme for DFS\nvoid dfs_recursive(node const& n) {\n // Here we are doing something...\n std::cout stack;\n stack.push(&n);\n\n while (stack.size() > 0) {\n auto const& temp = *stack.top();\n stack.pop();\n std::cout queue;\n queue.push(&n);\n\n while (queue.size() > 0) {\n auto const& temp = *queue.front();\n queue.pop();\n\n std::cout (), 0};\n }\n\n std::vector vec;\n std::generate_n(std::back_inserter(vec), num_child, [&] {\n return create_tree(num_row - 1, num_child);\n });\n\n return node{std::move(vec), num_row};\n}\n\nint main() {\n // Creating Tree in main\n auto root = create_tree(2, 3);\n auto binary_root = create_tree(3, 2);\n std::cout \nTree.cs\nusing System;\nusing System.Collections.Generic;\n\nnamespace TreeTraversal\n{\n public class Tree\n {\n public int Id { get; private set; }\n private List _children = new List();\n\n public Tree(int depthCount, int childrenCount)\n {\n Id = 1;\n\n if (depthCount > 0)\n {\n for (int i = 0; i ();\n stack.Push(this);\n\n while (stack.Count != 0)\n {\n Console.Write(stack.Peek().Id + \" \");\n var temp = stack.Pop();\n\n foreach (var c in temp._children)\n stack.Push(c);\n }\n }\n\n public void BFSQueue()\n {\n var queue = new Queue();\n queue.Enqueue(this);\n\n while (queue.Count != 0)\n {\n Console.Write(queue.Peek().Id + \" \");\n var temp = queue.Dequeue();\n\n foreach (var c in temp._children)\n queue.Enqueue(c);\n }\n }\n }\n}\n\nProgram.cs\nusing System;\n\nnamespace TreeTraversal\n{\n class Program\n {\n static void Main(string[] args)\n {\n var tree = new Tree(2, 3);\n Console.WriteLine(\"[#]\\nRecursive DFS:\");\n tree.DFSRecursive();\n Console.WriteLine();\n\n Console.WriteLine(\"[#]\\nRecursive Postorder DFS:\");\n tree.DFSRecursivePostorder();\n Console.WriteLine();\n\n Console.WriteLine(\"[#]\\nStack-based DFS:\");\n tree.DFSStack();\n Console.WriteLine();\n\n Console.WriteLine(\"[#]\\nQueue-based BFS:\");\n tree.BFSQueue();\n Console.WriteLine();\n\n tree = new Tree(3, 2);\n Console.WriteLine(\"[#]\\nRecursive Inorder DFS for Binary Tree:\");\n tree.DFSRecursiveInorderBinary();\n Console.WriteLine();\n }\n }\n}\n\nutility.h\n#ifndef UTILITY_H\n#define UTILITY_H\n\n#include \n#include \n#include \n#include \n\nstruct stack {\n void **data;\n size_t top, capacity, size;\n};\n\nstruct queue {\n void **data;\n size_t front, back, capacity;\n};\n\nstruct stack get_stack(size_t size) {\n struct stack stk;\n\n stk.data = malloc(4 * size);\n stk.capacity = 4;\n stk.top = 0;\n\n return stk;\n}\n\nbool stack_empty(struct stack *stk) {\n return stk->top == 0;\n}\n\nvoid stack_push(struct stack *stk, void *element) {\n if (stk->top == stk->capacity) {\n stk->capacity *= 2;\n stk->data = realloc(stk->data, stk->capacity * sizeof(stk->data[0]));\n }\n\n stk->data[stk->top++] = element;\n}\n\nvoid *stack_pop(struct stack *stk) {\n if (stack_empty(stk)) {\n return NULL;\n }\n\n return stk->data[--stk->top];\n}\n\nvoid free_stack(struct stack stk) {\n free(stk.data);\n}\n\nstruct queue get_queue(size_t size) {\n struct queue q;\n\n q.data = calloc(4, size);\n q.front = 0;\n q.back = 0;\n q.capacity = 4;\n\n return q;\n}\n\nbool queue_empty(struct queue *q) {\n return q->front == q->back;\n}\n\nvoid queue_resize(struct queue *q) {\n size_t size = sizeof(q->data[0]);\n void **tmp = calloc((q->capacity * 2), size);\n memcpy(tmp, q->data + q->front, (q->capacity - q->front) * size);\n memcpy(tmp + q->capacity - q->front, q->data, (q->front - 1) * size);\n\n free(q->data);\n\n q->data = tmp;\n q->back = q->capacity - 1;\n q->front = 0;\n q->capacity *= 2;\n}\n\nvoid enqueue(struct queue *q, void *element) {\n if (q->front == (q->back + 1) % q->capacity) {\n queue_resize(q);\n }\n\n q->data[q->back] = element;\n q->back = (q->back + 1) % q->capacity;\n}\n\nvoid *dequeue(struct queue *q) {\n if (queue_empty(q)) {\n return NULL;\n }\n\n void *ret = q->data[q->front];\n q->front = (q->front + 1) % q->capacity;\n\n return ret;\n}\n\nvoid free_queue(struct queue q) {\n free(q.data);\n}\n\n#endif //UTILITY_H\n\ntree_traversal.c\n#include \"utility.h\"\n\n#include \n#include \n#include \n\nstruct node {\n struct node *children;\n size_t children_size;\n int id;\n};\n\nstruct node create_tree(int rows, size_t num_children) {\n struct node n = {NULL, 0, rows};\n\n if (rows > 0) {\n n.children = (struct node*)malloc(num_children * sizeof(struct node));\n n.children_size = num_children;\n for (size_t i = 0; i 0) {\n for (size_t i = 0; i id);\n for (size_t i = 0; i children_size; ++i) {\n stack_push(&stk, &tmp->children[i]);\n }\n }\n\n free_stack(stk);\n}\n\nvoid bfs_queue(struct node n) {\n struct queue q = get_queue(sizeof(struct node*));\n enqueue(&q, &n);\n struct node *tmp;\n\n while (!queue_empty(&q)) {\n tmp = (struct node*)dequeue(&q);\n if (!tmp) {\n break;\n }\n\n printf(\"%d \", tmp->id);\n for (size_t i = 0; i children_size; ++i) {\n enqueue(&q, &tmp->children[i]);\n }\n }\n\n free_queue(q);\n}\n\nint main() {\n struct node root = create_tree(2, 3);\n\n printf(\"[#]\\nRecursive DFS:\\n\");\n dfs_recursive(root);\n printf(\"\\n\");\n\n printf(\"[#]\\nRecursive Postorder DFS:\\n\");\n dfs_recursive_postorder(root);\n printf(\"\\n\");\n\n printf(\"[#]\\nStack-based DFS:\\n\");\n dfs_stack(root);\n printf(\"\\n\");\n\n printf(\"[#]\\nQueue-based BFS:\\n\");\n bfs_queue(root);\n printf(\"\\n\");\n\n destroy_tree(root);\n struct node root_binary = create_tree(3, 2);\n\n printf(\"[#]\\nRecursive Inorder DFS for Binary Tree:\\n\");\n dfs_recursive_inorder_btree(root_binary);\n printf(\"\\n\");\n\n destroy_tree(root_binary);\n return 0;\n}\n\nTree.java\nimport java.util.ArrayList;\nimport java.util.LinkedList;\nimport java.util.Queue;\nimport java.util.Stack;\n\npublic class Tree {\n public Node root;\n\n public Tree(int rowCount, int childrenCount) {\n // this.root is the root node of the Tree\n this.root = new Node(rowCount);\n this.createAllChildren(this.root, rowCount-1, childrenCount);\n }\n\n\n public void dfsRecursive() {\n this.dfsRecursive(this.root);\n }\n\n private void dfsRecursive(Node node) {\n System.out.print(node.id + \" \");\n\n for (Node n : node.children) {\n dfsRecursive(n);\n }\n }\n\n\n public void dfsRecursivePostOrder() {\n this.dfsRecursivePostOrder(this.root);\n }\n\n private void dfsRecursivePostOrder(Node node) {\n for (Node n : node.children) {\n dfsRecursivePostOrder(n);\n }\n\n // Here we are doing something ...\n System.out.print(node.id + \" \");\n }\n\n\n public void dfsRecursiveInOrderBinary() {\n dfsRecursiveInOrderBinary(this.root);\n }\n\n private void dfsRecursiveInOrderBinary(Node node) {\n switch (node.children.size()) {\n case 2:\n dfsRecursiveInOrderBinary(node.children.get(0));\n System.out.print(node.id + \" \");\n dfsRecursiveInOrderBinary(node.children.get(1));\n break;\n case 1:\n dfsRecursiveInOrderBinary(node.children.get(0));\n System.out.print(node.id + \" \");\n break;\n case 0:\n System.out.print(node.id + \" \");\n break;\n default:\n System.err.println(\"Not a binary tree at dfsRecursiveInOrderBinary()!\");\n }\n }\n\n\n public void dfsStack() {\n Stack stack = new Stack();\n stack.push(this.root);\n\n Node tmp;\n\n while (stack.size() != 0) {\n System.out.print(stack.peek().id + \" \");\n tmp = stack.pop();\n\n for (Node c : tmp.children) {\n stack.push(c);\n }\n }\n }\n\n public void bfsQueue() {\n Queue queue = new LinkedList();\n queue.add(this.root);\n\n while (queue.size() != 0) {\n System.out.print(queue.peek().id + \" \");\n Node temp = queue.poll(); // return null if the queue is empty\n\n if (temp != null) {\n for (Node c : temp.children) {\n queue.add(c);\n }\n }\n }\n }\n\n\n private void createAllChildren(Node node, int rowCount, int childrenCount) {\n if (rowCount {\n public ArrayList children;\n public int id;\n\n public Node(int id) {\n this.children = new ArrayList();\n this.id = id;\n }\n\n @Override\n public int compareTo(Node other) {\n // Need to implement Comparable and override this\n // method because of the method BFSQueue() which uses Queues\n // and must know how to check if two nodes are the same or not\n return Integer.compare(this.id, other.id);\n }\n }\n\n public static void main(String[] args) {\n Tree tree = new Tree(2, 3);\n\n System.out.println(\"[#]\\nRecursive DFS:\");\n tree.dfsRecursive();\n System.out.println();\n\n System.out.println(\"[#]\\nRecursive Postorder DFS:\");\n tree.dfsRecursivePostOrder();\n System.out.println();\n\n\n System.out.println(\"[#]\\nStack-based DFS:\");\n tree.dfsStack();\n System.out.println();\n\n\n System.out.println(\"[#]\\nQueue-based BFS:\");\n tree.bfsQueue();\n System.out.println();\n\n\n // Uncommenting the following 2 lines will result in an exception thrown because at least one Node of the Tree has more than 2 children and therefor a DFSRecursiveInorderBinary doesn't work.\n //System.out.println(\"Using in-order binary recursive DFS : (fail)\");\n //tree.dfsRecursiveInOrderBinary();\n\n tree = new Tree(3, 2);\n System.out.println(\"[#]\\nRecursive Inorder DFS for Binary Tree:\");\n tree.dfsRecursiveInOrderBinary();\n System.out.println();\n }\n}\n\nfunction createTree(rows, children) {\n if (rows === 0) {\n return { id: rows, children: [] };\n }\n\n return {\n id: rows,\n children: [...Array(children).keys()].map(() => createTree(rows - 1, children))\n };\n}\n\nfunction dfsPreorder(tree) {\n if (!tree) {\n return;\n }\n\n process.stdout.write(tree.id + \" \");\n tree.children.forEach(dfsPreorder);\n}\n\nfunction dfsPostorder(tree) {\n if (!tree) {\n return;\n }\n\n tree.children.forEach(dfsPostorder);\n process.stdout.write(tree.id + \" \");\n}\n\nfunction dfsInorder(tree) {\n if (!tree) {\n return;\n }\n\n switch (tree.children.length) {\n case 2:\n dfsInorder(tree.children[0]);\n console.log(tree.id);\n dfsInorder(tree.children[1]);\n break;\n case 1:\n dfsInorder(tree.children[0]);\n console.log(tree.id);\n break;\n case 0:\n console.log(tree.id);\n break;\n default:\n throw new Error(\"Postorder traversal is only valid for binary trees\");\n }\n}\n\nfunction dfsIterative(tree) {\n const stack = [tree];\n while (stack.length > 0) {\n const current = stack.pop();\n process.stdout.write(current.id + \" \");\n stack.push(...current.children);\n }\n}\n\nfunction bfs(tree) {\n const queue = [tree];\n while (queue.length > 0) {\n const current = queue.shift();\n process.stdout.write(current.id + \" \");\n queue.push(...current.children);\n }\n}\n\nconst root = createTree(2, 3);\nconsole.log(\"[#]\\nRecursive DFS:\");\ndfsPreorder(root);\nconsole.log();\nconsole.log(\"[#]\\nRecursive Postorder DFS:\");\ndfsPostorder(root);\nconsole.log();\nconsole.log(\"[#]\\nStack-based DFS:\");\ndfsIterative(root);\nconsole.log();\nconsole.log(\"[#]\\nQueue-based BFS:\");\nbfs(root);\nconsole.log();\nconst root_binary = createTree(3, 2);\nconsole.log(\"[#]\\nRecursive Inorder DFS for Binary Tree:\");\ndfsInorder(root_binary);\nconsole.log();\n\nclass Node:\n def __init__(self):\n self.data = None\n self.children = []\n\ndef create_tree(node, num_row, num_child):\n node.data = num_row\n\n if num_row > 0:\n for i in range(num_child):\n child = create_tree(Node(), num_row-1, num_child)\n node.children.append(child)\n\n return node\n\n\ndef dfs_recursive(node):\n if node.data != None:\n print(node.data, end=' ')\n\n for child in node.children:\n dfs_recursive(child)\n\n\ndef dfs_recursive_postorder(node):\n for child in node.children:\n dfs_recursive_postorder(child)\n\n if node.data != None:\n print(node.data, end=' ')\n\n\n# This assumes only 2 children, but accounts for other possibilities\ndef dfs_recursive_inorder_btree(node):\n if len(node.children) == 2:\n dfs_recursive_inorder_btree(node.children[0])\n print(node.data, end=' ')\n dfs_recursive_inorder_btree(node.children[1])\n elif len(node.children) == 1:\n dfs_recursive_inorder_btree(node.children[0])\n print(node.data, end=' ')\n elif len(node.children) == 0:\n print(node.data, end=' ')\n else:\n print(\"Not a binary tree!\")\n\n\ndef dfs_stack(node):\n stack = [node]\n while stack:\n node = stack.pop()\n stack.extend(node.children)\n print(node.data, end=' ')\n\ndef bfs_queue(node):\n queue = [node]\n while queue:\n node = queue.pop(0)\n queue.extend(node.children)\n print(node.data)\n\n\ndef main():\n tree = create_tree(Node(), 2, 3)\n\n print(\"[#]\\nRecursive DFS:\")\n dfs_recursive(tree)\n print()\n\n print(\"[#]\\nRecursive Postorder DFS:\")\n dfs_recursive_postorder(tree)\n print()\n\n print(\"[#]\\nStack-based DFS:\")\n dfs_stack(tree)\n print()\n\n print(\"[#]\\nQueue-based BFS:\")\n bfs_queue(tree)\n print()\n\n binary_tree = create_tree(Node(), 3, 2)\n\n print(\"[#]\\nRecursive Inorder DFS for Binary Tree:\")\n dfs_recursive_inorder_btree(binary_tree)\n print()\n\nif __name__ == '__main__':\n main()\n\nThe code snippets were taken from this Scratch project\n\n \nuse std::collections::VecDeque;\n\n#[derive(Debug)]\nstruct Node {\n children: Vec,\n value: u64,\n}\n\nfn dfs_recursive(n: &Node) {\n print!(\"{} \", n.value);\n\n for child in &n.children {\n dfs_recursive(child);\n }\n}\n\nfn dfs_recursive_postorder(n: &Node) {\n for child in &n.children {\n dfs_recursive_postorder(child);\n }\n\n print!(\"{} \", n.value);\n}\n\nfn dfs_recursive_inorder_btree(n: &Node) {\n match &n.children[..] {\n [left, right] => {\n dfs_recursive_inorder_btree(left);\n print!(\"{} \", n.value);\n dfs_recursive_inorder_btree(right);\n }\n [left] => {\n dfs_recursive_inorder_btree(left);\n print!(\"{} \", n.value);\n }\n [] => print!(\"{} \", n.value),\n _ => print!(\"This is not a binary tree. \"),\n }\n}\n\nfn dfs_stack(n: &Node) {\n let mut stack = vec![n];\n\n while let Some(current) = stack.pop() {\n print!(\"{} \", current.value);\n stack.extend(¤t.children);\n }\n}\n\nfn bfs_queue(n: &Node) {\n let mut queue = VecDeque::new();\n queue.push_back(n);\n\n while let Some(current) = queue.pop_front() {\n print!(\"{} \", current.value);\n queue.extend(¤t.children);\n }\n}\n\nfn create_tree(num_row: u64, num_child: u64) -> Node {\n if num_row == 0 {\n return Node {\n children: vec![],\n value: 0,\n };\n }\n\n let children = (0..num_child)\n .map(|_| create_tree(num_row - 1, num_child))\n .collect();\n\n Node {\n children,\n value: num_row,\n }\n}\n\nfn main() {\n let root = create_tree(2, 3);\n\n println!(\"[#]\\nRecursive DFS:\");\n dfs_recursive(&root);\n println!();\n\n println!(\"[#]\\nRecursive Postorder DFS:\");\n dfs_recursive_postorder(&root);\n println!();\n\n println!(\"[#]\\nStack-based DFS:\");\n dfs_stack(&root);\n println!();\n\n println!(\"[#]\\nQueue-based BFS:\");\n bfs_queue(&root);\n println!();\n\n println!(\"[#]\\nRecursive Inorder DFS for Binary Tree:\");\n let root_binary = create_tree(3, 2);\n dfs_recursive_inorder_btree(&root_binary);\n println!();\n}\n\ndata Tree a = Node\n { node :: a,\n forest :: [Tree a]\n }\n deriving (Show)\n\ndfs :: Tree a -> [a]\ndfs (Node x ts) = x : concatMap dfs ts\n\ndfsPostOrder :: Tree a -> [a]\ndfsPostOrder (Node x ts) = concatMap dfsPostOrder ts ++ [x]\n\ndfsInOrder :: Tree a -> [a] -- For binary trees only\ndfsInOrder (Node x []) = [x]\ndfsInOrder (Node x [l]) = dfsInOrder l ++ [x] -- Single branch assumed to be left\ndfsInOrder (Node x [l, r]) = dfsInOrder l ++ [x] ++ dfsInOrder r\ndfsInOrder _ = error \"Not a binary tree\"\n\ndfsStack :: Tree a -> [a]\ndfsStack t = go [t]\n where\n go [] = []\n go ((Node x ts) : stack) = x : go (ts ++ stack)\n\nbfs :: Tree a -> [a]\nbfs (Node x ts) = x : go ts\n where\n go [] = []\n go ts = map node ts ++ go (concatMap forest ts)\n\ncreateTree :: Int -> Int -> Tree Int\ncreateTree 0 _ = Node 0 []\ncreateTree numRow numChild = Node numRow children\n where\n children = map (createTree (numRow - 1)) $ replicate numChild numChild\n\nmain = do\n let testTree = createTree 2 3\n showNodes = unwords . map show\n putStrLn \"[#]\\nRecursive DFS:\"\n putStrLn $ showNodes $ dfs testTree\n putStrLn \"[#]\\nRecursive Postorder DFS:\"\n putStrLn $ showNodes $ dfsPostOrder testTree\n putStrLn \"[#]\\nStack-based DFS:\"\n putStrLn $ showNodes $ dfsStack testTree\n putStrLn \"[#]\\nQueue-based BFS:\"\n putStrLn $ showNodes $ bfs testTree\n putStrLn \"[#]\\nRecursive Inorder DFS for Binary Tree:\"\n putStrLn $ showNodes $ dfsInOrder $ createTree 3 2\n\nclass Node {\n var value: Int\n var children: [Node]?\n\n init(value: Int, children: [Node]) {\n self.value = value\n self.children = children\n }\n}\n\nfunc createTree(numRows: Int, numChildren: Int) -> Node {\n let node = Node(value: numRows, children: [])\n\n if numRows > 0 {\n for _ in 1...numChildren {\n let child = createTree(numRows: numRows-1, numChildren: numChildren)\n node.children?.append(child)\n }\n }\n\n return node\n}\n\nfunc dfsRecursive(node: Node) {\n print(node.value, terminator:\" \")\n\n for child in node.children! {\n dfsRecursive(node: child)\n }\n}\n\nfunc dfsRecursivePostOrder(node: Node) {\n for child in node.children! {\n dfsRecursivePostOrder(node: child)\n }\n\n print(node.value, terminator:\" \")\n}\n\nfunc dfsRecursiveInOrderBinary(node: Node) {\n if node.children?.count == 2 {\n dfsRecursiveInOrderBinary(node: node.children![0])\n print(node.value, terminator:\" \")\n dfsRecursiveInOrderBinary(node: node.children![1])\n } else if node.children?.count == 1 {\n dfsRecursiveInOrderBinary(node: node.children![0])\n print(node.value, terminator:\" \")\n } else if node.children?.count == 0 {\n print(node.value, terminator:\" \")\n } else {\n print(\"Not a binary tree!\")\n }\n}\n\nfunc dfsStack(node: Node) {\n var stack = [node]\n var temp: Node\n\n while stack.count > 0 {\n temp = stack.popLast()!\n print(temp.value, terminator:\" \")\n\n for child in temp.children! {\n stack.append(child)\n }\n }\n}\n\nfunc bfsQueue(node: Node) {\n var queue = [node]\n var temp: Node\n\n while queue.count > 0 {\n temp = queue.remove(at: 0)\n print(temp.value, terminator:\" \")\n\n for child in temp.children! {\n queue.append(child)\n }\n }\n}\n\nfunc main() {\n let root = createTree(numRows: 2, numChildren: 3)\n\n print(\"[#]\\nRecursive DFS:\")\n dfsRecursive(node: root)\n print()\n\n print(\"[#]\\nRecursive Postorder DFS:\")\n dfsRecursivePostOrder(node: root)\n print()\n\n print(\"[#]\\nStack-based DFS:\")\n dfsStack(node: root)\n print()\n\n print(\"[#]\\nQueue-based BFS:\")\n bfsQueue(node: root)\n print()\n\n let rootBinary = createTree(numRows: 3, numChildren: 2)\n\n print(\"[#]\\nRecursive Inorder DFS for Binary Tree:\")\n dfsRecursiveInOrderBinary(node: rootBinary)\n print()\n}\n\nmain()\n\nid = $id;\n $this->children = $children;\n }\n\n public function getId(): int\n {\n return $this->id;\n }\n\n public function getChildren(): array\n {\n return $this->children;\n }\n\n public function addChild(Tree $child): void\n {\n $this->children[] = $child;\n }\n\n public function jsonSerialize(): array\n {\n return [\n 'id' => $this->id,\n 'children' => $this->children,\n ];\n }\n}\n\nclass TreeTraversal\n{\n public static function DFSRecursive(Tree $tree): void\n {\n echo $tree->getId() . ' ';\n foreach ($tree->getChildren() as $child) {\n static::DFSRecursive($child);\n }\n }\n\n public static function DFSRecursivePostorder(Tree $tree): void\n {\n foreach ($tree->getChildren() as $child) {\n static::DFSRecursivePostorder($child);\n }\n echo $tree->getId() . ' ';\n }\n\n public static function DFSRecursiveInorderBinary(Tree $tree): void\n {\n switch (count($tree->getChildren())) {\n case 2:\n static::DFSRecursiveInorderBinary($tree->getChildren()[0]);\n echo $tree->getId() . ' ';\n static::DFSRecursiveInorderBinary($tree->getChildren()[1]);\n break;\n case 1:\n static::DFSRecursiveInorderBinary($tree->getChildren()[0]);\n echo $tree->getId() . ' ';\n break;\n case 0:\n echo $tree->getId() . ' ';\n break;\n default:\n throw new InvalidArgumentException('Not a binary tree!');\n break;\n }\n }\n\n public static function DFSStack(Tree $tree): void\n {\n $stack = [$tree];\n $temp = null;\n\n while (null !== ($temp = array_pop($stack))) {\n echo $temp->getId() . ' ';\n foreach ($temp->getChildren() as $child) {\n $stack[] = $child;\n }\n }\n }\n\n public static function DFSQueue(Tree $tree): void\n {\n $stack = [$tree];\n $temp = null;\n\n while (null !== ($temp = array_shift($stack))) {\n echo $temp->getId() . ' ';\n foreach ($temp->getChildren() as $child) {\n $stack[] = $child;\n }\n }\n }\n}\n\nfunction generate_tree(int $numOfRows, int $numOfChildren): Tree\n{\n $node = new Tree($numOfRows);\n\n if ($numOfRows > 0) {\n for ($i = 0; $i addChild($child);\n }\n }\n\n return $node;\n}\n\n$node = generate_tree(2, 3);\n\necho '[#]' . PHP_EOL . 'Recursive DFS:' . PHP_EOL;\nTreeTraversal::DFSRecursive($node);\necho PHP_EOL;\n\necho '[#]' . PHP_EOL . 'Recursive Postorder DFS:' . PHP_EOL;\nTreeTraversal::DFSRecursivePostorder($node);\necho PHP_EOL;\n\necho '[#]' . PHP_EOL . 'Stack-based DFS:' . PHP_EOL;\nTreeTraversal::DFSStack($node);\necho PHP_EOL;\n\necho '[#]' . PHP_EOL . 'Queue-based BFS:' . PHP_EOL;\nTreeTraversal::DFSQueue($node);\necho PHP_EOL;\n\n// If you want to try to run binary order on a non-binary tree,\n// comment out the generation of the new tree below.\n// If you do that, an exception will be thrown\n$node = generate_tree(3, 2);\necho '[#]' . PHP_EOL . 'Recursive Inorder DFS for Binary Tree:' . PHP_EOL;\nTreeTraversal::DFSRecursiveInorderBinary($node);\necho PHP_EOL;\n\nclass Node \n property id, children \n def initialize(@id : Int32, @children : Array(Node))\n end \nend \n\ndef dfs_recursive(node) \n print \"#{node.id} \"\n node.children.each{ |child| dfs_recursive child } \nend\n\ndef dfs_recursive_postorder(node) \n node.children.each{ |child| dfs_recursive_postorder child }\n print \"#{node.id} \"\nend \n\ndef dfs_recursive_inorder_btree(node) \n case node.children.size\n when 2\n dfs_recursive_inorder_btree node.children[0]\n print \"#{node.id} \"\n dfs_recursive_inorder_btree node.children[1] \n when 1 \n dfs_recursive_inorder_btree node.children[0]\n print \"#{node.id} \"\n when 0 \n print \"#{node.id} \"\n else \n print \"Not a binary tree!\"\n end \nend \n\ndef dfs_stack(node) \n stack = [node] \n\n until stack.empty? \n temp = stack.pop \n print \"#{temp.id} \"\n temp.children.each{ |child| stack.push child } \n end \nend \n\ndef bfs_queue(node) \n queue = Deque.new [node]\n\n until queue.empty? \n temp = queue.shift\n print \"#{temp.id} \"\n temp.children.each{ |child| queue.push child }\n end \nend \n\ndef create_tree(levels, num_childs) \n\n children = [] of Node \n unless levels == 0 \n num_childs.times{children.push create_tree levels-1, num_childs } \n end \n\n Node.new(levels, children) \nend\n\ndef main \n root = create_tree levels: 2, num_childs: 3\n\n puts \"[#]\\nRecursive DFS:\"\n dfs_recursive root\n puts \n\n puts \"[#]\\nRecursive Postorder DFS:\" \n dfs_recursive_postorder root \n puts \n\n puts \"[#]\\nStack-based DFS:\"\n dfs_stack root \n puts \n\n puts \"[#]\\nQueue-based BFS:\"\n bfs_queue root \n puts \n\n root_bin = create_tree levels: 3, num_childs: 2\n\n puts \"[#]\\nRecursive Inorder DFS for Binary Tree:\"\n dfs_recursive_inorder_btree root_bin\n puts\nend \n\nmain\n\nObject subclass: #Node\n instanceVariableNames: 'children data'\n classVariableNames: ''\n package: ''\n\nNode>>children\n \"Children getter.\"\n ^ children\n\nNode>>children: newChildren\n \"Children setter.\"\n children := newChildren.\n\nNode>>data\n \"Data getter\"\n ^ data\n\nNode>>data: newData\n \"Data setter\"\n data := newData.\n\nNode>>dfsRecursive\n \"Recursive depth first search.\"\n Transcript show: data; cr.\n children collect: [ :child | child dfsRecursive ]\n\nNode>>dfsRecursivePostOrder\n \"Recursive depth first search (post-order).\"\n children collect: [ :child | (child dfsRecursivePostOrder)].\n Transcript show: data; cr.\n\nNode>>dfsInOrderBinaryTree\n \"Recursive depth first search on a binary tree in order.\"\n children size > 2 ifTrue: [\n Transcript show: 'This is not a binary tree!'; cr.\n ^self.\n ].\n children size = 2 ifTrue: [\n (children at: 1) dfsInOrderBinaryTree: value.\n ].\n Transcript show: data; cr.\n children size >= 1 ifTrue: [\n (children at: 0) dfsInOrderBinaryTree: value.\n ].\n ^self.\n\nNode>>dfsStack\n \"Depth-first search with a stack.\"\n | stack top |\n stack := Stack new.\n stack push: self.\n [stack size > 0] whileTrue: [\n top := stack pop.\n Transcript show: (top data); cr.\n top children reverseDo: [ :child |\n stack push: child.\n ].\n ].\n\nNode>>bfs\n \"A breadth-first tree search using queues.\"\n | queue current |\n queue := LinkedList with: self.\n [ queue size > 0 ] whileTrue: [\n current := queue first.\n queue removeFirst.\n Transcript show: (current data); cr.\n current children collect: [ :child |\n queue addLast: child\n ].\n ].\n\n| test |\ntest := Node new: 1 children: { Node new: 2.\n Node new: 3 children: { Node new: 4.\n Node new: 5. } }.\ntest dfsRecursive.\ntest dfsRecursivePostorder.\ntest dfsInOrderBinaryTree.\ntest dfsStack.\ntest bfs.\n\npackage main\n\nimport \"fmt\"\n\ntype node struct {\n id int\n children []*node\n}\n\nfunc dfsRecursive(n *node) {\n fmt.Printf(\"%d \", n.id)\n for _, child := range n.children {\n dfsRecursive(child)\n }\n}\n\nfunc dfsRecursivePostorder(n *node) {\n for _, child := range n.children {\n dfsRecursivePostorder(child)\n }\n fmt.Printf(\"%d \", n.id)\n}\n\nfunc dfsRecursiveInorderBtree(n *node) {\n switch len(n.children) {\n case 2:\n dfsRecursiveInorderBtree(n.children[0])\n fmt.Printf(\"%d \", n.id)\n dfsRecursiveInorderBtree(n.children[1])\n case 1:\n dfsRecursiveInorderBtree(n.children[0])\n fmt.Printf(\"%d \", n.id)\n case 0:\n fmt.Printf(\"%d \", n.id)\n default:\n fmt.Println(\"This is not a binary tree\")\n }\n}\n\nfunc dfsStack(n *node) {\n stack := []*node{n}\n\n for len(stack) > 0 {\n cur := stack[0]\n stack = stack[1:]\n fmt.Printf(\"%d \", cur.id)\n stack = append(cur.children, stack...)\n }\n}\n\nfunc bfsQueue(n *node) {\n queue := []*node{n}\n\n for len(queue) > 0 {\n cur := queue[0]\n queue = queue[1:]\n fmt.Printf(\"%d \", cur.id)\n queue = append(queue, cur.children...)\n }\n}\n\nfunc createTree(numRow, numChild int) *node {\n if numRow == 0 {\n return &node{id: 0}\n }\n\n cur := new(node)\n cur.id = numRow\n\n for x := 0; x \n.intel_syntax noprefix\n\n# System V calling convention cheatsheet\n# Params: rdi, rsi, rdx, rcx, r8, r9, xmm0-7\n# Return: rax (int 64 bits), rax:rdx (int 128 bits), xmm0 (float)\n# Callee cleanup: rbx, rbp, r12-15\n# Scratch: rax, rdi, rsi, rdx, rcx, r8, r9, r10, r11\n\n.section .rodata\n not_bt: .string \"This is not a binary tree.\\n\"\n fmt_tree: .string \"%d \\n\"\n\n .equ stack_size, 16\n .equ stack_array, 0\n .equ stack_top, 8\n .equ stack_cap, 12\n\n .equ queue_size, 20\n .equ queue_array, 0\n .equ queue_front, 8\n .equ queue_back, 12\n .equ queue_cap, 16\n\n .equ tree_children, 0\n .equ tree_num_children, 8\n .equ tree_value, 12\n .equ tree_size, 16\n.section .text\n .global main\n .extern printf, malloc, free, memcpy\n\n# rdi - stack ptr\nget_stack:\n push r12\n mov r12, rdi\n mov rdi, 32 # Creating a 32 byte array\n call malloc\n mov QWORD PTR [r12], rax # Saving the data into the stack\n mov DWORD PTR [r12 + 8], 0\n mov DWORD PTR [r12 + 12], 32\n pop r12\n ret\n\n# rdi - stack ptr\n# rsi - element ptr\nstack_push:\n push r12\n push r13\n push r14\n mov r12, rdi # Saving the variables\n mov r13, rsi\n mov r14d, DWORD PTR [r12 + 8]\n mov esi, DWORD PTR [r12 + 12]\n cmp rsi, r14 # Check if top is equal to capacity\n jne stack_push_append\n shl rsi, 1 # Calculate new capacity in bytes\n mov DWORD PTR [r12 + 12], esi # Saving new capcaity\n mov rdi, [r12]\n call realloc # Making the array bigger\n mov QWORD PTR [r12], rax\nstack_push_append:\n add r14, 8\n mov rax, QWORD PTR [r12]\n lea rax, [rax + r14]\n mov QWORD PTR [rax], r13 # Saving element and new top\n mov DWORD PTR [r12 + 8], r14d\n pop r14\n pop r13\n pop r12\n ret\n\n# rdi - stack ptr\n# RET rax - element ptr\nstack_pop:\n push r12\n mov r12d, DWORD PTR [rdi + 8] # Get top\n test r12, r12 # Check if top is zero\n jne stack_pop_element\n xor rax, rax # Return 0\n jmp stack_pop_return\nstack_pop_element:\n mov rax, [rdi]\n lea rax, [rax + r12] # Get the element\n mov rax, QWORD PTR [rax]\n sub r12, 8 # Subtract 1 from top and save it\n mov DWORD PTR [rdi + 8], r12d\nstack_pop_return:\n pop r12\n ret\n\n# rdi - stack ptr\nfree_stack:\n mov rdi, QWORD PTR [rdi]\n call free # Free stack array\n ret\n\n# rdi - queue ptr\nget_queue:\n push r12\n mov r12, rdi\n mov rdi, 32 # Create a 32 byte array\n call malloc\n mov QWORD PTR [r12], rax # Saving data to the queue pointer\n mov QWORD PTR [r12 + 8], 0\n mov DWORD PTR [r12 + 16], 32\n pop r12\n ret\n\n# rdi - queue ptr\nqueue_resize:\n push r12\n push r13\n push r14\n mov r12, rdi\n mov edi, DWORD PTR [r12 + 16] # Get new capacity and create new array\n shl rdi, 1\n call malloc\n mov r13, rax\n mov r14, QWORD PTR[r12]\n mov rdi, r13 # Copy data from front to capacity\n mov eax, DWORD PTR [r12 + 8]\n lea rsi, [r14 + rax]\n mov edx, DWORD PTR [r12 + 16]\n sub edx, DWORD PTR [r12 + 8]\n call memcpy\n mov eax, DWORD PTR [r12 + 16] # Copy data from start of array to front\n sub eax, DWORD PTR [r12 + 8]\n lea rdi, [r13 + rax]\n mov rsi, r14\n mov edx, DWORD PTR [r12 + 8]\n call memcpy\n mov rdi, r14 # New array has front at 0 and back at the old capacity\n call free # So free the old array then save the new queue\n mov QWORD PTR [r12], r13\n mov eax, DWORD PTR [r12 + 16]\n sub rax, 8\n mov DWORD PTR [r12 + 12], eax\n mov DWORD PTR [r12 + 8], 0\n mov eax, DWORD PTR [r12 + 16]\n shl rax, 1\n mov DWORD PTR [r12 + 16], eax\n pop r14\n pop r13\n pop r12\n ret\n\n# rdi - queue ptr\n# rsi - element\nenqueue:\n push r12\n push r13\n push r14\n push r15\n mov r12, rdi # Saving parameters\n mov r13, rsi\n mov r14d, DWORD PTR [rdi + 8]\n mov eax, DWORD PTR [rdi + 12]# Calculating new back\n add eax, 8\n mov edi, DWORD PTR [r12 + 16]\n cdq\n idiv edi\n cmp rdx, r14 # Check if front and new back are equal\n jne enqueue_append\n mov rdi, r12 # If so resize the queue\n call queue_resize\nenqueue_append:\n mov r14, QWORD PTR [r12] # Saving the element\n mov r15d, DWORD PTR [r12 + 12]\n lea r14, [r14 + r15]\n mov QWORD PTR [r14], r13\n mov r14d, DWORD PTR [r12 + 16]# Calculating new back and then saving it\n add r15, 8\n mov rax, r15\n cdq\n idiv r14d\n mov DWORD PTR [r12 + 12], edx\n pop r15\n pop r14\n pop r13\n pop r12\n ret\n\n# rdi - queue ptr\n# RET rax - element\ndequeue:\n push r12\n push r13\n mov r12d, DWORD PTR [rdi + 8] # Check if queue is empty\n mov r13d, DWORD PTR [rdi + 12]\n xor rax, rax\n cmp r12, r13\n je dequeue_return # if empty return null\n mov r12, QWORD PTR [rdi] # else return element pointer\n mov r13d, DWORD PTR [rdi + 8]\n lea r13, [r12 + r13]\n mov eax, DWORD PTR [rdi + 8]\n add eax, 8\n mov r12d, DWORD PTR [rdi + 16] # Calculate new front\n cdq\n idiv r12d\n mov DWORD PTR [rdi + 8], edx # Save new front\n mov rax, QWORD PTR [r13]\ndequeue_return:\n pop r13\n pop r12\n ret\n\n# rdi - queue ptr\nfree_queue:\n mov rdi, QWORD PTR [rdi] # Free queue array\n call free\n ret\n\n# rdi - levels\n# rsi - children_size\n# RET rax:rdx - the tree - children|value|children_size\ncreate_tree:\n push rbx\n push r12\n push r13\n push r14\n push r15\n mov r12, rdi\n mov r13, rsi\n test rdi, rdi\n jz create_tree_leaf\n mov r14, rsi # We'll allocate sizeof(tree) * children_size bytes of memory\n shl r14, 4 # save the size calculation to a callee-saved register so we can reuse it after the malloc\n mov rdi, r14\n call malloc\n mov r15, rax # Save the children address twice, once for the return value, once for the loop variable\n mov rbx, rax\n lea r14, [rax + r14] # Calculate the address of the element after last of the children array\ncreate_tree_children:\n cmp rbx, r14\n je create_tree_return\n lea rdi, [r12 - 1] # levels - 1\n mov rsi, r13\n call create_tree\n mov QWORD PTR [rbx], rax # Save the created tree to memory\n mov QWORD PTR [rbx + 8], rdx # The offset of children_size, writing out explicitly would've made the line way too long\n add rbx, tree_size\n jmp create_tree_children\ncreate_tree_leaf:\n mov r15, 0\n xor r13, r13 # Leaves won't have any children\ncreate_tree_return:\n mov rax, r15 # The children pointer will be in r15\n mov rdx, r12\n shl rdx, 32 # The tree's value will be the current \"levels\"\n shl r13, 4\n or rdx, r13 # Generate the return value by moving the value to the upper 32 bits\n pop r15\n pop r14\n pop r13\n pop r12\n pop rbx\n ret\n\n# rdi - children ptr\n# rsi - children size\nfree_tree:\n push r12\n push r13\n push r14\n push r15\n test rdi, rdi # Make sure the pointer is non-zero\n jz free_tree_return\n mov r12, rdi # Saving array\n lea r13, [r12 + rsi] # Get start and end of the array\n mov r14, r12\nfree_tree_free_kid:\n cmp r14, r13 # Loop thought the array and free all children\n je free_tree_free_array\n mov rdi, QWORD PTR [r14]\n mov esi, DWORD PTR [r14 + 8]\n call free_tree\n add r14, tree_size\n jmp free_tree_free_kid\nfree_tree_free_array:\n mov rdi, r12 # Free the array\n call free\nfree_tree_return:\n pop r15\n pop r14\n pop r13\n pop r12\n ret\n\n# rdi - children ptr\n# rsi - value|children_size\ndfs_recursive:\n push r12\n push r13\n mov r12, rdi\n mov r13, rsi\n mov rdi, OFFSET fmt_tree # Handle the current node\n shr rsi, 32 # The tree value is in the upper 32 bits\n xor rax, rax\n call printf\n mov r13d, r13d # Zero out the top 32 bits\n add r13, r12 # Pointer pointing after the last element of the children array\ndfs_recursive_children:\n cmp r12, r13 # If we reached the end, return\n je dfs_recursive_return\n mov rdi, QWORD PTR [r12]\n mov rsi, QWORD PTR [r12 + 8]\n call dfs_recursive\n add r12, tree_size\n jmp dfs_recursive_children\ndfs_recursive_return:\n pop r13\n pop r12\n ret\n\n# rdi - children ptr\n# rsi - value|children_size\ndfs_recursive_postorder:\n push r12\n push r13\n push r14\n mov r12, rdi\n mov r13, rsi\n mov r14, rsi\n mov r13d, r13d # Zero out the top 32 bits\n add r13, r12 # Pointer pointing after the last element of the children array\ndfs_recursive_po_children:\n cmp r12, r13 # If we reached the end, return\n je dfs_recursive_po_return\n mov rdi, QWORD PTR [r12]\n mov rsi, QWORD PTR [r12 + 8]\n call dfs_recursive_postorder\n add r12, tree_size\n jmp dfs_recursive_po_children\ndfs_recursive_po_return:\n mov rdi, OFFSET fmt_tree # Handle the current node\n mov rsi, r14\n shr rsi, 32 # The tree value is in the upper 32 bits\n xor rax, rax\n call printf\n pop r14\n pop r13\n pop r12\n ret\n\n# rdi - children ptr\n# rsi - value|children_size\ndfs_recursive_inorder_btree:\n push r12\n push r13\n mov r12, rdi\n mov r13, rsi\n mov rax, rsi\n mov eax, eax\n cmp rax, 0 # Check what type of tree it is.\n je dfs_recursive_bt_size0\n cmp rax, 16\n je dfs_recursive_bt_size1\n cmp rax, 32\n je dfs_recursive_bt_size2\n mov rdi, OFFSET not_bt # If the tree is not binary then print a warning\n xor rax, rax\n call printf\n jmp dfs_recursive_bt_return\ndfs_recursive_bt_size0:\n mov rdi, OFFSET fmt_tree # If the node is a leaf then print its id\n shr rsi, 32\n xor rax, rax\n call printf\n jmp dfs_recursive_bt_return\ndfs_recursive_bt_size1:\n mov rdi, QWORD PTR [r12] # If the node has 1 child then call the function and print the id\n mov rsi, QWORD PTR [r12 + 8]\n call dfs_recursive_inorder_btree\n mov rdi, OFFSET fmt_tree\n mov rsi, r13\n shr rsi, 32\n xor rax, rax\n call printf\n jmp dfs_recursive_bt_return\ndfs_recursive_bt_size2:\n mov rdi, QWORD PTR [r12] # Same as above just print id inbetween the calls\n mov rsi, QWORD PTR [r12 + 8]\n call dfs_recursive_inorder_btree\n mov rdi, OFFSET fmt_tree\n mov rsi, r13\n shr rsi, 32\n xor rax, rax\n call printf\n mov rdi, QWORD PTR [r12 + 16]\n mov rsi, QWORD PTR [r12 + 24]\n call dfs_recursive_inorder_btree\ndfs_recursive_bt_return:\n pop r13\n pop r12\n ret\n\n# rdi - children ptr\n# rsi - value|children_size\ndfs_stack:\n push r12\n push r13\n push r14\n sub rsp, 16 # Create stack\n mov r12, rsp\n push rsi # Save node to use as pointer\n push rdi\n mov rdi, r12\n call get_stack # Init stack\n mov rdi, r12\n mov rsi, rsp\n call stack_push # Push node\n mov rdi, r12 # Pop stack\n call stack_pop\ndfs_stack_loop:\n test rax, rax # Test if stack is empty\n jz dfs_stack_return\n mov r13, rax\n mov rdi, OFFSET fmt_tree # Print id\n mov esi, DWORD PTR [r13 + 12]\n xor rax, rax\n call printf\n mov eax, DWORD PTR [r13 + 8] # Get start and end of array\n mov r13, QWORD PTR [r13]\n lea r14, [r13 + rax]\ndfs_stack_push_child:\n cmp r13, r14 # Check if the pointers are the same\n je dfs_stack_end_push\n mov rdi, r12 # Push node into the stack\n mov rsi, r13\n call stack_push\n add r13, tree_size\n jmp dfs_stack_push_child\ndfs_stack_end_push:\n mov rdi, r12 # Pop stack\n call stack_pop\n jmp dfs_stack_loop\ndfs_stack_return:\n mov rdi, r12 # Free stack\n call free_stack\n add rsp, 32\n pop r14\n pop r13\n pop r12\n ret\n\n# rdi - children ptr\n# rsi - value|children_size\nbfs_queue:\n push r12\n push r13\n push r14\n sub rsp, 20 # Create queue\n mov r12, rsp\n push rsi # Save node to use as pointer\n push rdi\n mov rdi, r12\n call get_queue # Init queue\n mov rdi, r12\n mov rsi, rsp\n call enqueue # enqueue node\n mov eax, DWORD PTR [r12 + 8]\n mov edi, DWORD PTR [r12 + 12]\nbfs_queue_loop:\n cmp eax, edi\n je bfs_queue_return\n mov rdi, r12 # dequeue\n call dequeue\n test rax, rax # Test if queue is empty\n jz bfs_queue_return\n mov r13, rax\n mov rdi, OFFSET fmt_tree # Print id\n mov esi, DWORD PTR [r13 + 12]\n xor rax, rax\n call printf\n mov eax, DWORD PTR [r13 + 8] # Get start and end of array\n mov r13, QWORD PTR [r13]\n lea r14, [r13 + rax]\nbfs_queue_push_child:\n cmp r13, r14 # Check if the pointers are the same\n je bfs_queue_end_push\n mov rdi, r12 # enqueue node\n mov rsi, r13\n call enqueue\n add r13, tree_size\n jmp bfs_queue_push_child\nbfs_queue_end_push:\n mov eax, DWORD PTR [r12 + 8]\n mov edi, DWORD PTR [r12 + 12]\n jmp bfs_queue_loop\nbfs_queue_return:\n mov rdi, r12 # Free queue\n call free_queue\n add rsp, 36\n pop r14\n pop r13\n pop r12\n ret\n\nmain:\n push r12\n push r13\n mov rdi, 3\n mov rsi, 3\n call create_tree\n mov r12, rax\n mov r13, rdx\n mov rdi, rax\n mov rsi, rdx\n call bfs_queue\n mov rdi, r12\n mov rsi, r13\n mov esi, esi\n call free_tree\n pop r13\n pop r12\n ret\n\n🦃 ⏹ 🍇\n 🔘 ⏫\n\n ❗️ 🔡 ➡️ 🔡 🍇\n ↪️ 🐕 🙌 🆕⏹⏫❗️ 🍇\n ↩️ 🔤The given tree is not binary!🔤\n 🍉\n ↩️ 🔤🔤\n 🍉\n🍉\n\n🐇 🌲 🍇\n 🖍🆕 id 🔢\n 🖍🆕 children 🍨🐚🌲🍆\n\n 🆕 depth_count 🔢 children_count 🔢 🍇\n 1 ➡️ 🖍id\n 🍨🍆 ➡️ 🖍children\n\n 🌌🐕 depth_count children_count❗️\n 🍉\n\n 🔐 🆕 ⭐️ given_id 🔢 depth_count 🔢 children_count 🔢 🍇\n given_id ➡️ 🖍id\n 🍨🍆 ➡️ 🖍children\n\n 🌌🐕 depth_count children_count❗️\n 🍉\n\n ❗️ 🆔 ➡️ 🔢 🍇\n ↩️ id\n 🍉\n\n ❗️ 🧒 ➡️ 🍨🐚🌲🍆 🍇\n ↩️ children\n 🍉\n\n 📗 Depth-First Search Recursive pre-order 📗\n ❗️ 🌀 🍇\n 😀 🔡 id 10❗️❗️\n\n 🔂 child children 🍇\n 🌀 child❗️\n 🍉\n 🍉\n\n 📗 Depth-First Search Recursive post-order 📗\n ❗️ 🍥 🍇\n 🔂 child children 🍇\n 🍥 child❗️\n 🍉\n\n 😀 🔡 id 10❗️❗️\n 🍉\n\n 📗\n Depth-First Search Recursive Inorder Binary\n This assumes only 2 children.\n 📗\n ❗️ 🍭 ➡️ 🍬⏹ 🍇\n ↪️ 🐔 children❗️ ▶️ 2 🍇\n ↩️ 🆕⏹⏫❗️\n 🍉\n\n ↪️ 🐔 children❗️ ▶️ 0 🍇\n 🍭🐽 children 0❗️❗️\n 😀 🔡 id 10❗️❗️\n 🍭🐽 children 1❗️❗️\n 🍉\n 🙅 🍇\n 😀 🔡 id 10❗️❗️\n 🍉\n ↩️ 🤷‍♀️\n 🍉\n\n 📗 Depth-First Search Stack 📗\n ❗️ 🥞 🍇\n 🍨 🐕 🍆 ➡️ stack\n\n 🔁 ❎ 🐔 stack❗️ 🙌 0❗️ 🍇\n 🐽 stack 🐔 stack❗️ ➖ 1❗️ ➡️ temp\n 🐨 stack 🐔 stack❗️ ➖ 1❗️\n\n 😀 🔡 🆔 temp❗️ 10❗️❗️\n\n 🧒 temp❗️ ➡️ temp_children\n 🔂 child temp_children 🍇\n 🐻 stack child❗️\n 🍉\n 🍉\n 🍉\n\n 📗 Breadth-First Search Queue 📗\n ❗️ 🏢 🍇\n 🍨 🐕 🍆 ➡️ queue\n\n 🔁 ❎ 🐔 queue❗️ 🙌 0❗️ 🍇\n 🐽 queue 0❗️ ➡️ temp\n 🐨 queue 0❗️\n\n 😀 🔡 🆔 temp❗️ 10❗️❗️\n\n 🧒 temp❗️ ➡️ temp_children\n 🔂 child temp_children 🍇\n 🐻 queue child❗️\n 🍉\n 🍉\n 🍉\n\n 🔐 ❗️ 🌌 depth_count 🔢 children_count 🔢 🍇\n ↪️ ❎ depth_count ◀️🙌 1❗️ 🍇\n 🔂 i 🆕⏩⏩ 0 children_count❗️ 🍇\n 🐻 children 🆕🌲⭐️ 🤜id ✖️ 10 ➕ i ➕ 1🤛 🤜depth_count ➖ 1🤛 children_count❗️❗️\n 🍉\n 🍉\n 🍉\n🍉\n\n🏁 🍇\n 🆕🌲🆕 3 3❗️ ➡️ tree\n 😀 🔤Tree Traversal🔤️❗️\n 😀 🔤🌀 - Depth-First Search Recursive pre-order🔤❗️\n 🌀tree❗️\n 😀 🔤🍥 - Depth-First Search Recursive post-order🔤❗️\n 🍥tree❗️\n 😀 🔤🥞 - Depth-First Search Stack🔤❗️\n 🥞tree❗️\n 😀 🔤🏢 - Breadth-First Search Queue🔤❗️\n 🏢tree❗️\n\n 😀 🔤🍭 - Depth-First Search Recursive Inorder Binary - Error🔤❗️\n 💭 Calling the Depth-First Search Recursive Inorder Binary method here does\n 💭 result in an error, since \"tree\" is not a binary tree.\n ️↪️ 🍭tree❗️ ➡️ return 🍇\n 😀 🔡return❗❗️️\n 🍉\n\n 🆕🌲🆕 3 2❗️ ➡️ binary_tree\n 😀 🔤🍭 - Depth-First Search Recursive Inorder Binary🔤❗️\n ️↪️ 🍭binary_tree❗️ ➡️ return 🍇\n 😀 🔡return❗❗️️\n 🍉\n🍉\n\n;;;; Tree traversal in Common Lisp\n\n(defstruct node data children)\n\n(defun dfs-recursive (node)\n \"A depth first approach for printing out all values in a tree.\"\n (when (node-data node)\n (format t \"~a \" (node-data node)))\n (loop for child in (node-children node) do\n (dfs-recursive child)))\n\n(defun dfs-recursive-postorder (node)\n \"A depth first approach for printing out all values in a tree starting from the bottom.\"\n (loop for child in (node-children node) do\n (dfs-recursive-postorder child))\n (when (node-data node)\n (format t \"~a \" (node-data node))))\n\n(defun dfs-recursive-inorder-btree (node)\n \"A depth first search approach for printing all values in a binary tree.\"\n (case (length (node-children node))\n (2\n (dfs-recursive-inorder-btree (first (node-children node)))\n (format t \"~a \" (node-data node))\n (dfs-recursive-inorder-btree (second (node-children node))))\n (1\n (dfs-recursive-inorder-btree (first (node-children node)))\n (format t \"~a \" (node-data node)))\n (0\n (format t \"~a \" (node-data node)))\n (t\n (print \"Invalid binary tree.\"))))\n\n(defun dfs-stack (node)\n \"A depth first approach for printing out all values in a tree using a stack.\"\n (loop\n with stack = (list node)\n with temp = nil\n while (> (length stack) 0) do\n (format t \"~a \" (node-data (first stack)))\n (setf temp (pop stack))\n (loop for child in (node-children temp) do\n (push child stack))))\n\n(defun bfs-queue (node)\n \"A breadth first search approach for printing out all values in a tree.\"\n (loop\n with queue = (list node)\n with temp = nil\n while (> (length queue) 0) do\n (format t \"~a \" (node-data (first queue)))\n (setf temp (pop queue))\n ;; If the queue is empty, the queue should be filled with the children nodes.\n (if (eql queue nil)\n (setf queue (node-children temp))\n (nconc queue (node-children temp)))))\n\n(defun make-tree (num-rows num-child)\n \"Creates a simple tree, where every node has 'num-child' children and is 'num-rows' deep.\"\n ;; A tree with 0 rows can't be created.\n (if (eql num-rows 0)\n (make-node\n :data 0\n :children nil)\n (make-node\n :data num-rows\n :children (loop repeat num-child collect (make-tree (1- num-rows) num-child)))))\n\n;; A tree for testing\n(defvar tree (make-tree 2 3))\n\n;; A binary tree for testing\n(defvar binary-tree (make-tree 3 2))\n\n;; Should print: 3 2 1 1 1 2 1 1 1 2 1 1 1\n(format t \"[#]~%Recursive DFS:~%\")\n(dfs-recursive tree)\n(format t \"~%\")\n\n;; Should print: 1 1 1 2 1 1 1 2 1 1 1 2 3\n(format t \"[#]~%Recursive Postorder DFS:~%\")\n(dfs-recursive-postorder tree)\n(format t \"~%\")\n\n;; Should print: 3 2 1 1 1 2 1 1 1 2 1 1 1\n(format t \"[#]~%Stack-based DFS:~%\")\n(dfs-stack tree)\n(format t \"~%\")\n\n;; Should print: 3 2 2 2 1 1 1 1 1 1 1 1 1\n(format t \"[#]~%Queue-based BFS:~%\")\n(bfs-queue tree)\n(format t \"~%\")\n\n;; Should print: 1 2 1 3 1 2 1\n(format t \"[#]~%Recursive Inorder DFS for Binary Tree:~%\")\n(dfs-recursive-inorder-btree binary-tree)\n(format t \"~%\")\n\nmain()\n\n%% Functions\n\nfunction root = create_tree()\n node = @(k,v) containers.Map(k,v);\n\n node2 = node(2, {{}}); node3 = node(3, {{}}); node4 = node(4, {{}});\n node6 = node(6, {{}}); node7 = node(7, {{}}); node8 = node(8, {{}});\n node10 = node(10, {{}}); node11 = node(11, {{}}); node12 = node(12, {{}});\n\n node1 = node(1, {node2, node3, node4});\n node5 = node(5, {node6, node7, node8});\n node9 = node(9, {node10, node11, node12});\n\n root = node(0, {node1, node5, node9});\nend\n\nfunction root = create_btree()\n node = @(k,v) containers.Map(k,v);\n\n node2 = node(2, {{}}); node3 = node(3, {{}});\n node5 = node(5, {{}}); node6 = node(6, {{}});\n\n node1 = node(1, {node2, node3});\n node4 = node(4, {node5, node6});\n\n root = node(0, {node1, node4});\nend\n\nfunction DFS_recursive(n)\n\n cell_index = @(a, b) a{b};\n ID = cell_index(keys(n), 1);\n\n fprintf('%u ', ID);\n\n children = cell_index(values(n), 1);\n for i = children\n child = i{1};\n if ~isempty(child)\n DFS_recursive(child);\n end\n end\nend\n\nfunction DFS_recursive_postorder(n)\n\n cell_index = @(a, b) a{b};\n\n children = cell_index(values(n), 1);\n for i = children\n child = i{1};\n if ~isempty(child)\n DFS_recursive_postorder(child);\n end\n end\n\n ID = cell_index(keys(n), 1);\n fprintf('%u ', ID);\n\nend\n\nfunction DFS_recursive_inorder_btree(n)\n\n cell_index = @(a, b) a{b};\n ID = cell_index(keys(n), 1);\n children = cell_index(values(n), 1);\n\n if length(children) == 2\n DFS_recursive_inorder_btree(children{1})\n fprintf('%u ', ID)\n DFS_recursive_inorder_btree(children{2})\n elseif length(children) == 1\n if ~isempty(children{1})\n DFS_recursive_inorder_btree(children{1})\n end\n fprintf('%u ', ID)\n else\n fprintf(\"Not a binary tree!\")\n end\nend\n\nfunction DFS_stack(n)\n\n cell_index = @(a, b) a{b};\n node_stack = {n};\n\n while ~isempty(node_stack)\n\n parent = node_stack{end};\n node_stack(end) = [];\n\n ID = cell_index(keys(parent), 1);\n fprintf('%u ', ID);\n\n children = cell_index(values(parent), 1);\n\n for i = flip(children)\n child = i{1};\n if ~isempty(child)\n node_stack = {node_stack{:} child};\n end\n end\n end\nend\n\nfunction BFS_queue(n)\n\n cell_index = @(a, b) a{b};\n node_queue = {n};\n\n while ~isempty(node_queue)\n next_nodes = {};\n for parent_cell = node_queue\n parent = parent_cell{1};\n ID = cell_index(keys(parent), 1);\n fprintf('%u ', ID);\n children = cell_index(values(parent), 1);\n for i = children\n child = i{1};\n if ~isempty(child)\n next_nodes = {next_nodes{:}, child};\n end\n end\n end\n node_queue = next_nodes;\n end\nend\n\nfunction main()\n root = create_tree();\n rootb = create_btree();\n\n fprintf('\\nDFS Recursive\\n')\n DFS_recursive(root)\n\n fprintf('\\nDFS Recursive Postorder\\n')\n DFS_recursive_postorder(root)\n\n fprintf('\\nDFS Recursive Inorder Binary Tree\\n')\n DFS_recursive_inorder_btree(rootb)\n\n fprintf('\\nDFS Stack\\n')\n DFS_stack(root)\n\n fprintf('\\nBFS Queue\\n')\n BFS_queue(root) \n fprintf('\\n')\nend\n\nfrom collections import deque\n\ndata Node(value: int, children: Node[])\n\ndef dfs_recursive(Node(value, children)):\n \"\"\"A depth first approach for printing out all values in a tree.\"\"\"\n print(value, end=' ')\n for child in children:\n dfs_recursive(child)\n\ndef dfs_recursive_postorder(Node(value, children)):\n \"\"\"A depth first approach for printing out all values in a tree starting from the bottom.\"\"\"\n for child in children:\n dfs_recursive_postorder(child)\n print(value, end=' ')\n\ndef dfs_recursive_inorder_btree(Node(value, children)):\n \"\"\"A depth first search approach for printing all values in a binary tree.\"\"\"\n case len(children):\n match 2:\n dfs_recursive_inorder_btree(children[0])\n print(value, end=' ')\n dfs_recursive_inorder_btree(children[1])\n match 1:\n dfs_recursive_inorder_btree(children[0])\n print(value, end=' ')\n match 0:\n print(value, end=' ')\n else:\n print('Invalid binary tree')\n\ndef dfs_stack(node is Node):\n \"\"\"A depth first approach for printing out all values in a tree using a stack.\"\"\"\n stack = [node]\n while stack:\n current_node = stack.pop()\n print(current_node.value, end=' ')\n for child in current_node.children:\n stack.append(child)\n\ndef bfs_queue(node is Node):\n \"\"\"A breadth first search approach for printing out all values in a tree.\"\"\"\n queue = deque([node])\n while queue:\n current_node = queue.popleft()\n print(current_node.value, end=' ')\n for child in current_node.children:\n queue.append(child)\n\ndef create_tree(num_rows, num_child):\n \"\"\"Creates a simple tree, where every node has\n 'num_child' children and is 'num_rows' deep.\"\"\"\n if num_rows == 0:\n return Node(0, ())\n else:\n return Node(num_rows, tuple(create_tree(num_rows-1, num_child)\n for _ in range(num_child)))\n\n\nif __name__ =='__main__':\n # A ternary tree for testing\n tree = create_tree(2, 3)\n\n print(\"[#]\\nRecursive DFS:\")\n dfs_recursive(tree)\n print()\n\n print(\"[#]\\nRecursive Postorder DFS:\")\n dfs_recursive_postorder(tree)\n print()\n\n print(\"[#]\\nStack-based DFS:\")\n dfs_stack(tree)\n print()\n\n print(\"[#]\\nQueue-based BFS:\")\n bfs_queue(tree)\n print()\n\n # And a binary tree for testing\n binary_tree = create_tree(3, 2)\n\n print(\"[#]\\nRecursive Inorder DFS for Binary Tree:\")\n dfs_recursive_inorder_btree(binary_tree)\n print()\n\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"DFSpreorder\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"DFSpostorder\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"DFSinorder\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"BFSsimple\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/euclidean_algorithm/euclidean_algorithm.html":{"url":"contents/euclidean_algorithm/euclidean_algorithm.html","title":"Euclidean Algorithm","keywords":"","body":"Euclidean Algorithm\nComputer science is (almost by definition) a science about computers -- a device first conceptualized in the 1800's. Computers have become so revolutionary, that it is difficult to think of our lives today without them. That said, algorithms are much older and have existed in the world for millennia. Incredibly, a few of the algorithms created before the Common Era (AD) are still in use today. One such algorithm was first described in Euclid's Elements (~ 300 BC) and has come to be known as the Euclidean Algorithm.\nThe algorithm is a simple way to find the greatest common divisor (GCD) of two numbers, which is useful for a number of different applications (like reducing fractions). The first method (envisioned by Euclid) uses simple subtraction:\nfunction s:euclid_sub(a, b)\n let l:a = abs(a:a)\n let l:b = abs(a:b)\n\n while l:a != l:b\n if l:a > l:b\n let l:a -= l:b\n else\n let l:b -= l:a\n endif\n endwhile\n\n return l:a\nendfunction\n\nint euclid_sub(int a, int b) {\n a = abs(a);\n b = abs(b);\n\n while (a != b) {\n if (a > b) {\n a -= b;\n } else {\n b -= a;\n }\n }\n\n return a;\n}\n\npublic int EuclidSub(int a, int b)\n{\n // Math.Abs for negative number support\n a = Math.Abs(a);\n b = Math.Abs(b);\n\n while (a != b)\n {\n if (a > b)\n a = a - b;\n else\n b = b - a;\n }\n\n return a;\n}\n\n(defn euclid-sub [a b]\n (loop [i (Math/abs a) j (Math/abs b)]\n (if (= i j)\n i\n (if (> i j)\n (recur (- i j) j)\n (recur i (- j i))))))\n\nint euclid_sub(int a, int b) {\n a = std::abs(a);\n b = std::abs(b);\n\n while (a != b) {\n if (a > b) {\n a -= b;\n } else {\n b -= a;\n }\n }\n\n return a;\n}\n\npublic static int euclidSub(int a, int b) {\n a = Math.abs(a);\n b = Math.abs(b);\n\n while (a != b) {\n if (a > b) {\n a -= b;\n } else {\n b -= a;\n }\n }\n\n return a;\n}\n\nfun euclidSub(a: Int, b: Int): Int {\n var a = a.absoluteValue\n var b = b.absoluteValue\n\n while (a != b) {\n if (a > b) a -= b\n else b -= a\n }\n\n return a\n}\n\nfunction euclidSub(a, b) {\n a = Math.abs(a);\n b = Math.abs(b);\n\n while (a !== b) {\n if (a > b) {\n a -= b;\n } else {\n b -= a;\n }\n }\n\n return a;\n}\n\n(defun euclid-sub (a b)\n \"Finds the greatest common divsor for any two integers\"\n (defun euclid-sub* (a b)\n \"Finds the greatest common divisor for any two positive integers\"\n (if (eql a b)\n a\n (if (> a b)\n (euclid-sub* (- a b) b)\n (euclid-sub* a (- b a)))))\n (euclid-sub* (abs a) (abs b)))\n\ndef euclid_sub(a, b):\n\n a = abs(a)\n b = abs(b)\n\n if a == 0:\n return b\n elif b == 0:\n return a\n\n while a != b:\n if a > b:\n a -= b\n else:\n b -= a\n\n return a\n\neuclidSub :: Integer -> Integer -> Integer\neuclidSub a b = inner (abs a) (abs b)\n where\n inner x y\n -- if a = b, then the gcd is a\n | x == y = x\n -- if a \nfn euclid_sub(mut a: i64, mut b: i64) -> i64 {\n a = a.abs();\n b = b.abs();\n while a != b {\n if a \nlet euclid_sub a b =\n let rec inner a b =\n if a = b then\n a\n else if a \nfunc euclidSub(a, b int) int {\n a = abs(a)\n b = abs(b)\n\n for a != b {\n if a > b {\n a -= b\n } else {\n b -= a\n }\n }\n\n return a\n}\n\nfunc euclidSub(a: Int, b: Int) -> Int {\n var a = abs(a)\n var b = abs(b)\n\n while (a != b) {\n if (a > b) {\n a -= b\n } else {\n b -= a\n }\n }\n\n return a\n}\n\nfunction gcd = euclidSub(a,b)\n\n a = abs(a);\n b = abs(b);\n\n while a ~= b\n if a > b\n a = a - b;\n else\n b = b - a;\n end\n end\n\n gcd = a;\nend\n\nlocal function euclid_sub(a, b)\n a = math.abs(a)\n b = math.abs(b)\n\n while a ~= b do\n if a > b then\n a = a-b\n else\n b = b-a\n end\n end\n\n return a\nend\n\nfunction euclid_sub(a::Int64, b::Int64)\n a = abs(a)\n b = abs(b)\n\n while (a != b)\n if (a > b)\n a -= b\n else\n b -= a\n end\n end\n\n return a\nend\n\nfunc euclid_sub(in1, in2: int): int =\n var\n a = abs(in1)\n b = abs(in2)\n\n while a != b:\n if a > b:\n a -= b\n else:\n b -= a\n\n result = a\n\n\neuclid_sub:\n mov rax, rdi # Get abs of a\n sar rax, 31\n xor rdi, rax\n sub rdi, rax\n mov rax, rsi # Get abs of b\n sar rax, 31\n xor rsi, rax\n sub rsi, rax\n jmp check\nloop:\n cmp rdi, rsi # Find which is bigger\n jle if_true\n sub rdi, rsi # If a is bigger then a -= b\n jmp check\nif_true:\n sub rsi, rdi # Else b -= a\ncheck:\n cmp rsi, rdi # Check if a and b are not equal\n jne loop\n mov rax, rdi # Return results\n\nINTEGER FUNCTION euclid_sub(a, b)\n IMPLICIT NONE\n INTEGER, INTENT(INOUT) :: a, b\n\n a = ABS(a)\n b = ABS(b)\n\n DO WHILE (a /= b)\n\n IF (a > b) THEN\n a = a - b\n ELSE\n b = b - a\n END IF\n END DO\n\n euclid_sub = a\n\nEND FUNCTION euclid_sub\n\nfunction euclid_sub(int $a, int $b): int\n{\n $a = abs($a);\n $b = abs($b);\n\n while ($a !== $b) {\n if ($a > $b) {\n $a = $a - $b;\n } else {\n $b = $b - $a;\n }\n }\n\n return $a;\n}\n\n: euclid- ( a b -- gcd )\n [ abs ] bi@\n [ 2dup = ]\n [\n ! make sure the lower number is deeper\n 2dup >= [ swap ] when\n over -\n ! leaves us with stack { }\n ]\n until\n ! we have the GCD twice now, drop one\n drop\n;\n\nEuclidian algorithm subtraction method.\nEnter two positive integers. \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nThe \nend.\n\ndef euclid_sub(a: Int, b: Int): Int =\n (Math.abs(a), Math.abs(b)) match {\n case (0, _) | (_, 0) => 0\n case (x, y) if x euclid_sub(x, y - x)\n case (x, y) if x > y => euclid_sub(x - y, y)\n case _ => a\n\n(define (euclid_sub a b)\n (local ((define (euclid_sub* x y)\n (if (= x y)\n x\n (if (> x y)\n (euclid_sub* (- x y) y)\n (euclid_sub* x (- y x))\n )\n )\n )) (euclid_sub* (abs a) (abs b))\n )\n )\n\ndef gcd_minus(a, b)\n a = a.abs\n b = b.abs\n until a == b\n if a > b\n a -= b\n else\n b -= a\n end\n end\n a\nend\n\nInteger>>euclidSub: secondNumber\n \"Euclidean algorithm with subtraction\"\n | a b |\n a := self abs.\n b := secondNumber abs.\n [ a == b ] whileFalse: [ \n a > b ifTrue: [ \n a := a - b.\n ] ifFalse: [ \n b := b - a.\n ].\n ].\n ^a.\n\n🐇 ❗️ 🔼 a 🔢 b 🔢 ➡️ 🔢 🍇\n 💭 Use 🏧 (returns the absolute value) to support negative numbers.\n 🏧a ❗️ ➡️ 🖍🆕var_a\n 🏧b ❗️ ➡️ 🖍🆕var_b\n\n ️🔁 ❎ var_a 🙌 var_b ❗️ 🍇\n ↪️ var_a ▶️ var_b 🍇\n var_a ⬅️ ➖ var_b\n 🍉\n 🙅 🍇\n var_b ⬅️ ➖ var_a\n 🍉\n 🍉\n\n ↩️ var_a\n🍉\n\nHOW IZ I UKLIDSUP YR NUM1 AN YR NUM2\n NUM1 R I IZ ABZ YR NUM1 MKAY\n NUM2 R I IZ ABZ YR NUM2 MKAY\n\n IM IN YR LOOP \n BOTH SAEM NUM1 AN NUM2, O RLY?\n YA RLY, FOUND YR NUM1\n OIC \n\n DIFFRINT NUM1 AN SMALLR OF NUM1 AN NUM2, O RLY?\n YA RLY, NUM1 R DIFF OF NUM1 AN NUM2\n NO WAI, NUM2 R DIFF OF NUM2 AN NUM1\n OIC\n IM OUTTA YR LOOP\n\nIF U SAY SO\n\neuclid_sub() {\n local a\n local b\n a=$(abs \"$1\")\n b=$(abs \"$2\")\n\n while (( a != b )); do\n if (( a > b )); then\n ((a -= b))\n else\n ((b -= a))\n fi\n done\n printf \"%s\" \"$a\"\n}\n\n// Euclidean algorithm with subtraction\nint euclid_sub(int a, int b) {\n a = abs(a);\n b = abs(b);\n\n while (a != b) {\n if (a > b) {\n a -= b;\n } else {\n b -= a;\n }\n }\n\n return a;\n}\n\n\n \n\n(define (euclid-sub a b)\n (cond \n [(or (negative? a)(negative? b))(euclid-sub (abs a)(abs b))] \n [(eq? a b) a]\n [(> a b)(euclid-sub(- a b) b)]\n [else\n (euclid-sub a (- b a))]))\n\n\n \n\nleave one line empty:\nfunction Sub-Euclid($a, $b) {\n $a = [Math]::Abs($a)\n $b = [Math]::Abs($b)\n\n while ($a -ne $b) {\n if ($a -gt $b) {\n $a = $a - $b\n } else {\n $b = $b - $a\n }\n }\n\n return $a\n}\n\ndef euclid_sub(a is int, 0) = a\naddpattern def euclid_sub(0, b is int) = b\n\naddpattern def euclid_sub(a is int, b is int):\n if a \n\n\nHere, we simply line the two numbers up every step and subtract the lower value from the higher one every timestep. Once the two values are equal, we call that value the greatest common divisor. A graph of a and b as they change every step would look something like this:\n\n \n\n\nModern implementations, though, often use the modulus operator (%) like so\nfunction s:euclid_mod(a, b)\n let l:a = abs(a:a)\n let l:b = abs(a:b)\n\n while l:b != 0\n let l:c = l:b\n let l:b = l:a % l:b\n let l:a = l:c\n endwhile\n\n return l:a\nendfunction\n\nint euclid_mod(int a, int b) {\n a = abs(a);\n b = abs(b);\n\n while (b != 0) {\n int temp = b;\n b = a % b;\n a = temp;\n }\n\n return a;\n}\n\npublic int EuclidMod(int a, int b)\n{\n // Math.Abs for negative number support\n a = Math.Abs(a);\n b = Math.Abs(b);\n\n while (b != 0)\n {\n var temp = b;\n b = a % b;\n a = temp;\n }\n\n return a;\n}\n\n(defn euclid-mod [a b]\n (loop [i (Math/abs a) j (Math/abs b)]\n (if (zero? j)\n i\n (recur j (% i j)))))\n\n// Euclidean algorithm using modulus\nint euclid_mod(int a, int b) {\n a = std::abs(a);\n b = std::abs(b);\n\n while (b != 0) {\n a = std::exchange(b, a % b);\n }\n\n return a;\n}\n\npublic static int euclidMod(int a, int b) {\n while (b != 0) {\n int tmp = b;\n b = a % b;\n a = tmp;\n }\n\n return a;\n}\n\nfun euclidMod(a: Int, b: Int): Int {\n var a = a.absoluteValue\n var b = b.absoluteValue\n\n while (b != 0) {\n val tmp = b\n b = a % b\n a = tmp\n }\n\n return a\n}\n\nfunction euclidMod(a, b) {\n a = Math.abs(a);\n b = Math.abs(b);\n\n let temp;\n while (b !== 0) {\n temp = b;\n b = a % b;\n a = temp;\n }\n\n return a;\n}\n\n(defun euclid-mod (a b)\n \"Finds the greatest common divisor for any two integers\"\n (if (zerop b)\n (abs a)\n (euclid-mod b (mod a b))))\n\ndef euclid_mod(a, b):\n\n a = abs(a)\n b = abs(b)\n\n while b > 0:\n a, b = b, a % b\n\n return a\n\neuclidMod :: Integer -> Integer -> Integer\neuclidMod a b = inner (abs a) (abs b)\n where\n -- if a divides b, then gcd is a\n inner x 0 = x\n -- otherwise, recursively call inner with b and (a mod b) as new inputs\n inner x y = inner y (x `mod` y)\n\nfn euclid_rem(mut a: i64, mut b: i64) -> i64 {\n a = a.abs();\n b = b.abs();\n while b != 0 {\n let tmp = b;\n b = a % b;\n a = tmp;\n }\n\n a\n}\n\nlet euclid_mod a b =\n let rec inner a = function\n | 0 -> a\n | b -> inner b (a mod b)\n in (inner (abs a) (abs b))\n\nfunc euclidMod(a, b int) int {\n a = abs(a)\n b = abs(b)\n\n for b != 0 {\n a, b = b, a%b\n }\n\n return a\n}\n\nfunc euclidMod(a: Int, b: Int) -> Int {\n var a = abs(a);\n var b = abs(b);\n\n while (b != 0) {\n let temp = b\n b = a % b\n a = temp\n }\n\n return a\n}\n\nfunction gcd = euclidMod(a,b)\n\n a=abs(a);\n b=abs(b);\n\n while b > 0\n temp = b;\n b = mod(a,b);\n a = temp;\n end\n\n gcd = a;\nend\n\nlocal function euclid_mod(a, b)\n a = math.abs(a)\n b = math.abs(b)\n\n while b ~= 0 do\n a, b = b, a%b\n end\n\n return a\nend\n\nfunction euclid_mod(a::Int64, b::Int64)\n a = abs(a)\n b = abs(b)\n\n while(b != 0)\n b,a = a%b,b\n end\n\n return a\nend\n\nfunc euclid_mod(in1, in2: int): int =\n var\n a = abs(in1)\n b = abs(in2)\n\n while b != 0:\n let temp: int = b\n b = a mod b\n a = temp;\n\n result = a\n\n\n# rdi - a\n# rsi - b\n# RET rax - gcd of a and b\neuclid_mod:\n mov rax, rdi # Get abs of a\n sar rax, 31\n xor rdi, rax\n sub rdi, rax\n mov rax, rsi # Get abs of b\n sar rax, 31\n xor rsi, rax\n sub rsi, rax\n jmp mod_check\nmod_loop:\n xor rdx, rdx # Take the mod of a and b\n mov rax, rdi\n div rsi\n mov rdi, rsi # Set b to the mod of a and b\n mov rsi, rdx # Set a to b\nmod_check:\n cmp rsi, 0 # Check if b is non-zero\n jne mod_loop\n mov rax, rdi # Return the result\n\nINTEGER FUNCTION euclid_mod(a, b)\n IMPLICIT NONE\n INTEGER, INTENT(INOUT) :: a, b\n INTEGER :: temp\n\n DO WHILE (b > 0)\n temp = b\n b = MODULO(a,b)\n a = temp\n END DO\n\n euclid_mod = a\n\nEND FUNCTION euclid_mod\n\nfunction euclid_mod(int $a, int $b): int\n{\n $a = abs($a);\n $b = abs($b);\n\n while ($b !== 0) {\n list($b, $a) = [$a % $b, $b];\n }\n\n return $a;\n}\n\n: euclid% ( a b -- gcd )\n [ abs ] bi@ ! take both absolute values\n [ dup zero? ] ! check if `b` (on top) is 0\n [\n ! a b -> a b b -> b a b -> b a%b\n dup -rot mod\n ]\n until\n ! the zero is on top, so get rid of it\n drop\n;\n\nEuclidian algorithm modulo method.\nEnter two positive integers. \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nThe\nend.\n\n\ndef euclid_mod(a: Int, b: Int): Int =\n (Math.abs(a), Math.abs(b)) match {\n case (_, 0) => a\n case (a, b) => euclid_mod(b, a % b)\n\n(define (euclid_mod a b)\n (local ((define (euclid_mod* a b)\n (if (= 0 b)\n (abs a)\n (euclid_mod* b (modulo a b))\n )\n )) (euclid_mod* a b)\n )\n )\n\ndef gcd_mod(a, b)\n a = a.abs\n b = b.abs\n a, b = b, a%b until b.zero?\n a\nend\n\nInteger>>euclidMod: secondNumber\n \"Euclidean algorithm with modulus.\"\n | a b oldB |\n a := self abs.\n b := secondNumber abs.\n [ b == 0 ] whileFalse: [ \n oldB := b.\n b := a % b.\n a := oldB.\n ].\n ^a.\n\n🐇 ❗️ ⏫ a 🔢 b 🔢 ➡️ 🔢 🍇\n 💭 Use 🏧 (returns the absolute value) to support negative numbers.\n 🏧a ❗️ ➡️ 🖍🆕var_a\n 🏧b ❗️ ➡️ 🖍🆕var_b\n\n ️🔁 ❎ var_b 🙌 0 ❗️ 🍇\n var_b ➡️ temp\n var_a 🚮 var_b ➡️ 🖍var_b\n temp ➡️ 🖍var_a\n 🍉\n\n ↩️ var_a\n🍉\n\nHOW IZ I UKLIDMOD YR NUM1 AN YR NUM2\n NUM1 R I IZ ABZ YR NUM1 MKAY\n NUM2 R I IZ ABZ YR NUM2 MKAY\n\n IM IN YR LOOP \n BOTH SAEM NUM2 AN 0, O RLY?\n YA RLY, FOUND YR NUM1\n OIC\n\n I HAS A TMP ITZ NUM2\n NUM2 R MOD OF NUM1 AN NUM2\n NUM1 R TMP\n IM OUTTA YR LOOP\n\nIF U SAY SO\n\neuclid_mod() {\n local a\n local b\n a=$(abs \"$1\")\n b=$(abs \"$2\")\n\n while (( b != 0 )); do\n ((tmp = b))\n ((b = a % b))\n ((a = tmp))\n done\n printf \"%s\" \"$a\"\n}\n\n// Euclidean algorithm using modulus\nint euclid_mod(int a, int b) {\n int tmp;\n a = abs(a);\n b = abs(b);\n\n while (b != 0) {\n tmp = a % b;\n a = b;\n b = tmp;\n }\n\n return a;\n}\n\n\n \n\n(define (euclid-mod a b)\n (if (zero? b)\n a\n (euclid-mod b (modulo a b))))\n\n\n \n\nleave one line empty:\nfunction Mod-Euclid($a, $b) {\n $a = [Math]::Abs($a)\n $b = [Math]::Abs($b)\n\n while ($b -ne 0) {\n $tmp = $b\n $b = $a % $b\n $a = $tmp\n }\n\n return $a\n}\n\ndef euclid_mod(a is int, 0) = a\naddpattern def euclid_mod(0, b is int) = b\n\naddpattern def euclid_mod(a is int, b is int) = euclid_mod(b, a % b)\n\n\n\nHere, we set b to be the remainder of a%b and a to be whatever b was last timestep. Because of how the modulus operator works, this will provide the same information as the subtraction-based implementation, but when we show a and b as they change with time, we can see that it might take many fewer steps:\n\n \n\n\nThe Euclidean Algorithm is truly fundamental to many other algorithms throughout the history of computer science and will definitely be used again later. At least to me, it's amazing how such an ancient algorithm can still have modern use and appeal. That said, there are still other algorithms out there that can find the greatest common divisor of two numbers that are arguably better in certain cases than the Euclidean algorithm, but the fact that we are discussing Euclid two millennia after his death shows how timeless and universal mathematics truly is. I think that's pretty cool.\nVideo Explanation\nHere's a video on the Euclidean algorithm:\n\n\n\n\nExample Code\nfunction s:euclid_mod(a, b)\n let l:a = abs(a:a)\n let l:b = abs(a:b)\n\n while l:b != 0\n let l:c = l:b\n let l:b = l:a % l:b\n let l:a = l:c\n endwhile\n\n return l:a\nendfunction\n\nfunction s:euclid_sub(a, b)\n let l:a = abs(a:a)\n let l:b = abs(a:b)\n\n while l:a != l:b\n if l:a > l:b\n let l:a -= l:b\n else\n let l:b -= l:a\n endif\n endwhile\n\n return l:a\nendfunction\n\nlet s:check_1 = s:euclid_mod(64 * 67, 64 * 71)\nlet s:check_2 = s:euclid_sub(128 * 12, 128 * 77)\n\necho 'Modulus-based euclidean algorithm result:' s:check_1\necho 'subtraction-based euclidean algorithm result:' s:check_2\n\n#include \n#include \n\nint euclid_mod(int a, int b) {\n a = abs(a);\n b = abs(b);\n\n while (b != 0) {\n int temp = b;\n b = a % b;\n a = temp;\n }\n\n return a;\n}\n\nint euclid_sub(int a, int b) {\n a = abs(a);\n b = abs(b);\n\n while (a != b) {\n if (a > b) {\n a -= b;\n } else {\n b -= a;\n }\n }\n\n return a;\n}\n\nint main() {\n int check1 = euclid_mod(64 * 67, 64 * 81);\n int check2 = euclid_sub(128 * 12, 128 * 77);\n\n printf(\"[#]\\nModulus-based euclidean algorithm result:\\n%d\\n\", check1);\n printf(\"[#]\\nSubtraction-based euclidean algorithm result:\\n%d\\n\", check2);\n\n return 0;\n}\n\nEuclideanAlgorithm.cs\n// submitted by Julian Schacher (jspp)\nusing System;\n\nnamespace EuclideanAlgorithm\n{\n public class EuclideanAlgorithm\n {\n public int EuclidSub(int a, int b)\n {\n // Math.Abs for negative number support\n a = Math.Abs(a);\n b = Math.Abs(b);\n\n while (a != b)\n {\n if (a > b)\n a = a - b;\n else\n b = b - a;\n }\n\n return a;\n }\n\n public int EuclidMod(int a, int b)\n {\n // Math.Abs for negative number support\n a = Math.Abs(a);\n b = Math.Abs(b);\n\n while (b != 0)\n {\n var temp = b;\n b = a % b;\n a = temp;\n }\n\n return a;\n }\n }\n}\n\nProgram.cs\n// submitted by Julian Schacher (jspp)\nusing System;\n\nnamespace EuclideanAlgorithm\n{\n class Program\n {\n static void Main(string[] args)\n {\n var euclideanAlgorithm = new EuclideanAlgorithm();\n int check = euclideanAlgorithm.EuclidMod(64 * 67, 64 * 81);\n int check2 = euclideanAlgorithm.EuclidSub(128 * 12, 128 * 77);\n\n Console.WriteLine(\"[#]\\nModulus-based euclidean algorithm result:\");\n Console.WriteLine(check);\n Console.WriteLine(\"[#]\\nSubtraction-based euclidean algorithm result:\");\n Console.WriteLine(check2);\n }\n }\n}\n\n;; earthfail\n(defn euclid-sub [a b]\n (loop [i (Math/abs a) j (Math/abs b)]\n (if (= i j)\n i\n (if (> i j)\n (recur (- i j) j)\n (recur i (- j i))))))\n(defn euclid-mod [a b]\n (loop [i (Math/abs a) j (Math/abs b)]\n (if (zero? j)\n i\n (recur j (% i j)))))\n\n(print\n (euclid-sub (* 64 67)\n (* 64 81))\n (euclid-mod (* 128 12)\n (* 128 77)))\n\n#include \n#include \n#include \n\n// Euclidean algorithm using modulus\nint euclid_mod(int a, int b) {\n a = std::abs(a);\n b = std::abs(b);\n\n while (b != 0) {\n a = std::exchange(b, a % b);\n }\n\n return a;\n}\n\n// Euclidean algorithm with subtraction\nint euclid_sub(int a, int b) {\n a = std::abs(a);\n b = std::abs(b);\n\n while (a != b) {\n if (a > b) {\n a -= b;\n } else {\n b -= a;\n }\n }\n\n return a;\n}\n\nint main() {\n auto check1 = euclid_mod(64 * 67, 64 * 81);\n auto check2 = euclid_sub(128 * 12, 128 * 77);\n\n std::cout \n// submitted by lolatomroflsinnlos, modified by xam4lor\npublic class EuclideanAlgo {\n public static int euclidSub(int a, int b) {\n a = Math.abs(a);\n b = Math.abs(b);\n\n while (a != b) {\n if (a > b) {\n a -= b;\n } else {\n b -= a;\n }\n }\n\n return a;\n }\n\n public static int euclidMod(int a, int b) {\n while (b != 0) {\n int tmp = b;\n b = a % b;\n a = tmp;\n }\n\n return a;\n }\n\n public static void main(String[] args) {\n System.out.println(\"[#]\\nModulus-based euclidean algorithm result:\");\n System.out.println(euclidMod(64 * 67, 64 * 81));\n System.out.println(\"[#]\\nSubtraction-based euclidean algorithm result:\");\n System.out.println(euclidSub(128 * 12, 128 * 77));\n }\n}\n\nimport kotlin.math.absoluteValue\n\nfun euclidSub(a: Int, b: Int): Int {\n var a = a.absoluteValue\n var b = b.absoluteValue\n\n while (a != b) {\n if (a > b) a -= b\n else b -= a\n }\n\n return a\n}\n\nfun euclidMod(a: Int, b: Int): Int {\n var a = a.absoluteValue\n var b = b.absoluteValue\n\n while (b != 0) {\n val tmp = b\n b = a % b\n a = tmp\n }\n\n return a\n}\n\nfun main(args: Array) {\n println(\"[#]\\nModulus-based euclidean algorithm result:\")\n println(euclidMod(64 * 67, 64 * 81))\n println(\"[#]\\nSubtraction-based euclidean algorithm result:\")\n println(euclidSub(128 * 12, 128 * 77))\n}\n\nfunction euclidMod(a, b) {\n a = Math.abs(a);\n b = Math.abs(b);\n\n let temp;\n while (b !== 0) {\n temp = b;\n b = a % b;\n a = temp;\n }\n\n return a;\n}\n\nfunction euclidSub(a, b) {\n a = Math.abs(a);\n b = Math.abs(b);\n\n while (a !== b) {\n if (a > b) {\n a -= b;\n } else {\n b -= a;\n }\n }\n\n return a;\n}\n\nconsole.log('[#]\\nModulus-based euclidean algorithm result:')\nconsole.log(euclidMod(64 * 67, 64 * 81));\nconsole.log('[#]\\nSubtraction-based euclidean algorithm result:')\nconsole.log(euclidSub(128 * 12, 128 * 77));\n\n;;;; Euclidean algorithm implementation in Common Lisp\n\n(defun euclid-sub (a b)\n \"Finds the greatest common divsor for any two integers\"\n (defun euclid-sub* (a b)\n \"Finds the greatest common divisor for any two positive integers\"\n (if (eql a b)\n a\n (if (> a b)\n (euclid-sub* (- a b) b)\n (euclid-sub* a (- b a)))))\n (euclid-sub* (abs a) (abs b)))\n\n(defun euclid-mod (a b)\n \"Finds the greatest common divisor for any two integers\"\n (if (zerop b)\n (abs a)\n (euclid-mod b (mod a b))))\n\n(format T \"[#]~%Modulus-based euclidean algorithm result:~%\")\n(format T \"~d~%\" (euclid-sub (* 64 67) (* 64 81)))\n(format T \"[#]~%Subtraction-based euclidean algorithm result:~%\")\n(format T \"~d~%\" (euclid-mod (* 128 12) (* 128 77)))\n\n;; Quick test\n(assert\n (eql (euclid-sub (* 64 67) (* 64 81))\n (gcd (* 64 67) (* 64 81))))\n\n(assert\n (eql (euclid-mod (* 64 67) (* 64 81))\n (gcd (* 64 67) (* 64 81))))\n\ndef euclid_mod(a, b):\n\n a = abs(a)\n b = abs(b)\n\n while b > 0:\n a, b = b, a % b\n\n return a\n\ndef euclid_sub(a, b):\n\n a = abs(a)\n b = abs(b)\n\n if a == 0:\n return b\n elif b == 0:\n return a\n\n while a != b:\n if a > b:\n a -= b\n else:\n b -= a\n\n return a\n\nif __name__==\"__main__\":\n print('[#]\\nModulus-based euclidean algorithm result:'),\n print(euclid_mod(64 * 67, 64 * 81))\n print('[#]\\nSubtraction-based euclidean algorithm result:')\n print(euclid_sub(128 * 12, 128 * 77))\n\n-- Method 1: Euclid's original subtraction algorithm\n\neuclidSub :: Integer -> Integer -> Integer\neuclidSub a b = inner (abs a) (abs b)\n where\n inner x y\n -- if a = b, then the gcd is a\n | x == y = x\n -- if a Integer -> Integer\neuclidMod a b = inner (abs a) (abs b)\n where\n -- if a divides b, then gcd is a\n inner x 0 = x\n -- otherwise, recursively call inner with b and (a mod b) as new inputs\n inner x y = inner y (x `mod` y)\n\n-- _________________________________________________________________________\n\n-- Examples\n\nmain :: IO ()\nmain = do\n let chk1 = euclidMod (64 * 67) (64 * 81)\n chk2 = euclidSub (128 * 12) (128 * 77)\n putStrLn \"[#]\\nModulus-based euclidean algorithm result:\"\n print chk1\n putStrLn \"[#]\\nSubtraction-based euclidean algorithm result:\"\n print chk2\n\n// contributed by Nicole Mazzuca (ubsan)\n\nfn euclid_sub(mut a: i64, mut b: i64) -> i64 {\n a = a.abs();\n b = b.abs();\n while a != b {\n if a i64 {\n a = a.abs();\n b = b.abs();\n while b != 0 {\n let tmp = b;\n b = a % b;\n a = tmp;\n }\n\n a\n}\n\nfn main() {\n let chk1 = euclid_rem(64 * 67, 64 * 81);\n let chk2 = euclid_sub(128 * 12, 128 * 77);\n println!(\"[#]\\nModulus-based euclidean algorithm result:\\n{}\", chk1);\n println!(\"[#]\\nSubtraction-based euclidean algorithm result:\\n{}\", chk2);\n}\n\n(* contributed by Nicole Mazzuca (ubsan) *)\n\nlet euclid_mod a b =\n let rec inner a = function\n | 0 -> a\n | b -> inner b (a mod b)\n in (inner (abs a) (abs b))\n\nlet euclid_sub a b =\n let rec inner a b =\n if a = b then\n a\n else if a print_int |> print_newline;\n Printf.printf \"[#]\\nSubtraction-based euclidean algorithm result:\\n\";\n chk2 |> print_int |> print_newline\n\n// Submitted by Chinmaya Mahesh (chin123)\n\npackage main\n\nimport \"fmt\"\n\nfunc abs(a int) int {\n if a b {\n a -= b\n } else {\n b -= a\n }\n }\n\n return a\n}\n\nfunc main() {\n check1 := euclidMod(64*67, 64*81)\n check2 := euclidSub(128*12, 128*77)\n\n fmt.Println(\"[#]\\nModulus-based euclidean algorithm result:\")\n fmt.Println(check1)\n fmt.Println(\"[#]\\nSubtraction-based euclidean algorithm result:\")\n fmt.Println(check2)\n}\n\nfunc euclidSub(a: Int, b: Int) -> Int {\n var a = abs(a)\n var b = abs(b)\n\n while (a != b) {\n if (a > b) {\n a -= b\n } else {\n b -= a\n }\n }\n\n return a\n}\n\nfunc euclidMod(a: Int, b: Int) -> Int {\n var a = abs(a);\n var b = abs(b);\n\n while (b != 0) {\n let temp = b\n b = a % b\n a = temp\n }\n\n return a\n}\n\nfunc main() {\n print(\"[#]\\nModulus-based euclidean algorithm result:\")\n print(euclidMod(a: 64 * 67, b: 64 * 81))\n print(\"[#]\\nSubtraction-based euclidean algorithm result:\")\n print(euclidSub(a: 128 * 12, b: 128 * 77))\n}\n\nmain()\n\n// Submitted by Max Weinstein\n\nfunction gcd = euclidSub(a,b)\n\n a = abs(a);\n b = abs(b);\n\n while a ~= b\n if a > b\n a = a - b;\n else\n b = b - a;\n end\n end\n\n gcd = a;\nend\n\nfunction gcd = euclidMod(a,b)\n\n a=abs(a);\n b=abs(b);\n\n while b > 0\n temp = b;\n b = mod(a,b);\n a = temp;\n end\n\n gcd = a;\nend\n\nfunction euclid()\n ['[#] Modulus-based euclidean algorithm result: ',num2str(euclidMod(64 * 67, 64 * 81))]\n\n ['[#] Subtraction-based euclidean algorithm result: ',num2str(euclidSub(128 * 12, 128 * 77))]\nend\n\nlocal function euclid_sub(a, b)\n a = math.abs(a)\n b = math.abs(b)\n\n while a ~= b do\n if a > b then\n a = a-b\n else\n b = b-a\n end\n end\n\n return a\nend\n\nlocal function euclid_mod(a, b)\n a = math.abs(a)\n b = math.abs(b)\n\n while b ~= 0 do\n a, b = b, a%b\n end\n\n return a\nend\n\nlocal function main()\n print(\"[#]\\nModulus-based euclidean algorithm result:\")\n print(euclid_mod(64 * 67, 64 * 81))\n print(\"[#]\\nSubtraction-based euclidean algorithm result:\")\n print(euclid_sub(128 * 12, 128 * 77))\nend\n\nmain()\n\nfunction euclid_mod(a::Int64, b::Int64)\n a = abs(a)\n b = abs(b)\n\n while(b != 0)\n b,a = a%b,b\n end\n\n return a\nend\n\nfunction euclid_sub(a::Int64, b::Int64)\n a = abs(a)\n b = abs(b)\n\n while (a != b)\n if (a > b)\n a -= b\n else\n b -= a\n end\n end\n\n return a\nend\n\nfunction main()\n check1 = euclid_mod(64 * 67, 64 * 81);\n check2 = euclid_sub(128 * 12, 128 * 77);\n\n println(\"[#]\\nModulus-based euclidean algorithm result:\\n$(check1)\")\n println(\"[#]\\nSubtraction-based euclidean algorithm result:\\n$(check2)\")\n\nend\n\nmain()\n\nfunc euclid_mod(in1, in2: int): int =\n var\n a = abs(in1)\n b = abs(in2)\n\n while b != 0:\n let temp: int = b\n b = a mod b\n a = temp;\n\n result = a\n\nfunc euclid_sub(in1, in2: int): int =\n var\n a = abs(in1)\n b = abs(in2)\n\n while a != b:\n if a > b:\n a -= b\n else:\n b -= a\n\n result = a\n\nwhen isMainModule:\n echo \"[#]\\nModulus-based euclidean algorithm result:\"\n echo euclid_sub(64 * 67, 64 * 81)\n echo \"[#]\\nSubtraction-based euclidean algorithm result:\"\n echo euclid_mod(128 * 12, 128 * 77)\n\n.intel_syntax noprefix\n\n.section .rodata\n euclid_mod_fmt: .string \"[#]\\nModulus-based euclidean algorithm result:\\n%d\\n\"\n euclid_sub_fmt: .string \"[#]\\nSubtraction-based euclidean algorithm result:\\n%d\\n\"\n\n.section .text\n .global main\n .extern printf\n\n# rdi - a\n# rsi - b\n# RET rax - gcd of a and b\neuclid_mod:\n mov rax, rdi # Get abs of a\n sar rax, 31\n xor rdi, rax\n sub rdi, rax\n mov rax, rsi # Get abs of b\n sar rax, 31\n xor rsi, rax\n sub rsi, rax\n jmp mod_check\nmod_loop:\n xor rdx, rdx # Take the mod of a and b\n mov rax, rdi\n div rsi\n mov rdi, rsi # Set b to the mod of a and b\n mov rsi, rdx # Set a to b\nmod_check:\n cmp rsi, 0 # Check if b is non-zero\n jne mod_loop\n mov rax, rdi # Return the result\n ret\n\neuclid_sub:\n mov rax, rdi # Get abs of a\n sar rax, 31\n xor rdi, rax\n sub rdi, rax\n mov rax, rsi # Get abs of b\n sar rax, 31\n xor rsi, rax\n sub rsi, rax\n jmp check\nloop:\n cmp rdi, rsi # Find which is bigger\n jle if_true\n sub rdi, rsi # If a is bigger then a -= b\n jmp check\nif_true:\n sub rsi, rdi # Else b -= a\ncheck:\n cmp rsi, rdi # Check if a and b are not equal\n jne loop\n mov rax, rdi # Return results\n ret\n\nmain:\n mov rdi, 4288 # Call euclid_mod\n mov rsi, 5184\n call euclid_mod\n mov rdi, OFFSET euclid_mod_fmt # Print output\n mov rsi, rax\n xor rax, rax\n call printf\n mov rdi, 1536 # Call euclid_sub\n mov rsi, 9856\n call euclid_sub\n mov rdi, OFFSET euclid_sub_fmt # Print output\n mov rsi, rax\n xor rax, rax\n call printf\n xor rax, rax # Return 0\n ret\n\nINTEGER FUNCTION euclid_sub(a, b)\n IMPLICIT NONE\n INTEGER, INTENT(INOUT) :: a, b\n\n a = ABS(a)\n b = ABS(b)\n\n DO WHILE (a /= b)\n\n IF (a > b) THEN\n a = a - b\n ELSE\n b = b - a\n END IF\n END DO\n\n euclid_sub = a\n\nEND FUNCTION euclid_sub \n\nINTEGER FUNCTION euclid_mod(a, b)\n IMPLICIT NONE\n INTEGER, INTENT(INOUT) :: a, b\n INTEGER :: temp\n\n DO WHILE (b > 0)\n temp = b\n b = MODULO(a,b)\n a = temp\n END DO\n\n euclid_mod = a\n\nEND FUNCTION euclid_mod\n\nPROGRAM euclidean\n\n IMPLICIT NONE\n INTEGER :: a, b, euclid_sub, euclid_mod\n\n a = 64 * 67\n b = 64 * 81\n\n WRITE(*,'(a)') '[#]'\n WRITE(*,'(a)') 'Modulus-based euclidean algorithm result:'\n WRITE(*, '(g0)') euclid_mod(a, b)\n\n a = 128 * 12\n b = 128 * 77\n\n WRITE(*,'(a)') '[#]'\n WRITE(*,'(a)') 'Subtraction-based euclidean algorithm result:'\n WRITE(*, '(g0)') euclid_sub(a, b)\n\nEND PROGRAM euclidean\n\n $b) {\n $a = $a - $b;\n } else {\n $b = $b - $a;\n }\n }\n\n return $a;\n}\n\nfunction euclid_mod(int $a, int $b): int\n{\n $a = abs($a);\n $b = abs($b);\n\n while ($b !== 0) {\n list($b, $a) = [$a % $b, $b];\n }\n\n return $a;\n}\n\nprintf('[#]'.PHP_EOL.'Modulus-based euclidean algorithm result:'.PHP_EOL.'%s', euclid_mod(64 * 67, 64 * 81));\necho PHP_EOL;\nprintf('[#]'.PHP_EOL.'Subtraction-based euclidean algorithm result:'.PHP_EOL.'%s', euclid_sub(128 * 12, 128 * 77));\necho PHP_EOL;\n\n: euclid- ( a b -- gcd )\n [ abs ] bi@\n [ 2dup = ]\n [\n ! make sure the lower number is deeper\n 2dup >= [ swap ] when\n over -\n ! leaves us with stack { }\n ]\n until\n ! we have the GCD twice now, drop one\n drop\n;\n\n: euclid% ( a b -- gcd )\n [ abs ] bi@ ! take both absolute values\n [ dup zero? ] ! check if `b` (on top) is 0\n [\n ! a b -> a b b -> b a b -> b a%b\n dup -rot mod\n ]\n until\n ! the zero is on top, so get rid of it\n drop\n;\n\n42 56 euclid% . ! 14\n48 180 euclid% . ! 12\n\n42 56 euclid- . ! 14\n48 180 euclid- . ! 12\n\nHere is a readable version of the algorithms with comments. First, subtraction method:\nReading the input: a, b\n[SPACE][SPACE][SPACE][LF] push 0\n[SPACE][SPACE][SPACE][TAB][LF] push 1\n[TAB][LF][TAB][TAB] readi\n[TAB][LF][TAB][TAB] readi\n\nLoop: a, b => a, b-a\n[LF][SPACE][SPACE][LF] label_0:\n[SPACE][SPACE][SPACE][LF] push 0\n[TAB][TAB][TAB] retrieve\n[SPACE][SPACE][SPACE][TAB][LF] push 1\n[TAB][TAB][TAB] retrieve\n[TAB][SPACE][SPACE][TAB] sub\n[SPACE][LF][SPACE] dup\n[LF][TAB][SPACE][TAB][LF] jmp zero label_1\n[SPACE][LF][SPACE] dup\n[LF][TAB][TAB][TAB][SPACE][LF] jmp neg label_2\n[SPACE][SPACE][SPACE][LF] push 0\n[SPACE][LF][TAB] swap\n[TAB][TAB][SPACE] store\n[LF][SPACE][LF][LF] jmp label_0\n\nExit when a=b\n[LF][SPACE][SPACE][TAB][LF] label_1:\n[SPACE][SPACE][SPACE][LF] push 0\n[TAB][TAB][TAB] retrieve\n[TAB][LF][SPACE][TAB] printi\n[LF][LF][LF] end\n\nIf a>b: a, b => a-b, b\n[LF][SPACE][SPACE][TAB][SPACE][LF] label_2:\n[SPACE][SPACE][SPACE][LF] push 0\n[SPACE][LF][TAB] swap\n[TAB][SPACE][SPACE][TAB] sub\n[SPACE][SPACE][SPACE][TAB][LF] push 1\n[SPACE][LF][TAB] swap\n[TAB][TAB][SPACE] store\n[LF][SPACE][LF][LF] jmp label_0\n\nand modulo method:\nReading the input: a, b\n[SPACE][SPACE][SPACE][LF] push 0\n[SPACE][SPACE][SPACE][TAB][LF] push 1\n[TAB][LF][TAB][TAB] readi\n[TAB][LF][TAB][TAB] readi\n\nLoop: a, b => b, a%b\n[LF][SPACE][SPACE][LF] label_0:\n[SPACE][SPACE][SPACE][LF] push 0\n[TAB][TAB][TAB] retrieve\n[SPACE][LF][SPACE] dup\n[LF][TAB][SPACE][TAB][LF] jmp zero label_1\n[SPACE][SPACE][SPACE][TAB][LF] push 1\n[TAB][TAB][TAB] retrieve\n[SPACE][LF][TAB] swap\n[TAB][SPACE][TAB][TAB] mod\n[SPACE][SPACE][SPACE][LF] push 0\n[TAB][TAB][TAB] retrieve\n[SPACE][SPACE][SPACE][TAB][LF] push 1\n[SPACE][LF][TAB] swap\n[TAB][TAB][SPACE] store\n[SPACE][SPACE][SPACE][LF] push 0\n[SPACE][LF][TAB] swap\n[TAB][TAB][SPACE] store\n[LF][SPACE][LF][LF] jmp label_0\n\nExit when b=0\n[LF][SPACE][SPACE][TAB][LF] label_1:\n[SPACE][SPACE][SPACE][TAB][LF] push 1\n[TAB][TAB][TAB] retrieve\n[TAB][LF][SPACE][TAB] printi\n[LF][LF][LF][LF] end\n\nobject Euclid {\n\n def euclid_sub(a: Int, b: Int): Int =\n (Math.abs(a), Math.abs(b)) match {\n case (0, _) | (_, 0) => 0\n case (x, y) if x euclid_sub(x, y - x)\n case (x, y) if x > y => euclid_sub(x - y, y)\n case _ => a\n }\n\n def euclid_mod(a: Int, b: Int): Int =\n (Math.abs(a), Math.abs(b)) match {\n case (_, 0) => a\n case (a, b) => euclid_mod(b, a % b)\n }\n\n def main(args: Array[String]): Unit = {\n println(\"[#]\\nModulus-based euclidean algorithm result:\")\n println(euclid_mod(64 * 67, 64 * 81))\n println(\"[#]\\nSubtraction-based euclidean algorithm result:\")\n println(euclid_sub(128 * 12, 128 * 77))\n }\n\n}\n\n#lang racket\n\n(define (euclid_sub a b)\n (local ((define (euclid_sub* x y)\n (if (= x y)\n x\n (if (> x y)\n (euclid_sub* (- x y) y)\n (euclid_sub* x (- y x))\n )\n )\n )) (euclid_sub* (abs a) (abs b))\n )\n )\n\n(define (euclid_mod a b)\n (local ((define (euclid_mod* a b)\n (if (= 0 b)\n (abs a)\n (euclid_mod* b (modulo a b))\n )\n )) (euclid_mod* a b)\n )\n )\n\n(displayln \"[#]\\nModulus-based euclidean algorithm result:\")\n(displayln (euclid_sub (* 64 67) (* 64 81)))\n(displayln \"[#]\\nSubtraction-based euclidean algorithm result:\")\n(displayln (euclid_mod (* 128 12) (* 128 77)))\n\ndef gcd_mod(a, b)\n a = a.abs\n b = b.abs\n a, b = b, a%b until b.zero?\n a\nend\n\ndef gcd_minus(a, b)\n a = a.abs\n b = b.abs\n until a == b\n if a > b\n a -= b\n else\n b -= a\n end\n end\n a\nend\n\nprint \"[#]\\nModulus-based euclidean algorithm result:\\n\"\np gcd_mod(64 * 67, 64 * 81)\nprint \"[#]\\nSubtraction-based euclidean algorithm result:\\n\"\np gcd_minus(128 * 12, 128 * 77)\n\nInteger>>euclidSub: secondNumber\n \"Euclidean algorithm with subtraction\"\n | a b |\n a := self abs.\n b := secondNumber abs.\n [ a == b ] whileFalse: [ \n a > b ifTrue: [ \n a := a - b.\n ] ifFalse: [ \n b := b - a.\n ].\n ].\n ^a.\n\nInteger>>euclidMod: secondNumber\n \"Euclidean algorithm with modulus.\"\n | a b oldB |\n a := self abs.\n b := secondNumber abs.\n [ b == 0 ] whileFalse: [ \n oldB := b.\n b := a % b.\n a := oldB.\n ].\n ^a.\n\nTranscript show: ((64 * 67) euclidSub: (64 * 81)).\nTranscript cr.\nTranscript show: ((128 * 12) euclidMod: (128 * 77)).\n\n🐇 ⬆️ 🍇\n 🐇 ❗️ 🔼 a 🔢 b 🔢 ➡️ 🔢 🍇\n 💭 Use 🏧 (returns the absolute value) to support negative numbers.\n 🏧a ❗️ ➡️ 🖍🆕var_a\n 🏧b ❗️ ➡️ 🖍🆕var_b\n\n ️🔁 ❎ var_a 🙌 var_b ❗️ 🍇\n ↪️ var_a ▶️ var_b 🍇\n var_a ⬅️ ➖ var_b\n 🍉\n 🙅 🍇\n var_b ⬅️ ➖ var_a\n 🍉\n 🍉\n\n ↩️ var_a\n 🍉\n\n 🐇 ❗️ ⏫ a 🔢 b 🔢 ➡️ 🔢 🍇\n 💭 Use 🏧 (returns the absolute value) to support negative numbers.\n 🏧a ❗️ ➡️ 🖍🆕var_a\n 🏧b ❗️ ➡️ 🖍🆕var_b\n\n ️🔁 ❎ var_b 🙌 0 ❗️ 🍇\n var_b ➡️ temp\n var_a 🚮 var_b ➡️ 🖍var_b\n temp ➡️ 🖍var_a\n 🍉\n\n ↩️ var_a\n 🍉\n🍉\n\n🏁 🍇\n 😀 🔡 ️🔼🐇⬆️ 🤜64 ✖️ 67🤛 🤜64 ✖️ 81🤛 ❗️ 10 ❗️❗️\n 😀 🔡 ️⏫🐇⬆️ 🤜128 ✖️ 12🤛 🤜128 ✖️ 77🤛 ❗️ 10 ❗️❗️\n🍉\n\nHAI 1.2\n HOW IZ I ABZ YR NUM\n DIFFRINT NUM AN BIGGR OF NUM AN 0, O RLY?\n YA RLY, FOUND YR DIFF OF 0 AN NUM\n NO WAI, FOUND YR NUM\n OIC\n IF U SAY SO\n\n HOW IZ I UKLIDMOD YR NUM1 AN YR NUM2\n NUM1 R I IZ ABZ YR NUM1 MKAY\n NUM2 R I IZ ABZ YR NUM2 MKAY\n\n IM IN YR LOOP \n BOTH SAEM NUM2 AN 0, O RLY?\n YA RLY, FOUND YR NUM1\n OIC\n\n I HAS A TMP ITZ NUM2\n NUM2 R MOD OF NUM1 AN NUM2\n NUM1 R TMP\n IM OUTTA YR LOOP\n\n IF U SAY SO\n\n HOW IZ I UKLIDSUP YR NUM1 AN YR NUM2\n NUM1 R I IZ ABZ YR NUM1 MKAY\n NUM2 R I IZ ABZ YR NUM2 MKAY\n\n IM IN YR LOOP \n BOTH SAEM NUM1 AN NUM2, O RLY?\n YA RLY, FOUND YR NUM1\n OIC \n\n DIFFRINT NUM1 AN SMALLR OF NUM1 AN NUM2, O RLY?\n YA RLY, NUM1 R DIFF OF NUM1 AN NUM2\n NO WAI, NUM2 R DIFF OF NUM2 AN NUM1\n OIC\n IM OUTTA YR LOOP\n\n IF U SAY SO\n\n I HAS A CHECK1 ITZ I IZ UKLIDMOD YR PRODUKT OF 64 AN 67 AN YR PRODUKT OF 64 AN 81 MKAY\n I HAS A CHECK2 ITZ I IZ UKLIDSUP YR PRODUKT OF 128 AN 12 AN YR PRODUKT OF 128 AN 77 MKAY\n\n VISIBLE CHECK1\n VISIBLE CHECK2\nKTHXBYE\n\n#!/usr/bin/env bash\nabs() {\n local ret=$1\n if (( ret b )); then\n ((a -= b))\n else\n ((b -= a))\n fi\n done\n printf \"%s\" \"$a\"\n}\n\nresult=$(euclid_mod $((64 * 67)) $((64 * 81)))\necho -e \"[#]\\nModulus-based euclidean algorithm result:\\n$result\"\nresult=$(euclid_sub $((128 * 12)) $((128 * 77)))\necho -e \"[#]\\nSubtraction-based euclidean algorithm result:\\n$result\"\n\nimport std.stdio;\nimport std.math;\n\n// Euclidean algorithm using modulus\nint euclid_mod(int a, int b) {\n int tmp;\n a = abs(a);\n b = abs(b);\n\n while (b != 0) {\n tmp = a % b;\n a = b;\n b = tmp;\n }\n\n return a;\n}\n\n// Euclidean algorithm with subtraction\nint euclid_sub(int a, int b) {\n a = abs(a);\n b = abs(b);\n\n while (a != b) {\n if (a > b) {\n a -= b;\n } else {\n b -= a;\n }\n }\n\n return a;\n}\n\nvoid main()\n{\n auto check1 = euclid_mod(64 * 67, 64 * 81);\n auto check2 = euclid_sub(128 * 12, 128 * 77);\n\n writeln(\"[#]\\nModulus-based euclidean algorithm result:\\n\", check1);\n writeln(\"[#]\\nSubtraction-based euclidean algorithm result:\\n\", check2);\n}\n\nA text version of the program is provided for both versions.\nSubtraction\n\n \n\nCOMMAND STATE OF STACK\nin(number) A // Take A as an input\nduplicate AA // Start to take the absolute value of A\npush 1 1AA\nduplicate 11AA\nsubtract 0AA\ngreater 0/1A // 1 if A > 0, 0 if A 0, 1 if A 0, 0 if B 0, 1 if B B; 1 if true; 0 if false\n pointer BA // If A > B, DP goes one clockwise, otherwise, DP stays the same. \n\n // If A > B (DP has changed 1 clockwise)\n duplicate BBA\n push 3 3BBA\n push 1 13BBA\n roll BAB\n subtract AB // A = A - B\n push 2 2AB\n push 1 12AB\n roll BA\n // Go back to start of loop\n\n // If B > A (DP stayed the same)\n push 2 2BA\n push 1 12BA\n roll AB\n duplicate AAB\n push 3 3AAB\n push 1 13AAB\n roll ABA\n subtract BA // B = B - A\n // Go back to start of loop\n\n// Go down if a = b (end of while loop)\npop A\nout(number) - // Print out A when done.\nModulo\n\n \n\nCOMMAND STATE OF STACK\nin(number) A\nin(number) BA\n\n// Start of loop\nduplicate BBA\nnot 0/1 BA\nnot 1/0 BA\npointer BA\n\n // Go down if b ≠ 0\n duplicate TBA\n push 3 3TBA \n push 1 13TBA\n roll BAT\n mod BA // b = a mod b; a = t\n // Go back to the start of the loop\n\n// Go right if b = 0\npop A\nout(number) - // Print out A when done.\n(define (euclid-sub a b)\n (cond \n [(or (negative? a)(negative? b))(euclid-sub (abs a)(abs b))] \n [(eq? a b) a]\n [(> a b)(euclid-sub(- a b) b)]\n [else\n (euclid-sub a (- b a))]))\n\n(define (euclid-mod a b)\n (if (zero? b)\n a\n (euclid-mod b (modulo a b))))\n\n(display \"[#]\\nModulus-based euclidean algorithm result:\") (newline)\n(display (euclid-mod (* 64 67) (* 64 81))) (newline)\n\n(display \"[#]\\nSubtraction-based euclidean algorithm result:\") (newline)\n(display (euclid-sub (* 128 12) (* 128 77))) (newline)\n\nThe code snippets were taken from this Scratch project\n\n \n\nleave one line empty:\nfunction Sub-Euclid($a, $b) {\n $a = [Math]::Abs($a)\n $b = [Math]::Abs($b)\n\n while ($a -ne $b) {\n if ($a -gt $b) {\n $a = $a - $b\n } else {\n $b = $b - $a\n }\n }\n\n return $a\n}\n\nfunction Mod-Euclid($a, $b) {\n $a = [Math]::Abs($a)\n $b = [Math]::Abs($b)\n\n while ($b -ne 0) {\n $tmp = $b\n $b = $a % $b\n $a = $tmp\n }\n\n return $a\n}\n\nWrite-Host \"[#]`nSubtraction-based euclidean algorithm result:`n$(Mod-Euclid $(64 * 67) $(64 * 81))\"\nWrite-Host \"[#]`nModulus-based euclidean algorithm result:`n$(Sub-Euclid $(128 * 12) $(128 * 77))\"\n\ndef euclid_sub(a is int, 0) = a\naddpattern def euclid_sub(0, b is int) = b\n\naddpattern def euclid_sub(a is int, b is int):\n if a \n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"Euclidsub\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Euclidmod\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/matrix_methods/matrix_methods.html":{"url":"contents/matrix_methods/matrix_methods.html","title":"Matrix Methods","keywords":"","body":"Matrix Methods\nMathematics is the foundation for many areas of science and engineering, and it is not uncommon for these applications to require the manipulation of large matrices. Though these applications are not mathematics, they use mathematics in everything they do and the methods to manipulate matrices are certainly mathematical. For this reason, I feel we should tour many methods used to manipulate matrices into any usable form. For the most part, we can divide the mathematical matrix methods into the following categories:\n\nDiagonalization / Finding the Eigenvalues\nCreating upper and lower diagonal matrices\nSolving systems of Equations\n\nThere are certainly more methods out there, so don't be offended if I have failed to list one of your favorite types of algorithms. We'll be filling more in as we go along!\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/computational_geometry/computational_geometry.html":{"url":"contents/computational_geometry/computational_geometry.html","title":"Computational Geometry","keywords":"","body":"Computational Geometry\nWhen it comes to the different sectors of computational mathematics, there are none that bring me more joy than computational geometry.\nIn some sense, it is the foundation for almost every area of automatically generated two and three dimensional graphics.\nIf you have time to spend poring through some interesting research, I would definitely recommend going to the arXiv.org section for computational geometry.\nWe will add more to this section as the Archive evolves, so let me know of any algorithms that you would like to cover in the future!\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/gift_wrapping/gift_wrapping.html":{"url":"contents/gift_wrapping/gift_wrapping.html","title":"Gift Wrapping","keywords":"","body":"Gift Wrapping\nIf given a \"gift\", here defined as a random distribution of points in two or three dimensions, gift-wrapping algorithms allow programmers to find its convex hull -- the smallest convex shape that holds all interior points.\nThis is one of the many cases where the leap from two to three dimensions leads to an incredibly more complicated code.\nThat said, there is a rich history of algorithms to solve this problem.\nTo be fair, only the Jarvis March is classified as the gift wrapping algorithm; however, it's a neat name to give algorithms that solve for the convex hull of a distribution of points.\nStrictly speaking, though, the term is not entirely accurate for all convex hull methods.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/decision_problems/decision_problems.html":{"url":"contents/decision_problems/decision_problems.html","title":"Decision Problems","keywords":"","body":"Decision Problems\nI'll be honest here: I am not sure what section to put these problems in, so for now, they are in Computational Mathematics, but that may change in the near future.\nI'm also not sure whether we can classify these problems as decision problems at all; however, everything in this section is related to making informed decisions when assigning inputs to appropriate outputs.\nFor example, the Hungarian algorithm reads in a bunch of inputs (candidates for certain jobs or positions) and assigns each input to an output task while minimizing the cost associated with all inputs performing their designated task.\nOverall, these problems come up all over the place and are certainly worth studying in their own right!\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/physics_solvers/physics_solvers.html":{"url":"contents/physics_solvers/physics_solvers.html","title":"Physics Solvers","keywords":"","body":"Physics Solvers\nThere are certain algorithms that have been uniquely created to solve particular physical systems.\nFor example, the kinematic equation can be solved with Verlet integration and also with more general differential equation solvers.\nIn this section, we will place all algorithms and methods that are specific to physics and cannot be used in any other area.\nIt's worth noting that many algorithms used throughout the Archive can also be used to solve physics equations and physics lends itself more readily to computational methods than many other areas of scientific research, such as biology or chemistry.\nIn the future, we may also place several unique physical systems along with different methods to solve these systems.\nFor example, there are many different ways to solve the Schrödinger equation, heat equation, kinematic equation and several other systems that are unique to physics and there are benefits and drawbacks for solving certain physical systems in certain ways.\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/huffman_encoding/huffman_encoding.html":{"url":"contents/huffman_encoding/huffman_encoding.html","title":"Huffman Encoding","keywords":"","body":"Huffman Encoding\nIf there were ever a data compression method to take the world by storm, it would be Huffman encoding.\nIn fact, this was the method that got me into computational methods to begin with.\nI distinctly remember sitting in my data compression class and talking about the great information theorist Claude Shannon and Robert Fano, when suddenly my professor introduced a new kid to the mix: David Huffman.\nHe managed to rip the heart out of the methods described by leaders of the field and create a data compression method that was easier to understand and implement, while also providing more robust results, and apparently this was all done for a school project!\nIt was in that moment, I knew I would never amount to anything.\nI have since accepted that fact and moved on.\nHuffman encoding follows from the problem described in the Data Compression section.\nWe have a string that we want to encode into bits.\nHuffman encoding ensures that our encoded bitstring is as small as possible without losing any information.\nBecause it is both lossless and guarantees the smallest possible bit length, it outright replaces both Shannon and Shannon-Fano encoding in most cases, which is a little weird because the method was devised while Huffman was taking a course from Fano, himself!\nThe idea is somewhat straightforward in principle, but a little difficult to code in practice.\nBy creating a binary tree of the input alphabet, every branch can be provided a unique bit representation simply by assigning a binary value to each child and reading to a character in a leaf node if starting from the root node.\nSo now the question is: how do we create a binary tree?\nWell, here we build it from the bottom up like so:\n\nOrder all characters according to the frequency they appear in the input bitstring, with the most frequent character at the top of the list. Be sure to keep track of the frequencies, too!\nAdd the smallest two values together to create a new node with a new frequency.\nKeep doing step 2 until the tree is complete.\nRead the tree backwards from the root node and concatenate the final bitstring codeword. Keep all codewords and put them into your final set of codewords (sometimes called a codebook)\nEncode your phrase with the codebook.\n\nAnd that's it.\nHere's an image of what this might look like for the phrase bibbity_bobbity:\n\n \n\n\nThis will create a codebook that looks like this:\n\n\n\nCharacter\nBit Representation\n\n\n\n\nb\n0\n\n\ni\n100\n\n\nt\n101\n\n\ny\n110\n\n\no\n1110\n\n\n_\n1111\n\n\n\nand bibbity_bobbity becomes 01000010010111011110111000100101110.\nAs mentioned this uses the minimum number of bits possible for encoding.\nThe fact that this algorithm is both conceptually simple and provably useful is rather extraordinary to me and is why Huffman encoding will always hold a special place in my heart.\nVideo Explanation\nHere is a quick video explanation for Huffman encoding:\n\n\n\n\nExample Code\nIn code, this can be a little tricky. It requires a method to continually sort the nodes as you add more and more nodes to the system.\nThe most straightforward way to do this in some languages is with a priority queue, but depending on the language, this might be more or less appropriate.\nIn addition, to read the tree backwards, some sort of Depth First Search needs to be implemented.\nWhether you use a stack or straight-up recursion also depends on the language, but the recursive method is a little easier to understand in most cases.\nusing Test\n\n# This is for the PriorityQueue\nusing DataStructures\n\nstruct Leaf\n weight::Int64\n key::Char\nend\n\nstruct Branch\n right::Union{Leaf, Branch}\n left::Union{Leaf, Branch}\n weight::Int64\nend\n\nconst Node = Union{Leaf, Branch}\n\nfunction codebook_recurse!(leaf::Leaf, code::String,\n dict::Dict{Char,String})\n dict[leaf.key] = code\nend\n\nfunction codebook_recurse!(branch::Branch, code::String,\n dict::Dict{Char,String})\n codebook_recurse!(branch.left, string(code, \"1\"), dict)\n codebook_recurse!(branch.right, string(code, \"0\"), dict)\nend\n\n# This will depth-first search through the tree\n# to create bitstrings for each character.\n# Note: Any depth-first search method will work\n# This outputs encoding Dict to be used for encoding\nfunction create_codebook(n::Node)\n codebook = Dict{Char,String}()\n if isa(n, Leaf)\n codebook[n.key]=\"0\"\n else\n codebook_recurse!(n, \"\", codebook)\n end\n return codebook\nend\n\n# This outputs huffman tree to generate dictionary for encoding\nfunction create_tree(phrase::String)\n\n # creating weights\n weights = PriorityQueue()\n for i in phrase\n temp_string = string(i)\n if (haskey(weights, temp_string))\n weights[temp_string] += 1\n else\n weights[temp_string] = 1\n end\n end\n\n # Creating all nodes to iterate through\n nodes = PriorityQueue{Node, Int64}()\n while(length(weights) > 0)\n weight = peek(weights)[2]\n key = dequeue!(weights)[1]\n temp_node = Leaf(weight, key)\n enqueue!(nodes, temp_node, weight)\n end\n\n while(length(nodes) > 1)\n node1 = dequeue!(nodes)\n node2 = dequeue!(nodes)\n temp_node = Branch(node1, node2, node1.weight + node2.weight)\n enqueue!(nodes, temp_node, temp_node.weight)\n end\n\n huffman_tree = dequeue!(nodes)\n return huffman_tree\n\nend\n\nfunction encode(codebook::Dict{Char, String}, phrase::String)\n final_bitstring = \"\"\n for i in phrase\n final_bitstring = final_bitstring * codebook[i]\n end\n\n return final_bitstring\nend\n\nfunction decode(huffman_tree::Node, bitstring::String)\n current = huffman_tree\n final_string = \"\"\n for i in bitstring\n if isa(huffman_tree, Branch)\n if (i == '1')\n current = current.left\n else\n current = current.right\n end\n\n if (!isa(current, Branch))\n final_string *= string(current.key)\n current = huffman_tree\n end\n else\n final_string *= string(huffman_tree.key)\n end\n end\n\n return final_string\nend\n\nfunction two_pass_huffman(phrase::String)\n huffman_tree = create_tree(phrase)\n codebook = create_codebook(huffman_tree)\n bitstring = encode(codebook, phrase)\n final_string = decode(huffman_tree, bitstring)\n return final_string\nend\n\n@testset \"b-string tests\" begin\n @test two_pass_huffman(\"b\") == \"b\"\n @test two_pass_huffman(\"bbbbbbbb\") == \"bbbbbbbb\"\n @test two_pass_huffman(\"bibbity bobbity\") == \"bibbity bobbity\"\nend\n\nextern crate itertools;\n\nuse std::cmp::{Ord, Ordering, PartialOrd};\nuse std::collections::{BinaryHeap, HashMap};\n\nuse itertools::Itertools;\n\n#[derive(Debug)]\nenum HuffmanTree {\n Branch {\n count: i32,\n left: Box,\n right: Box,\n },\n Leaf {\n count: i32,\n value: char,\n },\n}\n\nimpl PartialEq for HuffmanTree {\n fn eq(&self, other: &Self) -> bool {\n self.count() == other.count()\n }\n}\n\nimpl Eq for HuffmanTree {}\n\nimpl PartialOrd for HuffmanTree {\n fn partial_cmp(&self, other: &Self) -> Option {\n other.count().partial_cmp(&self.count())\n }\n}\n\nimpl Ord for HuffmanTree {\n fn cmp(&self, other: &Self) -> Ordering {\n other.count().cmp(&self.count())\n }\n}\n\n#[derive(Debug)]\nstruct Codebook {\n codebook: HashMap,\n tree: HuffmanTree,\n}\n\nimpl HuffmanTree {\n pub fn from(input: &str) -> Self {\n let counts = input.chars().fold(HashMap::new(), |mut map, c| {\n *map.entry(c).or_insert(0) += 1;\n map\n });\n let mut queue = counts\n .iter()\n .map(|(&value, &count)| HuffmanTree::Leaf { value, count })\n .collect::>();\n\n while queue.len() > 1 {\n let left = queue.pop().unwrap();\n let right = queue.pop().unwrap();\n queue.push(HuffmanTree::Branch {\n count: left.count() + right.count(),\n left: Box::new(left),\n right: Box::new(right),\n })\n }\n\n queue.pop().expect(\"The Huffman tree has to have a root\")\n }\n\n pub fn count(&self) -> i32 {\n match *self {\n HuffmanTree::Branch { count, .. } => count,\n HuffmanTree::Leaf { count, .. } => count,\n }\n }\n\n pub fn make_codebook(self) -> Codebook {\n let mut codebook = HashMap::new();\n self.dfs(String::from(\"\"), &mut codebook);\n Codebook {\n codebook,\n tree: self,\n }\n }\n\n pub fn decode(&self, input: &str) -> String {\n let mut result = String::from(\"\");\n let mut start = 0;\n while !input[start..].is_empty() {\n start += self.decode_dfs(&input[start..], &mut result);\n }\n result\n }\n\n fn decode_dfs(&self, input: &str, result: &mut String) -> usize {\n let current = input.chars().next();\n match *self {\n HuffmanTree::Branch { ref left, .. } if current == Some('0') => {\n 1 + left.decode_dfs(&input[1..], result)\n }\n HuffmanTree::Branch { ref right, .. } if current == Some('1') => {\n 1 + right.decode_dfs(&input[1..], result)\n }\n HuffmanTree::Leaf { value, .. } => {\n result.push(value);\n 0\n }\n _ => panic!(\"Unexpected end of input\"),\n }\n }\n\n fn dfs(&self, code: String, codebook: &mut HashMap) {\n match *self {\n HuffmanTree::Branch {\n ref left,\n ref right,\n ..\n } => {\n left.dfs(code.clone() + \"0\", codebook);\n right.dfs(code.clone() + \"1\", codebook);\n }\n HuffmanTree::Leaf { value, .. } => {\n codebook.insert(value, code);\n }\n }\n }\n}\n\nimpl Codebook {\n fn encode(&self, input: &str) -> String {\n input.chars().map(|c| &self.codebook[&c]).join(\"\")\n }\n\n fn decode(&self, input: &str) -> String {\n self.tree.decode(input)\n }\n}\n\nfn main() {\n let input = \"bibbity bobbity\";\n\n let tree = HuffmanTree::from(input);\n let codebook = tree.make_codebook();\n let encoded = codebook.encode(input);\n let decoded = codebook.decode(&encoded);\n\n // Uncomment this line if you want to see the codebook/tree\n // println!(\"{:#?}\", codebook);\n println!(\"{}\", encoded);\n println!(\"{}\", decoded);\n}\n\n// Made by Guston and edited by Gathros\n#include \n#include \n#include \n#include \n\nstruct tree {\n struct tree* left;\n struct tree* right;\n\n int count;\n char value;\n};\n\nstruct bitstring_builder {\n char str[257];\n int next_index;\n};\n\nstruct codebook {\n char* codes[256];\n};\n\nstruct heap {\n struct tree** data;\n size_t length;\n size_t capacity;\n};\n\nbool is_leaf(const struct tree* t) {\n return !t->left && !t->right;\n}\n\nvoid swap(struct tree** lhs, struct tree** rhs) {\n struct tree* tmp = *lhs;\n *lhs = *rhs;\n *rhs = tmp;\n}\n\n/* The two concat functions are horribly inefficient */\nvoid concat(char** dst, const char* src) {\n size_t dst_len = strlen(*dst);\n size_t src_len = strlen(src);\n *dst = realloc(*dst, src_len + dst_len + 1);\n strcat(*dst, src);\n}\n\nvoid concat_char(char** dst, char c) {\n size_t len = strlen(*dst);\n *dst = realloc(*dst, len + 2);\n (*dst)[len] = c;\n (*dst)[len + 1] = '\\0';\n}\n\nchar* duplicate(const char* src) {\n size_t length = strlen(src);\n char* dst = malloc(length + 1);\n memcpy(dst, src, length + 1);\n return dst;\n}\n\nvoid heap_push(struct heap* heap, struct tree* value) {\n if (heap->capacity == heap->length) {\n heap->capacity = heap->capacity == 0 ? 4 : heap->capacity * 2;\n heap->data = realloc(heap->data, heap->capacity * sizeof(struct tree*));\n }\n heap->data[heap->length++] = value;\n\n size_t index = heap->length - 1;\n while (index) {\n size_t parent_index = (index - 1) / 2;\n if (heap->data[parent_index]->count data[index]->count) {\n break;\n }\n\n swap(&heap->data[parent_index], &heap->data[index]);\n index = parent_index;\n }\n}\n\nstruct tree* heap_pop(struct heap* heap) {\n if (!heap->length) {\n return NULL;\n }\n\n struct tree* result = heap->data[0];\n swap(&heap->data[0], &heap->data[--heap->length]);\n\n size_t index = 0;\n for (;;) {\n size_t target = index;\n size_t left = 2 * index + 1;\n size_t right = left + 1;\n\n if (left length &&\n heap->data[left]->count data[target]->count) {\n target = left;\n }\n\n if (right length &&\n heap->data[right]->count data[target]->count) {\n target = right;\n }\n\n if (target == index) {\n break;\n }\n\n swap(&heap->data[index], &heap->data[target]);\n index = target;\n }\n\n return result;\n}\n\nvoid heap_free(struct heap* heap) {\n free(heap->data);\n}\n\nstruct tree* generate_tree(const char* str) {\n int counts[256] = { 0 };\n\n for (; *str != '\\0'; ++str) {\n counts[(unsigned char)*str] += 1;\n }\n\n struct heap heap = { 0 };\n for (size_t i = 0; i value = (char)i;\n tree->count = counts[i];\n heap_push(&heap, tree);\n }\n }\n\n if (heap.length == 1) {\n struct tree* leaf = heap_pop(&heap);\n struct tree* root = calloc(0, sizeof(struct tree));\n root->left = leaf;\n root->count = leaf->count;\n heap_free(&heap);\n return root;\n }\n\n while (heap.length > 1) {\n struct tree* left = heap_pop(&heap);\n struct tree* right = heap_pop(&heap);\n struct tree* branch = calloc(1, sizeof(struct tree));\n branch->count = left->count + right->count;\n branch->left = left;\n branch->right = right;\n heap_push(&heap, branch);\n }\n\n struct tree* root = heap_pop(&heap);\n heap_free(&heap);\n return root;\n}\n\nvoid tree_free(struct tree* tree) {\n if (!tree) return;\n tree_free(tree->left);\n tree_free(tree->right);\n free(tree);\n}\n\nvoid codebook_recurse(const struct tree* tree,\n struct bitstring_builder* builder,\n struct codebook* codebook) {\n if (!tree) {\n return;\n }\n\n if (is_leaf(tree)) {\n builder->str[builder->next_index] = '\\0';\n codebook->codes[(unsigned char)tree->value] = duplicate(builder->str);\n return;\n }\n\n builder->str[builder->next_index++] = '0';\n codebook_recurse(tree->left, builder, codebook);\n builder->next_index -= 1;\n\n builder->str[builder->next_index++] = '1';\n codebook_recurse(tree->right, builder, codebook);\n builder->next_index -= 1;\n}\n\nstruct codebook generate_codebook(const struct tree* tree) {\n struct codebook codebook = { .codes = { 0 } };\n struct bitstring_builder builder = { .str = { 0 }, .next_index = 0 };\n codebook_recurse(tree, &builder, &codebook);\n return codebook;\n}\n\nvoid codebook_free(struct codebook* codebook) {\n int size = sizeof(codebook->codes) / sizeof(codebook->codes[0]);\n for (int i = 0; i codes[i]);\n }\n}\n\nconst char* get_code(const struct codebook* codebook, char c) {\n return codebook->codes[(unsigned char)c];\n}\n\nchar* encode(const char* input, struct tree** huffman_tree,\n struct codebook* codebook) {\n *huffman_tree = generate_tree(input);\n *codebook = generate_codebook(*huffman_tree);\n\n char* result = duplicate(get_code(codebook, *input));\n\n input += 1;\n\n for (; *input; ++input) {\n concat(&result, get_code(codebook, *input));\n }\n\n return result;\n}\n\nconst char* decode_recurse(const char* input, const struct tree* tree,\n char** result) {\n if (!tree) {\n return input;\n }\n\n if (is_leaf(tree)) {\n concat_char(result, tree->value);\n return input;\n }\n\n if (*input == '0') {\n return decode_recurse(input + 1, tree->left, result);\n } else {\n return decode_recurse(input + 1, tree->right, result);\n }\n}\n\nchar* decode(const char* input, const struct tree* tree) {\n char* result = calloc(1, 1);\n do {\n input = decode_recurse(input, tree, &result);\n } while (*input);\n return result;\n}\n\nint main() {\n struct tree* tree;\n struct codebook codebook;\n\n char* encoded = encode(\"bibbity bobbity\", &tree, &codebook);\n char* decoded = decode(encoded, tree);\n\n printf(\"Codebook:\\n\");\n for (int i = 0; i \nimport qualified Data.Map as M\nimport Data.List (insert, sort)\n\ndata Tree a = Leaf Int a\n | Node Int (Tree a) (Tree a)\n deriving (Show, Eq)\n\nfreq :: Tree a -> Int\nfreq (Leaf i _) = i\nfreq (Node i _ _) = i\n\ninstance (Eq a) => Ord (Tree a) where\n compare t1 t2 = compare (freq t1) (freq t2)\n\ngetFrequencies :: Ord a => [a] -> [(Int, a)]\ngetFrequencies = toSortedList . M.fromListWith (+) . flip zip (repeat 1)\n where toSortedList = sort . map swap . M.toList\n swap (a, i) = (i, a)\n\nbuildTree :: (Ord a) => [a] -> Maybe (Tree a)\nbuildTree = build . map (uncurry Leaf) . getFrequencies\n where build [] = Nothing\n build [t] = Just t\n build (t1:t2:ts) = build $ insert (Node (freq t1 + freq t2) t1 t2) ts\n\ndata Bit = Zero | One\n\ninstance Show Bit where\n show Zero = \"0\"\n show One = \"1\"\n\nencode :: (Ord a) => [a] -> (Maybe (Tree a), [Bit])\nencode s = (tree, msg)\n where\n tree = buildTree s\n msg = concatMap (table M.!) s\n table = case tree of\n Nothing -> M.empty\n Just t -> M.fromList $ mkTable (t, [])\n mkTable (Leaf _ a, p) = [(a, reverse p)]\n mkTable (Node _ t1 t2, p) = concatMap mkTable [(t1, Zero:p), (t2, One:p)]\n\ndecode :: (Ord a) => Maybe (Tree a) -> [Bit] -> [a]\ndecode Nothing _ = []\ndecode (Just t) m = path t m\n where path (Leaf _ a) m = a : path t m\n path (Node _ t1 _) (Zero: m) = path t1 m\n path (Node _ _ t2) (One: m) = path t2 m\n path _ _ = []\n\nmain = do\n let msg = \"bibbity bobbity\"\n (tree, encoded) = encode msg\n decoded = decode tree encoded\n putStrLn $ \"Endoding \\\"\" ++ msg ++ \"\\\": \" ++ concatMap show encoded\n putStrLn $ \"Length: \" ++ (show $ length encoded)\n putStrLn $ \"Decoding: \" ++ decoded\n\nHuffmanCoding.cs\n// submitted by Julian Schacher (jspp), thanks to gustorn for the help\nusing System;\nusing System.Collections.Generic;\nusing System.Linq;\n\nnamespace HuffmanCoding\n{\n public class EncodingResult\n {\n public string BitString { get; set; }\n public Dictionary Dictionary { get; set; }\n public HuffmanCoding.Node Tree { get; set; }\n\n public EncodingResult(string bitString, Dictionary dictionary, HuffmanCoding.Node tree)\n {\n this.BitString = bitString;\n this.Dictionary = dictionary;\n this.Tree = tree;\n }\n }\n\n public class HuffmanCoding\n {\n // The Node class used for the Huffman Tree.\n public class Node : IComparable\n {\n public Node LeftChild { get; set; }\n public Node RightChild { get; set; }\n public string BitString { get; set; } = \"\";\n public int Weight { get; set; }\n public string Key { get; set; }\n\n public bool IsLeaf => LeftChild == null && RightChild == null;\n\n // Creates a leaf. So just a node is created with the given values.\n public static Node CreateLeaf(char key, int weight) => new Node(key.ToString(), weight, null, null);\n // Creates a branch. Here a node is created by adding the keys and weights of both childs together.\n public static Node CreateBranch(Node leftChild, Node rightChild) => new Node(leftChild.Key + rightChild.Key, leftChild.Weight + rightChild.Weight, leftChild, rightChild);\n private Node(string key, int weight, Node leftChild, Node rightChild)\n {\n this.Key = key;\n this.Weight = weight;\n this.LeftChild = leftChild;\n this.RightChild = rightChild;\n }\n\n public int CompareTo(Node other) => this.Weight - other.Weight;\n }\n\n // Node with biggest value at the top.\n class NodePriorityList\n {\n public int Count => nodes.Count;\n\n private List nodes = new List();\n\n public NodePriorityList() { }\n public NodePriorityList(List givenNodes)\n {\n this.nodes = givenNodes.ToList();\n this.nodes.Sort();\n }\n\n public void Add(Node newNode)\n {\n var index = this.nodes.BinarySearch(newNode);\n if (index c)\n .Select(n => Node.CreateLeaf(n.Key, n.Count()))\n .ToList();\n\n // Convert list of nodes to a NodePriorityList.\n var nodePriorityList = new NodePriorityList(nodes);\n\n // Create Tree.\n while (nodePriorityList.Count > 1)\n {\n // Pop the two nodes with the smallest weights from the nodePriorityList and create a parentNode with the CreateBranch method. (This method adds the keys and weights of the childs together.)\n var leftChild = nodePriorityList.Pop();\n var rightChild = nodePriorityList.Pop();\n var parentNode = Node.CreateBranch(leftChild, rightChild);\n\n nodePriorityList.Add(parentNode);\n }\n\n return nodePriorityList.Pop();\n }\n\n\n private void CreateDictionary(Node node, string bitString, Dictionary localDictionary)\n {\n if (node.IsLeaf)\n localDictionary.Add(node.Key[0], bitString);\n else\n {\n if (node.LeftChild != null)\n CreateDictionary(node.LeftChild, bitString + '0', localDictionary);\n if (node.RightChild != null)\n CreateDictionary(node.RightChild, bitString + '1', localDictionary);\n }\n }\n\n private Dictionary CreateDictionary(Node root)\n {\n // We're using a string instead of a actual bits here, since it makes the code somewhat more readable and this is an educational example.\n var dictionary = new Dictionary();\n CreateDictionary(root, \"\", dictionary);\n return dictionary;\n }\n\n\n private string CreateBitString(string input, Dictionary dictionary)\n {\n // We're using a string right here. While no compression is achieved with a string, it's the easiest way to display what the compressed result looks like. Also this is just an educational example.\n var bitString = \"\";\n foreach (var character in input)\n bitString += dictionary[character];\n\n return bitString;\n }\n }\n}\n\nProgram.cs\n// submitted by Julian Schacher (jspp), thanks to gustorn for the help\nusing System.Collections;\nusing System.Collections.Generic;\n\nnamespace HuffmanCoding\n{\n class Program\n {\n static void Main(string[] args)\n {\n var huffmanCoding = new HuffmanCoding();\n\n var result = huffmanCoding.Encode(\"bibbity bobbity\");\n // The bitStrings are just strings and provide no compression. Look in HuffmanCoding.cs for explanation.\n // Print dictionary.\n foreach (var entry in result.Dictionary)\n System.Console.WriteLine($\"{entry.Key} {entry.Value}\");\n // Print BitString.\n System.Console.WriteLine($\"{result.BitString} count: {result.BitString.Length}\");\n\n var originalString = huffmanCoding.Decode(result);\n System.Console.WriteLine(originalString);\n }\n }\n}\n\nlocal function frequency_array(str)\n -- Collect all frequency values into a dict\n local map = {}\n for c in str:gmatch(\".\") do -- Iterate over each character in str\n map[c] = (map[c] or 0) + 1 -- Increment map[c] (default 0) by 1\n end\n\n -- We have a dict of frequencies but we want it in a sorted list\n -- Dump each key value pair into an array\n local arr = {}\n for k, v in pairs(map) do\n arr[#arr + 1] = {k, v}\n end\n table.sort(arr, function(a, b) return a[2] > b[2] end) -- Sort by frequency descending\n return arr\nend\n\nlocal function build_huffman_tree(message)\n\n if #message == 0 then return end\n\n local freq = frequency_array(message)\n\n while #freq > 1 do -- Repeat until we have only 1 node\n\n -- Take two of the least frequent nodes\n local node1, node2 = table.remove(freq), table.remove(freq)\n\n -- Group node values in first index, and sum of node frequencies in second\n local node3 = { {node1[1], node2[1] }, node1[2] + node2[2] }\n\n local i = 1\n while i \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\n#include \n\nusing std::begin;\nusing std::end;\n\nnamespace huffman {\n\n[[noreturn]] inline void unreachable() {\n std::cerr ;\n using bitstring = std::vector;\n\n // this is a flatmap between char and a bitstring\n // there should only ever be one character with a given\n // value at any time.\n using encoder_t = std::vector>;\n\n struct leaf final : node {\n char key;\n\n leaf(int freq, char key) : node(freq), key(key) {}\n };\n\n struct branch final : node {\n node_ptr lhs;\n node_ptr rhs;\n\n branch(node_ptr lhs, node_ptr rhs)\n : node(lhs->frequency + rhs->frequency), lhs(std::move(lhs)),\n rhs(std::move(rhs)) {}\n };\n\n // this allows us to share [codebook]s among encoded strings\n struct data {\n node_ptr decoder;\n encoder_t encoder;\n };\n std::shared_ptr underlying_;\n\npublic:\n template \n codebook(Iter const first, Iter const last);\n\n template \n std::vector encode(Iter first, Iter last) const;\n\n template \n std::string decode(Iter first, Iter last) const;\n};\n\nstruct encoded_string {\n codebook codes;\n std::vector string;\n\n explicit encoded_string(std::string const& s)\n : codes(begin(s), end(s)), string(codes.encode(begin(s), end(s))) {}\n\n encoded_string(codebook codes, std::string const& s)\n : codes(codes), string(codes.encode(begin(s), end(s))) {}\n\n std::string decoded() const {\n return codes.decode(begin(string), end(string));\n }\n};\n\n// --- implementation ---\ninline codebook::node::~node() {}\n\ninline std::vector with_new_bit(std::vector bits, bool b) {\n bits.push_back(b);\n return bits;\n}\n\ntemplate \ncodebook::codebook(Iter const first, Iter const last) {\n struct helper {\n static node_ptr make_decoder(Iter const first, Iter const last) {\n // in this part of the function, we build up a frequency list\n // sorted by frequency, descending\n auto freq = std::vector();\n\n std::for_each(first, last, [&freq](char c) {\n auto const it = std::find_if(\n begin(freq), end(freq), [c](auto const& p) { return p.key == c; });\n if (it != end(freq)) {\n // it's already in the list\n it->frequency += 1;\n } else {\n // it's not already in the list\n freq.emplace_back(1, c);\n }\n });\n\n if (freq.empty()) {\n throw std::invalid_argument(\"attempted to codebook an empty range\");\n }\n\n std::sort(begin(freq), end(freq), [](auto const& lhs, auto const& rhs) {\n return lhs.frequency > rhs.frequency;\n });\n\n auto ret = std::vector>();\n std::transform(\n begin(freq), end(freq), std::back_inserter(ret), [](auto const l) {\n return std::make_unique(l);\n });\n\n while (ret.size() > 1) {\n auto rhs = std::move(ret.back());\n ret.pop_back();\n auto lhs = std::move(ret.back());\n ret.pop_back();\n\n auto new_node =\n std::make_unique(std::move(lhs), std::move(rhs));\n auto const new_freq = new_node->frequency;\n\n // look for the first element with a smaller frequency\n auto const it =\n std::find_if(begin(ret), end(ret), [new_freq](auto const& n) {\n return n->frequency bits, encoder_t& out) {\n if (auto l = dynamic_cast(cur)) {\n out.push_back(std::make_pair(l->key, std::move(bits)));\n } else if (auto b = dynamic_cast(cur)) {\n encoder_rec(b->lhs.get(), with_new_bit(bits, 0), out);\n encoder_rec(b->rhs.get(), with_new_bit(std::move(bits), 1), out);\n } else {\n unreachable();\n }\n }\n\n static encoder_t make_encoder(node const& decoder) {\n auto ret = encoder_t();\n\n encoder_rec(&decoder, std::vector(), ret);\n\n return ret;\n }\n };\n\n auto decoder = helper::make_decoder(first, last);\n auto encoder = helper::make_encoder(*decoder);\n underlying_ = std::make_shared(\n data{std::move(decoder), std::move(encoder)});\n}\n\ntemplate \nstd::vector codebook::encode(Iter const first, Iter const last) const {\n std::vector ret;\n\n auto& encoder = underlying_->encoder;\n std::for_each(first, last, [&ret, &encoder](char c) {\n auto const it =\n std::find_if(begin(encoder), end(encoder), [c](auto const& p) {\n return p.first == c;\n });\n if (it != end(encoder)) {\n auto const& code = it->second;\n std::copy(begin(code), end(code), std::back_inserter(ret));\n } else {\n throw std::invalid_argument(\n \"The range has a character which was not in the huffman set\");\n }\n });\n\n return ret;\n}\n\ntemplate \nstd::string codebook::decode(Iter const first, Iter const last) const {\n std::string ret;\n\n node const* const top = underlying_->decoder.get();\n\n // returns a pair:\n // the second member is the decoded character\n // the first member is the place we've gotten to in the range\n // i.e., if [0] is an 'a', and we have\n // [it, last) = { 0, 1, 1, 0 }\n // we return (it', 'a') such that\n // [it', last) = { 1, 1, 0 }\n auto decode_single =\n [top](Iter it, Iter const last) -> std::pair {\n node const* current_node = top;\n\n for (; it != last; ++it) {\n if (auto l = dynamic_cast(current_node)) {\n return std::make_pair(it, l->key);\n } else if (auto b = dynamic_cast(current_node)) {\n if (*it) {\n current_node = b->rhs.get();\n } else {\n current_node = b->lhs.get();\n }\n } else {\n unreachable();\n }\n }\n\n if (auto l = dynamic_cast(current_node)) {\n return std::make_pair(last, l->key);\n } else {\n throw std::invalid_argument(\n \"The range was not encoded with this huffman set\");\n }\n };\n\n for (auto it = first; it != last;) {\n auto p = decode_single(it, last);\n it = p.first;\n ret.push_back(p.second);\n }\n\n return ret;\n}\n\n} // namespace huffman\n\nint main() {\n std::string to_be_encoded = R\"(bibbity bobbity)\";\n\n auto encoded = huffman::encoded_string(to_be_encoded);\n\n std::cout \n;; earthfail\n(ns experiments.core)\n\n;; get a vector with chars and frequencies\n\n(defn tree-string [st]\n \"take a string st and return the huffmantree with the frequency of\n each character included\"\n ;; vector of [character frequency] pair\n ;; for every char in string, added it to hash-map\n ;; with value one if it doesn't exist or increment its value\n (def cf-vec (vec\n (reduce (fn [m c]\n (assoc m c (inc (get m c 0))))\n {}\n st)))\n ;; make a sorted list with nodes with bigger frequencies first\n ;; take the last two which will help in dividing the tree\n ;; the first and last elements before and after\n ;; the smallest two in the tree shouldn't change\n (loop [tree (sort-by last > cf-vec)]\n (if ( tree)\n mid (take-last 2 sorted-tree)\n set-mid (set mid)\n func (complement (partial contains? set-mid))\n firsty (take-while func tree)\n [middle lasty] (split-at 2\n (drop-while func tree))]\n (recur\n (concat\n firsty\n ;; make a list with the two element in one list and\n ;; the sum of their frequencies e.g\n ;; '(((node1 f1) (node2 f2)) f1+f2)\n (list (list middle (reduce #(+ %1 (last %2)) 0 middle)))\n lasty))))))\n\n(defn remove-freq [tree]\n \"remove the frequencies in the huffmantree tree\"\n (cond\n (char? tree) tree ; check if this is a branch\n ;; if the tree is a node and frequency then ignore frequency\n (integer? (second tree)) (remove-freq (first tree)) ;remove the frequency\n ;; if the tree consists of two nodes then apply to both and combine\n :else (list (remove-freq (first tree))\n (remove-freq (second tree)))))\n\n(defn hash-tree [tree]\n \"make a hashmap with code for each letter as key and the letter as\n value\"\n (cond\n (char? tree) {\"\" tree}\n :else\n (let [left-map (hash-tree (first tree))\n right-map (hash-tree (second tree))\n func #(apply hash-map ; apply hash-map because\n ; interleave return a seq\n (interleave\n (map (partial str %2) (keys %1)) ;add 0 or 1\n ;to the start\n ;of the keys\n (vals %1)))]\n ;; add \"0\" to the keys of left nodes and \"1\" to the right nodes\n (merge (func left-map \"0\") (func right-map \"1\")))))\n\n\n(defn coder [s hash-coder]\n \"take a string s and return a coded string\"\n (apply str (map hash-coder s)))\n\n(defn decoder [s hash-decoder]\n \"takes a string s and a hash-map hash-decoder and decode s\"\n ;; code keyword in hashmap is for storing codes untill they are\n ;; complete and can be decoded with the decoder\n (get (reduce (fn [m code] ; reduce return {:message\n ; message,:code _}\n (let [new-code (str (m :code) code)]\n (if-let [letter (get hash-decoder new-code)]\n ;; if there is a letter then add it to :message\n ;; and revert :code to empty\n (assoc (update m :message #(str % letter))\n :code \"\")\n ;; if there is not a letter then just add the\n ;; code letter to the :code\n (update m :code #(str % code)))))\n {:message \"\",:code \"\"}\n s)\n :message)) ;extract :message value\n;; ----------------EXAMPLE----------------\n(def st \"(bibbity bobbity)\")\n\n(def hash-decoder (->>\n st\n tree-string\n remove-freq\n hash-tree))\n(def hash-coder (clojure.set/map-invert hash-decoder))\n(println \"coding...\")\n(def code (coder st hash-coder))\n(clojure.pprint/pprint code)\n\n(println \"\\ndecoding...\")\n(clojure.pprint/pprint (decoder code hash-decoder))\n\n# Huffman Encoding\n# Python 2.7+\n# Submitted by Matthew Giallourakis\n\nfrom collections import Counter\n\n# constructs the tree\ndef build_huffman_tree(message):\n\n # get sorted list of character and frequency pairs\n frequencies = Counter(message)\n trees = frequencies.most_common()\n\n # while there is more than one tree\n while len(trees) > 1:\n\n # pop off the two trees of least weight from the trees list\n tree_left,weight_left = trees.pop()\n tree_right,weight_right = trees.pop()\n\n # combine the nodes and add back to the nodes list\n new_tree = [tree_left, tree_right]\n new_weight = weight_left + weight_right\n\n # find the first tree that has a weight smaller than new_weight and returns its index in the list\n # If no such tree can be found, use len(trees) instead to append\n index = next((i for i, tree in enumerate(trees) if tree[1] code dictionary\n forward_dict = dict(codebook)\n\n # replace each character with its code\n for char in message:\n encoded_message += forward_dict[char]\n\n return encoded_message\n\n# decodes a message\ndef huffman_decode(codebook, encoded_message):\n\n decoded_message = ''\n key = ''\n\n # build a code -> char dictionary\n inverse_dict = dict([(v, k) for k, v in codebook])\n\n # for each bit in the encoding\n # if the bit is in the dictionary, replace the bit with the paired character\n # else look at the bit and the following bits together until a match occurs\n # move to the next bit not yet looked at\n for index, bit in enumerate(encoded_message):\n key += bit\n if key in inverse_dict:\n decoded_message += inverse_dict[key]\n key = ''\n\n return decoded_message\n\ndef main():\n\n # test example\n message = 'bibbity_bobbity'\n tree = build_huffman_tree(message)\n codebook = build_codebook(tree)\n encoded_message = huffman_encode(codebook, message)\n decoded_message = huffman_decode(codebook, encoded_message)\n\n print('message: ' + message)\n print('huffman tree: ' + str(tree))\n print('codebook: ' + str(codebook))\n print('encoded message: ' + encoded_message)\n print('decoded message: ' + decoded_message)\n\n # prints the following:\n #\n # message: bibbity_bobbity\n # huffman_tree: ['b', [[['_', 'o'], 'y'], ['t', 'i']]]\n # codebook: [('b', '0'), ('_', '1000'), ('o', '1001'),\n # ('y', '101'), ('t', '110'), ('i', '111')]\n # encoded_message: 01110011111010110000100100111110101\n # decoded_message: bibbity_bobbity\n\nif __name__ == '__main__':\n main()\n\nfunction encode(str) {\n const tree = createTree(str);\n const codebook = createCodebook(tree);\n return {\n string: [...str].map(c => codebook[c]).join(\"\"),\n tree,\n codebook\n };\n\n function createTree(str) {\n const chars = [...str];\n const charCounts = chars.reduce((counts, char) => {\n counts[char] = (counts[char] || 0) + 1;\n return counts;\n }, {});\n\n const nodes = Object.entries(charCounts).map(([key, weight]) => ({ key, weight }));\n const priorityQueue = makeQueue(nodes);\n while (priorityQueue.data.length > 1) {\n const left = priorityQueue.dequeue();\n const right = priorityQueue.dequeue();\n priorityQueue.enqueue({ weight: left.weight + right.weight, left, right });\n }\n return priorityQueue.dequeue();\n }\n\n function createCodebook(tree) {\n return recurse(tree, \"\", {});\n\n function recurse(node, bitstring, dict) {\n if (!node.left && !node.right) {\n dict[node.key] = bitstring;\n } else {\n if (node.left) {\n recurse(node.left, bitstring + \"0\", dict);\n }\n\n if (node.right) {\n recurse(node.right, bitstring + \"1\", dict);\n }\n }\n return dict;\n }\n }\n}\n\nfunction decode(bitstring, tree) {\n const result = [];\n let node = tree;\n\n for (const bit of [...bitstring]) {\n node = bit === \"0\" ? node.left : node.right;\n if (!node.left && !node.right) {\n result.push(node.key);\n node = tree;\n }\n }\n\n return result.join(\"\");\n}\n\n// This queue implementation is horribly inefficient, but a proper, heap-based implementation would\n// be longer that the algorithm itself\nfunction makeQueue(iterable) {\n return {\n data: [...iterable].sort((a, b) => a.weight - b.weight),\n enqueue(value) {\n const target = this.data.findIndex(x => x.weight > value.weight);\n if (target === -1) {\n this.data.push(value);\n } else {\n this.data = [...this.data.slice(0, target), value, ...this.data.slice(target)];\n }\n },\n dequeue() {\n return this.data.shift();\n }\n };\n}\n\nconst encoded = encode(\"bibbity bobbity\");\nconst decoded = decode(encoded.string, encoded.tree);\nconsole.log(encoded.string);\nconsole.log(decoded);\n\nimport java.util.*;\n\nclass Huffman {\n public static void main(String[] args) {\n HuffmanTree huffmanTree = new HuffmanTree(\"bibbity_bobbity\");\n huffmanTree.createTree();\n String encoded = huffmanTree.encode();\n System.out.println(\"Encoded String: \" + encoded);\n System.out.println(\"Decoded String: \" + huffmanTree.decode(encoded));\n }\n}\n\nclass TreeNode {\n String letter = \"\";\n int frequency = 0;\n TreeNode left = null, right = null;\n\n public TreeNode(String letter, int frequency) {\n this.letter = letter;\n this.frequency = frequency;\n }\n\n public TreeNode(int frequency, TreeNode left, TreeNode right) {\n this.frequency = frequency;\n this.left = left;\n this.right = right;\n }\n}\n\nclass HuffmanTree {\n private Map frequencyMap = new HashMap<>();\n private Map codeBook = new HashMap<>(), reverseCodeBook = new HashMap<>();\n private TreeNode root;\n private String stringToEncode;\n\n public HuffmanTree(String stringToEncode) {\n this.stringToEncode = stringToEncode;\n }\n\n public void createTree() {\n for (int i = 0; i priorityQueue = new PriorityQueue<>(Comparator.comparingInt(o -> o.frequency));\n for (Map.Entry m : frequencyMap.entrySet()) {\n priorityQueue.add(new TreeNode(m.getKey(), m.getValue()));\n }\n while (priorityQueue.size() > 1) {\n TreeNode left = priorityQueue.remove();\n TreeNode right = priorityQueue.remove();\n priorityQueue.add(new TreeNode(left.frequency + right.frequency, left, right));\n }\n root = priorityQueue.remove();\n }\n\n private void traverse(TreeNode node, StringBuilder code) {\n if (node.left == null && node.right == null) {\n codeBook.put(node.letter, code.toString());\n }\n if (node.left != null) {\n traverse(node.left, code.append(0));\n code.deleteCharAt(code.length() - 1);\n }\n if (node.right != null) {\n traverse(node.right, code.append(1));\n code.deleteCharAt(code.length() - 1);\n }\n }\n\n public void printCodeBook() {\n System.out.println(\"Code Book\");\n for (Map.Entry m : codeBook.entrySet()) {\n System.out.println(m.getKey() + \"\\t\" + m.getValue());\n }\n System.out.println();\n }\n\n private void CodeBookReverse() {\n for (Map.Entry m : codeBook.entrySet()) {\n reverseCodeBook.put(m.getValue(), m.getKey());\n }\n }\n\n public String encode() {\n traverse(root, new StringBuilder());\n StringBuilder encode = new StringBuilder();\n for (int i = 0; i \npackage main\n\nimport (\n \"container/heap\"\n \"fmt\"\n)\n\ntype node struct {\n freq int\n char rune\n left *node\n right *node\n}\n\ntype codebook map[rune]string\ntype nodeHeap []*node\n\nfunc (n nodeHeap) Len() int { return len(n) }\nfunc (n nodeHeap) Less(i, j int) bool { return n[i].freq > n[j].freq }\nfunc (n nodeHeap) Swap(i, j int) { n[i], n[j] = n[j], n[i] }\n\nfunc (n *nodeHeap) Push(x interface{}) {\n if node, ok := x.(*node); ok {\n *n = append(*n, node)\n } else {\n fmt.Printf(\"I got a node of Type %T\\n\", x)\n }\n}\n\nfunc (n *nodeHeap) Pop() interface{} {\n old := *n\n l := len(old)\n x := old[l-1]\n *n = old[0 : l-1]\n return x\n}\n\nfunc buildTree(message string) *node {\n freqMap := make(map[rune]*node)\n h := new(nodeHeap)\n heap.Init(h) // really needed?\n\n for _, char := range message {\n if _, ok := freqMap[char]; ok {\n freqMap[char].freq++\n } else {\n newNode := new(node)\n newNode.freq = 1\n newNode.char = char\n freqMap[char] = newNode\n heap.Push(h, newNode)\n }\n }\n\n for h.Len() > 1 {\n left, right := h.Pop().(*node), h.Pop().(*node)\n branch := new(node)\n branch.freq = right.freq + left.freq\n branch.left = left\n branch.right = right\n heap.Push(h, branch)\n }\n\n root := heap.Pop(h).(*node)\n return root\n}\n\nfunc codebookRecurse(node *node, cb *codebook, code []rune) {\n if node == nil {\n return\n }\n\n if node.left == nil && node.right == nil {\n (*cb)[node.char] = string(code)\n }\n\n code = append(code, '0')\n codebookRecurse(node.left, cb, code)\n code = append(code[:len(code)-1], '1')\n codebookRecurse(node.right, cb, code)\n}\n\nfunc encode(message string) (string, *node, codebook) {\n ret := \"\"\n root := buildTree(message)\n cb := generateCodebook(root)\n for _, char := range message {\n ret += cb[char]\n }\n\n return ret, root, cb\n}\n\nfunc decode(message string, root *node) string {\n cur := root\n ret := \"\"\n\n for _, char := range message {\n if cur == nil {\n return message\n }\n\n switch string(char) {\n case \"0\":\n if cur.left == nil {\n ret += string(cur.char)\n cur = root.left\n } else {\n cur = cur.left\n }\n case \"1\":\n if cur.right == nil {\n ret += string(cur.char)\n cur = root.right\n } else {\n cur = cur.right\n }\n }\n }\n\n if cur.char != 0 {\n ret += string(cur.char)\n }\n\n return ret\n}\n\nfunc generateCodebook(root *node) codebook {\n cb := make(codebook)\n codeArr := make([]rune, 0)\n codebookRecurse(root, &cb, codeArr)\n return cb\n}\n\nfunc main() {\n enc, root, cb := encode(\"bibbity_bobbity\")\n fmt.Println(\"Codebook:\")\n for r, c := range cb {\n fmt.Println(string(r), \"->\", c)\n }\n fmt.Println(\"\\nEncoded:\", enc)\n fmt.Println(\"Decoded:\", decode(enc, root))\n}\n\n.intel_syntax noprefix\n\n# System V calling convention cheatsheet\n# Params: rdi, rsi, rdx, rcx, r8, r9, xmm0-7\n# Return: rax (int 64 bits), rax:rdx (int 128 bits), xmm0 (float)\n# Callee cleanup: rbx, rbp, r12-15\n# Scratch: rax, rdi, rsi, rdx, rcx, r8, r9, r10, r11\n\n.section .rodata\n text: .string \"bibbity bobbity\"\n original: .string \"Original message: %s\\n\"\n encoded: .string \"Encoded message: \"\n decoded: .string \"Decoded message: %s\\n\"\n\n .equ bitstr_len, 32\n .equ bitstr_size, 40\n .equ codebook_size, 256 * bitstr_size\n\n .equ tree_left, 0\n .equ tree_right, 8\n .equ tree_count, 16\n .equ tree_value, 20\n .equ tree_size, 24\n\n .equ heap_len, 0\n .equ heap_data, 4\n .equ heap_size, 512 * 8 + 16 # 512 ptrs + 4 byte length + 12 byte padding\n .equ counts_size, 256 * 4\n\n .equ msg_len, 0\n .equ msg_data, 8\n.section .text\n .global main\n .extern printf, calloc, malloc, memset, puts\n\nmain:\n push r12\n push r13\n sub rsp, codebook_size + 16 # 8 extra bytes for the Huffman-tree ptr, 8 bytes for padding\n\n # Print the original text\n mov rdi, OFFSET original\n mov rsi, OFFSET text\n xor rax, rax\n call printf\n\n # First encode the text. This will also initialize the Huffman-tree and the codebook\n mov rdi, OFFSET text\n mov rsi, rsp\n lea rdx, [rsp + codebook_size]\n call encode\n mov r12, rax # Save the returned message ptr\n\n # Print the codebook and the encoded message\n mov rdi, rsp\n call print_codebook\n mov rdi, OFFSET encoded\n xor rax, rax\n call printf\n mov rdi, r12\n call print_message\n\n # Decode and print the message\n mov rdi, r12\n mov rsi, QWORD PTR [rsp + codebook_size]\n call decode\n mov r13, rax\n mov rdi, OFFSET decoded\n mov rsi, r13\n xor rax, rax\n call printf\n\n # Free allocated resources\n mov rdi, r12\n call free\n mov rdi, r13\n call free\n mov rdi, QWORD PTR [rsp + codebook_size]\n call free_tree\n\n add rsp, codebook_size + 16\n pop r13\n pop r12\n\n # Indiciate success with a 0 exit code\n xor rax, rax\n ret\n\n# rdi - text\n# rsi - codebook ptr\n# rdx - Huffman-tree ptr\n# RET rax - encoded message ptr\nencode:\n push r12\n push r13\n push r14\n mov r12, rdi # Save the original arguments\n mov r13, rsi\n mov r14, rdx\n call generate_tree # The text is already in rdi\n mov QWORD PTR [r14], rax # Save the Huffman-tree's root\n mov rdi, r13 # Set up the parameters for codebook generation: codebook ptr, Huffman-tree root\n mov rsi, rax\n call generate_codebook\n xor rax, rax\n xor r14, r14 # We'll use r14 to keep track of the length of the message\n mov rcx, r12 # Make a copy of the pointer to the message to be encoded\nencode_calculate_length:\n mov al, BYTE PTR [rcx]\n test al, al # If we're at the terminating null character then we're ready to encode\n jz encode_message\n lea rdx, [rax + 4*rax] # We get the codebook entry at the specific index\n lea r8, [r13 + 8*rdx]\n add r14, QWORD PTR [r8 + bitstr_len] # And add the encoded word length to the total\n inc rcx\n jmp encode_calculate_length\nencode_message:\n mov rdi, 1\n lea rsi, [r14 + 7] # Calculate the number of bytes we need to allocate to fit all the bits\n shr rsi, 3 # length % 8 rounded up = (length + 8 - 1) / 8\n lea rsi, [rsi + 8] # Make space for an 8-byte length field\n call calloc # Allocate the necessary memory, the message will be in rax\n mov QWORD PTR [rax], r14 # Save the length of the message\n # Registers:\n # - r12: text\n # - r13: codebook_ptr\n # - rax: message ptr\n # - free to use: rdi, rsi, rcx, rdx, r8, r9, r10, r11, r14\n xor r8, r8 # Bit offset\n lea r9, [rax + 8] # 8-byte message block\nencode_message_bits:\n xor rdi, rdi # We need to clear rdi because moving a single byte to dil doesn't do so\n mov dil, BYTE PTR [r12] # Iterate the message again\n test dil, dil # If we're at the the null terminator we're done\n jz encode_done\n lea rdx, [rdi + 4*rdi] # Get the codebook entry\n lea r10, [r13 + 8*rdx]\n mov r11, QWORD PTR [r10 + bitstr_len] # Load the bitstring length\n lea r14, [r10] # The bitstring qword we're currently processing\nencode_message_bits_qword:\n mov rdi, QWORD PTR [r14] # Calculate the first mask: [code qword] > [64 - bit offset]\n sub rcx, r8\n shr rsi, cl\n mov rcx, r11 # Copy the code length so we can manipulate it without destroying the original value\n sub rcx, 64\n jle encode_message_bits_try_overflow # If the length was less than or equal to 64, check if the code qword would overflow the current message block\n mov r11, rcx # We wanted to subtract 64 from the code length anyway\n lea r9, [r9 + 8] # Load the next message block\n or QWORD PTR [r9], rsi # Save the second mask to the new message block\n jmp encode_message_bits_qword\nencode_message_bits_try_overflow:\n add rcx, r8 # Calculate [code length] + [bit offset] - 64\n jl encode_calculate_new_bit_offset # If the result is less than 0 then we have no remaining bits -> calculate the new bit offset\n mov r8, rcx # Otherwise this also happens to be our new bit offset\n lea r9, [r9 + 8] # Load the next message block\n or QWORD PTR [r9], rsi # Save the second mask to the new message block\n inc r12 # Go to the next character in the input\n jmp encode_message_bits\nencode_calculate_new_bit_offset:\n lea r8, [r8 + r11] # Calculate the bit offset for the next code qword\n inc r12\n jmp encode_message_bits\nencode_done:\n pop r14\n pop r13\n pop r12\n ret\n\n# rdi - encoded message\n# rsi - Huffman-tree root (ptr)\n# RET rax - the decoded message\ndecode:\n push r12\n push r13\n push r14\n mov r12, rdi\n mov r13, rsi\n mov rdi, QWORD PTR [r12] # Load the length of the message\n mov r14, rdi # We'll use the length of the message as a loop counter later\n lea rdi, [rdi + 1] # The null terminator\n call malloc # This will usually be more than enough memory to contain the whole decoded message (we don't handle pathological cases right now)\n mov rdi, r12 # The single-character decoder doesn't touch rdi so we can hoist it before the loop\n xor rcx, rcx\n mov rdx, rax # The current byte in the output string\ndecode_loop:\n cmp rcx, r14 # The encoded message bit counter\n jge decode_done\n mov rsi, r13 # The current node in the Huffman-tree\ndecode_loop_char:\n test rsi, rsi # If the Huffman-tree node is null then we reached a dead-end -> start over\n jz decode_loop\n cmp QWORD PTR [rsi + tree_left], 0 # If the node has either a left or a right child, treat it as a branch\n jnz decode_loop_char_branch\n cmp QWORD PTR [rsi + tree_right], 0\n jnz decode_loop_char_branch\n mov r9d, DWORD PTR [rsi + tree_value] # Load the value in this node in case the next iteration needs it\n mov BYTE PTR [rdx], r9b # And save it to the output\n lea rdx, [rdx + 1] # Advance the output string\n jmp decode_loop\ndecode_loop_char_branch:\n mov r9, rcx # First, load the byte of the message the current bit is in\n shr r9, 3\n mov r10b, BYTE PTR [rdi + r9 + msg_data]\n mov r11, rcx # Save rcx in another register temporarily so we can restore it without push/pop\n and rcx, 7\n shr r10, cl # Get the bit we're interested in to position 0\n lea rcx, [r11 + 1] # Restore rcx and immediately add 1 to get the next bit to decode\n and r10, 0x1 # Zero out all other bits\n mov r8, rsi\n mov rsi, QWORD PTR [r8 + tree_left] # Take the left branch for 0, the right branch for a non-zero bit\n cmovnz rsi, QWORD PTR [r8 + tree_right]\n jmp decode_loop_char\ndecode_done:\n mov BYTE PTR [rdx], 0 # Write the null terminator at the end of the string\n pop r14\n pop r13\n pop r12\n ret\n\n# rdi - The starting address of the codebook we want to generate\n# rsi - Huffman-tree root (ptr)\ngenerate_codebook:\n push r12\n sub rsp, bitstr_size + 16 # 16 extra bytes for alignment\n mov r12, rsi\n xorps xmm0, xmm0 # Create a 0-initialized bitstring. This will be\n movaps XMMWORD PTR [rsp], xmm0 # used in the recursive function calls\n movaps XMMWORD PTR [rsp + 16], xmm0\n mov QWORD PTR [rsp + 32], 0\n xor rsi, rsi\n mov rdx, codebook_size\n call memset\n mov rdi, rax\n mov rsi, r12\n mov rdx, rsp\n call generate_codebook_recurse\n add rsp, bitstr_size + 16\n pop r12\n ret\n\n# rdi - The codebook's starting address\n# rsi - The current Huffman-tree node\n# rdx - The bitstring used for code generation\ngenerate_codebook_recurse:\n push rbp\n push r12\n push r13\n test rsi, rsi # If we reached a null pointer we're done\n jz generate_codebook_recurse_done\n mov r12, rsi\n cmp QWORD PTR [r12 + tree_left], 0 # If at least one of the children is not null\n jnz generate_codebook_branch # then we need to treat the current node as a branch\n cmp QWORD PTR [r12 + tree_right], 0\n jnz generate_codebook_branch\n mov r8d, DWORD PTR [r12 + tree_value] # Get the value of the current node\n movaps xmm0, XMMWORD PTR [rdx] # Get the values of the current bitstring into some registers\n movaps xmm1, XMMWORD PTR [rdx + 16]\n mov r9, QWORD PTR [rdx + 32]\n lea rax, [r8 + 4*r8] # The index calculation needs to add 40 * index. With lea arithmetic this can be represented as\n lea r10, [rdi + 8*rax] # base address + 8 * (5 * index). This is done in two lea instructions\n movups XMMWORD PTR [r10], xmm0 # And copy the data over to it\n movups XMMWORD PTR [r10 + 16], xmm1\n mov QWORD PTR [r10 + 32], r9\n jmp generate_codebook_recurse_done\ngenerate_codebook_branch:\n # First, calculate the necessary indices and bitmask to use for the bitstring\n mov r13, QWORD PTR [rdx + bitstr_len] # Load the current length of the bitstring\n mov rcx, r13 # This will be used to index into the bitstring data. We'll need two copies for it\n shr r13, 6 # We first get which 64 bit chunk of the bitstring we want to modify\n and rcx, 63 # Then the bit we want to change\n mov rbp, 1 # Generate the mask we'll use to set the correct bit\n shl rbp, cl\n # We'll start with the right branch\n or QWORD PTR [rdx + 8*r13], rbp # Set the bit\n inc QWORD PTR [rdx + bitstr_len] # Increase the bitstring length\n mov rsi, QWORD PTR [r12 + tree_right]\n call generate_codebook_recurse\n # Now we move on to the left branch: rbx - left child, r13 - bitstring index, rbp - mask\n not rbp\n and QWORD PTR [rdx + 8*r13], rbp\n mov rsi, QWORD PTR [r12 + tree_left]\n call generate_codebook_recurse\n dec QWORD PTR [rdx + bitstr_len] # Decrease the bitstring length\ngenerate_codebook_recurse_done:\n pop r13\n pop r12\n pop rbp\n ret\n\n# rdi - text\n# RET rax - Huffman-tree root (ptr)\ngenerate_tree:\n push r12\n push r13\n sub rsp, 5128 # 1024 bytes for the char counts, 4 bytes for heap length, 4096 bytes for the heap, 4 byte padding\n mov r12, rdi # Save the original text so it doesn't get clobbered\n mov rdi, rsp # Zero out the character counts and the heap length\n xor rsi, rsi\n mov rdx, 1040\n call memset\n xor rax, rax\ngenerate_tree_count_chars:\n mov al, BYTE PTR [r12]\n test al, al\n jz generate_tree_leaves_setup\n inc DWORD PTR [rsp + 4*rax]\n inc r12\n jmp generate_tree_count_chars\ngenerate_tree_leaves_setup:\n mov r12, 255 # The loop counter. We can only get here if the \"test\" on line 301 resulted in a zero so the next jl instruction will do the right thing\ngenerate_tree_leaves:\n jl generate_tree_one_leaf # If not then it's time to generate the branches\n mov r13d, DWORD PTR [rsp + 4*r12] # Load the count at the ith position\n test r13d, r13d # And check if it's zero\n jz generate_tree_leaves_counters # If it is we can skip this iteration\n mov rdi, 1 # If not, we need to allocate a new leaf node\n mov rsi, tree_size\n call calloc\n mov DWORD PTR [rax + tree_value], r12d # Save the value and the count to the tree\n mov DWORD PTR [rax + tree_count], r13d\n lea rdi, [rsp + counts_size] # Then push it onto the heap\n mov rsi, rax\n call heap_push\ngenerate_tree_leaves_counters:\n dec r12 # Decrement the loop counter and start over\n jmp generate_tree_leaves\ngenerate_tree_one_leaf:\n cmp DWORD PTR [rsp + counts_size], 1 # Check if there is only one element in the heap\n jne generate_tree_branches\n lea rdi, [rsp + counts_size] # Get the element\n call heap_pop\n mov r12, rax\n mov rdi, tree_size # Create the new tree node, the pointer to it will be in rax\n call malloc\n mov QWORD PTR [rax + tree_left], r12 # Save element in the left node\n mov ecx, DWORD PTR [r12 + tree_count] # Save element count in branch\n mov DWORD PTR [rax + tree_count], ecx\n jmp generate_tree_ret # Returning\ngenerate_tree_branches:\n cmp DWORD PTR [rsp + counts_size], 1 # Check if there are still at least two elements in the heap\n jle generate_tree_done # If not, we're done\n lea rdi, [rsp + counts_size] # Get the left child\n call heap_pop\n mov r12, rax\n lea rdi, [rsp + counts_size] # Get the right child\n call heap_pop\n mov r13, rax\n mov rdi, tree_size # Create the new tree node, the pointer to it will be in rax\n call malloc\n mov ecx, DWORD PTR [r12 + tree_count] # The new node's count: left count + right count\n add ecx, DWORD PTR [r13 + tree_count]\n mov QWORD PTR [rax + tree_left], r12 # Save the new node's fields: left, right, count (leave value unititialized, it shouldn't be used with branch nodes)\n mov QWORD PTR [rax + tree_right], r13\n mov DWORD PTR [rax + tree_count], ecx\n lea rdi, [rsp + counts_size] # Add the branch to the heap\n mov rsi, rax\n call heap_push\n jmp generate_tree_branches\ngenerate_tree_done:\n lea rdi, [rsp + counts_size] # The tree's root will be in rax after the pop\n call heap_pop\ngenerate_tree_ret:\n add rsp, 5128\n pop r13\n pop r12\n ret\n\n# rdi - heap ptr\n# rsi - tree ptr\nheap_push:\n lea rax, QWORD PTR [rdi + heap_data] # We load the heap's data ptr and length to the respective registers\n mov ecx, DWORD PTR [rdi + heap_len] # Load the current length\n lea edx, [ecx + 1] # First, calculate the new length (length + 1)\n mov DWORD PTR [rdi + heap_len], edx # Then save it\n mov QWORD PTR [rax + 8*rcx], rsi # And finally add the new value at the end of the array\nheap_push_sift_up:\n test rcx, rcx # Test if we got to the root (index == 0)\n jz heap_push_done\n lea rdx, [rcx - 1] # Calculate the parent index: (index - 1) / 2\n shr rdx, 1\n lea r8, [rax + 8*rcx] # Get the pointer to the current and parent elements\n lea r9, [rax + 8*rdx]\n mov r10, QWORD PTR [r8] # Load the current and the parent elements\n mov r11, QWORD PTR [r9]\n mov esi, DWORD PTR [r10 + tree_count] # Load the current tree's count\n cmp DWORD PTR [r11 + tree_count], esi # If parent count \nimport scala.collection.mutable.{Map, PriorityQueue}\n\nobject HuffmanEncoding {\n\n trait Node {\n var weight: Int\n }\n\n case class Leaf(char: Char, var weight: Int) extends Node\n\n case class Branch(left: Node, right: Node, var weight: Int) extends Node\n\n def createTree(phrase: String): Option[Node] = {\n\n val tree = PriorityQueue[Node]()(Ordering.by(-_.weight))\n tree ++= phrase\n .groupBy(identity)\n .mapValues(_.length)\n .map{\n case (char, count) => Leaf(char, count)\n }\n\n while (tree.size > 1) {\n val node1 = tree.dequeue()\n val node2 = tree.dequeue()\n tree += Branch(node1, node2, node1.weight + node2.weight)\n }\n\n tree.headOption\n }\n\n\n def createCodeBook(maybeRoot: Option[Node]): Map[Char, String] = {\n val codeBook = Map[Char, String]()\n\n def codeBookRecurse(node: Node, code: String): Unit =\n node match {\n case Leaf(symbol, _) => codeBook.put(symbol, code)\n case Branch(left, right, _) => {\n codeBookRecurse(left, code + \"0\")\n codeBookRecurse(right, code + \"1\")\n }\n }\n\n maybeRoot.foreach(c => codeBookRecurse(c, \"\"))\n\n codeBook\n }\n\n\n def encode(phrase: String, codeBook: Map[Char, String]): String = {\n phrase.flatMap(c => codeBook.getOrElse(c, \"?\"))\n }\n\n def decode(encoded: String, maybeRoot: Option[Node]): String = {\n val root = maybeRoot.getOrElse(Leaf('?', 0))\n var currentNode = root\n\n def chooseTreeBranch(bit: Char) =\n currentNode match {\n case Branch(left, right, _) =>\n currentNode = if (bit == '0') left else right\n case _ =>\n }\n\n def maybeGetACharacter =\n currentNode match {\n case Leaf(c, _) => {\n currentNode = root\n Some(c)\n }\n case _ => None\n }\n\n encoded\n .flatMap(bit => {\n chooseTreeBranch(bit)\n maybeGetACharacter\n })\n }\n\n def main(args: Array[String]): Unit = {\n val originalText = \"bibbity_bobbity\"\n println(\"Original Text: \" + originalText)\n\n val tree = createTree(originalText)\n val codeBook = createCodeBook(tree)\n println(\"CodeBook is: \" + codeBook)\n\n val encoded = encode(originalText, codeBook)\n println(\"Encoded text: \" + encoded)\n\n val decoded = decode(encoded, tree)\n println(\"Decoded text: \" + decoded)\n\n }\n\n}\n\nThe code snippet was taken from this scratch project\n\n \nfrom collections import Counter, deque\nfrom bisect import bisect\n\nclass Tree\n\ndata Empty() from Tree\ndata Leaf(char, n is int) from Tree:\n def __str__(self):\n return f'Leaf({self.char}, {self.n})'\n\n __repr__ = __str__\n\ndata Node(left is Tree, right is Tree) from Tree:\n def __str__(self):\n return f'Node({str(self.left)}, {str(self.right)})'\n __repr__ = __str__\n\ndef weight(Tree()) = 0\naddpattern def weight(Leaf(char, n)) = n\naddpattern def weight(Node(left, right)) = weight(left) + weight(right)\n\ndef build_huffman_tree(message):\n\n # get sorted list of character and frequency pairs\n frequencies = Counter(message)\n trees = frequencies.most_common() |> map$(t -> Leaf(*t)) |> reversed |> deque\n\n if not trees:\n return Empty()\n\n # while there is more than one tree\n while len(trees) > 1:\n\n # pop off the two trees of least weight from the trees list\n tree_left = trees.popleft()\n tree_right = trees.popleft()\n\n # combine the nodes and add back to the nodes list\n new_tree = Node(tree_left, tree_right)\n\n # find the first tree that has a weight smaller than new_weight\n # and returns its index in the list.\n # If no such tree can be found, use len(trees) instead to append\n index = bisect(trees |> map$(weight) |> list, weight(new_tree))\n\n # insert the new tree there\n trees.insert(index, new_tree)\n\n huffman_tree = trees[0]\n return huffman_tree\n\n\ndef build_codebook(Empty(), code='') = []\naddpattern def build_codebook(Leaf(char, n), code='') = [(char, code)]\naddpattern def build_codebook(Node(left, right), code='') = \n build_codebook(left, code+'0') + build_codebook(right, code+'1')\n\ndef huffman_encode(codebook, message):\n\n if len(codebook) == 1:\n return '0' * len(message)\n\n # build a char -> code dictionary\n forward_dict = dict(codebook)\n\n return ''.join(message |> map$(forward_dict[]))\n\ndef huffman_decode(codebook, encoded_message):\n\n decoded_message = []\n key = ''\n\n if not codebook:\n return ''\n elif len(codebook) == 1:\n return codebook[0][0] * len(encoded_message)\n\n # build a code -> char dictionary\n inverse_dict = dict((v, k) for k, v in codebook)\n\n # for each bit in the encoding\n # if the bit is in the dictionary, replace the bit with the paired\n # character else look at the bit and the following bits together\n # until a match occurs move to the next bit not yet looked at.\n if encoded_message == '':\n return inverse_dict['']\n\n for bit in encoded_message:\n key += bit\n if key in inverse_dict:\n decoded_message.append(inverse_dict[key])\n key = ''\n\n return ''.join(decoded_message)\n\n\nif __name__ == '__main__':\n # test example\n message = 'bibbity_bobbity'\n tree = build_huffman_tree(message)\n codebook = build_codebook(tree)\n encoded_message = huffman_encode(codebook, message)\n decoded_message = huffman_decode(codebook, encoded_message)\n\n print('message:', message)\n print('huffman tree:', tree)\n print('codebook:', codebook)\n print('encoded message:', encoded_message)\n print('decoded message:', decoded_message)\n\n # prints the following:\n #\n # message: bibbity_bobbity\n # huffman_tree: Node(Leaf(b, 6), Node(Node(Leaf(y, 2), Leaf(t, 2)),\n # Node(Node(Leaf(o, 1), Leaf(_, 1)), Leaf(i, 3))))\n # codebook: [('b', '0'), ('y', '100'), ('t', '101'),\n # ('o', '1100'), ('_', '1101'), ('i', '111')]\n # encoded_message: 01110011110110011010110000111101100\n # decoded_message: bibbity_bobbity\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"huffman_tree\" was created by Julian Schacher and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/computer_graphics/computer_graphics.html":{"url":"contents/computer_graphics/computer_graphics.html","title":"Computer Graphics","keywords":"","body":"Computer Graphics\nOf all areas of computer science research, none have had more of an immediate impact on multimedia than computer graphics.\nThis sub-field is distinctly different than computational science in that it focuses on the appearance of realistic details, instead of computing those details precisely.\nWhere a computational scientist might spend years writing software that runs on the fastest computers known to man to simulate climate, the computer graphics researcher might apply machine learning to create fluid simulations that look good enough to the untrained eye.\nIn the end, the computational scientist will have a plot and the computer graphics researcher will have a beautifully rendered simulation.\nThough I may have painted computer graphics to be a bit hand-wavey, that could not be further from the truth!\nInstead, I would argue that this field of research provides the closest approximation to realistic visualizations that desktop hardware can currently support.\nMany art and video game studios are interested in telling a complete story via computational media, and this simply would not be possible without the rigorous efforts of researchers from around the world.\nThis is why Pixar hires researchers and will actively publish their findings after their movies are released.\nThough the boundary between computer science research fields is a bit vague, for the purposes of the Algorithm Archive, we will broadly classify computer graphics as anything with direct applications to images or fields that can be represented as images.\nConvolutions, for example, would not be considered part of computer graphics because they are used widely in all areas of computer science research; however, Canny edge detection will be.\nWe will also be covering a wide range of applications that are used for rendering high-resolution graphics and computational art.\nAs with all sections to the Algorithm Archive, this is a work in progress and subject to change, so feel free to let me know what you think!\n"},"contents/quantum_information/quantum_information.html":{"url":"contents/quantum_information/quantum_information.html","title":"Quantum Information","keywords":"","body":"Quantum Information\nQuantum information theory is... intense.\nIt requires a strong and fundamental understanding of classical information theory and quantum mechanics.\nIt is not obvious in any way and deserves many textbooks on it's own.\nIn fact, there are numerous textbooks on the subject already.\nThe purpose of this section isn't to outdo any of that fundamental knowledge.\nInstead, we will attempt to distill the knowledge into a short, intuitive summary, with the hopes of helping people to understand more about the topic and pursue it further on their own.\nAt the time of writing, true quantum computers do not exist.\nWe do have some systems that are able to simulate qubits, they are not truly universal quantum computers.\nThe closest market-ready system we currently have is D-WAVE, which boasts an impressive 128 qubits!\nThere are many places to start an introduction to quantum information theory, so we'll go through it one step at a time:\n\nQuantum bitlogic: what is a qubit and how is it different than a classical bit?\nQuantum gates and quantum circuits: How do you fundamentally build a quantum algorithm?\nQuantum computers in the wild: Current experimental techniques to create a quantum computer and what makes them ill-suited as real quantum computers\nA survey of current quantum algorithms: There are a number of algorithms that promise fantastic advantages when performed on quantum computers and should really shake up the industry when they are finally experimentally realized.\n\nAs a note, item 3 might seem out of place for a book on algorithms, and I would tend to agree; however, at this point there is a phenomenal amount of research being done to realize the first truly quantum computer and there are a number of potential systems that could work for this purpose.\nThese systems will change how we think about and interface with quantum computation in the future and it is important to discuss where the field might be heading and when we can expect quantum computers at home.\nNow, there are not too many languages that can compile quantum code.\nA while ago, we tried to make a quantum circuit compiler, which was modeled after the SPICE circuit simulator, but this was far from a computer language.\nAt this point in time, it is impossible to tell what quantum computing languages will look like when we finally have a truly quantum machine, so for the time being, we will not ask for community code for the chapters related to quantum information.\nbasically, it's hard to imagine how to would adequately implement Shor's algorithm in C.\nAs always, this section will be updated as we add more algorithms to the list.\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/stable_marriage_problem/stable_marriage_problem.html":{"url":"contents/stable_marriage_problem/stable_marriage_problem.html","title":"Stable Marriage Problem","keywords":"","body":"The Stable Marriage Problem\nImagine you have two groups, each of size n.\nEach individual within a group has an internal ranking associated with all members of the opposing group.\nThe Stable Matching Problem attempts to unite both groups into stable pairs.\nIn this case, a set of pairs is considered stable if there are no pairs that like each other more than their current partners.\nThis doesn't mean that everyone gets their top choices, but if an individual prefers someone else who also prefers them back, the set of pairs is not stable.\nNow, this is often told as a story.\nOne group is male, the other is female, and everyone gets married, hence the name the Stable Marriage Problem.\nThis problem is solved by the Gale-Shapley algorithm, which can be simply described as follows:\n\nAll the men propose to their top choice of women.\nThe women become tentatively engaged to their top choice of the men who have proposed to them.\nAll rejected men propose to their next choice, and the women again select whichever man they prefer, possibly rejecting the one they were already engaged to.\n\nThis process continues until all individuals are paired, which means that this algorithm guarantees stable matching and also has a \\mathcal{O}(n^2) runtime.\nTo be clear, even though this algorithm seems conceptually simple, it is rather tricky to implement correctly.\nI do not at all claim that the code provided here is efficient and we will definitely be coming back to this problem in the future when we have more tools under our belt.\nI am incredibly interested to see what you guys do and how you implement the algorithm.\nVideo Explanation\nHere is a video describing the stable marriage problem:\n\n\n\n\nExample Code\nclass Person\n def initialize(id, name, prefs)\n @id = id\n @name = name\n @prefs = prefs\n @partner = nil\n @choices = 0\n end\n\n def lonely?\n @partner.nil?\n end\n\n def propose(partners)\n unless self.lonely?\n raise '%s is not lonely!' % self.name\n end\n choice = @prefs[@choices]\n partners[choice].onPropose(self)\n @choices += 1\n end\n\n def to_s\n \"#{@name.rjust(20)}: #{self.lonely? && \"Lonely\" || @partner.name}\"\n end\n\n def self.generate(size, prefix, r)\n Array.new(size){|i|\n Person.new(\n i,\n \"#{prefix} #{i}\",\n (0 ... size).to_a.shuffle(random: r)\n )\n }\n end\n\n protected\n attr_reader :id, :name\n attr_writer :partner\n\n # Acts upon a given Proposal\n def onPropose(partner)\n unless self.lonely?\n offer = score(partner)\n current = score(@partner)\n return unless offer > current \n @partner.partner = nil\n end\n @partner = partner\n partner.partner = self\n end\n\n private\n # Determines the preference of a given partner\n def score(partner)\n return 0 if partner.nil?\n @prefs.size - @prefs.index(partner.id)\n end\nend\n\n# Deterministic Output, feel free to change seed\nr = Random.new(42)\n\n# Determines Output Columns\nmen = Person.generate(4, \"Man\", r)\nwomen = Person.generate(4, \"Woman\", r)\n\n# Assume no Name is longer than 20 characters\nspacer = '-' * (20 * 2 + 2)\n\n# Solve the Problem\n1.step do |round|\n singles = men.select(&:lonely?)\n singles.each do |m|\n m.propose(women)\n end\n\n break if singles.empty?\n\n puts \"Round #{round}\"\n puts spacer\n puts men, women\n puts spacer\nend\n\nusing Random\n\nconst mnames = [\"A\", \"B\", \"C\", \"D\"]\nconst wnames = [\"E\", \"F\", \"G\", \"H\"]\n\nconst Preferences = Dict{String,Vector{String}}\nconst Pairs = Dict{String,String}\n\n# Returns a name => preference list dictionary, in decreasing order of preference\nfunction genpreferences(mannames::Vector{String}, womannames::Vector{String})\n men = Dict(map(m -> (m, shuffle(womannames)), mannames))\n women = Dict(map(w -> (w, shuffle(mannames)), womannames))\n return men, women\nend\n\n# Returns if `person` prefers the `first` candidate over the `second` one.\n# This translates to `first` appearing *sooner* in the preference list\nprefers(prefs, person, first, second) =\n findfirst(m -> m == first, prefs[person]) m == second, prefs[person])\n\nisfree(person, pairs) = !haskey(pairs, person)\n\nfunction galeshapley(men::Preferences, women::Preferences)\n mentowomen = Dict{String,String}()\n womentomen = Dict{String,String}()\n while true\n bachelors = [m for m in keys(men) if isfree(m, mentowomen)]\n if length(bachelors) == 0\n return mentowomen, womentomen\n end\n\n for bachelor in bachelors\n for candidate in men[bachelor]\n if isfree(candidate, womentomen)\n mentowomen[bachelor] = candidate\n womentomen[candidate] = bachelor\n break\n elseif prefers(women, candidate, bachelor, womentomen[candidate])\n delete!(mentowomen, womentomen[candidate])\n mentowomen[bachelor] = candidate\n womentomen[candidate] = bachelor\n break\n end\n end\n end\n end\nend\n\nfunction isstable(men::Preferences, women::Preferences, mentowomen::Pairs, womentoman::Pairs)\n for (husband, wife) in mentowomen\n for candidate in men[husband]\n if candidate != wife &&\n prefers(men, husband, candidate, wife) &&\n prefers(women, candidate, husband, womentoman[candidate])\n return false\n end\n end\n end\n return true\nend\n\nfunction main()\n men, women = genpreferences(mnames, wnames)\n mentowomen, womentomen = galeshapley(men, women)\n println(mentowomen)\n println(isstable(men, women, mentowomen, womentomen) ? \"Stable\" : \"Unstable\")\nend\n\nmain()\n\n# Submitted by Marius Becker\n# Updated by Amaras\n\n\nfrom random import shuffle\nfrom copy import copy\nfrom string import ascii_uppercase, ascii_lowercase\n\n\ndef main():\n # Set this to however many men and women you want, up to 26\n num_pairs = 5\n\n # Create all Person objects\n men = [Person(name) for name in ascii_uppercase[:num_pairs]]\n women = [Person(name) for name in ascii_lowercase[:num_pairs]]\n\n # Set everyone's preferences\n for man in men:\n man.preference = copy(women)\n shuffle(man.preference)\n\n for woman in women:\n woman.preference = copy(men)\n shuffle(woman.preference)\n\n # Run the algorithm\n stable_marriage(men, women)\n\n # Print preferences and the result\n print('Preferences of the men:')\n for man in men:\n print(man)\n\n print()\n\n print('Preferences of the women:')\n for woman in women:\n print(woman)\n\n print('\\n')\n\n print('The algorithm gave this solution:')\n for man in men:\n print(f'{man.name} + {man.partner.name}')\n\n\ndef stable_marriage(men, women):\n \"\"\"Finds pairs with stable marriages\"\"\"\n\n while True:\n # Let every man without a partner propose to a woman\n for man in men:\n if not man.has_partner:\n man.propose_to_next()\n\n # Let the women pick their favorites\n for woman in women:\n woman.pick_preferred()\n\n # Continue only when someone is still left without a partner\n if all((man.has_partner for man in men)):\n return\n\n\nclass Person:\n\n def __init__(self, name):\n self.name = name\n self.preference = []\n self.candidates = []\n self.pref_index = 0\n self._partner = None\n\n @property\n def next_choice(self):\n \"\"\"Return the next person in the own preference list\"\"\"\n try:\n return self.preference[self.pref_index]\n except IndexError:\n return None\n\n def propose_to_next(self):\n \"\"\"Propose to the next person in the own preference list\"\"\"\n person = self.next_choice\n person.candidates.append(self)\n self.pref_index += 1\n\n def pick_preferred(self):\n \"\"\"Pick a new partner or stay with the old one if they are preferred\"\"\"\n # Iterate own preferences in order\n for person in self.preference:\n # Pick the first person that's either a new candidate or the\n # current partner\n if person == self.partner:\n break\n elif person in self.candidates:\n self.partner = person\n break\n\n # Rejected candidates don't get a second chance\n self.candidates.clear()\n\n @property\n def partner(self):\n return self._partner\n\n # The call self.partner = person sets self._partner as person\n # However, since engagement is symmetrical, self._partner._partner\n # (which is then person._partner) also needs to be set to self\n @partner.setter\n def partner(self, person):\n \"\"\"Set a person as the new partner and sets the partner of that\n person as well\"\"\"\n\n # Do nothing if nothing would change\n if person != self._partner:\n # Remove self from current partner\n if self._partner is not None:\n self._partner._partner = None\n\n # Set own and the other person's partner\n self._partner = person\n if self._partner is not None:\n self._partner._partner = self\n\n # This allows use of self.has_partner instead of self.has_partner()\n @property\n def has_partner(self):\n \"\"\"Determine whether this person currently has a partner or not.\"\"\"\n return self.partner is not None\n\n # This allows the preferences to be printed more elegantly\n def __str__(self):\n return f'{self.name}: {\", \".join(p.name for p in self.preference)}'\n\n\nif __name__ == '__main__':\n main()\n\nimport Data.Map as M (Map, (!))\nimport qualified Data.Map as M\nimport Data.List (elemIndex)\nimport Control.Monad.State\n\nstableMatching :: (Ord a, Ord b) => [(a, [b])] -> [(b, [a])] -> [(a, b)]\nstableMatching men women = evalState (propose (M.fromList women) men) M.empty\n\npropose :: (Ord a, Ord b) => Map b [a] ->\n [(a, [b])] ->\n State (Map b (a, [b])) [(a, b)]\npropose _ [] = get >>= return . map (\\(w, (m,_)) -> (m, w)) . M.assocs\npropose women ((man, pref):bachelors) = do\n let theOne = head pref\n couples do\n modify $ M.insert theOne (man, (tail pref))\n propose women bachelors\n Just (boyfriend, planB) -> do\n let rank x = elemIndex x (women!theOne)\n if rank boyfriend \n#include \n#include \n#include \n#include \n#include \n\nstruct person {\n size_t id;\n struct person *partner;\n size_t *prefers;\n size_t index;\n};\n\nvoid shuffle(size_t *array, size_t size) {\n for (size_t i = size - 1; i > 0; --i) {\n size_t j = (size_t)rand() % (i + 1);\n size_t tmp = array[i];\n array[i] = array[j];\n array[j] = tmp;\n }\n}\n\nvoid create_group(struct person *group, size_t size) {\n for (size_t i = 0; i 0) {\n struct person *man = bachelors[bachelors_size - 1];\n struct person *woman = &women[man->prefers[man->index]];\n\n if (!woman->partner) {\n woman->partner = man;\n man->partner = woman;\n bachelors[--bachelors_size] = NULL;\n } else if (!prefers_partner(woman->prefers, woman->partner->id, man->id,\n size)) {\n\n woman->partner->index++;\n bachelors[bachelors_size - 1] = woman->partner;\n woman->partner = man;\n man->partner = woman;\n } else {\n man->index++;\n }\n }\n}\n\nvoid free_group(struct person *group, size_t size) {\n for (size_t i = 0; i id);\n }\n\n free_group(men, 5);\n free_group(women, 5);\n}\n\n#include \n#include \n#include \n#include \n#include \n#include \n\n// this header is so that we can use `not` and `and` on MSVC\n#include \n\n#include \n\nusing std::size_t;\n\n/*\n we use these to generate random numbers in this program.\n this makes the program simpler,\n by not having to pass around random number generators.\n*/\nstatic thread_local std::random_device global_random_device;\nstatic thread_local std::mt19937 global_rng(global_random_device());\n\nstruct person {\n /*\n this is a poor person's std::optional,\n but since we're attempting to be compileable on C++14,\n we won't worry too much about it.\n */\n bool finished;\n size_t preference;\n\n std::vector preference_list;\n};\n\n/*\n this function generates a list of people with size `number_of_partners`.\n\n each person's `preference_list` will be a randomly sorted list of\n the numbers in the range [0, number_of_partners),\n with no duplicates.\n*/\nstd::vector make_person_list(size_t number_of_partners) {\n auto random_pref_list = [&] {\n std::vector ret(number_of_partners);\n std::iota(begin(ret), end(ret), size_t(0));\n std::shuffle(begin(ret), end(ret), global_rng);\n\n return ret;\n };\n\n std::vector ret;\n std::generate_n(std::back_inserter(ret), number_of_partners, [&] {\n return person{false, 0, random_pref_list()};\n });\n\n return ret;\n}\n\ntemplate \nvoid stable_match(LeadIter leads, LeadIter leads_end, FollowIter follows) {\n // for each index in the leads' preference list, we'll go through this\n size_t const number_of_partners = leads_end - leads;\n for (size_t proposal_index = 0; proposal_index > proposals(number_of_partners);\n\n // for each lead, we'll make a proposal to their favorite follow\n for (size_t i = 0; i \nclass Person {\n constructor(name) {\n this.name = name;\n }\n\n get hasFiance() {\n return !!this.fiance;\n }\n\n prefers(other) {\n return this.preferences.indexOf(other) 0) {\n const guy = bachelors.shift();\n for (const girl of guy.preferences) {\n if (!girl.hasFiance) {\n guy.engageTo(girl);\n break;\n } else if (girl.prefers(guy)) {\n bachelors.push(girl.fiance);\n guy.engageTo(girl);\n break;\n }\n }\n }\n}\n\nfunction shuffle(iterable) {\n const array = [...iterable];\n for (let i = array.length - 1; i > 0; i--) {\n const j = Math.floor(Math.random() * (i + 1));\n [array[i], array[j]] = [array[j], array[i]];\n }\n return array;\n}\n\nconst guys = [...\"ABCDE\"].map(name => new Person(name));\nconst girls = [...\"FGHIJ\"].map(name => new Person(name));\n\nconsole.log(\"Guys\");\nfor (const guy of guys) {\n guy.preferences = shuffle(girls);\n console.log(`${guy.name}: ${guy.preferences.map(p => p.name).join()}`)\n}\n\nconsole.log(\"\\nGirls\");\nfor (const girl of girls) {\n girl.preferences = shuffle(guys);\n console.log(`${girl.name}: ${girl.preferences.map(p => p.name).join()}`)\n}\n\nstableMarriage(guys, girls);\n\nconsole.log(\"\\nPairings\");\nfor (const guy of guys) {\n console.log(`${guy.name}: ${guy.fiance.name}`);\n}\n\nGaleShapleyAlgorithm.cs\n// submitted by Julian Schacher (jspp) with great help by gustorn and Marius Becker\nusing System.Collections.Generic;\n\nnamespace StableMarriageProblem\n{\n public static class GaleShapleyAlgorithm\n where TFollow : Person\n where TLead : Person\n {\n public static void RunGaleShapleyAlgorithm(List follows, List leads)\n {\n // All follows are lonely.\n var lonelyFollows = new List(follows);\n\n // Carry on until there are no lonely follows anymore.\n while (lonelyFollows.Count > 0)\n {\n // Let every lonely follow propose to their current top choice.\n foreach (var lonelyFollow in lonelyFollows)\n {\n lonelyFollow.ProposeToNext();\n }\n\n // Look which follows have a partner now and which don't.\n var newLonelyFollows = new List();\n foreach (var follow in follows)\n {\n if (follow.Partner == null)\n newLonelyFollows.Add(follow);\n }\n lonelyFollows = newLonelyFollows;\n }\n }\n }\n}\n\nPerson.cs\n// submitted by Julian Schacher (jspp) with great help by gustorn and Marius Becker\nusing System.Collections.Generic;\n\nnamespace StableMarriageProblem\n{\n public class Person\n where TSelf : Person\n where TPref : Person\n {\n public string Name { get; set; }\n public TPref Partner { get; set; }\n public IList Choices { get; set; }\n // CurrentTopChoice equals the Choice in Choices that is the TopChoice,\n // if already tried women are not counted.\n public int CurrentTopChoiceIndex { get; set; } = 0;\n\n public Person(string name) => Name = name;\n\n public void ProposeToNext()\n {\n var interest = GetNextTopChoice();\n\n // If the interest has no partner or prefers this person,\n // change interest's partner to this person.\n if (interest.Partner == null ||\n interest.Choices.IndexOf(this as TSelf) Choices[CurrentTopChoiceIndex++];\n }\n}\n\nProgram.cs\n// submitted by Julian Schacher (jspp) with great help by gustorn and Marius Becker\nusing System;\nusing System.Collections.Generic;\n\nnamespace StableMarriageProblem\n{\n class Program\n {\n static void Main(string[] args)\n {\n Console.WriteLine(\"GaleShapleyAlgorithm\");\n // Using men and women as an example.\n var men = new List()\n {\n new Man(\"A\"),\n new Man(\"B\"),\n new Man(\"C\"),\n new Man(\"D\"),\n new Man(\"E\")\n };\n var women = new List()\n {\n new Woman(\"F\"),\n new Woman(\"G\"),\n new Woman(\"H\"),\n new Woman(\"I\"),\n new Woman(\"J\"),\n };\n\n var random = new Random();\n\n foreach (var man in men)\n {\n man.Choices = new List(women).Shuffle(random);\n Console.WriteLine(man.Name + \":\");\n foreach (var choice in man.Choices)\n Console.Write(choice.Name);\n Console.WriteLine();\n }\n foreach (var woman in women)\n {\n woman.Choices = new List(men).Shuffle(random);\n Console.WriteLine(woman.Name + \":\");\n foreach (var choice in woman.Choices)\n Console.Write(choice.Name);\n Console.WriteLine();\n }\n\n GaleShapleyAlgorithm.RunGaleShapleyAlgorithm(women, men);\n\n foreach (var woman in women)\n {\n Console.WriteLine(woman.Name + \" : \" + woman?.Partner.Name);\n }\n }\n }\n\n public class Man : Person\n {\n public Man(string name) : base(name) { }\n }\n\n public class Woman : Person\n {\n public Woman(string name) : base(name) { }\n }\n}\n\nListExtensions.cs\nusing System;\nusing System.Collections.Generic;\n\nnamespace StableMarriageProblem\n{\n public static class ListExtensions\n {\n public static IList Shuffle(this IList list, Random rng)\n {\n for (var i = 0; i \nimport java.util.List;\nimport java.util.ArrayList;\nimport java.util.Collections;\n\nclass StableMarriage {\n\n /*\n * Use the stable marriage algorithm to find stable pairs from the\n * lists of men and women.\n */\n public static void findStableMarriages(List women, List men) {\n // We might have more men/women than women/men. In this case, not everybody can\n // get a mate. We should aim to give every member of the less numerous gender a mate,\n // as this is always possible.\n List leastCommonGender = women.size() System.out.println(w + \" married to \" + w.getMate()));\n }\n\n public static void main(String[] args) {\n int nPairs = 5;\n List women = new ArrayList<>();\n List men = new ArrayList<>();\n for (char i = 'A'; i {\n w.receiveOptions(men);\n System.out.println(w + \" prefers \" + w.getPreferredMates());\n });\n men.forEach(m -> {\n m.receiveOptions(women);\n System.out.println(m + \" prefers \" + m.getPreferredMates());\n });\n\n findStableMarriages(women, men);\n }\n\n}\n\nclass Person {\n private final String name;\n protected Person mate;\n protected List preferredMates;\n\n public Person(String name) {\n this.name = name;\n }\n\n public boolean isLonely() {\n return mate == null;\n }\n\n public void setMate(Person mate) {\n // Only set mates if there is a change.\n if (this.mate != mate) {\n // Remove old mates mate.\n if (this.mate != null)\n this.mate.mate = null;\n\n // Set the new mate.\n this.mate = mate;\n\n // If new mate is someone, update their mate.\n if (mate != null)\n mate.mate = this;\n }\n }\n\n public Person getMate() {\n return mate;\n }\n\n public void receiveOptions(List mates) {\n // Preferences are subjective.\n preferredMates = new ArrayList<>(mates);\n Collections.shuffle(preferredMates);\n }\n\n public List getPreferredMates() {\n return preferredMates;\n }\n\n public String toString() {\n return getClass().getName() + \"(\" + name + \")\";\n }\n}\n\nclass Woman extends Person {\n private List suitors = new ArrayList<>();\n\n public Woman(String name) {\n super(name);\n }\n\n public void recieveProposal(Man suitor) {\n suitors.add(suitor);\n }\n\n public void chooseMate() {\n for (Person mostDesired : preferredMates) {\n if (mostDesired == mate || suitors.contains(mostDesired)) {\n setMate(mostDesired);\n break;\n }\n }\n }\n}\n\nclass Man extends Person {\n public Man(String name) {\n super(name);\n }\n\n public void propose() {\n if (!preferredMates.isEmpty()) {\n Woman fiance = (Woman) preferredMates.remove(0);\n fiance.recieveProposal(this);\n }\n }\n}\n\nname = $name;\n }\n\n public function getName(): string\n {\n return $this->name;\n }\n\n public function setPreferences(array $preferences): void\n {\n $this->preferences = $preferences;\n }\n\n public function getMatch(): ?Person\n {\n return $this->match;\n }\n\n public function getPreferences(): array\n {\n return $this->preferences;\n }\n\n public function isSingle(): bool\n {\n return $this->match === null;\n }\n\n public function unmatch(): void\n {\n $this->match = null;\n }\n\n public function setMatch(Person $match): void\n {\n if ($this->match !== $match) {\n if ($this->match !== null) {\n $this->match->unmatch();\n }\n $this->match = $match;\n $match->setMatch($this);\n }\n }\n\n public function propose(): void\n {\n if (!empty($this->preferences)) {\n $fiance = array_shift($this->preferences);\n $fiance->receiveProposal($this);\n }\n }\n\n public function receiveProposal(Person $man): void\n {\n $this->suitors[] = $man;\n }\n\n public function chooseMatch(): void\n {\n foreach ($this->preferences as $preference) {\n if ($preference === $this->match || in_array($preference, $this->suitors)) {\n $this->setMatch($preference);\n break;\n }\n }\n\n $this->suitors = [];\n }\n\n public function __toString(): string\n {\n return $this->name;\n }\n}\n\nfunction stable_marriage(array $men, array $women): void\n{\n do {\n foreach ($men as $man) {\n if ($man->isSingle()) {\n $man->propose();\n }\n }\n\n foreach ($women as $woman) {\n $woman->chooseMatch();\n }\n\n $unmarried = false;\n foreach ($women as $woman) {\n if ($woman->isSingle()) {\n $unmarried = true;\n break;\n }\n }\n\n } while ($unmarried);\n}\n\n$groupSize = 10;\n$men = [];\n$women = [];\n\nfor ($i = 1; $i setPreferences($preferences);\n printf('%s\\'s choices: %s', $man->getName(), implode(',', $man->getPreferences()));\n echo PHP_EOL;\n}\necho PHP_EOL;\nforeach ($women as $woman) {\n $preferences = $men;\n shuffle($preferences);\n $woman->setPreferences($preferences);\n printf('%s\\'s choices: %s', $woman->getName(), implode(',', $woman->getPreferences()));\n echo PHP_EOL;\n}\necho PHP_EOL;\n\nstable_marriage($men, $women);\nforeach ($women as $woman) {\n printf('%s is married to %s', $woman, $woman->getMatch());\n echo PHP_EOL;\n}\n\nimport scala.collection.mutable._\n\nobject StableMarriage {\n\n var bachelors = Queue[Man]()\n\n case class Man(name: String, var preferences: List[Woman] = List()) {\n def propose(): Unit = preferences match {\n case woman :: remainingPreferences => {\n if (woman.prefers(this)) {\n bachelors ++= woman.fiance\n woman.fiance = Some(this)\n }\n else\n bachelors.enqueue(this)\n preferences = remainingPreferences\n }\n case _ =>\n }\n }\n\n case class Woman(name: String, var preferences: List[Man] = List(), var fiance: Option[Man] = None) {\n def prefers(man: Man): Boolean =\n fiance match {\n case Some(otherMan) => preferences.indexOf(man) true //always prefer any man over nobody\n }\n }\n\n def findStableMatches(men: Man*): Unit = {\n bachelors = men.to[Queue]\n while (bachelors.nonEmpty)\n bachelors.dequeue.propose()\n }\n}\n\nobject StableMarriageExample {\n\n val a = StableMarriage.Man(\"Adam\")\n val b = StableMarriage.Man(\"Bart\")\n val c = StableMarriage.Man(\"Colm\")\n val x = StableMarriage.Woman(\"Xena\")\n val y = StableMarriage.Woman(\"Yeva\")\n val z = StableMarriage.Woman(\"Zara\")\n\n a.preferences = List(y, x, z)\n b.preferences = List(y, z, x)\n c.preferences = List(x, z, y)\n x.preferences = List(b, a, c)\n y.preferences = List(c, a, b)\n z.preferences = List(a, c, b)\n\n\n def main(args: Array[String]): Unit = {\n\n StableMarriage.findStableMatches(a, b, c)\n\n List(x, y, z).foreach(\n w => Console.println(\n w.name\n + \" is married to \"\n + w.fiance.getOrElse(StableMarriage.Man(\"Nobody\")).name))\n }\n\n}\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/flood_fill/flood_fill.html":{"url":"contents/flood_fill/flood_fill.html","title":"Flood Fill","keywords":"","body":"Flood Fill\nFlood fill is a method that is surprisingly useful in a large number of different situations and keeps finding me wherever I go.\nWhen I was completing my PhD, I had an idea to track superfluid vortices by using flood fill as a way to help mask out unnecessary features of the simulation.\nWhen I was making a terminal game, I thought of creating an animation that was just flood fill in disguise.\nWhen I decided to play minesweeper or Go with my girlfriend, flood fill was used in both!\nFlood fill is probably most commonly known as the \"Bucket Fill\" application in most art programs [1].\nIt's usually indicated by an icon that looks like a bucket and is known to fill in any enclosed area, as shown below:\n\n \n\n\nBecause flood fill is incredibly common, there are a large number of variations to the method, some of which are more optimal than others.\nFor this chapter, we will cover the basics: how to fill a domain in a quick and dirty way.\nIn subsequent chapters, we will continue our journey by creating more and more efficient flood fill methods, including scanline-based and fixed memory methods [2].\nI have decided to split the chapter up for a few important reasons:\n\nI did not want to flood the Algorithm Archive with flood fill methods all at the same time.\nI feel it's worth letting each chapter sit for a bit while we savor it's unique flavor.\nMany users are implementing versions of each algorithm in their own languages and it is difficult to review and submit code for chapters with a lot of code chunks.\nSeveral sub-chapters with less code is easier for everyone.\nI am kinda under a time-constraint right now and wanted to make sure we regularly get content into the Algorithm Archive.\n\nSo, without further a-do, let's hop right into it!\nWhat does flood fill do?\nFlood fill is essentially composed of 2 parts:\n\nDetermining the extents of the domain to fill\nWalking through all elements within a domain and changing some property\n\nFor the purposes of this chapter, we will be using a set of floating-point values that range from 0 to 1 instead of a color-space like RGB.\nThough bucket fill is always used in art programs in some sort of color space, flood fill is more general and can be used in a space with any type of element.\nAs such, it makes sense to use a simpler element type so we can better understand the method.\nSo how do we go about finding the extents of the domain to fill?\nHere, a domain will be defined as any connected set of elements in an n-dimensional space whose values do not vary beyond a predefined threshold.\nAs an example, if we take a circle embedded into a 2-dimensional grid, we have 3 separate domains:\n\nInside the circle where all elements are 0.\nThe circle, itself, where the elements are set to 0.75.\nOutside the circle where all elements are similarly 0.\n\n\n \n\n\nThough there are some more complicated ways to determine the extents of the domain, we will not focus on this aspect of the flood fill method for the remainder of this chapter and instead leave it for subsequent chapters.\nSo now we will focus on the process of walking through each element in the domain and changing some property.\nDomain traversal\nAs before, the simplest example to work with is that of an image, where each element in our domain is a single pixel.\nHere, we can connect each pixel to all other pixels in its vicinity, like so:\n\n \n\n\nIn this image, a border is shown between each individual pixel and a grid is superimposed to show how each pixel is connected to its neighbors.\nThis means that each element has 4 neighbors: north, south, east, and west.\nWe could also include northeast, southeast, southwest, and northwest if we wanted to do an 8-way fill, but we will restrict the discussion to the 4-way fill for now, as the method is essentially the same and slightly easier to understand with fewer elements to worry about.\nBy connecting each pixel to its neighbors in this way, the flood fill operation becomes a process of graph traversal, not too dissimilar from the tree traversal methods described before.\nThis means that after selecting our initial location, we can then traverse through all elements in either a depth-first or breadth-first fashion.\nWe will be covering the following this chapter:\n\nFinding all neighbors\nDepth-first node traversal\nBreadth-first node traversal and small-scale optimizations\n\nSo let's start by discussing how we might go about finding the neighbors to fill.\nFinding all neighbors\nThe first step of this method is to query the location of all possible neighbors.\nAt first glance, this seems rather straightforward.\nOne simply needs to look up, down, left, and right of the current location and add those elements to the list of neighbors if they are:\n\nOn the canvas\nHave a value close enough to the old value we would like to replace\n\nIn code, this might look like this:\nfunction find_neighbors(canvas, loc::CartesianIndex, old_val, new_val)\n\n # Finding north, south, east, west neighbors\n possible_neighbors = [loc + CartesianIndex(0, 1),\n loc + CartesianIndex(1, 0),\n loc + CartesianIndex(0, -1),\n loc + CartesianIndex(-1, 0)]\n\n # Exclusing neighbors that should not be colored\n neighbors = []\n for possible_neighbor in possible_neighbors\n if inbounds(size(canvas), possible_neighbor) &&\n canvas[possible_neighbor] == old_val\n push!(neighbors, possible_neighbor)\n end\n end\n\n return neighbors\nend\n\nint find_neighbors(struct canvas c, struct point p, int old_val, \n struct point *neighbors) {\n int cnt = 0;\n struct point points[4] = {\n {p.x, p.y + 1},\n {p.x + 1, p.y},\n {p.x, p.y - 1},\n {p.x - 1, p.y}\n };\n\n for (int i = 0; i \nauto find_neighbors(\n std::vector> const& grid,\n CartesianIndex loc,\n float old_value,\n float /* new_value */) {\n\n const std::vector possible_neighbors{\n {loc[0], loc[1] + 1},\n {loc[0] + 1, loc[1]},\n {loc[0], loc[1] - 1},\n {loc[0] - 1, loc[1]}};\n\n std::vector neighbors;\n\n for (auto const& possible_neighbor : possible_neighbors) {\n const auto size = CartesianIndex{\n static_cast(grid[0].size()), static_cast(grid.size())};\n const auto x = static_cast(possible_neighbor[0]);\n const auto y = static_cast(possible_neighbor[1]);\n if (inbounds(size, possible_neighbor) && grid[x][y] == old_value) {\n neighbors.push_back(possible_neighbor);\n }\n }\n\n return neighbors;\n}\n\ndef find_neighbors(canvas, p, old_val, new_val):\n # north, south, east, west neighbors\n possible_neighbors = [\n Point(p.x, p.y+1),\n Point(p.x+1, p.y),\n Point(p.x-1, p.y),\n Point(p.x, p.y-1)\n ]\n\n # exclude the neighbors that go out of bounds and should not be colored\n neighbors = []\n for possible_neighbor in possible_neighbors:\n if inbounds(canvas.shape, possible_neighbor):\n if canvas[possible_neighbor] == old_val:\n neighbors.append(possible_neighbor)\n return neighbors\n\ndef find_neighbours(canvas, location is Point, old_value):\n possible_neighbours = ((Point(0, 1), Point(1, 0), Point(0, -1), Point(-1, 0))\n |> map$(location.__add__))\n\n yield from possible_neighbours |> filter$(x -> (inbounds(canvas.shape, x)\n and canvas[x] == old_value))\n\n\n\n\nThis code is set up to return a vector of elements to then use for subsequent sections.\nDepth-first node traversal\nNow that we have the ability to find all neighboring elements, we can proceed to traverse through those nodes in the most straightforward way: recursion.\nIn code, it might look like this:\nfunction recursive_fill!(canvas, loc::CartesianIndex, old_val, new_val)\n\n if (old_val == new_val)\n return\n end\n\n canvas[loc] = new_val\n\n possible_neighbors = find_neighbors(canvas, loc, old_val, new_val)\n for possible_neighbor in possible_neighbors\n recursive_fill!(canvas, possible_neighbor, old_val, new_val)\n end\nend\n\nvoid recursive_fill(struct canvas c, struct point p, int old_val,\n int new_val) {\n\n if (old_val == new_val) {\n return;\n }\n\n c.data[p.x + c.max_x * p.y] = new_val;\n\n struct point neighbors[4];\n int cnt = find_neighbors(c, p, old_val, neighbors);\n\n for (int i = 0; i \nvoid recursive_fill(\n std::vector>& grid,\n CartesianIndex loc,\n float old_value,\n float new_value) {\n if (old_value == new_value) {\n return;\n }\n\n const auto x = static_cast(loc[0]);\n const auto y = static_cast(loc[1]);\n\n grid[x][y] = new_value;\n\n const auto possible_neighbors = find_neighbors(grid, loc, old_value, new_value);\n for (auto const& possible_neighbor : possible_neighbors) {\n recursive_fill(grid, possible_neighbor, old_value, new_value);\n }\n}\n\ndef recursive_fill(canvas, p, old_val, new_val):\n if old_val == new_val:\n return\n\n canvas[p] = new_val\n\n neighbors = find_neighbors(canvas, p, old_val, new_val)\n for neighbor in neighbors:\n recursive_fill(canvas, neighbor, old_val, new_val)\n\ndef recursive_fill(canvas, location is Point, old_value, new_value):\n if new_value == old_value or not inbounds(canvas.shape, location):\n return\n\n canvas[location] = new_value\n # consume is important here, because otherwise, the recursive function is not called again\n consume(\n find_neighbours(canvas, location, old_value)\n |> map$(recursive_fill$(canvas, ?, old_value, new_value))\n )\n\n\n\nThe above code continues recursing through available neighbors as long as neighbors exist, and this should work so long as we are adding the correct set of neighbors.\nAdditionally, it is possible to do the same type of traversal by managing a stack, like so:\nfunction stack_fill!(canvas, loc::CartesianIndex, old_val, new_val)\n if new_val == old_val\n return\n end\n\n s = Stack{CartesianIndex}()\n push!(s, loc)\n\n while length(s) > 0\n current_loc = pop!(s)\n if canvas[current_loc] == old_val\n canvas[current_loc] = new_val\n possible_neighbors = find_neighbors(canvas, current_loc,\n old_val, new_val)\n for neighbor in possible_neighbors\n push!(s,neighbor)\n end\n end\n\n end\nend\n\nvoid stack_fill(struct canvas c, struct point p, int old_val, int new_val) {\n if (old_val == new_val) {\n return;\n }\n\n struct stack stk = get_stack();\n stack_push(&stk, p);\n\n while (!stack_empty(stk)) {\n struct point cur_loc = stack_pop(&stk);\n if (c.data[cur_loc.x + c.max_x * cur_loc.y] == old_val) {\n c.data[cur_loc.x + c.max_x * cur_loc.y] = new_val;\n\n struct point neighbors[4];\n int cnt = find_neighbors(c, cur_loc, old_val, neighbors);\n\n for (int i = 0; i \nvoid stack_fill(\n std::vector>& grid,\n CartesianIndex loc,\n float old_value,\n float new_value) {\n if (old_value == new_value) {\n return;\n }\n\n auto s = std::stack{};\n s.push(loc);\n\n while (s.size() > 0) {\n const auto current_loc = s.top();\n s.pop();\n\n const auto x = static_cast(current_loc[0]);\n const auto y = static_cast(current_loc[1]);\n\n if (grid[x][y] == old_value) {\n grid[x][y] = new_value;\n const auto possible_neighbors =\n find_neighbors(grid, current_loc, old_value, new_value);\n for (auto const& neighbor : possible_neighbors) {\n s.push(neighbor);\n }\n }\n }\n}\n\ndef stack_fill(canvas, p, old_val, new_val):\n if old_val == new_val:\n return\n\n stack = [p]\n\n while stack:\n cur_loc = stack.pop()\n canvas[cur_loc] = new_val\n stack += find_neighbors(canvas, cur_loc, old_val, new_val)\n\ndef stack_fill(canvas, location is Point, old_value, new_value):\n if new_value == old_value or not inbounds(canvas.shape, location):\n return\n\n stack = [location]\n\n while stack:\n current_location = stack.pop()\n if canvas[current_location] == old_value:\n canvas[current_location] = new_value\n stack.extend(find_neighbours(canvas, current_location, old_value))\n\n\n\nThis is ultimately the same method of traversal as before; however, because we are managing our own data structure, there are a few distinct differences:\n\nThe manually managed stack could be slightly slower and potentially more memory-intensive\nIt is easy to reach the maximum recursion depth on certain hardware with the recursive method, so it is best to use the stack-based implementation in those cases.\n\nIf we were to use either of these methods to fill a circle embedded in a two dimensional domain, we would see the following\n\n\n \nYour browser does not support the video tag.\n\n\n\nHere, we see that these methods will traverse through one direction first before filling from there.\nThis is potentially the easiest method to write, but it is not the most intuitive fill pattern.\nI suspect that if someone was asked to fill the contents of the circle on their own, they would fill it more evenly from the center, like so:\n\n\n \nYour browser does not support the video tag.\n\n\n\nThis is simply another traversal strategy known as breadth-first traversal and comes with its own set of caveats.\nWe will discuss this further in the next subsection\nBreadth-first node traversal and small-scale optimizations\nBreadth-first node traversal is as simple as switching the stack in the depth-first strategy with a queue.\nThe code would look something like this:\nfunction queue_fill!(canvas, loc::CartesianIndex, old_val, new_val)\n if new_val == old_val\n return\n end\n\n q = Queue{CartesianIndex}()\n enqueue!(q, loc)\n\n # Coloring the initial location\n canvas[loc] = new_val\n\n while length(q) > 0\n current_loc = dequeue!(q)\n\n possible_neighbors = find_neighbors(canvas, current_loc,\n old_val, new_val)\n\n # Coloring as we are enqueuing neighbors\n for neighbor in possible_neighbors\n canvas[neighbor] = new_val\n enqueue!(q,neighbor)\n end\n\n end\nend\n\nvoid queue_fill(struct canvas c, struct point p, int old_val, int new_val) {\n if (old_val == new_val) {\n return;\n }\n\n struct queue q = get_queue(sizeof(struct point *));\n enqueue(&q, p);\n\n while (!queue_empty(q)) {\n struct point cur_loc = dequeue(&q);\n if (c.data[cur_loc.x + c.max_x * cur_loc.y] == old_val) {\n c.data[cur_loc.x + c.max_x * cur_loc.y] = new_val;\n\n struct point neighbors[4];\n int cnt = find_neighbors(c, cur_loc, old_val, neighbors);\n\n for (int i = 0; i \nvoid queue_fill(\n std::vector>& grid,\n CartesianIndex loc,\n float old_value,\n float new_value) {\n if (old_value == new_value) {\n return;\n }\n\n auto q = std::queue{};\n q.push(loc);\n const auto x = static_cast(loc[0]);\n const auto y = static_cast(loc[1]);\n grid[x][y] = new_value;\n\n while (q.size() > 0) {\n const auto current_loc = q.front();\n q.pop();\n const auto possible_neighbors =\n find_neighbors(grid, current_loc, old_value, new_value);\n for (auto const& neighbor : possible_neighbors) {\n const auto neighbor_x = static_cast(neighbor[0]);\n const auto neighbor_y = static_cast(neighbor[1]);\n grid[neighbor_x][neighbor_y] = new_value;\n q.push(neighbor);\n }\n }\n}\n\ndef queue_fill(canvas, p, old_val, new_val):\n if old_val == new_val:\n return\n\n q = Queue()\n q.put(p)\n\n canvas[p] = new_val\n\n while not q.empty():\n cur_loc = q.get()\n neighbors = find_neighbors(canvas, cur_loc, old_val, new_val)\n\n for neighbor in neighbors:\n canvas[neighbor] = new_val\n q.put(neighbor)\n\ndef queue_fill(canvas, location is Point, old_value, new_value):\n if new_value == old_value or not inbounds(canvas.shape, location):\n return\n\n queue = deque()\n queue.append(location)\n\n canvas[location] = new_value\n\n while queue:\n current_location = queue.popleft()\n for neighbour in find_neighbours(canvas, current_location, old_value):\n canvas[neighbour] = new_value\n queue.append(neighbour)\n\n\n\nNow, there is a small trick in this code that must be considered to make sure it runs optimally.\nNamely, the nodes must be colored when they are being enqueued, not when visiting the node.\nAt least for me, it was not immediately obvious why this would be the case, but let me try to explain.\nLet's imagine that we decided to write code that colored all neighboring nodes only when visiting them.\nWhen querying all possible neighbors, we will add 4 elements to the queue for the north, south, east, and west neighbors of the initial node, as shown below:\n\n \n\n\nNow let's imagine we travel east first.\nIt then enqueues three more nodes: north, south, and east again.\nThis is shown below:\n\n \n\n\nIt does not enqueue its west neighbor because this has already been colored.\nAt this stage, we will have six nodes ready to be colored and 2 that are already colored.\nNow let's say we travel north next.\nThis node will enqueue three more nodes: west, north, and east, as shown below:\n\n \n\n\nThe problem is that the east element has already been enqueued for coloring by the previous node!.\nThis shared element is colored in red.\nAs we progress through all four initial neighbors, we will find 4 nodes that are doubly enqueued: all directions diagonal to the initial location!\nThis is again shown below:\n\n \n\n\nAs the number of nodes increases, so does the number of duplicate nodes.\nA quick fix is to color the nodes when they are being enqueued like in the example code above.\nWhen doing this, duplicates will not be enqueued with a breadth-first scheme because they will already be colored when other nodes are trying to find their neighbors.\nThis created a node connection pattern like so:\n\n \n\n\nAs some final food for thought: why wasn't this a problem with the depth-first strategy?\nThe simple answer is that it actually was an issue, but it was way less prevalent.\nWith the depth-first strategy, a number of unnecessary nodes are still pushed to the stack, but because we consistently push one direction before spreading out to other directions, it is more likely that the nodes have filled neighbors when they are looking for what to fill around them.\nSimply put: depth-first traversal is slightly more efficient in this case unless you can color as querying for neighbors, in which case breadth-first is more efficient.\nConclusions\nAs stated before, the method discussed in this chapter is just the tip of the iceberg and many other flood fill methods exist that are likely to be more efficient for most purposes.\nThese will all be covered in subsequent chapters which will come out somewhat regularly throughout the next few months, lest we flood that archive with flood fill methods.\nVideo Explanation\nHere is a video describing tree traversal:\n\n\n\n\nExample Code\nThe example code for this chapter will be the simplest application of flood fill that still adequately tests the code to ensure it is stopping at boundaries appropriately.\nFor this, we will create a two dimensional array of floats, all starting at 0.0, and then set a single vertical line of elements at the center to be 1.0.\nAfter, we will fill in the left-hand side of the array to be all ones by choosing any point within the left domain to fill.\nusing DataStructures\nusing Test\n\n# Function to check to make sure we are on the canvas\nfunction inbounds(canvas_size, loc)\n\n # Make sure we are not beneath or to the left of the canvas\n if minimum(Tuple(loc)) canvas_size[2]\n return false\n\n # Make sure we are not above the canvas\n elseif loc[1] > canvas_size[1]\n return false\n else\n return true\n end\nend\n\nfunction find_neighbors(canvas, loc::CartesianIndex, old_val, new_val)\n\n # Finding north, south, east, west neighbors\n possible_neighbors = [loc + CartesianIndex(0, 1),\n loc + CartesianIndex(1, 0),\n loc + CartesianIndex(0, -1),\n loc + CartesianIndex(-1, 0)]\n\n # Exclusing neighbors that should not be colored\n neighbors = []\n for possible_neighbor in possible_neighbors\n if inbounds(size(canvas), possible_neighbor) &&\n canvas[possible_neighbor] == old_val\n push!(neighbors, possible_neighbor)\n end\n end\n\n return neighbors\nend\n\nfunction stack_fill!(canvas, loc::CartesianIndex, old_val, new_val)\n if new_val == old_val\n return\n end\n\n s = Stack{CartesianIndex}()\n push!(s, loc)\n\n while length(s) > 0\n current_loc = pop!(s)\n if canvas[current_loc] == old_val\n canvas[current_loc] = new_val\n possible_neighbors = find_neighbors(canvas, current_loc,\n old_val, new_val)\n for neighbor in possible_neighbors\n push!(s,neighbor)\n end\n end\n\n end\nend\n\n\nfunction queue_fill!(canvas, loc::CartesianIndex, old_val, new_val)\n if new_val == old_val\n return\n end\n\n q = Queue{CartesianIndex}()\n enqueue!(q, loc)\n\n # Coloring the initial location\n canvas[loc] = new_val\n\n while length(q) > 0\n current_loc = dequeue!(q)\n\n possible_neighbors = find_neighbors(canvas, current_loc,\n old_val, new_val)\n\n # Coloring as we are enqueuing neighbors\n for neighbor in possible_neighbors\n canvas[neighbor] = new_val\n enqueue!(q,neighbor)\n end\n\n end\nend\n\nfunction recursive_fill!(canvas, loc::CartesianIndex, old_val, new_val)\n\n if (old_val == new_val)\n return\n end\n\n canvas[loc] = new_val\n\n possible_neighbors = find_neighbors(canvas, loc, old_val, new_val)\n for possible_neighbor in possible_neighbors\n recursive_fill!(canvas, possible_neighbor, old_val, new_val)\n end\nend\n\nfunction main()\n\n # Creation of a 5x5 grid with a single row of 1.0 elements \n grid = zeros(5,5)\n grid[3,:] .= 1\n\n # Create solution grid\n answer_grid = zeros(5,5)\n answer_grid[1:3, :] .= 1\n\n # Start filling at 1,1\n start_loc = CartesianIndex(1,1)\n\n @testset \"Fill Methods\" begin\n # Use recursive method and reinitialize grid\n recursive_fill!(grid, start_loc, 0.0, 1.0)\n @test grid == answer_grid\n\n grid[1:2,:] .= 0\n\n # Use queue method and reinitialize grid\n queue_fill!(grid, start_loc, 0.0, 1.0)\n @test grid == answer_grid\n\n grid[1:2,:] .= 0\n\n # Use stack method and reinitialize grid\n stack_fill!(grid, start_loc, 0.0, 1.0)\n @test grid == answer_grid\n end\n\nend\n\nmain()\n\n#include \n#include \n#include \n\nstruct canvas {\n int max_x, max_y;\n int *data;\n};\n\nstruct point {\n int x, y;\n};\n\nstruct stack {\n size_t top, capacity;\n struct point *data;\n};\n\nstruct queue {\n size_t front, back, capacity;\n struct point *data;\n};\n\nint inbounds(struct point p, struct canvas c) {\n return (p.x = c.max_y || p.x >= c.max_x) ? 0 : 1;\n}\n\nint find_neighbors(struct canvas c, struct point p, int old_val, \n struct point *neighbors) {\n int cnt = 0;\n struct point points[4] = {\n {p.x, p.y + 1},\n {p.x + 1, p.y},\n {p.x, p.y - 1},\n {p.x - 1, p.y}\n };\n\n for (int i = 0; i top == stk->capacity) {\n stk->capacity *= 2;\n stk->data = realloc(stk->data, stk->capacity * sizeof(stk->data[0]));\n }\n\n stk->data[stk->top++] = element;\n}\n\nstruct point stack_pop(struct stack *stk) {\n return stk->data[--stk->top];\n}\n\nvoid free_stack(struct stack stk) {\n free(stk.data);\n}\n\nvoid stack_fill(struct canvas c, struct point p, int old_val, int new_val) {\n if (old_val == new_val) {\n return;\n }\n\n struct stack stk = get_stack();\n stack_push(&stk, p);\n\n while (!stack_empty(stk)) {\n struct point cur_loc = stack_pop(&stk);\n if (c.data[cur_loc.x + c.max_x * cur_loc.y] == old_val) {\n c.data[cur_loc.x + c.max_x * cur_loc.y] = new_val;\n\n struct point neighbors[4];\n int cnt = find_neighbors(c, cur_loc, old_val, neighbors);\n\n for (int i = 0; i front == (q->back + 1) % q->capacity) {\n size_t size = sizeof(q->data[0]);\n struct point *tmp = calloc((q->capacity * 2), size);\n memcpy(tmp, q->data + q->front, (q->capacity - q->front) * size);\n memcpy(tmp + q->capacity - q->front, q->data, (q->front - 1) * size);\n\n free(q->data);\n\n q->data = tmp;\n q->back = q->capacity - 1;\n q->front = 0;\n q->capacity *= 2;\n }\n\n q->data[q->back] = element;\n q->back = (q->back + 1) % q->capacity;\n}\n\nstruct point dequeue(struct queue *q) {\n struct point ret = q->data[q->front];\n q->front = (q->front + 1) % q->capacity;\n\n return ret;\n}\n\nvoid free_queue(struct queue q) {\n free(q.data);\n}\n\nvoid queue_fill(struct canvas c, struct point p, int old_val, int new_val) {\n if (old_val == new_val) {\n return;\n }\n\n struct queue q = get_queue(sizeof(struct point *));\n enqueue(&q, p);\n\n while (!queue_empty(q)) {\n struct point cur_loc = dequeue(&q);\n if (c.data[cur_loc.x + c.max_x * cur_loc.y] == old_val) {\n c.data[cur_loc.x + c.max_x * cur_loc.y] = new_val;\n\n struct point neighbors[4];\n int cnt = find_neighbors(c, cur_loc, old_val, neighbors);\n\n for (int i = 0; i \n#include \n#include \n#include \n#include \n#include \n#include \n\nusing CartesianIndex = std::array;\n\nauto inbounds(CartesianIndex size, CartesianIndex loc) {\n if (loc[0] = size[0] || loc[1] >= size[1]) {\n return false;\n }\n return true;\n}\n\nauto find_neighbors(\n std::vector> const& grid,\n CartesianIndex loc,\n float old_value,\n float /* new_value */) {\n\n const std::vector possible_neighbors{\n {loc[0], loc[1] + 1},\n {loc[0] + 1, loc[1]},\n {loc[0], loc[1] - 1},\n {loc[0] - 1, loc[1]}};\n\n std::vector neighbors;\n\n for (auto const& possible_neighbor : possible_neighbors) {\n const auto size = CartesianIndex{\n static_cast(grid[0].size()), static_cast(grid.size())};\n const auto x = static_cast(possible_neighbor[0]);\n const auto y = static_cast(possible_neighbor[1]);\n if (inbounds(size, possible_neighbor) && grid[x][y] == old_value) {\n neighbors.push_back(possible_neighbor);\n }\n }\n\n return neighbors;\n}\n\nvoid recursive_fill(\n std::vector>& grid,\n CartesianIndex loc,\n float old_value,\n float new_value) {\n if (old_value == new_value) {\n return;\n }\n\n const auto x = static_cast(loc[0]);\n const auto y = static_cast(loc[1]);\n\n grid[x][y] = new_value;\n\n const auto possible_neighbors = find_neighbors(grid, loc, old_value, new_value);\n for (auto const& possible_neighbor : possible_neighbors) {\n recursive_fill(grid, possible_neighbor, old_value, new_value);\n }\n}\n\nvoid queue_fill(\n std::vector>& grid,\n CartesianIndex loc,\n float old_value,\n float new_value) {\n if (old_value == new_value) {\n return;\n }\n\n auto q = std::queue{};\n q.push(loc);\n const auto x = static_cast(loc[0]);\n const auto y = static_cast(loc[1]);\n grid[x][y] = new_value;\n\n while (q.size() > 0) {\n const auto current_loc = q.front();\n q.pop();\n const auto possible_neighbors =\n find_neighbors(grid, current_loc, old_value, new_value);\n for (auto const& neighbor : possible_neighbors) {\n const auto neighbor_x = static_cast(neighbor[0]);\n const auto neighbor_y = static_cast(neighbor[1]);\n grid[neighbor_x][neighbor_y] = new_value;\n q.push(neighbor);\n }\n }\n}\n\nvoid stack_fill(\n std::vector>& grid,\n CartesianIndex loc,\n float old_value,\n float new_value) {\n if (old_value == new_value) {\n return;\n }\n\n auto s = std::stack{};\n s.push(loc);\n\n while (s.size() > 0) {\n const auto current_loc = s.top();\n s.pop();\n\n const auto x = static_cast(current_loc[0]);\n const auto y = static_cast(current_loc[1]);\n\n if (grid[x][y] == old_value) {\n grid[x][y] = new_value;\n const auto possible_neighbors =\n find_neighbors(grid, current_loc, old_value, new_value);\n for (auto const& neighbor : possible_neighbors) {\n s.push(neighbor);\n }\n }\n }\n}\n\nint main() {\n\n const std::vector> grid{\n {0, 0, 1, 0, 0},\n {0, 0, 1, 0, 0},\n {0, 0, 1, 0, 0},\n {0, 0, 1, 0, 0},\n {0, 0, 1, 0, 0}};\n\n const std::vector> solution_grid{\n {1, 1, 1, 0, 0},\n {1, 1, 1, 0, 0},\n {1, 1, 1, 0, 0},\n {1, 1, 1, 0, 0},\n {1, 1, 1, 0, 0}};\n\n const CartesianIndex start_loc{1, 1};\n\n auto test_grid = grid;\n recursive_fill(test_grid, start_loc, 0.0, 1.0);\n assert(test_grid == solution_grid);\n\n test_grid = grid;\n queue_fill(test_grid, start_loc, 0.0, 1.0);\n assert(test_grid == solution_grid);\n\n test_grid = grid;\n stack_fill(test_grid, start_loc, 0.0, 1.0);\n assert(test_grid == solution_grid);\n\n return EXIT_SUCCESS;\n}\n\nfrom collections import namedtuple\nfrom queue import Queue\nimport numpy as np\n\nPoint = namedtuple(\"Point\", \"x y\")\n\ndef inbounds(canvas_shape, p):\n return min(p) >= 0 and p.x \nfrom collections import deque\nimport numpy as np\n\n\ndata Point(x, y):\n def __add__(self, other is Point) = Point(self.x + other.x, self.y + other.y)\n\n\n# This function is necessary, because negative indices wrap around the\n# array in Coconut.\ndef inbounds(canvas_shape, location is Point) =\n min(location) >= 0 and location.x map$(location.__add__))\n\n yield from possible_neighbours |> filter$(x -> (inbounds(canvas.shape, x)\n and canvas[x] == old_value))\n\n\ndef stack_fill(canvas, location is Point, old_value, new_value):\n if new_value == old_value or not inbounds(canvas.shape, location):\n return\n\n stack = [location]\n\n while stack:\n current_location = stack.pop()\n if canvas[current_location] == old_value:\n canvas[current_location] = new_value\n stack.extend(find_neighbours(canvas, current_location, old_value))\n\n\ndef queue_fill(canvas, location is Point, old_value, new_value):\n if new_value == old_value or not inbounds(canvas.shape, location):\n return\n\n queue = deque()\n queue.append(location)\n\n canvas[location] = new_value\n\n while queue:\n current_location = queue.popleft()\n for neighbour in find_neighbours(canvas, current_location, old_value):\n canvas[neighbour] = new_value\n queue.append(neighbour)\n\n\ndef recursive_fill(canvas, location is Point, old_value, new_value):\n if new_value == old_value or not inbounds(canvas.shape, location):\n return\n\n canvas[location] = new_value\n # consume is important here, because otherwise, the recursive function is not called again\n consume(\n find_neighbours(canvas, location, old_value)\n |> map$(recursive_fill$(canvas, ?, old_value, new_value))\n )\n\n\ndef test_grid(initial_canvas, final_canvas, function):\n canvas = initial_canvas.copy() # ensure the initial_canvas is unchanged\n function(canvas)\n return (canvas == final_canvas).all()\n\ndef test():\n from collections import namedtuple\n\n TestResults = namedtuple('TestResults', 'passes failures')\n pass_count = failure_count = 0\n\n grid = np.zeros((5, 5))\n grid[2,:] = 1\n solution_grid = np.zeros((5, 5))\n solution_grid[:3,] = 1\n\n starting_location = Point(0, 0)\n\n recursive_test_func = recursive_fill$(?, starting_location, 0, 1)\n # The following is manual unit testing of the function\n if test_grid(grid, solution_grid, recursive_test_func):\n pass_count += 1\n print('.', end='')\n else:\n failure_count += 1\n print('F', end='')\n\n stack_test_func = stack_fill$(?, starting_location, 0, 1)\n if test_grid(grid, solution_grid, stack_test_func):\n print('.', end='')\n pass_count += 1\n else:\n print('F', end='')\n failure_count += 1\n\n queue_test_func = queue_fill$(?, starting_location, 0, 1)\n if test_grid(grid, solution_grid, queue_test_func):\n print('.', end='')\n pass_count += 1\n else:\n print('F', end='')\n failure_count += 1\n\n print()\n print(TestResults(pass_count, failure_count))\n\nif __name__ == '__main__':\n # Testing setup\n test()\n\n\n\n\nBibliography\n1.Bucket Fill in Gimp, 2020.2.Torbert, Shane, Applied computer science, Springer, 2016.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"Example Bucket Fill\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Circle Domains\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Grid 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Grid 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Grid 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Grid 4\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Grid 5\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Grid 6\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Stack Fill\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Queue Fill\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n"},"contents/jarvis_march/jarvis_march.html":{"url":"contents/jarvis_march/jarvis_march.html","title":"Jarvis March","keywords":"","body":"Jarvis March\nThe first two-dimensional convex hull algorithm was originally developed by R. A. Jarvis in 1973 [1].\nThough other convex hull algorithms exist, this algorithm is often called the gift-wrapping algorithm.\nThe idea behind this algorithm is simple.\nIf we start with a random distribution of points, we can find the convex hull by first starting with the left-most point and using the origin to calculate an angle between every other point in the simulation.\nAs a note, the \"angle\" can be roughly approximated with a cross-product or a dot product, which is common for some implementations here.\nWhichever point has the largest interior angle is chosen as the next point in the convex hull and we draw a line between the two points.\nFrom there, we use the two known points to again calculate the angle between all other points in the simulation.\nWe then choose the point with the largest interior angle and move the simulation forward.\nWe keep repeating this process until we have returned to our original point.\nThe set of points chosen in this simulation will be the convex hull.\nAs we might expect, this algorithm is not incredibly efficient and has a runtime of \\mathcal{O}(nh), where n is the number of points and h is the size of the hull.\nAs a note, the Jarvis March can be generalized to higher dimensions.\nSince this algorithm, there have been many other algorithms that have advanced the field of two-dimensional gift-wrapping forward, including the Graham Scan and Chan's Algorithm, which will be discussed in due time.\nBibliography\n1.Jarvis, Ray A, On the identification of the convex hull of a finite set of points in the plane, Elsevier, 1973.\nExample Code\nJarvisMarch.cs\n// submitted by Julian Schacher (jspp) with great help by gustorn\nusing System;\nusing System.Collections.Generic;\nusing System.Linq;\n\nnamespace JarvisMarch\n{\n public struct Vector\n {\n public readonly int x;\n public readonly int y;\n\n public Vector(int xValue, int yValue)\n {\n this.x = xValue;\n this.y = yValue;\n }\n\n public override bool Equals(object obj) => obj is Vector v && this.x == v.x && this.y == v.y;\n public override int GetHashCode() => (17 * 23 + this.x) * 23 + this.y;\n\n public static bool operator==(Vector a, Vector b) => a.Equals(b);\n public static bool operator!=(Vector a, Vector b) => !(a == b);\n }\n\n public class JarvisMarch\n {\n public List Run(List points)\n {\n var convexHull = new List();\n\n // Set the intial pointOnHull to the point of the list, where the x-position is the lowest.\n var pointOnHull = points.Aggregate((leftmost, current) => leftmost.x \n {\n // Returns true, if potentialNextPointOnHull is equal to the current pointOnHull or if the current point is left of the line defined by pointOnHull and potentialNextPointOnHull.\n if (potentialNextPointOnHull == pointOnHull || IsLeftOf(pointOnHull, potentialNextPointOnHull, current))\n return current;\n return potentialNextPointOnHull;\n });\n\n // Check if the gift wrap is completed.\n } while (pointOnHull != convexHull[0]);\n\n return convexHull;\n }\n\n // Returns true, if p is left of the line defined by a and b.\n private bool IsLeftOf(Vector a, Vector b, Vector p) => (b.x - a.x) * (p.y - a.y) > (p.x - a.x) * (b.y - a.y);\n }\n}\n\nProgram.cs\n// submitted by Julian Schacher (jspp) with great help by gustorn\nusing System;\nusing System.Collections.Generic;\n\nnamespace JarvisMarch\n{\n class Program\n {\n static void Main(string[] args)\n {\n System.Console.WriteLine(\"JarvisMarch\");\n // Example list of points.\n // The points are represented by vectors here, but that doesn't really matter.\n var points = new List()\n {\n new Vector(-5, 2),\n new Vector(5, 7),\n new Vector(-6, -12),\n new Vector(-14, -14),\n new Vector(9, 9),\n new Vector(-1, -1),\n new Vector(-10, 11),\n new Vector(-6, 15),\n new Vector(-6, -8),\n new Vector(15, -9),\n new Vector(7, -7),\n new Vector(-2, -9),\n new Vector(6, -5),\n new Vector(0, 14),\n new Vector(2, 8),\n };\n var jarvisMarch = new JarvisMarch();\n var giftWrap = jarvisMarch.Run(points);\n\n // Print the points of the gift wrap.\n foreach (var point in giftWrap)\n System.Console.WriteLine($\"{point.x}, {point.y}\");\n }\n }\n}\n\nstruct Pos\n x::Float64\n y::Float64\nend\n\nfunction jarvis_cross(point1::Pos, point2::Pos, point3::Pos)\n vec1 = Pos(point2.x - point1.x, point2.y - point1.y)\n vec2 = Pos(point3.x - point2.x, point3.y - point2.y)\n ret_cross = vec1.x*vec2.y - vec1.y*vec2.x\n return ret_cross*ret_cross\nend\n\nfunction jarvis_march(points::Vector{Pos})\n hull = Vector{Pos}()\n\n # sorting array based on leftmost point\n sort!(points, by = item -> item.x)\n push!(hull, points[1])\n\n i = 1\n curr_point = points[2]\n\n # Find cross product between points\n curr_product = jarvis_cross(Pos(0,0), hull[1], curr_point)\n while (curr_point != hull[1])\n for point in points\n product = 0.0\n if (i == 1)\n if (hull[i] != point)\n product = jarvis_cross(Pos(0,0), hull[i], point)\n end\n else\n if (hull[i] != point && hull[i-1] != point)\n product = jarvis_cross(hull[i-1], hull[i], point)\n end\n end\n if (product > curr_product)\n curr_point = point\n curr_product = product\n end\n end\n push!(hull, curr_point)\n curr_product = 0\n i += 1\n end\n\n return hull\nend\n\nfunction main()\n\n points = [Pos(2,1.5), Pos(1, 1), Pos(2, 4), Pos(3, 1)]\n hull = jarvis_march(points)\n println(hull)\nend\n\nmain()\n\nimport Data.List (sort, maximumBy)\nimport Data.Function (on)\n\ntype Point = (Double, Double)\n\nangle :: Point -> Point -> Point -> Double\nangle a@(xa, ya) b@(xb, yb) c@(xc, yc)\n | a==b || c==b = 0\n | theta [Point]\njarvisMarch [] = []\njarvisMarch pts = p0 : wrap (x, y-1) p0\n where p0@(x, y)= minimum pts\n wrap p1 p2\n | pm == p0 = []\n | otherwise = pm : wrap p2 pm\n where pm = maximumBy (compare `on` angle p1 p2) pts\n\nmain = do\n let pts = filter (\\(x,y) -> x^2+y^2\n#include \n#include \n#include \n\nstruct point {\n double x,y;\n};\n\nstruct point left_most_point(struct point *points, size_t num_points) {\n struct point ret = points[0];\n\n for (size_t i = 0; i 0.0) {\n end_point = points[j];\n }\n }\n\n i++;\n hull_point = end_point;\n } while (!equal(end_point, hull_points[0]));\n\n return i;\n}\n\nint main() {\n struct point points[] = {\n { -5.0, 2.0 },\n { 5.0, 7.0 },\n { -6.0, -12.0 },\n { -14.0, -14.0 },\n { 9.0, 9.0 },\n { -1.0, -1.0 },\n { -10.0, 11.0 },\n { -6.0, 15.0 },\n { -6.0, -8.0 },\n { 15.0, -9.0 },\n { 7.0, -7.0 },\n { -2.0, -9.0 },\n { 6.0, -5.0 },\n { 0.0, 14.0 },\n { 2.0, 8.0 }\n };\n struct point hull_points[15];\n\n size_t num_hull_points = jarvis_march(points, hull_points, 15);\n\n printf(\"The Hull points are:\\n\");\n for (size_t i = 0; i \nfunction jarvisMarch(points) {\n const hull = [];\n\n let pointOnHull = points.reduce((leftmost, current) => leftmost.x (p.x - a.x) * (b.y - a.y);\n}\n\nconst points = [\n { x: -5, y: 2 },\n { x: 5, y: 7 },\n { x: -6, y: -12 },\n { x: -14, y: -14 },\n { x: 9, y: 9 },\n { x: -1, y: -1 },\n { x: -10, y: 11 },\n { x: -6, y: 15 },\n { x: -6, y: -8 },\n { x: 15, y: -9 },\n { x: 7, y: -7 },\n { x: -2, y: -9 },\n { x: 6, y: -5 },\n { x: 0, y: 14 },\n { x: 2, y: 8 }\n];\n\nconst convexHull = jarvisMarch(points);\nconvexHull.forEach(p => console.log(`(${p.x}, ${p.y})`));\n\n# Is the turn counter clockwise?\ndef ccw(p1, p2, p3):\n return (p3[1] - p1[1]) * (p2[0] - p1[0]) \\\n >= (p2[1] - p1[1]) * (p3[0] - p1[0])\n\n\ndef jarvis_march(gift):\n n = len(gift) # Number of points in list\n point_on_hull = min(gift) # leftmost point in gift\n hull = [point_on_hull] # leftmost point guaranteed to be in hull\n\n while True:\n # Candidate for next point in hull\n endpoint = gift[0]\n for j in range(1, n):\n if endpoint == point_on_hull \\\n or not ccw(gift[j], hull[-1], endpoint):\n endpoint = gift[j]\n\n point_on_hull = endpoint\n\n # Check if we have completely wrapped gift\n if hull[0] == endpoint:\n break\n else:\n hull.append(point_on_hull)\n\n return hull\n\n\ndef main():\n test_gift = [\n (-5, 2), (5, 7), (-6, -12), (-14, -14), (9, 9),\n (-1, -1), (-10, 11), (-6, 15), (-6, -8), (15, -9),\n (7, -7), (-2, -9), (6, -5), (0, 14), (2, 8)\n ]\n hull = jarvis_march(test_gift)\n\n print(\"The points in the hull are:\")\n for point in hull:\n print(point)\n\n\nif __name__ == \"__main__\":\n main()\n\n#include \n#include \n#include \n\nstruct Point\n{\n double x, y;\n\n bool operator==(const Point& b) const\n {\n return x == b.x && y == b.y;\n }\n\n bool operator!=(const Point& b) const\n {\n return !(*this == b);\n }\n};\n\nstd::vector jarvis_march(const std::vector& points)\n{\n std::vector hull_points;\n\n if(points.empty())\n return hull_points;\n\n // Left most point\n auto first_point_it = std::min_element(points.begin(), points.end(), [](const Point& a, const Point& b){ return a.x (p3.x - p1.x) * (p2.y - p1.y);\n }\n );\n }\n while(*next_point_it != *first_point_it);\n\n return hull_points;\n}\n\nint main() {\n std::vector points = {\n { -5.0, 2.0 },\n { 5.0, 7.0 },\n { -6.0, -12.0 },\n { -14.0, -14.0 },\n { 9.0, 9.0 },\n { -1.0, -1.0 },\n { -10.0, 11.0 },\n { -6.0, 15.0 },\n { -6.0, -8.0 },\n { 15.0, -9.0 },\n { 7.0, -7.0 },\n { -2.0, -9.0 },\n { 6.0, -5.0 },\n { 0.0, 14.0 },\n { 2.0, 8.0 }\n };\n\n auto hull_points = jarvis_march(points);\n\n std::cout \n;;;; Jarvis March implementation\n\n(defstruct (point (:constructor make-point (x y))) x y)\n\n(defun is-left-p (p1 p2 p3)\n \"Checks if the point p3 is to the left of the line p1 -> p2\"\n (>\n (*\n (- (point-y p3) (point-y p1))\n (- (point-x p2) (point-x p1)))\n (*\n (- (point-y p2) (point-y p1))\n (- (point-x p3) (point-x p1)))))\n\n(defun next-point-on-hull (p1 p2 gift)\n \"Finds the next point on the convex hull of a gift\"\n (if (null gift)\n p2\n (if (is-left-p p1 p2 (first gift))\n (next-point-on-hull p1 (first gift) (rest gift))\n (next-point-on-hull p1 p2 (rest gift)))))\n\n(defun leftmost-point (gift)\n \"Returns the lefmost point of a gift\"\n (reduce \n (lambda (p1 p2)\n (if (\nimport java.util.*;\n\npublic class JarvisMarch {\n\n static class Point {\n private double x;\n private double y;\n\n public Point(double a, double b) {\n x = a;\n y = b;\n }\n\n public double getX() {\n return x;\n }\n public double getY() {\n return y;\n }\n\n public boolean equals(Point p) {\n if (p.getX() == x && p.getY() == y) {\n return true;\n } else {\n return false;\n }\n }\n public double magnitude() {\n return Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2));\n }\n }\n\n //find the angle by creating two vectors and then using a property of dot products\n private static double angle(Point a, Point b, Point c) {\n Point ab = new Point(b.getX() - a.getX(), b.getY() - a.getY());\n Point bc = new Point(c.getX() - b.getX(), c.getY() - b.getY());\n return Math.acos(-1 * ((ab.getX() * bc.getX()) + (ab.getY() * bc.getY())) /\n (ab.magnitude() * bc.magnitude()));\n }\n\n public static ArrayList jarvisMarch(ArrayList arr) {\n ArrayList hull = new ArrayList();\n Point pointOnHull = new Point(Double.MAX_VALUE, 0);\n\n //find leftmost point\n for (Point p: arr) {\n if (p.getX() angle(endpoint, pointOnHull, ref)) { //found a point that makes a greater angle\n endpoint = p;\n }\n }\n pointOnHull = endpoint;\n if (pointOnHull.equals(hull.get(0))) { //add next point to hull if not equal to the leftmost point\n break;\n } else {\n hull.add(pointOnHull);\n }\n }\n return hull;\n }\n\n public static void main(String[] args) {\n\n //test array setup\n ArrayList gift = new ArrayList();\n gift.add(new Point(-5, 2));\n gift.add(new Point(5, 7));\n gift.add(new Point(-6, -12));\n gift.add(new Point(-14, -14));\n gift.add(new Point(9, 9));\n gift.add(new Point(-1, -1));\n gift.add(new Point(-10, 11));\n gift.add(new Point(-6, 15));\n gift.add(new Point(-6, -8));\n gift.add(new Point(15, -9));\n gift.add(new Point(7, -7));\n gift.add(new Point(-2, -9));\n gift.add(new Point(6, -5));\n gift.add(new Point(0, 14));\n gift.add(new Point(2, 8));\n\n //print initial array of points\n System.out.println(\"Gift:\");\n for (Point p: gift) {\n System.out.println(\"[\" + p.getX() + \", \" + p.getY() + \"]\");\n }\n\n //find and print the array of points in the hull\n ArrayList hull = jarvisMarch(gift);\n System.out.println(\"Wrapping:\");\n for (Point p: hull) {\n System.out.println(\"[\" + p.getX() + \", \" + p.getY() + \"]\");\n }\n }\n\n}\n\npackage main\n\nimport (\n \"fmt\"\n)\n\ntype point struct {\n x, y float64\n}\n\nfunc leftMostPoint(points []point) point {\n ret := points[0]\n\n for _, p := range points {\n if (p.x = (p2.y-p1.y)*(p3.x-p1.x)\n}\n\nfunc jarvisMarch(points []point) []point {\n hullPoints := make([]point, 0)\n hullPoint := leftMostPoint(points)\n hullPoints = append(hullPoints, hullPoint)\n\n for {\n endPoint := points[0]\n\n for _, p := range points[1:] {\n if endPoint.equal(hullPoint) || !counterClockWise(p, hullPoints[len(hullPoints)-1], endPoint) {\n endPoint = p\n }\n }\n\n hullPoint = endPoint\n\n if endPoint.equal(hullPoints[0]) {\n break\n }\n\n hullPoints = append(hullPoints, hullPoint)\n }\n return hullPoints\n}\n\nfunc main() {\n points := []point{{-5, 2}, {5, 7}, {-6, -12}, {-14, -14}, {9, 9},\n {-1, -1}, {-10, 11}, {-6, 15}, {-6, -8}, {15, -9},\n {7, -7}, {-2, -9}, {6, -5}, {0, 14}, {2, 8},\n }\n\n hullPoints := jarvisMarch(points)\n fmt.Println(\"The hull points are:\")\n\n for _, p := range hullPoints {\n fmt.Printf(\"x=%f y=%f\\n\", p.x, p.y)\n }\n}\n\nstruct Point {\n x int\n y int\n}\n\nfn left_most_point(points []Point) Point {\n mut ret := points[0]\n\n for p in points {\n if (p.x = (p2.y-p1.y) * (p3.x-p1.x)\n}\n\nfn jarvis_march(points []Point) []Point {\n mut hull_point := left_most_point(points)\n mut hull_points := [hull_point]\n\n\n for {\n mut end_point := points[0]\n\n for i := 1; i \n\ntype Point = (i64, i64);\n\n// Is the turn counter clockwise?\nfn turn_counter_clockwise(p1: Point, p2: Point, p3: Point) -> bool {\n (p3.1 - p1.1) * (p2.0 - p1.0) >= (p2.1 - p1.1) * (p3.0 - p1.0)\n}\n\nfn jarvis_march(gift: &[Point]) -> Option> {\n // There can only be a convex hull if there are more than 2 points\n if gift.len() \ndata point(x=0, y=0):\n def __str__(self):\n return f'({self.x}, {self.y})'\n\n# Is the turn counter-clockwise?\ndef counter_clockwise(p1 is point, p2 is point, p3 is point) =\n (p3.y - p1.y) * (p2.x - p1.x) >= (p2.y - p1.y) * (p3.x - p1.x)\n\n\ndef jarvis_march(gift: point[]) -> point[]:\n point_on_hull = min(gift) # The leftmost point in the gift\n hull = [point_on_hull] # It is guaranteed it will be on the hull.\n\n while True:\n # Candidate for the next point in the hull\n endpoint = gift[0]\n for p in gift:\n if (endpoint == point_on_hull\n or not counter_clockwise(p, hull[-1], endpoint)):\n endpoint = p\n\n point_on_hull = endpoint\n\n # Check if the gift is completely covered.\n if hull[0] == endpoint:\n return hull\n hull.append(point_on_hull)\n\n\nif __name__ == '__main__':\n test_gift = [\n (-5, 2), (5, 7), (-6, -12), (-14, -14), (9, 9),\n (-1, -1), (-10, 11), (-6, 15), (-6, -8), (15, -9),\n (7, -7), (-2, -9), (6, -5), (0, 14), (2, 8)\n ] |> map$(t -> point(*t)) |> list\n hull = jarvis_march(test_gift)\n\n print(\"[#] The points in the hull are:\")\n for point in hull:\n print(point)\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/graham_scan/graham_scan.html":{"url":"contents/graham_scan/graham_scan.html","title":"Graham Scan","keywords":"","body":"Graham Scan\nAt around the same time of the Jarvis March, R. L. Graham was also developing an algorithm to find the convex hull of a random set of points [1].\nUnlike the Jarvis March, which is an \\mathcal{O}(nh) operation, the Graham Scan is \\mathcal{O}(n\\log(n)), where n is the number of points and h is the size for the hull.\nThis means that the complexity of the Graham Scan is not output-sensitive; moreover, there are some cases where the Jarvis March is more optimal, depending on the size of the hull and the number of points to wrap.\nRather than starting at the leftmost point like the Jarvis March, the Graham scan starts at the bottom.\nWe then sort the distribution of points based on the angle between the bottom-most point, the origin, and each other point.\nAfter sorting, we go through point-by-point, searching for points that are on the convex hull and throwing out any other points.\nWe do this by looking for counter-clockwise rotations.\nIf an angle between three points turns inward, the shape is obviously not convex, so we can throw that result out.\nWe can find whether a rotation is counter-clockwise with trigonometric functions or by using a cross-product, like so:\nfunction ccw(a::Point, b::Point, c::Point)\n return ((b.x - a.x)*(c.y - a.y) - (b.y - a.y)*(c.x - a.x))\nend\n\nccw :: Point -> Point -> Point -> Double\nccw (xa, ya) (xb, yb) (xc, yc) = (xb - xa) * (yc - ya) - (yb - ya) * (xc - xa)\n\ndouble ccw(struct point a, struct point b, struct point c) {\n return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);\n}\n\nfunction ccw(a, b, c) {\n return (b.x - a.x) * (c.y - a.y) - (c.x - a.x) * (b.y - a.y);\n}\n\ndef counter_clockwise(p1, p2, p3):\n \"\"\"Is the turn counter-clockwise?\"\"\"\n return (p3[1] - p1[1]) * (p2[0] - p1[0]) >= (p2[1] - p1[1]) * (p3[0] - p1[0])\n\nfunc counterClockwise(p1, p2, p3 point) bool {\n return (p3.y-p1.y)*(p2.x-p1.x) >= (p2.y-p1.y)*(p3.x-p1.x)\n}\n\nstatic double ccw(Point a, Point b, Point c) {\n return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);\n}\n\n(defun ccw (p1 p2 p3)\n \"Determines if a turn between three points is counterclockwise\"\n (-\n (*\n (- (point-y p2) (point-y p1))\n (- (point-x p3) (point-x p1)))\n (*\n (- (point-y p3) (point-y p1))\n (- (point-x p2) (point-x p1)))))\n\ndouble ccw(const point& a, const point& b, const point& c) {\n return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);\n}\n\ndata point(x=0, y=0):\n def angle(self, other):\n \"\"\"Computes the angle between the two points\"\"\"\n match point(x1, y1) in other:\n return atan2(y1 - self.y, x1 - self.x)\n\nfn counter_clockwise(a: &Point, b: &Point, c: &Point) -> f64 {\n (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x)\n}\n\n\n\nIf the output of this function is 0, the points are collinear.\nIf the output is positive, then the points form a counter-clockwise \"left\" turn.\nIf the output is negative, then the points form a clockwise \"right\" turn.\nWe basically do not want clockwise rotations, because this means we are at an interior angle.\n\nTo save memory and expensive append() operations, we ultimately look for points that should be on the hull and swap them with the first elements in the array.\nIf there are M elements on the hull, then the first M elements in our output random distribution of points will be the hull.\nIn the end, the code should look something like this:\nfunction graham_scan!(points::Vector{Point})\n N = length(points)\n\n # Place the lowest point at the start of the array\n sort!(points, by = item -> item.y)\n\n # Sort all other points according to angle with that point\n other_points = sort(points[2:end], by = item -> atan(item.y - points[1].y,\n item.x - points[1].x))\n\n # Place points sorted by angle back into points vector\n for i in 1:length(other_points)\n points[i+1] = other_points[i]\n end\n\n # M will be the point on the hull\n M = 2\n for i = 1:N\n while (ccw(points[M-1], points[M], points[i]) 2)\n M -= 1\n # All points are collinear\n elseif (i == N)\n break\n else\n i += 1\n end\n end\n\n # ccw point found, updating hull and swapping points\n M += 1\n points[i], points[M] = points[M], points[i]\n end\n\n return points[1:M]\nend\n\ngrahamScan :: [Point] -> [Point]\ngrahamScan [] = []\ngrahamScan pts = wrap sortedPts [p0]\n where p0@(x, y)= minimumBy (compare `on` snd) pts\n sortedPts = sortOn (\\(px, py) -> atan2 (py-y) (px-x) ) $ filter (/=p0) pts\n wrap [] ps = ps\n wrap (s:ss) [p] = wrap ss [s, p]\n wrap (s:ss) (p1:p2:ps)\n | ccw s p1 p2 > 0 = wrap (s:ss) (p2:ps)\n | otherwise = wrap ss (s:p1:p2:ps)\n\nsize_t graham_scan(struct point *points, size_t size) {\n qsort(points, size, sizeof(struct point), cmp_points);\n polar_angles_sort(points, points[0], size);\n\n struct point tmp_points[size + 1];\n memcpy(tmp_points + 1, points, size * sizeof(struct point));\n tmp_points[0] = tmp_points[size];\n\n size_t m = 1;\n for (size_t i = 2; i 1) {\n m--;\n continue;\n } else if (i == size) {\n break;\n } else {\n i++;\n }\n }\n\n m++;\n struct point tmp = tmp_points[i];\n tmp_points[i] = tmp_points[m];\n tmp_points[m] = tmp;\n }\n\n memcpy(points, tmp_points + 1, size * sizeof(struct point));\n\n return m;\n}\n\nfunction grahamScan(points) {\n // First, sort the points so the one with the lowest y-coordinate comes first (the pivot)\n points = [...points].sort((a, b) => (a.y - b.y));\n const pivot = points[0];\n\n // Then sort all remaining points based on the angle between the pivot and itself\n const hull = points.slice(1).sort((a, b) => polarAngle(a, pivot) - polarAngle(b, pivot));\n\n // The pivot is always on the hull\n hull.unshift(pivot);\n\n let n = hull.length;\n let m = 1;\n for (let i = 2; i 1) {\n m -= 1;\n } else if (m === i) {\n break;\n } else {\n i += 1;\n }\n }\n\n m += 1;\n [hull[i], hull[m]] = [hull[m], hull[i]];\n }\n\n return hull.slice(0, m + 1);\n}\n\ndef graham_scan(gift):\n gift = list(set(gift)) # Remove duplicate points\n start = min(gift, key=lambda p: (p[1], p[0])) # Must be in hull\n gift.remove(start)\n\n s = sorted(gift, key=lambda point: polar_angle(start, point))\n hull = [start, s[0], s[1]]\n\n # Remove points from hull that make the hull concave\n for pt in s[2:]:\n while not counter_clockwise(hull[-2], hull[-1], pt):\n del hull[-1]\n hull.append(pt)\n\n return hull\n\nfunc grahamScan(points []point) []point {\n sort.Slice(points, func(a, b int) bool {\n return points[a].y \nstatic List grahamScan(List gift) {\n gift = gift.stream()\n .distinct()\n .sorted(Comparator.comparingDouble(point -> -point.y))\n .collect(Collectors.toList());\n\n Point pivot = gift.get(0);\n\n // Sort the remaining Points based on the angle between the pivot and itself\n List hull = gift.subList(1, gift.size());\n hull.sort(Comparator.comparingDouble(point -> polarAngle(point, pivot)));\n\n // The pivot is always on the hull\n hull.add(0, pivot);\n\n int n = hull.size();\n int m = 1;\n\n for (int i = 2; i 1) {\n m--;\n } else if (m == 1) {\n break;\n } else {\n i++;\n }\n }\n m++;\n\n Point temp = hull.get(i);\n hull.set(i, hull.get(m));\n hull.set(m, temp);\n }\n return hull.subList(0, m + 1);\n}\n\n(defun atan2 (y x)\n \"Calculates the angle of a point in the euclidean plane in radians\"\n (cond\n ((> x 0) (atan y x))\n ((and (= y 0)) (+ (atan y x) pi))\n ((and ( y 0)) (/ pi 2))\n ((and (eql x 0) ( (length gift) 0)'.\n (if gift\n (labels ((wrap (sorted-points hull)\n (if sorted-points\n ;; This covers the case where the hull has one or more element.\n ;; We aren't concerned about the hull being empty, because then the gift must\n ;; also be empty and this function is never given an empty gift.\n (if (rest hull)\n (if (\nstd::vector graham_scan(std::vector& points) {\n // selecting lowest point as pivot\n size_t low_index = 0;\n for (size_t i = 1; i 1) {\n m--;\n continue;\n } else if (i == points.size()) {\n break;\n } else {\n i++;\n }\n }\n m++;\n std::swap(points[i], points[m]);\n }\n return std::vector(points.begin(), points.begin() + m + 1);\n}\n\ndef graham_scan(gift):\n gift = list(set(gift)) # Remove the duplicate points if any.\n start = min(gift, key=(p -> (p.x, p.y)))\n gift.remove(start)\n\n s = sorted(gift, key=(point -> start.angle(point)))\n hull = [start, s[0], s[1]]\n\n # Remove the hull points that make the hull concave\n for point in s[2:]:\n while not counter_clockwise(hull[-2], hull[-1], point):\n del hull[-1]\n hull.append(point)\n return hull\n\nfn graham_scan(mut points: Vec) -> Vec {\n if points.is_empty() {\n return Vec::new();\n }\n\n // Unwrap is safe because length is > 0\n let start = *points.iter().min().unwrap();\n points.retain(|a| a != &start);\n points.sort_unstable_by(|a, b| polar_angle(&start, a).partial_cmp(&polar_angle(&start, b)).unwrap());\n\n let mut hull: Vec = vec![start, points[0], points[1]];\n\n for pt in points[2..points.len()].iter() {\n while counter_clockwise(&hull[hull.len() - 2], &hull[hull.len() - 1], pt) \n\n\nBibliography\n1.Graham, Ronald L, An efficient algorithm for determining the convex hull of a finite planar set, Elsevier, 1972.\nExample Code\nstruct Point\n x::Float64\n y::Float64\nend\n\nfunction ccw(a::Point, b::Point, c::Point)\n return ((b.x - a.x)*(c.y - a.y) - (b.y - a.y)*(c.x - a.x))\nend\n\nfunction graham_scan!(points::Vector{Point})\n N = length(points)\n\n # Place the lowest point at the start of the array\n sort!(points, by = item -> item.y)\n\n # Sort all other points according to angle with that point\n other_points = sort(points[2:end], by = item -> atan(item.y - points[1].y,\n item.x - points[1].x))\n\n # Place points sorted by angle back into points vector\n for i in 1:length(other_points)\n points[i+1] = other_points[i]\n end\n\n # M will be the point on the hull\n M = 2\n for i = 1:N\n while (ccw(points[M-1], points[M], points[i]) 2)\n M -= 1\n # All points are collinear\n elseif (i == N)\n break\n else\n i += 1\n end\n end\n\n # ccw point found, updating hull and swapping points\n M += 1\n points[i], points[M] = points[M], points[i]\n end\n\n return points[1:M]\nend\n\nfunction main()\n # This hull is just a simple test so we know what the output should be\n points = [\n Point(-5,2), Point(5,7), Point(-6,-12), Point(-14,-14), Point(9,9),\n Point(-1,-1), Point(-10,11), Point(-6,15), Point(-6,-8), Point(15,-9),\n Point(7,-7), Point(-2,-9), Point(6,-5), Point(0,14), Point(2,8)\n ]\n hull = graham_scan!(points)\n println(hull)\nend\n\nmain()\n\nimport Data.List (sortOn, minimumBy)\nimport Data.Function (on)\n\ntype Point = (Double, Double)\n\nccw :: Point -> Point -> Point -> Double\nccw (xa, ya) (xb, yb) (xc, yc) = (xb - xa) * (yc - ya) - (yb - ya) * (xc - xa)\n\ngrahamScan :: [Point] -> [Point]\ngrahamScan [] = []\ngrahamScan pts = wrap sortedPts [p0]\n where p0@(x, y)= minimumBy (compare `on` snd) pts\n sortedPts = sortOn (\\(px, py) -> atan2 (py-y) (px-x) ) $ filter (/=p0) pts\n wrap [] ps = ps\n wrap (s:ss) [p] = wrap ss [s, p]\n wrap (s:ss) (p1:p2:ps)\n | ccw s p1 p2 > 0 = wrap (s:ss) (p2:ps)\n | otherwise = wrap ss (s:p1:p2:ps)\n\nmain = do\n -- We build the set of points of integer coordinates within a circle of radius 5\n let pts = [(x,y) | x\n#include \n#include \n#include \n#include \n#include \n\nstruct point {\n double x, y;\n};\n\nint cmp_points(const void *a, const void *b) {\n struct point* pa = (struct point*) a;\n struct point* pb = (struct point*) b;\n\n if (pa->y > pb->y) {\n return 1;\n } else if (pa->y y) {\n return -1;\n } else {\n return 0;\n }\n}\n\ndouble ccw(struct point a, struct point b, struct point c) {\n return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);\n}\n\ndouble polar_angle(struct point origin, struct point p) {\n return atan2(p.y - origin.y, p.x - origin.x);\n}\n\nvoid polar_angles_sort(struct point *points, struct point origin, size_t size) {\n if (size pivot_angle) {\n j--;\n }\n\n if (i >= j) {\n break;\n }\n\n struct point tmp = points[i];\n points[i] = points[j];\n points[j] = tmp;\n\n i++;\n j--;\n }\n\n polar_angles_sort(points, origin, i);\n polar_angles_sort(points + i, origin, size - i);\n}\n\nsize_t graham_scan(struct point *points, size_t size) {\n qsort(points, size, sizeof(struct point), cmp_points);\n polar_angles_sort(points, points[0], size);\n\n struct point tmp_points[size + 1];\n memcpy(tmp_points + 1, points, size * sizeof(struct point));\n tmp_points[0] = tmp_points[size];\n\n size_t m = 1;\n for (size_t i = 2; i 1) {\n m--;\n continue;\n } else if (i == size) {\n break;\n } else {\n i++;\n }\n }\n\n m++;\n struct point tmp = tmp_points[i];\n tmp_points[i] = tmp_points[m];\n tmp_points[m] = tmp;\n }\n\n memcpy(points, tmp_points + 1, size * sizeof(struct point));\n\n return m;\n}\n\nint main() {\n struct point points[] = {{-5, 2}, {5, 7}, {-6, -12}, {-14, -14}, {9, 9},\n {-1, -1}, {-10, 11}, {-6, 15}, {-6, -8}, {15, -9},\n {7, -7}, {-2, -9}, {6, -5}, {0, 14}, {2, 8}};\n size_t num_initial_points = 15;\n\n printf(\"Points:\\n\");\n for (size_t i = 0; i \nfunction grahamScan(points) {\n // First, sort the points so the one with the lowest y-coordinate comes first (the pivot)\n points = [...points].sort((a, b) => (a.y - b.y));\n const pivot = points[0];\n\n // Then sort all remaining points based on the angle between the pivot and itself\n const hull = points.slice(1).sort((a, b) => polarAngle(a, pivot) - polarAngle(b, pivot));\n\n // The pivot is always on the hull\n hull.unshift(pivot);\n\n let n = hull.length;\n let m = 1;\n for (let i = 2; i 1) {\n m -= 1;\n } else if (m === i) {\n break;\n } else {\n i += 1;\n }\n }\n\n m += 1;\n [hull[i], hull[m]] = [hull[m], hull[i]];\n }\n\n return hull.slice(0, m + 1);\n}\n\nfunction polarAngle(a, b) {\n return Math.atan2(a.y - b.y, a.x - b.x);\n}\n\nfunction ccw(a, b, c) {\n return (b.x - a.x) * (c.y - a.y) - (c.x - a.x) * (b.y - a.y);\n}\n\nconst points = [\n { x: -5, y: 2 },\n { x: 5, y: 7 },\n { x: -6, y: -12 },\n { x: -14, y: -14 },\n { x: 9, y: 9 },\n { x: -1, y: -1 },\n { x: -10, y: 11 },\n { x: -6, y: 15 },\n { x: -6, y: -8 },\n { x: 15, y: -9 },\n { x: 7, y: -7 },\n { x: -2, y: -9 },\n { x: 6, y: -5 },\n { x: 0, y: 14 },\n { x: 2, y: 8 },\n];\n\nconst convexHull = grahamScan(points);\nconsole.log(\"The points in the hull are:\");\nconvexHull.forEach(p => console.log(`(${p.x}, ${p.y})`));\n\nfrom math import atan2\n\n\ndef counter_clockwise(p1, p2, p3):\n \"\"\"Is the turn counter-clockwise?\"\"\"\n return (p3[1] - p1[1]) * (p2[0] - p1[0]) >= (p2[1] - p1[1]) * (p3[0] - p1[0])\n\n\ndef polar_angle(ref, point):\n \"\"\"Find the polar angle of a point relative to a reference point\"\"\"\n return atan2(point[1] - ref[1], point[0] - ref[0])\n\n\ndef graham_scan(gift):\n gift = list(set(gift)) # Remove duplicate points\n start = min(gift, key=lambda p: (p[1], p[0])) # Must be in hull\n gift.remove(start)\n\n s = sorted(gift, key=lambda point: polar_angle(start, point))\n hull = [start, s[0], s[1]]\n\n # Remove points from hull that make the hull concave\n for pt in s[2:]:\n while not counter_clockwise(hull[-2], hull[-1], pt):\n del hull[-1]\n hull.append(pt)\n\n return hull\n\n\ndef main():\n test_gift = [\n (-5, 2),\n (5, 7),\n (-6, -12),\n (-14, -14),\n (9, 9),\n (-1, -1),\n (-10, 11),\n (-6, 15),\n (-6, -8),\n (15, -9),\n (7, -7),\n (-2, -9),\n (6, -5),\n (0, 14),\n (2, 8),\n ]\n hull = graham_scan(test_gift)\n\n print(\"The points in the hull are:\")\n for point in hull:\n print(point)\n\n\nmain()\n\npackage main\n\nimport (\n \"fmt\"\n \"math\"\n \"sort\"\n)\n\ntype point struct {\n x, y int\n}\n\nfunc counterClockwise(p1, p2, p3 point) bool {\n return (p3.y-p1.y)*(p2.x-p1.x) >= (p2.y-p1.y)*(p3.x-p1.x)\n}\n\nfunc polarAngle(ref, point point) float64 {\n return math.Atan2(float64(point.y-ref.y), float64(point.x-ref.x))\n}\n\nfunc grahamScan(points []point) []point {\n sort.Slice(points, func(a, b int) bool {\n return points[a].y \nimport java.util.ArrayList;\nimport java.util.Comparator;\nimport java.util.List;\nimport java.util.stream.Collectors;\n\npublic class GrahamScan {\n\n static class Point {\n public double x;\n public double y;\n\n public Point(double x, double y) {\n this.x = x;\n this.y = y;\n }\n\n @Override\n public boolean equals(Object o) {\n if (o == null) return false;\n if (o == this) return true;\n if (!(o instanceof Point)) return false;\n Point p = (Point)o;\n return p.x == this.x && p.y == this.y;\n }\n }\n\n static double ccw(Point a, Point b, Point c) {\n return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);\n }\n\n static double polarAngle(Point origin, Point p) {\n return Math.atan2(p.y - origin.y, p.x - origin.x);\n }\n\n static List grahamScan(List gift) {\n gift = gift.stream()\n .distinct()\n .sorted(Comparator.comparingDouble(point -> -point.y))\n .collect(Collectors.toList());\n\n Point pivot = gift.get(0);\n\n // Sort the remaining Points based on the angle between the pivot and itself\n List hull = gift.subList(1, gift.size());\n hull.sort(Comparator.comparingDouble(point -> polarAngle(point, pivot)));\n\n // The pivot is always on the hull\n hull.add(0, pivot);\n\n int n = hull.size();\n int m = 1;\n\n for (int i = 2; i 1) {\n m--;\n } else if (m == 1) {\n break;\n } else {\n i++;\n }\n }\n m++;\n\n Point temp = hull.get(i);\n hull.set(i, hull.get(m));\n hull.set(m, temp);\n }\n return hull.subList(0, m + 1);\n }\n\n public static void main(String[] args) {\n ArrayList points = new ArrayList<>();\n\n points.add(new Point(-5, 2));\n points.add(new Point(5, 7));\n points.add(new Point(-6, -12));\n points.add(new Point(-14, -14));\n points.add(new Point(9, 9));\n points.add(new Point(-1, -1));\n points.add(new Point(-10, 11));\n points.add(new Point(-6, 15));\n points.add(new Point(-6, -8));\n points.add(new Point(15, -9));\n points.add(new Point(7, -7));\n points.add(new Point(-2, -9));\n points.add(new Point(6, -5));\n points.add(new Point(0, 14));\n points.add(new Point(2, 8));\n\n List convexHull = grahamScan(points);\n\n convexHull.forEach(p -> System.out.printf(\"% 1.0f, % 1.0f\\n\", p.x, p.y));\n }\n}\n\n;;;; Graham scan implementation in Common Lisp\n\n(defstruct (point (:constructor make-point (x y))) x y)\n\n(defun ccw (p1 p2 p3)\n \"Determines if a turn between three points is counterclockwise\"\n (-\n (*\n (- (point-y p2) (point-y p1))\n (- (point-x p3) (point-x p1)))\n (*\n (- (point-y p3) (point-y p1))\n (- (point-x p2) (point-x p1)))))\n\n(defun atan2 (y x)\n \"Calculates the angle of a point in the euclidean plane in radians\"\n (cond\n ((> x 0) (atan y x))\n ((and (= y 0)) (+ (atan y x) pi))\n ((and ( y 0)) (/ pi 2))\n ((and (eql x 0) ( (length gift) 0)'.\n (if gift\n (labels ((wrap (sorted-points hull)\n (if sorted-points\n ;; This covers the case where the hull has one or more element.\n ;; We aren't concerned about the hull being empty, because then the gift must\n ;; also be empty and this function is never given an empty gift.\n (if (rest hull)\n (if (\n#include \n#include \n#include \n#include \n\nstruct point {\n double x;\n double y;\n};\n\nstd::ostream& operator& points) {\n for (auto p : points) {\n os graham_scan(std::vector& points) {\n // selecting lowest point as pivot\n size_t low_index = 0;\n for (size_t i = 1; i 1) {\n m--;\n continue;\n } else if (i == points.size()) {\n break;\n } else {\n i++;\n }\n }\n m++;\n std::swap(points[i], points[m]);\n }\n return std::vector(points.begin(), points.begin() + m + 1);\n}\n\nint main() {\n std::vector points = {{-5, 2},\n {5, 7},\n {-6, -12},\n {-14, -14},\n {9, 9},\n {-1, -1},\n {-10, 11},\n {-6, 15},\n {-6, -8},\n {15, -9},\n {7, -7},\n {-2, -9},\n {6, -5},\n {0, 14},\n {2, 8}};\n std::cout hull = graham_scan(points);\n std::cout \nfrom math import atan2\n\n\ndata point(x=0, y=0):\n def angle(self, other):\n \"\"\"Computes the angle between the two points\"\"\"\n match point(x1, y1) in other:\n return atan2(y1 - self.y, x1 - self.x)\n def __str__(self):\n return f'({self.x}, {self.y})'\n\n# Is the turn counter-clockwise?\ndef counter_clockwise(p1, p2, p3) =\n (p3.y - p1.y) * (p2.x - p1.x) >= (p2.y - p1.y) * (p3.x - p1.x)\n\n\ndef graham_scan(gift):\n gift = list(set(gift)) # Remove the duplicate points if any.\n start = min(gift, key=(p -> (p.x, p.y)))\n gift.remove(start)\n\n s = sorted(gift, key=(point -> start.angle(point)))\n hull = [start, s[0], s[1]]\n\n # Remove the hull points that make the hull concave\n for point in s[2:]:\n while not counter_clockwise(hull[-2], hull[-1], point):\n del hull[-1]\n hull.append(point)\n return hull\n\n\nif __name__ == '__main__':\n test_gift = [\n (-5, 2),\n (5, 7),\n (-6, -12),\n (-14, -14),\n (9, 9),\n (-1, -1),\n (-10, 11),\n (-6, 15),\n (-6, -8),\n (15, -9),\n (7, -7),\n (-2, -9),\n (6, -5),\n (0, 14),\n (2, 8),\n ] |> map$(p -> point(*p)) |> list\n hull = graham_scan(test_gift)\n \"The points in the hull are:\" |> print\n \"\\n\".join(map(str, hull)) |> print\n\nuse std::cmp::Ordering;\n\n#[derive(Debug, PartialEq, Copy, Clone)]\nstruct Point {\n x: f64,\n y: f64,\n}\n\nimpl Eq for Point {}\n\nimpl PartialOrd for Point {\n fn partial_cmp(&self, other: &Self) -> Option {\n if self.y == other.y {\n self.x.partial_cmp(&other.x)\n } else {\n self.y.partial_cmp(&other.y)\n }\n }\n}\n\n// Defines an order for Points so they can be sorted\nimpl Ord for Point {\n fn cmp(&self, other: &Self) -> Ordering {\n // Neither field of Point will be NaN, so this is safe\n self.partial_cmp(other).unwrap()\n }\n}\n\n// Determines whether the angle abc is clockwise, counter-clockwise or colinear\n// result > 0 : counter-clockwise\n// result = 0 : colinear\n// result f64 {\n (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x)\n}\n\n// Calculate the polar angle of a point relative to a reference point.\nfn polar_angle(reference: &Point, point: &Point) -> f64 {\n (point.y - reference.y).atan2(point.x - reference.x)\n}\n\nfn graham_scan(mut points: Vec) -> Vec {\n if points.is_empty() {\n return Vec::new();\n }\n\n // Unwrap is safe because length is > 0\n let start = *points.iter().min().unwrap();\n points.retain(|a| a != &start);\n points.sort_unstable_by(|a, b| polar_angle(&start, a).partial_cmp(&polar_angle(&start, b)).unwrap());\n\n let mut hull: Vec = vec![start, points[0], points[1]];\n\n for pt in points[2..points.len()].iter() {\n while counter_clockwise(&hull[hull.len() - 2], &hull[hull.len() - 1], pt) \n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/data_compression/data_compression.html":{"url":"contents/data_compression/data_compression.html","title":"Data Compression","keywords":"","body":"Data Compression\nI'll be honest, data compression used to be an incredibly hot topic, but kids these days usually have incredibly powerful devices that do not seem to be memory-limited at all.\nBecause of this, it seems odd to talk about data compression as a field of intense debate and development.\nIt would naively seem that better hardware means that there are less restrictions on programmers and less of a need to search for new and unique ways to compress their data; however, this is far from the case.\nThat said, there will always be new devices on the market that require minimizing data storage.\nIn fact, some of the most revolutionary algorithms and methods in existence today fall in the category of data compression.\nFrom lossless data compression with Huffman encoding to genetic compression algorithms and machine learning, there is a lot to learn about this field, and we'll go through it piece-by-piece.\nAll that said, no discussion about data compression is complete without first discussing the information, itself -- specifically how information is represented in computer systems.\nNow, we've discussed this in some depth before with bitlogic, but there is much more to the story than what we let on before.\nLet's start with a working definition of information:\nInformation is a representation of certainty.\nThis might seem like a silly, hand-wavey definition, but hear me out.\nIf I am uncertain about something, I will ask a question.\nThe answer to this question could be any number of things, but it will contain information from an individual with some level of certainty.\nFor example, let's pretend you have been furiously coding for months in your mother's basement (it happens).\nAt some point, you realize you haven't gone outside and are completely unaware of the day, month, or even year!\nAs your mother slips food under your door one day, you reach out to her and ask, \"What's it like outside today?\"\nOverjoyed at the prospect of her child finally leaving their room, your mother might say, \"It's bright, sunny and warm. A perfect day to go outside and relax!\"\nThis provides you a lot of information, and to some degree of certainty you can conclude it is summer.\nOf course, after this interaction you do not acknowledge your mother's existence after her answer and go back to coding.\nYou have the information you need.\nNo reason to overcomplicate things with further human contact.\nSee, information is defined in a number of different places for a number of different reasons, so for our purposes, we will define the unit of information to be the bit, a simple binary 1 or 0.\nTaking the example mentioned before (assuming you can take your mother at face-value), you were provided 3 true statements:\n\nIt is bright\nIt is sunny\nIt is warm\n\nWith this information, you assumed that it was probably summer.\nUnfortunately, your assumption about it being summer is not information.\nIt might be a logical conclusion, but it was not provided as a \"fact.\"\nThis is an important distinction between what we might colloquially describe as information and what information theory requires.\nInformation theory works with measurements -- binary absolutes.\nNow, we can clearly say that with some probability it is summer, but this is a different story altogether, which we will undoubtedly discuss in the future.\nFor now, let's talk about a simple representation of information on computer systems.\nImagine you have a simple alphabet with only 2 characters in it, a and b.\nIn this case, there are plenty of ways you can represent these characters in bits, but the most obvious way might look like this:\n\n\n\nCharacter\nBit Representation\n\n\n\n\na\n0\n\n\nb\n1\n\n\n\nSo long as you don't add any new characters to the mix, this is a perfectly valid set of codewords.\nIf you get the bitstring 0111101, you can easily decode it as abbbbab.\nBut what if you wanted to add a third character, c?\nWell, it's clear that c cannot be either 0 or 1, but because of the way we have defined the set of codewords above, it actually cannot be any combination of 0 or 1 either.\nFor example, if we defined c to be 01 and we were provided the bitstring 0111101, we could interpret this string as either abbbbab or cbbbc!\nNow, we could use context or other information provided to distinguish these two possible cases, but it is clear that we need to think more deeply about our set of codewords in this case.\nFirst, let's think a bit about decoding.\nFor our purposes, we do not want to think when decoding.\nNo matter what the bitstring is that we need to decode, we want to be able to read bit-by-bit until we find a match in our set of codewords and move on.\nBasically, we do not want any ambiguity in our set of codewords.\nThe code for c should not contain the code for a or b!\nIn this way, our set of codewords should be prefix-free.\nNo word should appear as a prefix to another word.\nIf we wanted a good, prefix-free set of codewords for 4 characters (a, b, c, and d), it might look like this:\n\n\n\nCharacter\nBit Representation\n\n\n\n\na\n00\n\n\nb\n01\n\n\nc\n10\n\n\nd\n11\n\n\n\nWe can decode any even bitstring with this set.\n0100101010110100 is bacccdba.\nThis is great, but now we have another question: given a string of characters, can we construct a set of codewords that minimizes the number of bits in its corresponding bitstring?\nThis is the heart of data compression!\nFirst things first, let's define a simple measure for how compressed the data is.\nLet's take the following set of characters: abbcccdddd.\nIf we were to put all the letters in a bag and pull one out at random, we would have the following probabilities of pulling out any of the letters:\n\n\n\nCharacter\nProbability\n\n\n\n\na\n.1\n\n\nb\n.2\n\n\nc\n.3\n\n\nd\n.4\n\n\n\nThis basically means that we are far more likely to pull out a d than an a, and if we are trying to minimize the length of our encoded bitstring, the length of the bit representation for d should probably be shorter than the bit representation for a.\nUltimately, to compress our encoded bitstring, we want to minimize the following quantity:\n\nL(C(W)) = \\sum_{i=0}^{n}w_i\\times \\text{length}(c_i)\n\nWhere C is the characters of our alphabet and c_i is codeword for a single character, W is related to the probability of pulling that character out of a bag and w_i is an individual probability of getting a specific character, and L is a vague, unitless quantity to determine the overall length and is usually used to determine compression ratios.\nTo show how this works, let's consider encoding the word abbcccdddd with two different alphabets:\n\n\n\nCharacter\nProbability\nBit Representation 1\nBit Representation 2\n\n\n\n\na\n.1\n00\n000\n\n\nb\n.2\n01\n001\n\n\nc\n.3\n10\n01\n\n\nd\n.4\n11\n1\n\n\n\nIn this case:\n\n\\begin{align}\nL_1 &= 0.1\\times 2 + 0.2 \\times 2 + 0.3 \\times 2 + 0.4 \\times 2 = 2 \\\\\nL_2 &= 0.1\\times 3 + 0.2 \\times 3 + 0.3 \\times 2 + 0.4 \\times 1 = 1.9\n\\end{align}\n\nHere, it's clear that L_2 , and thus the second set of codewords compresses our data more than the first.\nThis measure can be used as a direct test of certain simple data compression techniques, notably those created by Shannon, Fano, and Huffman, which will be covered soon!\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/cryptography/cryptography.html":{"url":"contents/cryptography/cryptography.html","title":"Cryptography","keywords":"","body":"Cryptography\nHumans have almost always been interested in sending secret messages that only the sender and receiver understand.\nThe reason for this is obvious: secret messages should remain secret.\nThe easiest way for this to happen is to talk behind closed doors, but that simply doesn't work if the sender and receiver are separated by a significant distance.\nIn this case, they need to rely on a messenger or mailman to send the message.\nFor simplicity, let's assume they are sending a written letter for the purpose of negotiating war tactics in ancient Greece or Rome.\nObviously, the message can remain secret if both the sender and receiver also trust the messenger; however, what if the messenger is actually an evil spy?\nWhat if the messenger is killed and the letter is stolen?\nWhat if (in an elaborate ruse), some third party slips into the messenger's tent in the dead-of-night and replaces the letter with another one entirely different?\nThese are all important questions cryptography addresses.\nThe idea is simple: we procedurally scramble the message we are sending and only provide the unscrambling procedure to trusted parties.\nIn this way, the message would seem like utter gobbledygook to anyone other than the sender and receiver.\nIt doesn't matter if the messenger is evil.\nThey cannot read the message anyway.\nIt's also fine if the message is replaced, because then the receiver won't be able to properly decode the message and can just ask for another message to be sent (probably on another path with a different messenger).\nUnsurprisingly, a very early method of encryption was supposedly developed by Julius Caeser and called the \"Caesar Cipher\" [1].\nHere, every character in the message is replaced by another character based on some pre-defined table or chart that only the sender and receiver have.\nThe table is created by simply rotating the alphabet by n spaces, where n is chosen in a discussion between the sender and receiver before-hand.\n\n\n\nn\n0\n2\n14\n18\n21\n24\n\n\n\n\na\na\nc\no\ns\nv\ny\n\n\nb\nb\nd\np\nt\nw\nz\n\n\nc\nc\ne\nq\nu\nx\na\n\n\nd\nd\nf\nr\nv\ny\nb\n\n\ne\ne\ng\ns\nw\nz\nc\n\n\nf\nf\nh\nt\nx\na\nd\n\n\ng\ng\ni\nu\ny\nb\ne\n\n\nh\nh\nj\nv\nz\nc\nf\n\n\ni\ni\nk\nw\na\nd\ng\n\n\nj\nj\nl\nx\nb\ne\nh\n\n\nk\nk\nm\ny\nc\nf\ni\n\n\nl\nl\nn\nz\nd\ng\nj\n\n\nm\nm\no\na\ne\nh\nk\n\n\nn\nn\np\nb\nf\ni\nl\n\n\no\no\nq\nc\ng\nj\nm\n\n\np\np\nr\nd\nh\nk\nn\n\n\nq\nq\ns\ne\ni\nl\no\n\n\nr\nr\nt\nf\nj\nm\np\n\n\ns\ns\nu\ng\nk\nn\nq\n\n\nt\nt\nv\nh\nl\no\nr\n\n\nu\nu\nw\ni\nm\np\ns\n\n\nv\nv\nx\nj\nn\nq\nt\n\n\nw\nw\ny\nk\no\nr\nu\n\n\nx\nx\nz\nl\np\ns\nv\n\n\ny\ny\na\nm\nq\nt\nw\n\n\nz\nz\nb\nn\nr\nu\nx\n\n\n\nIt is certainly not the most complicated scheme out there, but it is generally the first encryption scheme people come up with when trying to encode secret messages to one another.\nHonestly, I remember sending messages back and forth to friends in elementary school, but we would never provide the necessary table to decode the message.\nInstead, we would provide enough text that they could find the table themselves from context.\nIf a bunch of elementary school kids can figure out how to break this encryption scheme, it cannot be too robust.\nIn fact, it's interesting to see how the field of cryptography has grown since the Caesar cipher was developed.\nIn the cryptographic literature, there is always a sender, receiver, and eavesdropper.\nFor some reason beyond my own comprehension, the first two people are almost always given the names Alice (sender) and Bob (receiver).\nMeanwhile, the attacker or eavesdropper is usually called either Eve or Charlie\nThese names are consistent even with quantum cryptography, so they are here to stay.\nIn general, there are two different types of encryption: symmetric and asymmetric.\nBoth of which are described in the following sections.\nCryptographic systems are a cornerstone to modern information technology and lie at the heart of everything from WiFi to online banking.\nIf an attacker manages to crack modern cryptographic algorithms, they could cause serious damage.\nFor this reason, it is important to keep a few things in mind:\n\nBecause cryptography has become such an advanced field cryptographic systems should be analyzed by trained professionals and have undergo extensive testing and vetting.\n This means that whenever possible, one should use a widely accepted cryptography library instead of writing their own cypher.\nKerckhoffs's principle says that when determining the robustness of a cryptographic system it should be assumed that the attacker knows the encryption and decryption algorithm [2].\n This does not include any pre-shared or secret keys.\nWith the advances in technology, cryptography often hits its limits.\n Many formerly state-of-the-art hashing algorithms have become obsolete because the computers used to crack them have gotten faster and better.\n Another field that cryptography will have to face is quantum computing.\n Quantum computers will have a big impact on cryptography and especially asymmetric cryptography.\n This whole set of problems is summarized in the field of post-quantum cryptography [3].\n\nSymmetric Cryptography\nSymmetric cryptography is called symmetric because the key that is used is the same for encrypting and decrypting. \nFor this to work Alice and Bob both need the same key, which they have to share before communicating. \nSome examples for symmetric cryptography are:\n\nCeasar Cipher: Alice and Bob rotate the alphabet by n characters and use that as a table to encode and decode their message [1].\nRot13: This is a special case of the Caeser Cipher where the alphabet is rotated by 13, hence the name \"Rot13\" [4]\nPermutation Cipher: Here we choose a permutation \\pi (i.e. \\pi=(3,1,2,4)) and reorder the the letters according to that \\pi which is the key [5].\nXOR encryption: This method works on bit strings and combines the message and a key of equal bit length with the XOR operator [6].\n To decrypt, simply XOR again with the same key.\nDES or Data Encryption Standard: This is a newer encryption algorithm which was standardized in 1977 [7]. \n It has since been deemed insecure and is superseded by AES.\nAES or Advanced Encryption Standard: The actual algorithm is called \"Rijndael\" [8]. \n Like with XOR or DES we generate a bit string (depending on which AES you use 128/192 or 256 bit long) which is your key.\nBlowfish: This algorithm was also a good contender for the AES but lost to Rijndael [9].\n\nThis section is currently a work-in-progress, and all of these methods will have corresponding chapters in the near future.\nAsymmetric Cryptography\nAsymmetric cryptography is sometimes called \"public key cryptography\" (or PK cryptography in short) because Bob and Alice both need a shared public key and a private key they keep to themselves.\nThese algorithms are called asymmetric because what is encrypted with the public key can only be decrypted with the private key and vice versa. \nThis can be used for a number of different applications, like digital signing, encrypted communication, or secretly sharing keys.\nFor example, if Alice wants to send a message to Bob and this message has to be kept private, Alice will encrypt the message with Bob's public key.\nNow only Bob can decrypt the message again and read it.\nIf Charlie were to alter Alice's message, Bob couldn't decrypt it anymore.\nIf Bob wants to make sure the message is actually from Alice, Alice can encrypt the already encrypted message with her private key again.\nThis is to keep Charlie from sending forged or altered messages since Bob couldn't decrypt that layer with Alice's public key.\nSome examples for public key cryptography:\n\nRSA: This algorithm calculates a public and a private key from two very large primes [10]. \n It is (hopefully) near impossible to factor the product of two such primes in a feasible amount of time.\nECC or Elliptic-curve cryptography: Here you calculate the private and public key from two points on an elliptic curve [11]. \n This has the positive side effect that you need smaller numbers than non-ECC algorithms like RSA to achieve the same level of security.\n\nThis section is currently a work-in-progress. These methods will also have corresponding chapters in the near future.\nBibliography\n1.Wikipedia: Ceasar Cipher, 2022.2.Wikipedia: Kerckhoffs's principle, 2022.3.Wikipedia: Post-quantum Cryptography, 2022.4.Wikipedia: ROT13, 2022.5.Crypto Corner: Permutation Cipher, 2022.6.Wikipedia: XOR cipher, 2022.7.Wikipedia: Data Encryption Standard, 2022.8.Wikipedia: Advanced Encryption Standard, 2022.9.Wikipedia: Blowfish (cipher), 2022.10.Wikipedia: RSA (cryptosystem), 2022.11.Wikipedia: Elliptic-curve cryptography, 2022.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nThe text of this chapter was written by Liikt and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by Liikt and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n"},"contents/taylor_series_expansion/taylor_series_expansion.html":{"url":"contents/taylor_series_expansion/taylor_series_expansion.html","title":"Taylor Series","keywords":"","body":"NOTE: Incomplete!\nTaylor Series Expansion\nI have been formally trained as a physicist. In my mind, there are several mathematical topics that blur the boundary between mathematics and physics. Taylor Series Expansions are one of those topics.\nOn the one hand, I can see how the expansion could be considered purely mathematical. I mean, here is the definition:\n\nf(x) \\simeq \\sum_{n=0}^{\\infty} \\frac{f^{(n)}(a)}{n!}(x-a)^n\n\nwhere f(x) is some function along real or complex space, a is the point that we are expanding from, and f^{(n)}(x) denotes the n^{\\text{th}} derivative of f(x).\nFrom this perspective, the expansion just looks like a bunch of derivatives strung together! Where's the physics? Well, let's expand this series for the first few derivatives:\n\nf(x) \\simeq f(a) + \\frac{df(a)}{dx}(x-a)\n + \\frac{1}{2}\\frac{d^2f(a)}{dx^2}(x-a)^2\n\nIf we substitute the derivatives for their physical quantities with f(x) \\rightarrow x(t), expanding from 0, and set\n\n\\begin{align}\n\\frac{dx(t)}{dt} &= \\text{velocity} = v(t) \\\\\n\\frac{d^2x(t)}{dt^2} &= \\text{acceleration} = a \\\\\n\\end{align}\n\nThe Taylor series expansion turns into one of the most common formulas in classical physics, the kinematic equation!\n\nx(t) \\simeq x_0 + v_0t\n + \\frac{1}{2}at^2\n\nNote that here, we assume the acceleration to be constant, but it could technically have higher order terms.\nTruth be told, the Taylor Series Expansion can be found in the most unusual places and is used as the foundation of many different algorithms throughout this book. At first, it might not seem obvious why, but we can approximate almost any smooth function with a Taylor Series Expansion, and the more terms we include, the better our approximation becomes! For example, take Figure 1. Any function can be approximated as a sum of all the derivatives for that function. If we evaluate these derivatives at any point, we closely approximate the actual function.\n\n \n\n\nThis shows the true power of the Taylor Series Expansion. It allows us to more easily tackle complicated functions by approximating them as functions we can actually use and imagine!\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"Taylor Approximation\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/convolutions/convolutions.html":{"url":"contents/convolutions/convolutions.html","title":"Convolutions","keywords":"","body":"Convolutions\nTo put it bluntly, convolutions can be confusing.\nSome might even call them convoluted!\n(Get it? Because we are talking about convolutions? A wise man once told me that all good jokes need additional clarification.)\nNot only are convolutions hard to describe, but if they are not used in practice, it is hard to understand why they would ever be needed.\nI am going to do what I can to describe them in an intuitive way; however, I may need to come back to this in the future.\nLet me know if there is anything here that is unclear, and I will do what I can to clear it up.\nAs always, we should start at the start.\nIf you take two functions f and g, there are a number of ways you can combine them.\nAll basic operations can do this (addition, subtraction, multiplication, and division), but there are also special operations that only work with functions and do not work on standard variables or numbers.\nFor example, f \\circ g is a composition of the two functions, where you plug g(x) into f.\nA convolution is another function-related operation, and is often notated with a star (*) operator, where\n\nf*g=c\n\nprovides a third function, c, that is a blended version of f and g.\nAs a rather important side-note: there is an incredibly similar operation known as a correlation which will be discussed in the near future.\nNow we are left with a rather vague question: how do we blend functions?\nTo answer this question, we will need to show off a few simple graphics and animations in the Convolutions in 1D section while also discussing the mathematical definition of convolutions.\nAfter, there will be a brief discussion on an interesting application of one dimensional convolutions in integer multiplication in the Multiplication as a Convolution section.\nWe will then move on to the most stereotypical application of convolutions in the Convolutions of Images section, where we will also discuss two important filters: the Gaussian kernel and the Sobel operator.\nAs a note: convolutions can be extended to n-dimensions, but after seeing how they are extended to two dimensions, it should be possible for the reader to extend it to three dimensions and beyond if that is needed, so we will not cover that in great detail here unless is is useful for another algorithm.\nIn addition, we will be touching on a rather difficult but powerful topic with the Convolutional Theorem section where convolutions can be computed by using Fourier transforms.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/convolutions/1d/1d.html":{"url":"contents/convolutions/1d/1d.html","title":"Convolutions in 1D","keywords":"","body":"Convolutions in 1D\nAs mentioned in the introductory section for convolutions, convolutions allow mathematicians to \"blend\" two seemingly unrelated functions; however, this definition is not very rigorous, so it might be better to think of a convolution as a method to apply a filter to a signal or image.\nThis, of course, brings up more questions: what is a filter? What is a signal? How is this all related to images?\nFor this, we will start with some predefined signal.\nIt does not matter too much what it is, so we will pick a square wave where everything is set to zero except for a few elements at the center, which will be set to one.\nThis signal can be treated as an array, or a black and white, one-dimensional image where everything is black except for a white strip at the center.\nWe will also introduce a filter, which will be a simple triangle wave that goes to 1.\nBoth of these are shown below:\n\n \n \n\n\nSo now we have a signal and a filter.\nHow do we apply the filter to the signal?\nThe easiest way to do this is to iterate through every point in the signal and blend it with neighboring elements, where each neighboring element is weighted based on the filter value.\nSo in the case where the triangle wave is only 3 elements ([0.5, 1, 0.5]), the output at each point would be\n\nC_n = \\frac{A_{n-1}}{2} + A_{n} + \\frac{A_{n+1}}{2},\n\nwhere C is the output value, A is the input array (a signal or image), and n is an iterable element through that signal.\nIn this way, the \"application of a filter,\" is simply a multiplication of the triangle wave centered around each point of the input array, followed by in integral or sum of the output.\nIn some sense, this means we will shift the filter, then multiply and sum every step.\nThis can be seen in the following animation:\n\n\n \nYour browser does not support the video tag.\n\n\n\nHere, the purple, dashed line is the output convolution C, the vertical line is the iteration n, the blue line is the original signal, the red line is the filter, and the green area is the signal multiplied by the filter at that location.\nThe convolution at each point is the integral (sum) of the green area for each point.\nIf we extend this concept into the entirety of discrete space, it might look like this:\n(f*g)[n] = \\sum_{m = -\\infty}^{\\infty}f[m]g[n-m] = \\sum_{m = -\\infty}^{\\infty}f[n-m]g[m]\nWhere f[n] and g[n] are arrays of some form.\nThis means that the convolution can calculated by shifting either the filter along the signal or the signal along the filter.\nThis can be read as we said before: every step, we shift the filter, multiply, and sum.\nThere is, of course, a small caveat here.\nWhy are we subtracting m?\nCertainly, if we wanted to \"shift the filter along the signal,\" we could also do so by adding m instead, but that is actually an entirely separate operation known as a correlation, which will be discussed at a later time.\nThe simplest interpretation for this equation is the same as the animation: we reverse the second array, and move it through the first array one step at a time, performing a simple element-wise multiplication and summation at each step.\nWith this in mind, we can almost directly transcribe the discrete equation into code like so:\nfunction convolve_linear(signal::Array{T, 1}, filter::Array{T, 1},\n output_size) where {T \nstatic double[] ConvolveLinear(double[] signal, double[] filter, int outputSize)\n{\n // Convolutional output.\n var output = new double[outputSize];\n var sum = 0.0;\n\n for (var i = 0; i \ndef convolve_linear(signal, filter_array, output_size):\n out = np.zeros(output_size)\n s = 0\n\n for i in range(output_size):\n for j in range(max(0, i - len(filter_array)), i + 1):\n if j \n\n\nThe easiest way to reason about this code is to read it as you might read a textbook.\nFor each element in the output domain, we are summing a certain subsets of elements from i-length(filter) to i after multiplying it by the reversed filter (filter[i-j]).\nIn this way, it is precisely the same as the mathematical notation mentioned before.\nIn contrast to the animation, where the filter continuously reappears on the left edge of the screen, the code we have written for this part of the chapter requires the user to specify what they expect the output array length to be.\nDetermining what should happen at the edges of the convolution is a somewhat hotly debated topic and differs depending on what the user actually wants, so we will be discussing this in greater detail later in this chapter.\nAs an important note, if we were to extend the convolution into continuous space, we might write something like:\n(f*g)(x) = \\int_{-\\infty}^{\\infty}f(\\xi)g(x-\\xi)d\\xi = \\int_{-\\infty}^{\\infty}f(x-\\xi)g(\\xi)d\\xi\nNote that in this case, x and \\xi are not necessarily spatial elements, but the interpretation is otherwise the same as before.\nAt this stage, the mathematics and code might still be a little opaque, so it is a good idea to play around a bit and think about how this operation might be used in practice with a few different filters.\nPlaying with filters\nHonestly, the best way to learn how convolutions work is by using them for a number of different signals and filters, so\nlet us extend the previous triangle filter a bit further by convolving a square wave with a relatively sharp Gaussian, which can be seen in the following animation:\n\n\n \nYour browser does not support the video tag.\n\n\n\nIn practice, the convolutional output here is very similar to the triangle wave we showed before.\nThe final convolved image looks a lot like the square, except that its boundaries have been smoothed out or \"blurred.\"\nIn practice whenever a Gaussian filter is used, it will always blur the other convolved signal, which is why a convolution with a Gaussian is also called a blurring operation.\nThis operation is used very often when dealing with two-dimensional images, and we will discuss common kernels found in the wild in the next section.\nStill, it is interesting to see the blurring operation in action by convolving a random distribution with a larger Gaussian filter:\n\n\n \nYour browser does not support the video tag.\n\n\n\nIn this animation, the final convolution is so blurred that it does not seem related to the random input signal at all!\nIn fact, this animation seems to blend much more when compared to the previous Gaussian and the triangle wave animations.\nThis is because the Gaussian is wider than the previous to filters.\nIn general, the wider the filter, the stronger the blurring effect.\nSo what happens if we convolve a Gaussian with another Gaussian?\nWell, that is shown below:\n\n\n \nYour browser does not support the video tag.\n\n\n\nAs one might expect, the output is a blurrier Gaussian, which is essentially just wider.\nIf you were paying particularly close attention to the visualization, you might have noticed that the green area inside this visualization does not properly line up with the overlap of the two arrays.\nDon't worry!\nThis is exactly what should happen!\nRemember that the convolution requires a multiplication of the signal and filter, which was the same as the overlap when the signal was a square wave; however, in the case of two distinct signals, we should expect the multiplied output to look somewhat distinct.\nLet us extend this concept to one final example of a square wave convolved with a triangular, sawtooth function that looks like this:\n\n \n\n\nThis is the first non-symmetric filter of this chapter, and its convolution would look like this:\n\n\n \nYour browser does not support the video tag.\n\n\n\nNon-symmetric filters are useful for testing convolutions to ensure that the output is correct, so it might be worthwhile to linger on this animation for a bit longer.\nNotice how the convolution has an accelerating, positive slope when the reversed sawtooth function interacts with the square.\nThis makes sense as the smallest part of the triangle interacts first.\nSimilarly, there is a negatively accelerating slope when the sawtooth function leaves the square.\nDealing with boundaries\nIn all of the animations, we have shown the filter constantly reappearing on the left edge of the screen, which is not always the best thing to do at the boundaries.\nIn fact, these boundary conditions are somewhat non-trivial to code, so for this section, we will start with relatively simple boundary conditions that were introduced in the previous code example.\nSimple boundaries\nIn general, if a user wants to see a full convolution between two signals, the output size must be the size of the two signals put together, otherwise, we cannot iterate through the entire convolutional output domain.\nFor example, here is random noise again convolved with a Gaussian function, but with non-periodic boundaries:\n\n\n \nYour browser does not support the video tag.\n\n\n\nThis shows the full, unbounded convolution of the two signals, where\nwe clearly see a \"ramp up\" and \"ramp down\" phase at the start and end of the animation.\nThat said, there are many applications where the user actually needs to specify the output domain to be another length, such as the size of one of the input signals.\nIn this case, the simplest boundary would be to assume that whenever the filter hits the end of the image, it simply disappears.\nAnother way to think about this is that the signal only exists for the domain we specify it over, and is all 0s outside of this domain; therefore, the filter does not sum any signal from elements beyond its scope.\nAs an example, let's take the same example as before:\n\n\n \nYour browser does not support the video tag.\n\n\n\nSimilar to the case without boundary conditions, this convolution needs to \"ramp up,\" but it does not need to \"ramp down.\"\nThis is because the convolution output no longer extends past the bounds of the original signal so the bounded convolution is a subset of the full convolution.\nMore than that, the convolution does not go all the way to 0 on the right side.\nThis means that we are actually ignoring a rather important part of the convolution!\nThis is 100% true; however, if the signal is large and the filter is small (as is the case with most of image processing), we do not really care that much about the bits of the convolution we missed.\nIn addition, there is a way to center the convolution by modifying the location where the filter starts.\nFor example, we could have half of the filter already existing and overlapping with the signal for the very first computed point of the convolution.\nFor this reason, simple bounds are used frequently when performing convolutions on an image.\nIn the previous code snippet, we were able to perform both a bounded and unbounded convolution.\nHere it is again for clarity:\nfunction convolve_linear(signal::Array{T, 1}, filter::Array{T, 1},\n output_size) where {T \nstatic double[] ConvolveLinear(double[] signal, double[] filter, int outputSize)\n{\n // Convolutional output.\n var output = new double[outputSize];\n var sum = 0.0;\n\n for (var i = 0; i \ndef convolve_linear(signal, filter_array, output_size):\n out = np.zeros(output_size)\n s = 0\n\n for i in range(output_size):\n for j in range(max(0, i - len(filter_array)), i + 1):\n if j \n\n\nHere, the main difference between the bounded and unbounded versions is that the output array size is smaller in the bounded case.\nFor an unbounded convolution, the function would be called with a the output array size specified to be the size of both signals put together:\n# full convolution, output will be the size of x + y - 1\nfull_linear_output = convolve_linear(x, y, length(x) + length(y) - 1)\n\n// Full convolution, output will be the size of x + y - 1.\nvar fullLinearOutput = ConvolveLinear(x, y, x.Length + y.Length - 1);\n\n# full convolution, output will be the size of x + y - 1\nfull_linear_output = convolve_linear(x, y, len(x) + len(y) - 1)\n\n\n\nOn the other hand, the bounded call would set the output array size to simply be the length of the signal\n# simple boundaries\nsimple_linear_output = convolve_linear(x, y, length(x))\n\n// Simple boundaries.\nvar simpleLinearOutput = ConvolveLinear(x, y, x.Length);\n\n# simple boundaries\nsimple_linear_output = convolve_linear(x, y, len(x))\n\n\n\nFinally, as we mentioned before, it is possible to center bounded convolutions by changing the location where we calculate the each point along the filter.\nThis can be done by modifying the following line:\nfor j = max(1, i-length(filter)):i\n\nfor (var j = Math.Max(0, i - filter.Length); j \nfor j in range(max(0, i - len(filter_array)), i + 1):\n\n\n\nHere, j counts from i-length(filter) to i.\nTo center the convolution, it would need to count from i-(length(filter)/2) to i+(length(filter)/2) instead.\nI think this is a good place to stop discussions on simple boundary conditions.\nNow let us talk a bit more in detail about the case where we want the filter to continuously reappear every loop.\nThis case is known as the \"periodic boundary condition\" and was used for the visualizations at the start of this chapter.\nPeriodic boundary conditions\nThough periodic boundary conditions are more complicated that those mentioned in the previous section, they are still relatively straightforward to implement.\nWith these conditions, the filter will wrap itself around to the other end of the signal whenever it hits a boundary.\nIn this way, the signal is periodic, with an identical copy of itself acting as left and right neighbors.\nThose neighbors then have other neighbors, and those then have more neighbors, creating a sea of signals extending to infinity and beyond in both directions.\nFor us, this means that when the filter leaves one edge of the domain, it simply appears on the other, opposite edge.\nThis particular convolution is known as a cyclic convolution and is also the most common output of convolutions that work via the convolutional theorem, which will be discussed in another section.\nFor clarity: here is the same cyclic visualization we showed above with a random distribution and a Gaussian signal.\n\n\n \nYour browser does not support the video tag.\n\n\n\nIn code, this typically amounts to using some form of modulus operation, as shown here:\nfunction convolve_cyclic(signal::Array{T, 1},\n filter::Array{T, 1}) where {T \nstatic double[] ConvolveCyclic(double[] signal, double[] filter)\n{\n var outputSize = Math.Max(signal.Length, filter.Length);\n\n // Convolutional output.\n var output = new double[outputSize];\n var sum = 0.0;\n\n for (var i = 0; i \ndef convolve_cyclic(signal, filter_array):\n output_size = max(len(signal), len(filter_array))\n out = np.zeros(output_size)\n s = 0\n\n for i in range(output_size):\n for j in range(output_size):\n if(mod1(i - j, output_size) \n\n\nThis is essentially the same as before, except for the modulus operations, which allow us to work on a periodic domain.\nAs a final note before continuing: dealing with boundaries is tricky business and can dramatically change the behavior of the output convolution.\nFor this reason, it is important to think about what types of boundaries will work best for what you, the programmer, actually need.\nThe selection of boundary conditions will be a common trope for a large portion of computer graphics and physics algorithms where researchers often need to present and simulate data on an array of some sort.\nExample Code\nFor the code associated with this chapter, we have used the convolution to generate a few files for the full convolution, along with the periodic and simple boundary conditions discussed in this chapter.\nusing DelimitedFiles\nusing LinearAlgebra\n\nfunction convolve_cyclic(signal::Array{T, 1},\n filter::Array{T, 1}) where {T \nusing System;\nusing System.IO;\n\nnamespace Convolution1D\n{\n public class Convolution1D\n {\n // Creates a sawtooth function with the given length.\n static double[] CreateSawtooth(int length)\n {\n var array = new double[length];\n for (var i = 0; i = 0.\n static int Mod(int x, int y) => ((x % y) + y) % y;\n\n static double[] ConvolveCyclic(double[] signal, double[] filter)\n {\n var outputSize = Math.Max(signal.Length, filter.Length);\n\n // Convolutional output.\n var output = new double[outputSize];\n var sum = 0.0;\n\n for (var i = 0; i \nimport numpy as np\n\ndef mod1(x, y): return ((x % y) + y) % y\n\ndef convolve_cyclic(signal, filter_array):\n output_size = max(len(signal), len(filter_array))\n out = np.zeros(output_size)\n s = 0\n\n for i in range(output_size):\n for j in range(output_size):\n if(mod1(i - j, output_size) \n\n\nAt a test case, we have chosen to use two sawtooth functions, which should produce the following images:\n\n\n\nDescription\nImage\n\n\n\n\nSimple Boundaries\n\n\n\nFull\n\n\n\nCyclic\n\n\n\n\nAs a sanity check, make sure that the bounded convolution is a subset of the full convolution.\nIn this example, the bounded convolution is the start of the full convolution, but it is entirely possible it could be the middle or somewhere else entirely depending on how you counted within the inner, summation loop for the convolution.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nImages/Graphics\n\nThe image \"Square Wave\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Triangle Wave\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Triangle Square Convolution\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Gaussian Square Convolution\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Gaussian Random Convolution\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Double Convolution\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Sawtooth Wave\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Sawtooth Square Convolution\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Full Random Convolution\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Simple Random Convolution\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Simple Linear\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Full Linear\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Cyclic\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/convolutions/multiplication/multiplication.html":{"url":"contents/convolutions/multiplication/multiplication.html","title":"Multiplication as a Convolution","keywords":"","body":"Multiplication as a convolution\nAs a brief aside, we will touch on a rather interesting side topic: the relation between integer multiplication and convolutions\nAs an example, let us consider the following multiplication: 123 \\times 456 = 56088.\nIn this case, we might line up the numbers, like so:\n\n\\begin{matrix}\n&&1&2&3 \\\\\n&\\times &4&5&6 \\\\\n\\hline\n5 & 6 & 0 & 8 & 8\n\\end{matrix}\n\nHere, each column represents another power of 10, such that in the number 123, there is 1 100, 2 10s, and 3 1s.\nSo let us use a similar notation to perform the convolution, by reversing the second set of numbers and moving it to the right, performing an element-wise multiplication at each step:\n\n\\begin{matrix}\n&&&\\color{red}1&2&3 \\\\\n\\times &6&5&\\color{red}4&& \\\\\n\\hline\n\\end{matrix}\\\\\n\\color{red}{1}\\times\\color{red}{4} = 4\n\n\n\\begin{matrix}\n&&&\\color{red}1&\\color{green}2&3 \\\\\n\\times &&6&\\color{red}5&\\color{green}4& \\\\\n\\hline\n\\end{matrix}\\\\\n\\color{red}1\\times\\color{red}5+\\color{green}2\\times\\color{green}4=13\n\n\n\\begin{matrix}\n&&&\\color{red}1&\\color{green}2&\\color{blue}3 \\\\\n\\times &&&\\color{red}6&\\color{green}5&\\color{blue}4 \\\\\n\\hline\n\\end{matrix}\\\\\n\\color{red}1\\times\\color{red}6+\\color{green}2\\times\\color{green}5+\\color{blue}3\\times\\color{blue}4=28\n\n\n\\begin{matrix}\n&&1&\\color{green}2&\\color{blue}3& \\\\\n\\times &&&\\color{green}6&\\color{blue}5&4 \\\\\n\\hline\n\\end{matrix}\\\\\n\\color{green}2\\times\\color{green}6+\\color{blue}3\\times\\color{blue}5=27\n\n\n\\begin{matrix}\n&1&2&\\color{blue}3&& \\\\\n\\times &&&\\color{blue}6&5&4 \\\\\n\\hline\n\\end{matrix}\\\\\n\\color{blue}3\\times\\color{blue}6=18\n\nFor these operations, any blank space should be considered a 0.\nIn the end, we will have a new set of numbers:\n\n\\begin{matrix}\n&&1&2&3 \\\\\n&\\times &4&5&6 \\\\\n\\hline\n4 & 13 & 28 & 27 & 18\n\\end{matrix}\n\nNow all that is left is to perform the carrying operation by moving any number in the 10s digit to its left-bound neighbor.\nFor example, the numbers [4, 18]=[4+1, 8]=[5,8] or 58.\nFor these numbers, \n\n\\begin{matrix}\n&4 & 13 & 28 & 27 & 18\\\\\n=&4+1 & 3+2 & 8+2 & 7+1 & 8\\\\\n=&5 & 5 & 10 & 8 & 8\\\\\n=&5 & 5+1 & 0 & 8 & 8\\\\\n=&5 & 6 & 0 & 8 & 8\n\\end{matrix}\n\nWhich give us 123\\times456=56088, the correct answer for integer multiplication.\nI am not suggesting that we teach elementary school students to learn convolutions, but I do feel this is an interesting fact that most people do not know: integer multiplication can be performed with a convolution.\nThis will be discussed in further detail when we talk about the Schonhage-Strassen algorithm, which uses this fact to perform multiplications for incredibly large integers.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/convolutions/convolutional_theorem/convolutional_theorem.html":{"url":"contents/convolutions/convolutional_theorem/convolutional_theorem.html","title":"Convolutional Theorem","keywords":"","body":"Convolutional Theorem\nImportant note: this particular section will be expanded upon after the Fourier transform and Fast Fourier Transform (FFT) chapters have been revised.\nNow, let me tell you about a bit of computational magic:\nConvolutions can be performed with Fourier Transforms!\nThis is crazy, but it is also incredibly hard to explain, so let me do my best.\nAs described in the chapter on Fourier Transforms, Fourier Transforms allow programmers to move from real space to frequency space.\nWhen we transform a wave into frequency space, we can see a single peak in frequency space related to the frequency of that wave.\nNo matter what function we send into a Fourier Transform, the frequency-space image can be interpreted as a series of different waves with a specified frequency.\nEach of these waves is parameterized by another e^{2\\pi i k n / N} term, where k is the element's value in the frequency domain, n is its value in the time domain, and N is the overall length of the signal.\nIn this way, each wave can be seen as a complex exponential.\nSo here's the idea: if we take two functions f(x) and g(x) and move them to frequency space to be \\hat f(\\xi) and \\hat g(\\xi), we can then multiply those two functions and transform them back into to blend the signals together.\nIn this way, we will have a third function that relates the frequency-space images of the two input functions.\nThis is known as the convolution theorem which looks something like this:\n\\mathcal{F}(f*g) = \\mathcal{F}(f) \\cdot \\mathcal{F}(g)\nWhere \\mathcal{F} denotes the Fourier Transform.\nAt first, this might not seem particularly intuitive, but remember that frequency space is essentially composed of a set of exponentials.\nAs mentioned in the section about Multiplication as a Convolution, multiplication in base 10 space is also a convolution.\nThe convolutional theorem extends this concept into multiplication with any set of exponentials, not just base 10.\nObviously, this description is still lacking a bit of explanation, but I promise we will add more when revising the Fourier transform sections!\nBy using a Fast Fourier Transform (FFT) in code, this can take a standard convolution on two arrays of length n, which is an \\mathcal{O}(n^2) process, to \\mathcal{O}(n\\log(n)).\nThis means that the convolution theorem is fundamental to creating fast convolutional methods for certain large inputs.\n# using the convolutional theorem\nfunction convolve_fft(signal1::Array{T}, signal2::Array{T}) where {T \n\n\nThis method also has the added advantage that it will always output an array of the size of your signal; however, if your signals are not of equal size, we need to pad the smaller signal with zeros.\nAlso note that the Fourier Transform is a periodic or cyclic operation, so there are no real edges in this method, instead the arrays \"wrap around\" to the other side, creating a cyclic convolution like we showed in the periodic boundary condition case for the one-dimensional convolution.\nExample Code\nFor this example code, we will be using two sawtooth functions as we did in the chapter on one-dimensional convolutions:\nusing FFTW\nusing LinearAlgebra\nusing DelimitedFiles\n\n# using the convolutional theorem\nfunction convolve_fft(signal1::Array{T}, signal2::Array{T}) where {T \nfrom scipy.fft import fft, ifft\nimport numpy as np\n\n# using the convolutional theorem\ndef convolve_fft(signal1, signal2):\n return ifft(np.multiply(fft(signal1),fft(signal2)))\n\n# Sawtooth functions\nx = [float(i)/200 for i in range(1,101)]\ny = [float(i)/200 for i in range(1,101)]\n\nx /= np.linalg.norm(x)\ny /= np.linalg.norm(y)\n\n# Convolving the two signals\nfft_output = convolve_fft(x, y)\n\nnp.savetxt(\"fft.dat\", np.real(fft_output))\n\n\n\nThis should produce the following output:\n\n \n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nImages/Graphics\n\nThe image \"Cyclic\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/plotting/plotting.html":{"url":"contents/plotting/plotting.html","title":"Plotting","keywords":"","body":"Plotting\nPlotting is an essential tool for visualizing and understanding important details of several algorithms and methods and is necessary for studies in various areas of computational science.\nFor many languages, such as python, julia, and matlab, it is relatively straightforward to create simple plots for various types of data; however, for several other languages, like Fortran, C/C++, and java, plotting can be a chore.\nBecause the Algorithm Archive strives to be language agnostic, we do not want to favor any particular set of languages and have decided instead to output all data that needs plotting into a file format that can easily be read in by various plotting scripts separate from the algorithm implementations.\nIf you are implementing any algorithm in a language found on this page, you should be able to modify your existing code to allow for on-the-fly plotting.\nOtherwise, please use the language of your choice to write the initial implementation and output the data to a file before using one of the scripts available here for plotting.\nThis chapter aims to explain how to plot several different types of data and will be updated as more algorithms require more complex plotting schemes.\nThough many complex file formats exist, we will be mainly storing data for plotting in simple ASCII text.\nIf you wish to use these plotting scripts for other file formats or projects unrelated to the Algorithm Archive, some modification will be necessary.\nIn addition, each plotting language used in this chapter will likely have many features we are not currently using, so there may be methods to create stunning visualizations that we are ignoring here.\nPlotting a series of functions\nTo begin, let's write a simple script that allows for plotting a sine wave\nplot sin(x) with lines\n\nWhere x is a range from negative to positive 10.\nTo plot from the terminal, you can either:\n\nenter the gnuplot REPL (Read, Evaluate, Print, Loop -- the gnuplot shell) by using the gnuplot command and type the above command manually.\nwrite the command in an external script (let's call it script.gp) and run it with gnuplot script.gp -. The - will keep the terminal open in the background so the image stays up. If your plotting script outputs a .png file, the - is unnecessary.\n\nThis command will create a plot that looks like this:\n\n \n\n\nFor most gnuplot scripts, this command is written in short-hand.\nThe phrase with lines is abbreviated to simply w l and plot is sometimes written as simply p, so the following command would also work:\np sin(x) w l\n\n\nFrom here, it is rather straightforward to add more plots.\nFor example, let's add in a cosine function.\nIn this case, we need to add the following line to our script:\nplot sin(x) with lines\nreplot cos(x) with lines\n\nWhich will create an image that looks like this:\n\n \n\n\nIf you would prefer to plot everything on a single line (which will become more relevant when plotting directly to an image file), then you can use the following command:\np sin(x) w l, cos(x) w l\n\n\nIn some sense, this chapter is meant as a guide so users can better understand plotting in their language of choice.\nAs such, it is important to first understand how to perform a few basic tasks:\n\nChanging auxiliary features of the plot such as: title, axis, labels, x/ytic values, and plot dimensions\nPlotting multiple functions at the same time\nOutputting the plot to file\n\nAt the end of this chapter, we will discuss the scatter plot; however, additional plotting techniques may be covered in the near future for specific algorithms and methods.\nChanging auxiliary features\nBeauty is in the eye of the beholder, but it is rare for people to call plots \"beautiful.\"\nThat said, there are plenty of things you can do to more clearly represent your data, and if your data is beautiful, so be it!\nIn this section, we'll show you some small-scale modifications you can make to the plot we have already generated to make it little cleaner, but there are plenty of other ways to spruce up your plot that we are not covering here.\nBe sure to look at the documentation [1] for plotting in your language of choice if you want to do anything more complicated.\nx and y range\nAll data that can be plotted has a scope at which the important features are more clear.\nIt is sometimes important to zoom in or zoom out to highlight particular facets of the data available.\nThis can be simply done by modifying the x and y ranges in your plotter of choice, like so:\nset xrange [0:10]\nset yrange [0:1]\nplot sin(x) w l, cos(x) w l\nHere, the keywords xrange and yrange are known by gnuplot and take a range from [n:m], where n and m are real units in the plot, itself.\nFor this script, we generate a plot that looks like this:\n\n \n\n\nx and y tics\nIn addition to changing the plot scales, it is also important to notify your audience of what these scales actually mean.\nTo help guide the reader's eye and better understand what the plot represents, plotters provide tics (little notches) on the x and y axes.\nAs such, it is important to update the x and y tics with appropriate scales and labels.\nFirstly, to remove x and y tics, use\nunset xtics\nunset ytics\nThis will create a plot that looks like this:\n\n \n\n\nIf you want to set particular x or y tic values, use\nset xtics 0, 5, 10\nset ytics (\"bottom\" 0 , \"top\" 1)\nwhich creates a plot that looks like this:\n\n \n\n\nHere, we are selecting 3 values to use for the x-axis and using words or phrases for the \"bottom\" and \"top\" of the y-axis.\nTo be clear: we are not condoning the behavior of having mismatched x and y tic values by using words or phrases along the y axis and numbers along the x axis.\nThis is simply meant as a showcase for using gnuplot in this way.\nAs a note: there is a lot of information here we missed, specifically format specifiers, which allow users to modify the format of the numbers in their plots (to be in floating point, scientific notation, or something else).\nThis can be found in the documentation, along with anything else that is missed here.\n\n\nlogscale\nIn addition to changing the values of the x and y tics, we can also change the axes to plot in log-scale by using the following command:\nset logscale x\nset logscale y\n\n\nAs a simple example, let's take the exp(x) function.\nIn gnuplot, we can plot this by using p exp(x) w l, which will create the following:\n\n \n\n\nNow let's plot the same function with log-scale along the y axis:\n\n \n\n\nHere, we see what we expect: exp(x) is a straight line when the y axis is in log-scale.\nWhen we use log-scale on the sine and cosine waves from before, we get the following:\n\n \n\n\nThis is an awful plot, so it is only fitting that we use it as out example for the a few more plots in this chapter.\nlabels, titles, and legends\nMany researchers are very particular about labels.\nLabels need to be in the right spot, say the right stuff, and be interpreted in the right way.\nAs such, most plotters have a lot of options for labels, including LaTeX-like formatting for academic journals and such.\nThere are also multiple labels associated with each plot.\nEvery line has a label, often held in a box called a legend, and the plot, itself, has a title.\nlabels\nFirst, let's change the labels associated with each data set or function.\np sin(x) w l title \"sine wave\", cos(x) w l title \"cos(x)\"\n\n \n\n\nHere, we show that we can modify the data labels to be whatever we want.\nNote that for LaTeX-like math in the label, we might need to change the output to TeX, which will be shown later.\nFor now, let's move on to discuss what we can to with all of the labels in the legend\nlegend\nFirst things first, you should probably use a legend, unless you are a legend yourself and don't need one... In which case you can use the following:\nset nokey\nwhich will produce a plot that looks like this:\n\n \n\n\nAdmittedly, you are probably not important enough to remove the legend and doing so will prevent readers from understanding the data you are plotting, so this should be used sparingly.\nInstead, you should probably try to move the legend out of the way of the data, which can be done in a number of ways.\nIn gnuplot, it is possible to specify where we place the legend by using certain keywords, like top, bottom, left, right, and center, like so:\nset key top left\nwhich will produce a plot that looks like this:\n\n \n\n\nIn addition, we can specify exact coordinates in the plot to place the legend.\nFor example, if we wanted the legend to be at the position (1,0.5), then we would use the following command:\nset key at 1, 0.5\nwhich will produce a plot that looks like this:\n\n \n\n\nThis is certainly an awful place to put a legend for this plot, but this command could be useful for other plots.\n\n\ntitles\nObviously, in addition to labels, we can also provide a title for the entire plot, like so:\nset title \"Gnuplot Test\"\n\n \n\n\nsquare output\nMany times, plotting data in a 6:9 (or worse, 16:9) aspect ratio can feel like a misrepresentation of the data.\nFor whatever reason, I was told time and time again as a fledgling researcher that there is no need for widescreen plots and that I should set the output to square whenever possible.\nThat can be done by using\nset size square\nwhich will output the following plot:\n\n \n\n\nline and point types\nFinally, it's important to show your individuality by choosing your own point and line types.\nTo find all the point or line types available in gnuplot, simply open the REPL and run the test command, which outputs something that looks like this:\n\n \n\n\nAs a note, changing the line color is not mentioned in the test image above, this can be done with the linecolor command, which takes an argument in a color space like rgb.\nIf we would like to use a dashed black line for the sine function and purple crosses for cosine, we would use something like this:\np sin(x) with lines dashtype 2 linecolor rgb \"black\" title \"sin(x)\"\nrep cos(x) w p pt 17 lc rgb \"purple\" t \"cos(x)\"\nThis will create a plot that looks like this:\n\n \n\n\nWith this script, we are using a bunch of aliases, which can be found in the following section.\nFor now, it is clear that you can make your plot look however you like without too much trouble.\nThere are also a bunch of cool features that you can learn by looking up examples on the gnuplot site.\n\n\ngnuplot aliases\nAs we have seen in this chapter, it is common to use several aliases with gnuplot, and I have tried to introduce these slowly in the above text.\nHere are all the aliases stated explicitly:\n\n\n\ncommand\nalias\n\n\n\n\nplot\np\n\n\nreplot\nrep\n\n\nwith lines\nw l\n\n\nwith points\nw p\n\n\nlinecolor\nlc\n\n\npointtype\npt\n\n\ntitle\nt\n\n\n\nWe will add more aliases to this table as they are used in the Algorithm Archive.\n\n\nOutputting the plot to file\nAt this point, all the scripts have shown so far will output an image directly to your computer screen; however, it is important to note that you can use any of the above methods when outputting to a file as well.\nFor the most part, if you want to output any of the above scripts to a file, you simply need to run the following commands:\nset terminal pngcairo\nset output \"check.png\"\nIn this case, we are changing the REPL type to work with png images with the Cairo back-end, which is a vector drawing library in C.\nWe are also setting the output to \"check.png\".\nIf we would like to set the resolution of the output image, we could do the following:\nset terminal pngcairo size 640, 480\nAs an example, here is the script for the image we generated above:\nset terminal pngcairo size 640, 480\nset output \"sine_cosine_plot.png\"\nset xrange [0:10]\nset yrange [0:1]\nset logscale x\nset logscale y\nset key at 1,0.5\nset title \"Gnuplot Test\"\nset size square\n\nplot sin(x) with lines dashtype 2 linecolor rgb \"black\" title \"sin(x)\", \\\n cos(x) w p pt 17 lc rgb \"purple\" t \"cos(x)\"\n\nAs mentioned above, for a lot of scientific papers and articles, it is worth outputting images into a format that is used commonly for typesetting, such as LaTeX.\nThere are multiple ways to create TeX output with gnuplot by using different REPL modes like epslatex.\nThe easiest method to generate a pdf output with gnuplot that uses LaTeX would be to create a standalone TeX file, like so\nset terminal epslatex standalone size 10cm, 10cm\nset output \"check.tex\"\nThis can be quickly turned into a pdf with the pdflatex check.tex command.\nFor example, if we run the following script:\nset terminal epslatex standalone size 12cm, 8cm\nset output \"out.tex\"\n\np exp(x)\n\nand then run\ngnuplot file.gp\npdflatex out.tex\nWe will have a standalone pdf that uses LaTeX features in the file out.pdf.\nThis file should look like this:\n\n \n\n\nNote that in this process, we create auxiliary files like *.eps and *.aux, which are expected with LaTeX.\nIf you would like to directly read the output .tex file from gnuplot into another LaTeX document, you can use the same command as above without the standalone option, like so:\nset terminal epslatex size 10cm, 10cm\nset output \"check.tex\"\nThis will output another \"check.tex\" file that can be used by other LaTeX documents, and here is an example tex file to do that:\n\\documentclass[11pt]{article}\n\n\\usepackage{gnuplottex}\n\\begin{document}\n\n\\input{out}\n\n\\end{document}\n\nAs a note, the units for the epslatex terminal are real units in terms of cm, inches, or whatever other measurement LaTeX takes.\nAs such, you will probably want to make sure the size of the output image from gnuplot actually fits in the document you want to create.\n\n\nPlotting data from a file\nEach algorithm in the Algorithm Archive that requires plotting will also output a data file to use for this purpose.\nEven though there are plenty of complex data formats to write to and read from, for the purposes of this text, we will focus on simple ASCII data.\nThis is not preferred for any data-intensive task and there are a large number of different storage formats and file types available to choose from for your specific purposes; however, the Algorithm Archive intends to provide the simplest explanation of algorithms and methods and we do not want to over-complicate the process with file input and output.\nIf multiple data sets are required to be plotted, they will also be provided a new file, usually with a zero-padded name such as file_0000.dat, file_0001.dat, file_0002.dat, and so on.\nWe will assume that your plotter of choice has limited three dimensional capabilities and will instead focus on the data format for one and two-dimensional data here\nOne-dimensional output\nIn the case of one-dimensional output, the data file will have all numbers separated by a newline, such as in this case:\n0.5877852522924731\n0.9510565162951535\n0.9510565162951536\n0.5877852522924732\n1.2246467991473532e-16\n-0.587785252292473\n-0.9510565162951535\n-0.9510565162951536\n-0.5877852522924734\n-2.4492935982947064e-16\nFor the purposes of the Algorithm Archive, we will call these data files .dat files; however, the file extension does not matter and you can just as well name the files .tsv or .csv depending on your tastes.\nGnuplot can read in this file in the same way it can plot functions above.\nSo we can use the following command:\nplot \"sample_data.dat\" with lines\nWhich will provide the following output:\n\n \n\n\nTwo-dimensional image output\nIn the case of two-dimensional image output, the data file be similar, but this time, each number will be separated by a tab for different column entries and a newline for rows, as shown here:\n1.0 2.0 3.0\n4.0 5.0 6.0\n7.0 8.0 9.0\nIt is expected that the number of columns does not vary in each row and that we are working with an n \\times m matrix which can be simply plotted as a series of pixels that scale in color according to some defined color bar.\nTo create 2 dimensional plots in Gnuplot, we need to set the view to 2 dimensional and then do a 3 dimensional plot with the splot function that we set to a matrix image, like so:\nset view map\nsplot \"sample_data.dat\" matrix with image\n\n \n\n\nchanging the color bar\nFor plotting images from data files, we will often need to specify how we color the image by setting a custom color bar\nIn Gnuplot, there are not many predefined themes, but it is fairly easy to set your own theme for coloring a 2 dimensional image.\nThis is done by setting a palette and there are repositories online that have a number of palettes to choose from.\nSimply put, a palette is a number line where you can set a color to be associated with whatever value you like, like in this example:\nset view map\nset palette defined (0 0 0 1, 1 'red', 2 '#00FF00')\nsplot \"2d_sample_low_res.dat\" matrix with image\nThe integer value corresponds to the location of the color on the color bar and the color can be set as either a recognized word (blue, red, green, etc.), HTML notation ('#FF0000', '#00FF00', '#0000FF', etc.), or RGB colors (1 0 0, 0 1 0, 0 0 1, etc.).\nThis example will output the following plot:\n\n \n\n\n\nScatter Plots\nThe scatter plot is another useful method for visualizing data that plots each point in an n -dimensional space.\nFor the purposes of the Algorithm Archive, this space is mainly two-dimensional; however, scatter plots in three-dimensions may also be used for visualizing three-dimensional datasets.\nWe will update this section if three-dimensional scatter plots are required.\nFor the purposes of the Algorithm Archive, scatter plot data will be output as a series of x and y pairs, where each row has an x and a y value, separated by a tab character.\nFor example, a data file might look like this:\n0.7972009737623846 0.3548405553754319\n0.8661873069668018 0.13307711243511333\n0.7605752608745506 0.8686860241215444\n0.7796784902862803 0.35589625594005647\n0.23842162678327328 0.18541942067815853\n0.23648916187439406 0.6351126027850458\n0.6075688534409027 0.789554555806735\n0.361307926046027 0.6338943724188091\n0.3692102429804389 0.40610861857701597\n0.30699091691896263 0.27999628668153087\nFor three-dimensional scatter plots, there might be a third, z dimension.\nIn gnuplot, scatter plots are easy to generate with the provided data format, for example, you could use the following command:\np \"scatterplot_data.dat\" pt 7\nWhich will create the following image\n\n \n\n\nHere, we have chosen pointtype 7, simply because it is easier to see when compared to the default crosses.\n\n\nHistograms\nMany different algorithms will output data as a series of points that must be organized into separate bins before anyone can make sense of the data.\nFor example, here are 10 values from a set of 100 randomly generated integers between 1 and 9:\n2\n5\n5\n5\n1\n3\n2\n6\n3\n1\n6\nSomeone might ask, \"How many 1s show up in this string of numbers?\"\nSimilarly, someone might want to know how many 1s we have in comparison to the number of 2s (or 3s or 4s, etc).\nTo do this, we would create a set of bins and then iterate through the data, adding one to a bin every time we find a corresponding number.\nNote that the bins do not necessarily need to be sequential integer values and that for floating point numbers, the input might need to be rounded.\nYou can even histograms objects or anything that else that can be categorized.\nFor the data that we have shown above, we might create a histogram that looks like this:\n\n \n\n\nAnd here is a plotting script to generate it:\n# This is the size of each bin\nbin_width = 1;\n\n# This takes the data and determins which bin id it should fall into\nbin_id(x) = floor(x/bin_width)\n\n# This modifies each bin to be the correct width and also centers it over the \n# correct number\nbin(x) = bin_width * ( bin_id(x) + 0.5 )\n\n# Starts the y-axis at 0\nset yrange [0:]\n\n# Removes legend\nunset key\n\n# Sets a fill style for \"fillsteps\"\nset style fill solid 1.00 border\n\n# The column number to be histogrammed is 1, change $1 to another number if \n# you want to plot another column\nplot '../../data/rand.dat' u (bin($1)):(1) t 'data' smooth frequency w fillsteps\n\nFor this, we are using a fill style to use with fillsteps so the histogram is colored, but if you just want a line, you could remove the fill style and use histeps instead.\nAs another note, we are using t 'data' smooth frequency, which essentially turns the input numbers into a small, binned array to plot.\n\n\nNote that this code rounds the input in the case of floating point numbers.\nIf you are interested in seeing this type of plot generate fractal patterns, please look at the chapter on iterated function systems.\nConclusions\nPlotting is a powerful tool that is essential for most of computational science.\nHere, we have provided all of the essential skills to plot any data that comes from the Algorithm Archive, and we will strive to provide the plotting scripts we used whenever possible.\nBibliography\n1.Williams, T and Kelley, C, Gnuplot 5.0: An Interactive Plotting Program, Official Gnuplot Documentation, 2015.\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"gnuplot_sine_wave\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_wave\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_wave_range\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_notics\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_customtics\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"exp_fn\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"exp_fn_log\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_log\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_label\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_nokey\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_movekey\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_movekey2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_title\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_sine_cosine_square\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_test\" was created by the gnuplot test command, and gnuplot has this copyright.\nThe image \"gnuplot_sine_cosine_linetype\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_exp_tex\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_1d_sample\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_2d_sample\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_2d_sample_colorbar\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_scatterplot\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"gnuplot_histogram\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n\n\nPull Requests\nThe following pull requests have modified the text or graphics of this chapter:\n\n622: Initial PR for chapter\n\n"},"contents/monte_carlo_integration/monte_carlo_integration.html":{"url":"contents/monte_carlo_integration/monte_carlo_integration.html","title":"Monte Carlo","keywords":"","body":"Monte Carlo Integration\nMonte Carlo methods were some of the first methods I ever used for research, and when I learned about them, they seemed like some sort of magic.\nTheir premise is simple: random numbers can be used to integrate arbitrary shapes embedded into other objects.\nNowadays, \"Monte Carlo\" has become a bit of a catch-all term for methods that use random numbers to produce real results, but it all started as a straightforward method to integrate objects.\nNo matter how you slice it, the idea seems a bit crazy at first.\nAfter all, random numbers are random.\nHow could they possibly be used to find non-random values?\nWell, imagine you have a square.\nThe area of the square is simple, \\text{Area}_{\\text{square}} = \\text{length} \\times \\text{width}.\nSince it's a square, the \\text{length} and \\text{width} are the same, so the formula is technically just \\text{Area}_{\\text{square}} = \\text{length}^2.\nIf we embed a circle into the square with a radius r = \\tfrac{length}{2} (shown below), then its area is \\text{Area}_{\\text{circle}}=\\pi r^2.\nFor simplicity, we can also say that \\text{Area}_{\\text{square}}=4r^2.\n\n \n\n\nNow, let's say we want to find the area of the circle without an equation.\nAs we said before, it's embedded in the square, so we should be able to find some ratio of the area of the square to the area of the circle:\n\n\\text{Ratio} = \\frac{\\text{Area}_{\\text{circle}}}{\\text{Area}_{\\text{square}}}\n\nThis means,\n\n\\text{Area}_{\\text{circle}} = \\text{Area}_{\\text{square}}\\times\\text{Ratio} = 4r^2 \\times \\text{ratio}\n\nSo, if we can find the \\text{Ratio} and we know r, we should be able to easily find the \\text{Area}_{\\text{circle}}.\nThe question is, \"How do we easily find the \\text{Ratio}?\"\nWell, one way is with random sampling.\nWe basically just pick a bunch of points randomly in the square, and\neach point is tested to see whether it's in the circle or not:\nfunction in_circle(x_pos::Float64, y_pos::Float64)\n\n # Setting radius to 1 for unit circle\n radius = 1\n return x_pos^2 + y_pos^2 \n(defn in-circle? [pv r]\n \"take a vector representing point and radius return true if the\n point is inside the circle\"\n (>\n pv\n (map #(* % %))\n (reduce +))\n (* r r)))\n\nbool in_circle(double x, double y) {\n return x * x + y * y \n/**\n * Check if the point (x, y) is within a circle of a given radius.\n * @param x coordinate one\n * @param y coordinate two\n * @param r radius of the circle (optional)\n * @return true if (x, y) is within the circle.\n */\ninline bool in_circle(double x, double y, double r = 1) {\n return x * x + y * y \nfunction inCircle(xPos, yPos) {\n // Setting radius to 1 for unit circle\n let radius = 1;\n return xPos * xPos + yPos * yPos \ninCircle (x, y) = x^2 + y^2 \nfn in_circle(x: f64, y: f64, radius: f64) -> bool {\n x * x + y * y \nbool inCircle(real x, real y)\n{\n return x ^^ 2 + y ^^ 2 \nfunc inCircle(x, y float64) bool {\n return x*x+y*y \nin_circle \nprivate static boolean inCircle(double x, double y) {\n return x * x + y * y \nfunc inCircle(x: Double, y: Double, radius: Double) -> Bool {\n return (x*x) + (y*y) \ndef in_circle(x, y, radius = 1):\n \"\"\"Return True if the point is in the circle and False otherwise.\"\"\"\n return (x*x + y*y) \npublic bool IsInMe(Point point) => Math.Pow(point.X, 2) + Math.Pow(point.Y, 2) \nproc in_circle(x, y, radius: float): bool =\n return x * x + y * y \ndef in_circle(x, y, radius=1)\n # Check if coords are in circle via Pythagorean Thm\n return (x*x + y*y) \nFUNCTION in_circle(pos_x, pos_y, r)\n IMPLICIT NONE\n REAL(16), INTENT(IN) :: pos_x, pos_y, r\n LOGICAL :: in_circle\n\n in_circle = (pos_x ** 2 + pos_y ** 2) \n[ ! in-circle check\n [ 2 ^ ] bi@ + ! get the distance from the center\n 1 \n❗️ 📥 point ☝️ ➡️ 👌 🍇\n 📪 point❗️ ➡️ point_x\n 📫 point❗️ ➡️ point_y\n ↩️ 🤜point_x ✖️ point_x ➕ point_y ✖️ point_y🤛 ◀️ 🤜radius ✖️ radius🤛\n🍉\n\nfunction in_circle(float $positionX, float $positionY, float $radius = 1): bool\n{\n return pow($positionX, 2) + pow($positionY, 2) \nlocal function in_circle(x, y)\n return x*x + y*y \n(define (in-circle x y)\n \"Checks if a point is in a unit circle\"\n (\ndef inCircle(x: Double, y: Double) = x * x + y * y \n(defun in-circle-p (x y)\n \"Checks if a point is in a unit circle\"\n (\n# xmm0 - x\n# xmm1 - y\n# RET rax - bool\nin_circle:\n mulsd xmm0, xmm0 # Calculate x * x + y * y\n mulsd xmm1, xmm1\n addsd xmm0, xmm1\n movsd xmm1, one # Set circle radius to 1\n xor rax, rax\n comisd xmm1, xmm0 # Return bool xmm0 \ninCircle() {\n local ret\n local mag\n ((ret = 0))\n if (($1 ** 2 + $2 ** 2 \nprivate fun inCircle(x: Double, y: Double, radius: Double = 1.0) = (x * x + y * y) \n% a 2 by n array, rows are xs and ys\nxy_array = rand(2, n); \n\n% square every element in the array\nsquares_array = xy_array.^2; \n\n% sum the xs and ys and check if it's in the quarter circle\nincircle_array = sum(squares_array)\n\n \ndata point(x, y):\n def __abs__(self) = (self.x, self.y) |> map$(pow$(?, 2)) |> sum |> math.sqrt\n\ndef in_circle(p is point, radius = 1):\n \"\"\"Return True if the point is in the circle and False otherwise.\"\"\"\n return abs(p) \nfunction Is-InCircle($x, $y, $radius=1) {\n return ([Math]::Pow($x, 2) + [Math]::Pow($y, 2)) -lt [Math]::Pow($radius, 2)\n}\n\n\n\nIf it's in the circle, we increase an internal count by one, and in the end,\n\n\\text{Ratio} = \\frac{\\text{count in circle}}{\\text{total number of points used}}\n\nIf we use a small number of points, this will only give us a rough approximation, but as we start adding more and more points, the approximation becomes much, much better (as shown below)!\n\n \n\n\nThe true power of Monte Carlo comes from the fact that it can be used to integrate literally any object that can be embedded into the square.\nAs long as you can write some function to tell whether the provided point is inside the shape you want (like in_circle() in this case), you can use Monte Carlo integration!\nThis is obviously an incredibly powerful tool and has been used time and time again for many different areas of physics and engineering.\nI can guarantee that we will see similar methods crop up all over the place in the future!\nVideo Explanation\nHere is a video describing Monte Carlo integration:\n\n\n\n\nExample Code\nMonte Carlo methods are famous for their simplicity.\nIt doesn't take too many lines to get something simple going.\nHere, we are just integrating a circle, like we described above; however, there is a small twist and trick.\nInstead of calculating the area of the circle, we are instead trying to find the value of \\pi, and\nrather than integrating the entire circle, we are only integrating the upper right quadrant of the circle from 0 .\nThis saves a bit of computation time, but also requires us to multiply our output by 4.\nThat's all there is to it!\nFeel free to submit your version via pull request, and thanks for reading!\n# function to determine whether an x, y point is in the unit circle\nfunction in_circle(x_pos::Float64, y_pos::Float64)\n\n # Setting radius to 1 for unit circle\n radius = 1\n return x_pos^2 + y_pos^2 \n(ns monte-carlo.core)\n\n(defn in-circle? [pv r]\n \"take a vector representing point and radius return true if the\n point is inside the circle\"\n (>\n pv\n (map #(* % %))\n (reduce +))\n (* r r)))\n\n(defn rand-point [r]\n \"return a random point from (0,0) inclusive to (r,r) exclusive\"\n (repeatedly 2 #(rand r)))\n\n(defn monte-carlo [n r]\n \"take the number of random points and radius return an estimate to\npi\"\n (*' 4 (/ n)\n (loop [i n count 0]\n (if (zero? i)\n count\n (recur (dec i)\n (if (in-circle? (rand-point r) r)\n (inc count)\n count))))))\n\n(defn -main []\n (let [constant-pi Math/PI\n computed-pi (monte-carlo 10000000 2) ;; this may take some time on lower end machines\n difference (Math/abs (- constant-pi computed-pi))\n error (* 100 (/ difference constant-pi))]\n (println \"world's PI: \" constant-pi\n \",our PI: \" (double computed-pi)\n \",error: \" error)))\n\n#include \n#include \n#include \n#include \n#include \n\nbool in_circle(double x, double y) {\n return x * x + y * y \n#include \n#include \n#include \n\nconstexpr double PI = 3.14159265358979323846264338;\n\n/**\n * Check if the point (x, y) is within a circle of a given radius.\n * @param x coordinate one\n * @param y coordinate two\n * @param r radius of the circle (optional)\n * @return true if (x, y) is within the circle.\n */\ninline bool in_circle(double x, double y, double r = 1) {\n return x * x + y * y dist(0, 1);\n\n unsigned count = 0;\n for (unsigned i = 0; i \n// submitted by xam4lor\nfunction inCircle(xPos, yPos) {\n // Setting radius to 1 for unit circle\n let radius = 1;\n return xPos * xPos + yPos * yPos \nimport System.Random\n\nmonteCarloPi :: RandomGen g => g -> Int -> Float\nmonteCarloPi g n = count $ filter inCircle $ makePairs\n where makePairs = take n $ toPair (randomRs (0, 1) g :: [Float])\n toPair (x:y:rest) = (x, y) : toPair rest\n inCircle (x, y) = x^2 + y^2 \n// Submitted by jess 3jane\n\nextern crate rand;\n\nuse std::f64::consts::PI;\n\nfn in_circle(x: f64, y: f64, radius: f64) -> bool {\n x * x + y * y f64 {\n let mut count = 0;\n\n for _ in 0..n {\n let x = rand::random();\n let y = rand::random();\n if in_circle(x, y, 1.0) {\n count += 1;\n }\n }\n\n // return our pi estimate\n (4 * count) as f64 / n as f64\n}\n\nfn main() {\n let pi_estimate = monte_carlo(10000000);\n\n println!(\n \"Percent error is {:.3}%\",\n (100.0 * (pi_estimate - PI).abs() / PI)\n );\n}\n\n///Returns true if a point (x, y) is in the circle with radius r\nbool inCircle(real x, real y)\n{\n return x ^^ 2 + y ^^ 2 tuple!(\"x\", \"y\")(uniform01, uniform01))\n .take(n)\n .count!(a => inCircle(a.x, a.y));\n return piCount * 4.0 / n;\n}\n\nvoid main()\n{\n import std.math : abs, PI;\n import std.stdio : writeln;\n\n auto p = monteCarloPI(100_000);\n writeln(\"Estimated pi: \", p);\n writeln(\"Percent error: \", abs(p - PI) * 100 / PI);\n}\n\n// Submitted by Chinmaya Mahesh (chin123)\n\npackage main\n\nimport (\n \"fmt\"\n \"math\"\n \"math/rand\"\n \"time\"\n)\n\nfunc inCircle(x, y float64) bool {\n return x*x+y*y \n\nin_circle \nimport java.util.Random;\n\npublic class MonteCarlo {\n\n public static void main(String[] args) {\n double piEstimation = monteCarlo(1000);\n System.out.println(\"Estimated pi value: \" + piEstimation);\n System.out.printf(\"Percent error: \" + 100 * Math.abs(piEstimation - Math.PI) / Math.PI);\n }\n\n // function to check whether point (x,y) is in unit circle\n private static boolean inCircle(double x, double y) {\n return x * x + y * y \nfunc inCircle(x: Double, y: Double, radius: Double) -> Bool {\n return (x*x) + (y*y) Double {\n let radius: Double = 1\n var piCount = 0\n var randX: Double\n var randY: Double\n\n for _ in 0...n {\n randX = Double.random(in: 0..\nimport math\nimport random\n\n\ndef in_circle(x, y, radius = 1):\n \"\"\"Return True if the point is in the circle and False otherwise.\"\"\"\n return (x*x + y*y) \nMonteCarlo.cs\nusing System;\n\nnamespace MonteCarloIntegration\n{\n public class MonteCarlo\n {\n public double Run(int samples)\n {\n var circle = new Circle(1.0);\n var count = 0;\n var random = new Random();\n\n for (int i = 0; i \nCircle.cs\nusing System;\n\nnamespace MonteCarloIntegration\n{\n public struct Point\n {\n public double X { get; set; }\n public double Y { get; set; }\n\n public Point(double x, double y)\n {\n this.X = x;\n this.Y = y;\n }\n }\n\n public class Circle\n {\n public double Radius { get; private set; }\n\n public Circle(double radius) => this.Radius = Math.Abs(radius);\n\n public bool IsInMe(Point point) => Math.Pow(point.X, 2) + Math.Pow(point.Y, 2) \nProgram.cs\nusing System;\n\nnamespace MonteCarloIntegration\n{\n class Program\n {\n static void Main(string[] args)\n {\n var monteCarlo = new MonteCarlo();\n System.Console.WriteLine(\"Running with 10,000,000 samples.\");\n var piEstimate = monteCarlo.Run(10000000);\n System.Console.WriteLine($\"The estimate of pi is: {piEstimate}\");\n System.Console.WriteLine($\"The percent error is: {Math.Abs(piEstimate - Math.PI) / Math.PI * 100}%\");\n }\n }\n}\n\nimport random\nimport math\n\nrandomize()\n\nproc in_circle(x, y, radius: float): bool =\n return x * x + y * y \ndef in_circle(x, y, radius=1)\n # Check if coords are in circle via Pythagorean Thm\n return (x*x + y*y) \nFUNCTION in_circle(pos_x, pos_y, r)\n IMPLICIT NONE\n REAL(16), INTENT(IN) :: pos_x, pos_y, r\n LOGICAL :: in_circle\n\n in_circle = (pos_x ** 2 + pos_y ** 2) \nUSING: locals random math.ranges math.functions ;\n\n:: monte-carlo ( n in-shape?: ( x y -- ? ) -- % )\n n [ drop random-unit random-unit in-shape? call ] count n /\n; inline\n\n! Use the monte-carlo approximation to calculate pi\n: monte-carlo-pi ( n -- pi-approx )\n [ ! in-circle check\n [ 2 ^ ] bi@ + ! get the distance from the center\n 1 float\n;\n\nUSING: math.constants ;\n10000000 monte-carlo-pi ! Approximate pi\ndup . ! Print the approximation\npi - pi / 100 * >float abs . ! And the error margin\n\n🐇 ☝️ 🍇\n 🖍🆕 x 💯\n 🖍🆕 y 💯\n\n 🆕 🍼 x 💯 🍼 y 💯 🍇 🍉\n\n ❗️ 📪 ➡️ 💯 🍇\n ↩️ x\n 🍉\n\n ❗️ 📫 ➡️ 💯 🍇\n ↩️ y\n 🍉\n🍉\n\n🐇 🌕 🍇\n 🖍🆕 radius 💯\n\n 🆕 given_radius 💯 🍇\n 🏧 given_radius❗️ ➡️ 🖍radius\n 🍉\n\n ❗️ 📥 point ☝️ ➡️ 👌 🍇\n 📪 point❗️ ➡️ point_x\n 📫 point❗️ ➡️ point_y\n ↩️ 🤜point_x ✖️ point_x ➕ point_y ✖️ point_y🤛 ◀️ 🤜radius ✖️ radius🤛\n 🍉\n🍉\n\n🐇 🤡 🍇\n 🐇 ❗️ 🏃‍♀️ samples 🔢 ➡️ 💯 🍇\n 🆕🌕🆕 1.0 ❗️ ➡️ circle\n 0 ➡️ 🖍🆕 count\n\n 🆕🎰🆕 ❗️ ➡️ random\n\n 🔂 i 🆕⏩⏩ 0 samples❗️ 🍇\n 🆕☝️🆕 💯 random❗️ 💯 random❗️❗️ ➡️ point\n ↪️ 📥 circle point❗️ 🍇\n count ⬅️ ➕ 1\n 🍉\n 🍉\n\n ↩️ 4.0 ✖️ 💯 count❗️ ➗ 💯samples❗️\n 🍉\n🍉\n\n🏁 🍇\n 😀 🔤Running with 10,000,000 samples.🔤❗️\n 🏃‍♀️🐇🤡 10000000❗️ ➡️ pi_estimate\n 😀 🍪🔤The estimate of pi is: 🔤 🔡 pi_estimate 10❗🍪❗️\n 🏧 🤜pi_estimate ➖ 🥧🕊💯 ❗️🤛❗️ ➗ 🥧🕊💯 ❗️ ✖️ 100 ➡️ percent_error\n 😀 🍪🔤The percent error is: 🔤 🔡 percent_error 10❗ 🔤%🔤🍪❗️\n🍉\n\n\n-- function to determine whether an x, y point is in the unit circle\nlocal function in_circle(x, y)\n return x*x + y*y \n#lang racket/base\n\n(require racket/local)\n(require racket/math)\n\n(define (in-circle x y)\n \"Checks if a point is in a unit circle\"\n (string pi-estimate)))\n(displayln (string-append \"Estimate (float): \" (number->string (real->single-flonum pi-estimate))))\n(displayln (string-append \"Error:\" (number->string (* (/ (abs (- pi-estimate pi)) pi) 100))))\n\nobject MonteCarlo {\n\n def inCircle(x: Double, y: Double) = x * x + y * y \n;;;; Monte carlo integration to approximate pi\n\n(defun in-circle-p (x y)\n \"Checks if a point is in a unit circle\"\n (\n.intel_syntax noprefix\n\n.section .rodata\n pi: .double 3.141592653589793\n one: .double 1.0\n four: .double 4.0\n hundred: .double 100.0\n rand_max: .long 4290772992\n .long 1105199103\n fabs_const: .long 4294967295\n .long 2147483647\n .long 0\n .long 0\n estimate_fmt: .string \"The estaimate of pi is %lf\\n\"\n error_fmt: .string \"Percentage error: %0.2f\\n\"\n\n.section .text\n .global main\n .extern printf, srand, time, rand\n\n# xmm0 - x\n# xmm1 - y\n# RET rax - bool\nin_circle:\n mulsd xmm0, xmm0 # Calculate x * x + y * y\n mulsd xmm1, xmm1\n addsd xmm0, xmm1\n movsd xmm1, one # Set circle radius to 1\n xor rax, rax\n comisd xmm1, xmm0 # Return bool xmm0 \n#!/usr/bin/env bash\ninCircle() {\n local ret\n local mag\n ((ret = 0))\n if (($1 ** 2 + $2 ** 2 \nimport java.util.Random\n\nprivate fun inCircle(x: Double, y: Double, radius: Double = 1.0) = (x * x + y * y) ) {\n val piEstimate = monteCarlo(100000)\n println(\"Estimated pi value: $piEstimate\")\n val percentError = 100 * Math.abs(piEstimate - Math.PI) / Math.PI\n println(\"Percent error: $percentError\")\n}\n\npi_estimate = monte_carlo(10000000);\n\nfprintf(\"The pi estimate is: %f\\n\", pi_estimate);\nfprintf(\"Percent error is: %f%%\\n\", 100 * abs(pi_estimate - pi) / pi);\n\nfunction pi_estimate=monte_carlo(n)\n\n % a 2 by n array, rows are xs and ys\n xy_array = rand(2, n); \n\n % square every element in the array\n squares_array = xy_array.^2; \n\n % sum the xs and ys and check if it's in the quarter circle\n incircle_array = sum(squares_array)\nThe code snippets were taken from this scratch project\n\n \nimport math\nimport random\n\ndata point(x, y):\n def __abs__(self) = (self.x, self.y) |> map$(pow$(?, 2)) |> sum |> math.sqrt\n\ndef in_circle(p is point, radius = 1):\n \"\"\"Return True if the point is in the circle and False otherwise.\"\"\"\n return abs(p) map$(-> point(random.uniform(0, radius), random.uniform(0, radius)))\n |> filter$(in_circle$(?, radius))\n |> tuple\n |> len) * 4 / n_samples\n\nif __name__ == '__main__':\n\n samples = 100_000\n\n print(f\"Using {samples:_} samples.\")\n\n pi_estimate = monte_carlo(samples)\n percent_error = 100*abs(math.pi - pi_estimate)/math.pi\n\n print(\"The estimate of pi is: {:.3f}\".format(pi_estimate))\n print(\"The percent error is: {:.3f}\".format(percent_error))\n\nfunction Is-InCircle($x, $y, $radius=1) {\n return ([Math]::Pow($x, 2) + [Math]::Pow($y, 2)) -lt [Math]::Pow($radius, 2)\n}\n\nfunction Monte-Carlo([int]$n) {\n $PiCount = 0;\n for ($i = 0; $i -lt $n; $i++) {\n $x = Get-Random -Minimum 0.0 -Maximum 1.0\n $y = Get-Random -Minimum 0.0 -Maximum 1.0\n\n if (Is-InCircle $x $y) {\n $PiCount++\n }\n }\n return 4.0 * $PiCount / $n\n}\n\n# This could take some time\n$PiEstimate = Monte-Carlo 10000000\nWrite-Host \"The pi estimate is: $PiEstimate\"\nWrite-Host \"Percent error is: $(100 * [Math]::Abs($PiEstimate - ([Math]::PI)) / ([Math]::PI))\"\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"squarecircle\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe animation \"simplemontecarlo\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/bitlogic/bitlogic.html":{"url":"contents/bitlogic/bitlogic.html","title":"Bit Logic","keywords":"","body":"Bit Logic\nWe write code in a language that makes a little sense to us, but does not make sense at all to our computer without a compiler to transform the code we write into a language the computer can understand.\nIn the end, whenever we write code, all of the data structures we write are transformed into binary strings of 1's and 0's to be interpreted by our computer.\nThat said, it's not always obvious how this happens, so let's start the simple case of integer numbers.\nIntegers\nFor integer numbers, 0 is still 0 and 1 is still 1; however, for 2, we need to use 2 digits because binary only has 0's and 1's. When we get to 4, we'll need 3 digits and when we get to 8, we'll need 4. Every time we cross a power of 2, we'll need to add a new digit. Here's a table of the first 10 integers in binary:\n\n\n\nInteger Number\nBinary Number\n\n\n\n\n0\n0000\n\n\n1\n0001\n\n\n2\n0010\n\n\n3\n0011\n\n\n4\n0100\n\n\n5\n0101\n\n\n6\n0110\n\n\n7\n0111\n\n\n8\n1000\n\n\n9\n1001\n\n\n\nThe easiest way to interpret a binary string is to imagine that each digit is a power of 2 and add them together. For example, take the number 13, with a bitstring 1101:\n\n\n\n1\n1\n0\n1\n\n\n\n\n2^3\n2^2\n2^1\n2^0\n\n\n8\n4\n2\n1\n\n\n\nWe have 1 2^3 = 8, 1 2^2 = 4, 0 2^1 = 2 and 1 2^0 = 1, adding together to 13.\nThough this might seem straightforward, it is essential to understanding several operations that will be done on bits later.\nFor now, let's talk about the only trick to integer values: negative numbers!\nThere are a few ways to represent negative numbers.\nFor example, if we are using 8 bits, we might use the first of the 8 bits to be a sign bit, whose only purpose is telling the computer whether the number is positive or negative.\nAnother method is to \"roll over\" to negative numbers when the bit count gets too high, for example:\n\n\n\nInteger Number\nBinary Number\n\n\n\n\n126\n01111110\n\n\n127\n01111111\n\n\n-128\n10000000\n\n\n-127\n10000001\n\n\n\nUltimately, integer numbers are not that difficult to deal with in binary, so let's move onto something more complicated: floating-point numbers!\nFloating-point Numbers\nFloats are numbers with a decimal point.\n9.125 is a float. 9.000 is a float. 9 is an integer.\nHere are a few floats and their integer representations:\n\n\n\nFloating-point Number\nBinary Number\n\n\n\n\n9.125\n1001.001\n\n\n10.25\n1010.01\n\n\n1.00\n1\n\n\n\nThe idea is similar to before: Each digit represents a power of 2; however, this time any digit after the decimal point counts negative.\nSo for 9.125, we have 1 2^3 = 8, 1 2^0 = 1, and 1 2^{-3} = \\frac{1}{8}.\nNow, how is this actually implemented on your computer?\nWell, one way is with the IEEE 754 Floating-point Arithmetic Standard.\nFor 32 bits, the first bit is the sign bit, the next 8 bits tell us about the number's exponent, and the next 23 are called the mantissa and hold the binary string, itself. Now, there are a few points to keep in mind:\n\nBecause the exponent is being represented in 8 bits, we only have 256 values to play with. This means that the largest exponent we can represent (in single precision) is 128 and the smallest is -127. For this reason, we will add 127 to the power of every floating-point number. So, 1 = 1 \\times 2^{0}. The exponent stored is 0+127 = 127.\n\nWe normalize every bitstring to the first 1 available. For example: 9.125 = 1.001001 \\times 2^{3} and the biased exponent is 3+127=130, 8.25 = 1.00001 \\times 2^{130}, 0.5 = 1 \\times 2^{126} \\ldots This means that there will always be a leading 1 in our bitstring. This means that the first 1 is redundant and can be removed from the mantissa.\n\n\nSo here are a few floating-point numbers and their corresponding bitstrings:\n\n\n\nFloat\nSign\nExponent\nMantissa\n\n\n\n\n9.125\n0\n10000010\n00100100000000000000000\n\n\n- 5.25\n1\n10000001\n01010000000000000000000\n\n\n- 4096.625\n1\n10001011\n00000000000010100000000\n\n\n\nNow that we know how to represent integers and floating-point numbers, let's move on to operations, starting with bitshift operators\nBitshift Operators: >\nBitshift operators do what their name implies: they shift a string of bits one digit to the left (>).\nThis has the somewhat profound effect of multiplying or dividing the value by 2, which makes sense when you consider that each digit represents a power of 2.\nBecause of the somewhat complicated nature of floating-point numbers, bitshift operators usually only work on integer numbers, like so:\n\n\n\nOperation\nInteger\nBitstring\n\n\n\n\nNone\n10\n00001010\n\n\nBitshift left, \n20\n00010100\n\n\nBitshift right, >>\n5\n00000101\n\n\n\nThere are more complicated things that can be done with the bitshift operators; however, we'll leave that discussion for another day!\nLogic gates\nIn addition to the bitshift operations, there are a number of logical operations that can be performed on one or two bits together.\nThese operations are called gates, and follow somewhat straightforward logic.\nThe AND gate, for example, reads in 2 bits and will only output a 1 value if both inputs are 1. This can be seen in the corresponding truth table:\n\n \n\n\nThe OR gate will output 1 if either input bits are 1:\n\n \n\n\nThe exclusive OR or XOR gate is the same as the OR gate, but will not output 1 if both bits are 1:\n\n \n\n\nThe NOT gate simply flips the input bit:\n\n \n\n\nBy combining the NOT and AND gates, we get the NAND gate:\n\n \n\n\nAnd NOT and OR create NOR:\n\n \n\n\nThere are a few other gates, but this is enough for most things. We'll add more as the need arises!\nThat's about it for bitlogic. I realize it was a bit long, but this is absolutely essential to understanding how computers think and how to use programming as an effective tool!\nVideo Explanation\nHere is a video describing the contents of this chapter:\n\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"ANDgate\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"ORgate\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"XORgate\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"NOTgate\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"NANDgate\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"NORgate\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/box_muller/box_muller_rejection.html":{"url":"contents/box_muller/box_muller_rejection.html","title":"How costly is rejection sampling?","keywords":"","body":"Just how costly is rejection sampling anyway?\nLet's imagine we want to have a final Gaussian distribution with n particles in it.\nWith the Cartesian Box—Muller method, this is easy: start the initial distribution(s) with n particles and then do the transform.\nThings can be just as easy with the Polar Box—Muller method as well, so long as we start with a uniformly distributed circle instead of a uniformly distributed square.\nThat is to say, so long as we do the rejection sampling before-hand, the Polar Box—Muller method will always be more efficient.\nTo be fair, there are methods to generate a uniform distribution of points within a circle without rejection sampling, but let's assume that we require rejection sampling for this example\nThis means that someone somehow needs to do the rejection sampling for the Polar method, which is sometimes a painful process.\nThis also means that the Box—Muller method can be used to teach some of the fundamentals of General-Purpose GPU computing.\nNote that because of the specificity of this problem, all the code in this subsection will be in Julia and using the package KernelAbstractions.jl, which allows us to execute the same kernels on either CPU or GPU hardware depending on how we configure things.\nLet's first consider the case where we do the rejection sampling as a part of the polar Box—Muller kernel instead of as a pre-processing step.\nIn this case, we can imagine 2 separate ways of writing our kernel:\n\nWith replacement: In this case, we absolutely require the final number of points in our Gaussian distribution to be n, so if we find a point outside of the unit circle while running the kernel, we will \"re-roll\" again for a new point that is within the circle.\nWithout replacement: This means that we will start with a uniform distribution of n points, but end with a Gaussian of m points. In this case, if we find a point outside of the unit circle while running the kernel, we just ignore it by setting the output values to NaNs (or something similar).\n\nOK, so first with replacement:\n@kernel function polar_muller_replacement!(input_pts, output_pts, sigma, mu)\n tid = @index(Global, Linear)\n @inbounds r_0 = input_pts[tid, 1]^2 + input_pts[tid, 2]^2\n\n while r_0 > 1 || r_0 == 0\n p1 = rand()*2-1\n p2 = rand()*2-1\n r_0 = p1^2 + p2^2\n end\n\n @inbounds output_pts[tid,1] = sigma * input_pts[tid,1] *\n sqrt(-2 * log(r_0) / r_0) + mu\n @inbounds output_pts[tid,2] = sigma * input_pts[tid, 2] *\n sqrt(-2 * log(r_0) / r_0) + mu\nend\n\nThis is an awful idea for a number of reasons.\nHere are a few:\n\nIf we find a point outside of the unit circle, we have to continually look for new points until we do find one inside of the circle. Because we are running this program in parallel, where each thread transforms one point at a time, some threads might take literally forever to find a new point (if we are really unlucky).\nTo generate new points, we need to re-generate a uniform distribution, but what if our uniform distribution is not random? What if it's a grid (or something similar) instead? In this case, we really shouldn't look for a new point on the inside of the circle as all those points have already been accounted for.\nThe rand() function is kinda tricky on some parallel platforms (like GPUs) and might not work out of the box. In fact, the implementation shown above can only be run on the CPU.\n\nOK, fine.\nI don't think anyone expected a kernel with a while loop inside of it to be fast.\nSo what about a method without replacement?\nSurely there is no problem if we just ignore the while loop altogether!\nWell, the problem with this approach is a bit less straightforward, but first, code:\n@kernel function polar_muller_noreplacement!(input_pts, output_pts, sigma, mu)\n tid = @index(Global, Linear)\n @inbounds r_0 = input_pts[tid, 1]^2 + input_pts[tid, 2]^2\n\n # this method is only valid for points within the unit circle\n if r_0 == 0 || r_0 > 1\n @inbounds output_pts[tid,1] = NaN\n @inbounds output_pts[tid,2] = NaN\n else\n @inbounds output_pts[tid,1] = sigma * input_pts[tid,1] *\n sqrt(-2 * log(r_0) / r_0) + mu\n @inbounds output_pts[tid,2] = sigma * input_pts[tid, 2] *\n sqrt(-2 * log(r_0) / r_0) + mu\n end\n\nend\n\nTo start discussing why a polar kernel without replacement is also a bad idea, let's go back to the Monte Carlo chapter, where we calculated the value of \\pi by embedding it into a circle.\nThere, we found that the probability of a randomly chosen point falling within the unit circle to be \\frac{\\pi r^2}{(2r)^2} = \\frac{pi}{4} \\sim 78.54\\%, shown in the visual below:\n\n \n\n\nThis means that a uniform distribution of points within a circle will reject \\sim 21.46\\% of points on the square.\nThis also means that if we have a specific n value we want for the final distribution, we will need \\frac{1}{0.7853} \\sim 1.273 \\times more input values on average!\nNo problem!\nIn this hypothetical case, we don't need exactly n points, so we can just start the initial distributions with 1.273 \\times n points, right?\nRight.\nThat will work well on parallel CPU hardware, but on the GPU this will still have an issue.\nOn the GPU, computation is all done in parallel, but there is a minimum unit of parallelism called a warp.\nThe warp is the smallest number of threads that can execute something in parallel and is usually about 32.\nThis means that if an operation is queued, all 32 threads will do it at the same time.\nIf 16 threads need to execute something and the other 16 threads need to execute something else, this will lead to warp divergence where 2 actions need to be performed instead of 1:\n\n \n\n\nIn this image, every odd thread needs to perform the pink action, while the even threads need to perform the blue action.\nThis means that 2 separate parallel tasks will be performed, one for the even threads, another for the odd threads.\nThis means that if \\ell separate operations are queued, it could take \\ell\\times as long for all the threads to do their work!\nThis is why if statements in a kernel can be dangerous!\nIf used improperly, they can cause certain threads in a warp to do different things!\nSo let's imagine that the above image is part of a larger array of values, such that there are a bunch of warps with the same divergence issue.\nIn this case, we could sort the array before-hand so that all even elements come before all odd elements.\nThis would mean that the warps will almost certainly not diverge because the elements queued will all be of the same type and require the same operations.\nUnfortunately, this comes at the cost of a sorting operation which is prohibitively expensive.\nIf we look at the above kernel, we are essentially asking 21.47\\% of our threads to do something different than everyone else, and because we are usually inputting a uniform random distribution, this means that most warps will have to queue up 2 parallel actions instead of 1.\nEssentially, we need to pick our poison:\n\nSlow \\sin and \\cos operations with the Cartesian method\nWarp divergence with the Polar method\n\nThe only way to know which is better is to perform benchmarks, which we will show in a bit, but there is one final scenario we should consider: what about doing the rejection sampling as a pre-processing step?\nThis would mean that we pre-initialize the polar kernel with a uniform distribution of points in the unit circle.\nThis means no warp divergence, so we can get the best of both worlds, right?\nWell, not exactly.\nThe polar Box—Muller method will definitely be faster, but again: someone somewhere needed to do rejection sampling and if we include that step into the process, things become complicated again.\nThe truth is that this pre-processing step is difficult to get right, so it might require a chapter in it's own right.\nIn many cases, it's worth spending a little time before-hand to make sure subsequent operations are fast, but in this case, we only have a single operation, not a set of operations.\nThe Box—Muller method will usually only be used once at the start of the simulation, which means that the pre-processing step of rejection sampling might end up being overkill.\nNo matter the case, benchmarks will show the true nature of what we are dealing with here:\n\n\n\nMethod\nCPU\nGPU\n\n\n\n\nCartesian\n385.819 \\pm 1.9ms\n19.347 \\pm 0.618ms\n\n\nPolar without replacement\n273.308 \\pm 2.81ms\n26.712 \\pm 0.592ms\n\n\nPolar with replacement\n433.644 \\pm 2.64ms\nNA\n\n\n\nThese were run with an Nvidia GTX 970 GPU and a Ryzen 3700X 16 core CPU.\nFor those interested, the code can be found below.\nFor these benchmarks, we used Julia's inbuilt benchmarking suite from BenchmarkTools, making sure to sync the GPU kernels with CUDA.@sync.\nWe also ran with 4096^2 input points.\nHere, we see an interesting divergence in the results.\nOn the CPU, the polar method is always faster, but on the GPU, both methods are comparable.\nI believe this is the most important lesson to be learned from the Box—Muller method: sometimes, no matter how hard you try to optimize your code, different hardware can provide radically different results!\nIt's incredibly important to benchmark code to make sure it is actually is as performant as you think it is!\nFull Script\nusing KernelAbstractions\nusing CUDA\n\nif has_cuda_gpu()\n using CUDAKernels\nend\n\nfunction create_grid(n, endpoints; AT = Array)\n\n grid_extents = endpoints[2] - endpoints[1]\n\n # number of points along any given axis\n # For 2D, we take the sqrt(n) and then round up\n axis_num = ceil(Int, sqrt(n))\n\n # we are now rounding n up to the nearest square if it was not already one\n if sqrt(n) != axis_num\n n = axis_num^2\n end \n\n # Distance between each point\n dx = grid_extents / (axis_num)\n\n # This is warning in the case that we do not have a square number\n if sqrt(n) != axis_num\n println(\"Cannot evenly divide \", n, \" into 2 dimensions!\")\n end \n\n # Initializing the array, particles along the column, dimensions along rows\n a = AT(zeros(n, 2))\n\n # This works by firxt generating an N dimensional tuple with the number\n # of particles to be places along each dimension ((10,10) for 2D and n=100)\n # Then we generate the list of all CartesianIndices and cast that onto a\n # grid by multiplying by dx and subtracting grid_extents/2\n for i = 1:axis_num\n for j = 1:axis_num\n a[(i - 1) * axis_num + j, 1] = i * dx + endpoints[1]\n a[(i - 1) * axis_num + j, 2] = j * dx + endpoints[1]\n end\n end\n\n return a\nend\n\nfunction create_rand_dist(n, endpoints; AT = Array)\n grid_extents = endpoints[2] - endpoints[1]\n return(AT(rand(n,2)) * grid_extents .+ endpoints[1]) \nend\n\n# This function reads in a pair of input points and performs the Cartesian\n# Box--Muller transform\n@kernel function polar_muller_noreplacement!(input_pts, output_pts, sigma, mu)\n tid = @index(Global, Linear)\n @inbounds r_0 = input_pts[tid, 1]^2 + input_pts[tid, 2]^2\n\n # this method is only valid for points within the unit circle\n if r_0 == 0 || r_0 > 1\n @inbounds output_pts[tid,1] = NaN\n @inbounds output_pts[tid,2] = NaN\n else\n @inbounds output_pts[tid,1] = sigma * input_pts[tid,1] *\n sqrt(-2 * log(r_0) / r_0) + mu\n @inbounds output_pts[tid,2] = sigma * input_pts[tid, 2] *\n sqrt(-2 * log(r_0) / r_0) + mu\n end\n\nend\n\n@kernel function polar_muller_replacement!(input_pts, output_pts, sigma, mu)\n tid = @index(Global, Linear)\n @inbounds r_0 = input_pts[tid, 1]^2 + input_pts[tid, 2]^2\n\n while r_0 > 1 || r_0 == 0\n p1 = rand()*2-1\n p2 = rand()*2-1\n r_0 = p1^2 + p2^2\n end\n\n @inbounds output_pts[tid,1] = sigma * input_pts[tid,1] *\n sqrt(-2 * log(r_0) / r_0) + mu\n @inbounds output_pts[tid,2] = sigma * input_pts[tid, 2] *\n sqrt(-2 * log(r_0) / r_0) + mu\nend\n\n\nfunction polar_box_muller!(input_pts, output_pts, sigma, mu;\n numthreads = 256, numcores = 4,\n f = polar_muller_noreplacement!)\n if isa(input_pts, Array)\n kernel! = f(CPU(), numcores)\n else\n kernel! = f(CUDADevice(), numthreads)\n end\n kernel!(input_pts, output_pts, sigma, mu, ndrange=size(input_pts)[1])\nend\n\n\n@kernel function cartesian_kernel!(input_pts, output_pts, sigma, mu)\n tid = @index(Global, Linear)\n\n @inbounds r = sqrt(-2 * log(input_pts[tid,1]))\n @inbounds theta = 2 * pi * input_pts[tid, 2]\n\n @inbounds output_pts[tid,1] = sigma * r * cos(theta) + mu\n @inbounds output_pts[tid,2] = sigma * r * sin(theta) + mu\nend\n\nfunction cartesian_box_muller!(input_pts, output_pts, sigma, mu;\n numthreads = 256, numcores = 4)\n if isa(input_pts, Array)\n kernel! = cartesian_kernel!(CPU(), numcores)\n else\n kernel! = cartesian_kernel!(CUDADevice(), numthreads)\n end\n\n kernel!(input_pts, output_pts, sigma, mu, ndrange=size(input_pts)[1])\nend\n\nfunction main()\n\n input_pts = create_rand_dist(4096^2,[0,1])\n output_pts = create_rand_dist(4096^2,[0,1])\n\n wait(cartesian_box_muller!(input_pts, output_pts, 1, 0))\n @time wait(cartesian_box_muller!(input_pts, output_pts, 1, 0))\n wait(polar_box_muller!(input_pts, output_pts, 1, 0))\n @time wait(polar_box_muller!(input_pts, output_pts, 1, 0))\n\n if has_cuda_gpu()\n input_pts = create_rand_dist(4096^2,[0,1], AT = CuArray)\n output_pts = create_rand_dist(4096^2,[0,1], AT = CuArray)\n\n wait(cartesian_box_muller!(input_pts, output_pts, 1, 0))\n CUDA.@time wait(cartesian_box_muller!(input_pts, output_pts, 1, 0))\n wait(polar_box_muller!(input_pts, output_pts, 1, 0))\n CUDA.@time wait(polar_box_muller!(input_pts, output_pts, 1, 0))\n end\n\nend\n\nmain()\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n"},"contents/convolutions/2d/2d.html":{"url":"contents/convolutions/2d/2d.html","title":"Convolutions of Images (2D)","keywords":"","body":"Convolutions on Images\nFor this section, we will no longer be focusing on signals, but instead images (arrays filled with elements of red, green, and blue values).\nThat said, for the code examples, greyscale images may be used such that each array element is composed of some floating-point value instead of color.\nIn addition, we will not be discussing boundary conditions too much in this chapter and will instead be using the simple boundaries introduced in the section on one-dimensional convolutions.\nThe extension of one-dimensional convolutions to two dimensions requires a little thought about indexing and the like, but is ultimately the same operation.\nHere is an animation of a convolution for a two-dimensional image:\n\n\n \nYour browser does not support the video tag.\n\n\n\nIn this case, we convolved the image with a 3x3 square filter, all filled with values of \\frac{1}{9}.\nThis created a simple blurring effect, which is somewhat expected from the discussion in the previous section.\nIn code, a two-dimensional convolution might look like this:\nfunction convolve_linear(signal::Array{T, 2}, filter::Array{T, 2},\n output_size) where {T \ndef convolve_linear(signal, filter, output_size):\n out = np.zeros(output_size)\n sum = 0\n\n for i in range(output_size[0]):\n for j in range(output_size[1]):\n for k in range(max(0, i-filter.shape[0]), i+1):\n for l in range(max(0, j-filter.shape[1]), j+1):\n with suppress(IndexError):\n sum += signal[k, l] * filter[i-k, j-l]\n out[i, j] = sum\n sum = 0\n\n return out\n\n\n\nThis is very similar to what we have shown in previous sections; however, it essentially requires four iterable dimensions because we need to iterate through each axis of the output domain and the filter.\nAt this stage, it is worth highlighting common filters used for convolutions of images.\nIn particular, we will further discuss the Gaussian filter introduced in the previous section, and then introduce another set of kernels known as Sobel operators, which are used for naïve edge detection or image derivatives.\nThe Gaussian kernel\nThe Gaussian kernel serves as an effective blurring operation for images.\nAs a reminder, the formula for any Gaussian distribution is\n\ng(x,y) = \\frac{1}{2\\pi\\sigma^2}e^{-\\frac{x^2+y^2}{2\\sigma^2}},\n\nwhere \\sigma is the standard deviation and is a measure of the width of the Gaussian.\nA larger \\sigma means a larger Gaussian; however, remember that the Gaussian must fit onto the filter, otherwise it will be cut off!\nFor example, if you are using a 3\\times 3 filter, you should not be using \\sigma = 10.\nSome definitions of \\sigma allow users to have a separate deviation in x and y to create an ellipsoid Gaussian, but for the purposes of this chapter, we will assume \\sigma_x = \\sigma_y.\nAs a general rule of thumb, the larger the filter and standard deviation, the more \"smeared\" the final convolution will be.\nAt this stage, it is important to write some code, so we will generate a simple function that returns a Gaussian kernel with a specified standard deviation and filter size.\nfunction create_gaussian_kernel(kernel_size)\n\n kernel = zeros(kernel_size, kernel_size)\n\n # The center must be offset by 0.5 to find the correct index\n center = kernel_size * 0.5 + 0.5\n\n sigma = sqrt(0.1*kernel_size)\n\n for i = 1:kernel_size\n for j = 1:kernel_size\n kernel[i,j] = exp(-((i-center)^2 + (j-center)^2) / (2*sigma^2))\n end\n end\n\n return normalize(kernel)\n\nend\n\ndef create_gaussian_kernel(kernel_size):\n kernel = np.zeros((kernel_size, kernel_size))\n\n # The center must be offset by 0.5 to find the correct index\n center = kernel_size*0.5 + 0.5\n\n sigma = np.sqrt(0.1*kernel_size)\n\n def kernel_function(x, y):\n return np.exp(-((x-center+1)**2 + (y-center+1)**2)/(2*sigma**2))\n\n kernel = np.fromfunction(kernel_function, (kernel_size, kernel_size))\n return kernel / np.linalg.norm(kernel)\n\n\n\nThough it is entirely possible to create a Gaussian kernel whose standard deviation is independent on the kernel size, we have decided to enforce a relation between the two in this chapter.\nAs always, we encourage you to play with the code and create your own Gaussian kernels any way you want!\nAs a note, all the kernels will be scaled (normalized) at the end by the sum of all internal elements.\nThis ensures that the output of the convolution will not have an obnoxious scale factor associated with it.\nBelow are a few images generated by applying a kernel generated with the code above to a black and white image of a circle.\n\n \n\n\n\nIn (a), we show the original image, which is just a white circle at the center of a 50\\times 50 grid.\nIn (b), we show the image after convolution with a 3\\times 3 kernel.\nIn (c), we show the image after convolution with a 20\\times 20 kernel.\nHere, we see that (c) is significantly fuzzier than (b), which is a direct consequence of the kernel size.\nThere is a lot more that we could talk about, but now is a good time to move on to a slightly more complicated convolutional method: the Sobel operator.\nThe Sobel operator\nThe Sobel operator effectively performs a gradient operation on an image by highlighting areas where a large change has been made.\nIn essence, this means that this operation can be thought of as a naïve edge detector.\nEssentially, the n-dimensional Sobel operator is composed of n separate gradient convolutions (one for each dimension) that are then combined together into a final output array.\nAgain, for the purposes of this chapter, we will stick to two dimensions, which will be composed of two separate gradients along the x and y directions.\nEach gradient will be created by convolving our image with their corresponding Sobel operator:\n\n\\begin{align}\nS_x &= \\left(\\begin{bmatrix}\n1 \\\\\n2 \\\\\n1 \\\\\n\\end{bmatrix} \\otimes [1~0~-1]\n\\right) = \\begin{bmatrix}\n1 & 0 & -1 \\\\\n2 & 0 & -2 \\\\\n1 & 0 & -1 \\\\\n\\end{bmatrix}\\\\\n\nS_y &= \\left(\n\\begin{bmatrix}\n1 \\\\\n0 \\\\\n-1 \\\\\n\\end{bmatrix} \\otimes [1~2~1]\n\\right) = \\begin{bmatrix}\n1 & 2 & 1 \\\\\n0 & 0 & 0 \\\\\n-1 & -2 & -1 \\\\\n\\end{bmatrix}.\n\\end{align}\n\nThe gradients can then be found with a convolution, such that:\n\n\\begin{align}\nG_x &= S_x*A \\\\\nG_y &= S_y*A.\n\\end{align}\n\nHere, A is the input array or image.\nFinally, these gradients can be summed in quadrature to find the total Sobel operator or image gradient:\n\nG_{\\text{total}} = \\sqrt{G_x^2 + G_y^2}\n\nSo let us now show what it does in practice:\n\n \n\n\nIn this diagram, we start with the circle image on the right, and then convolve it with the S_x and S_y operators to find the gradients along x and y before summing them in quadrature to get the final image gradient.\nHere, we see that the edges of our input image have been highlighted, showing outline of our circle.\nThis is why the Sobel operator is also known as naïve edge detection and is an integral component to many more sophisticated edge detection methods like one proposed by Canny [1].\nIn code, the Sobel operator involves first finding the operators in x and y and then applying them with a traditional convolution:\nfunction create_sobel_operators()\n Sx = [1.0, 2.0, 1.0]*[-1.0 0.0 1.0] / 9\n Sy = [-1.0, 0.0, 1.0]*[1.0 2.0 1.0] / 9\n\n return Sx, Sy\nend\n\nfunction compute_sobel(signal)\n Sx, Sy = create_sobel_operators()\n\n Gx = convolve_linear(signal, Sx, size(signal) .+ size(Sx))\n Gy = convolve_linear(signal, Sy, size(signal) .+ size(Sy))\n\n return sqrt.(Gx.^2 .+ Gy.^2)\nend\n\ndef create_sobel_operators():\n Sx = np.dot([[1.0], [2.0], [1.0]], [[-1.0, 0.0, 1.0]]) / 9\n Sy = np.dot([[-1.0], [0.0], [1.0]], [[1.0, 2.0, 1.0]]) / 9\n\n return Sx, Sy\n\ndef sum_matrix_dimensions(mat1, mat2):\n return (mat1.shape[0] + mat2.shape[0], \n mat1.shape[1] + mat2.shape[1])\n\ndef compute_sobel(signal):\n Sx, Sy = create_sobel_operators()\n\n Gx = convolve_linear(signal, Sx, sum_matrix_dimensions(signal, Sx))\n Gy = convolve_linear(signal, Sy, sum_matrix_dimensions(signal, Sy))\n\n return np.sqrt(np.power(Gx, 2) + np.power(Gy, 2))\n\n\n\nWith that, I believe we are at a good place to stop discussions on two-dimensional convolutions.\nWe will definitely return to this topic in the future as new algorithms require more information.\nExample Code\nFor the code in this section, we have modified the visualizations from the one-dimensional convolution chapter to add a two-dimensional variant for blurring an image of random white noise.\nWe have also added code to create the Gaussian kernel and Sobel operator and apply it to the circle, as shown in the text.\nusing DelimitedFiles\nusing LinearAlgebra\n\nfunction convolve_linear(signal::Array{T, 2}, filter::Array{T, 2},\n output_size) where {T \nimport numpy as np\nfrom contextlib import suppress\n\n\ndef convolve_linear(signal, filter, output_size):\n out = np.zeros(output_size)\n sum = 0\n\n for i in range(output_size[0]):\n for j in range(output_size[1]):\n for k in range(max(0, i-filter.shape[0]), i+1):\n for l in range(max(0, j-filter.shape[1]), j+1):\n with suppress(IndexError):\n sum += signal[k, l] * filter[i-k, j-l]\n out[i, j] = sum\n sum = 0\n\n return out\n\n\ndef create_gaussian_kernel(kernel_size):\n kernel = np.zeros((kernel_size, kernel_size))\n\n # The center must be offset by 0.5 to find the correct index\n center = kernel_size*0.5 + 0.5\n\n sigma = np.sqrt(0.1*kernel_size)\n\n def kernel_function(x, y):\n return np.exp(-((x-center+1)**2 + (y-center+1)**2)/(2*sigma**2))\n\n kernel = np.fromfunction(kernel_function, (kernel_size, kernel_size))\n return kernel / np.linalg.norm(kernel)\n\n\ndef create_sobel_operators():\n Sx = np.dot([[1.0], [2.0], [1.0]], [[-1.0, 0.0, 1.0]]) / 9\n Sy = np.dot([[-1.0], [0.0], [1.0]], [[1.0, 2.0, 1.0]]) / 9\n\n return Sx, Sy\n\ndef sum_matrix_dimensions(mat1, mat2):\n return (mat1.shape[0] + mat2.shape[0], \n mat1.shape[1] + mat2.shape[1])\n\ndef compute_sobel(signal):\n Sx, Sy = create_sobel_operators()\n\n Gx = convolve_linear(signal, Sx, sum_matrix_dimensions(signal, Sx))\n Gy = convolve_linear(signal, Sy, sum_matrix_dimensions(signal, Sy))\n\n return np.sqrt(np.power(Gx, 2) + np.power(Gy, 2))\n\n\ndef create_circle(image_resolution, grid_extents, radius):\n out = np.zeros((image_resolution, image_resolution))\n\n for i in range(image_resolution):\n x_position = ((i * grid_extents / image_resolution)\n - 0.5 * grid_extents)\n for j in range(image_resolution):\n y_position = ((j * grid_extents / image_resolution)\n - 0.5 * grid_extents)\n if x_position ** 2 + y_position ** 2 \n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nBibliography\n1.Canny, John, A computational approach to edge detection, Ieee, 1986.\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nImages/Graphics\n\nThe image \"8bit Heart\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Circle Blur\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Sobel Filters\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"2D Convolution\" was created by James Schloss and Grant Sanderson and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/cooley_tukey/cooley_tukey.html":{"url":"contents/cooley_tukey/cooley_tukey.html","title":"FFT","keywords":"","body":"What Makes a Fourier Transform Fast?\nIf there were ever an algorithm to radically change the landscape of computer science and engineering by making seemingly impossible problems possible, it would be the Fast Fourier Transform (FFT).\nOn the surface, the algorithm seems like a simple application of recursion, and in principle, that is exactly what it is; however, the Fourier Transform is no ordinary transform -- it allows researchers and engineers to easily bounce back and forth between real space and frequency space and is the heart of many physics and engineering applications.\nFrom calculating superfluid vortex positions to super-resolution imaging, Fourier Transforms lay at the heart of many scientific disciplines and are essential to many algorithms we will cover later in this book.\nSimply put, the Fourier Transform is a beautiful application of complex number systems; however, it would rarely be used today if not for the ability to quickly perform the operation with Fast Fourier Transform, first introduced by the great Frederick Gauss in 1805 and later independently discovered by James Cooley and John Tukey in 1965 [1].\nGauss (of course) already had too many things named after him and Cooley and Tukey both had cooler names, so the most common algorithm for FFTs today is known as the Cooley-Tukey algorithm.\nWhat is a Fourier Transform?\nTo an outsider, the Fourier Transform looks like a mathematical mess -- certainly a far cry from the heroic portal between two domains I have depicted it to be; however, like most things, it's not as bad as it initially appears to be.\nSo, here it is in all it's glory!\nF(\\xi) = \\int_{-\\infty} ^\\infty f(x) e^{-2 \\pi i x \\xi} dx\nand\nf(x) = \\int_{-\\infty} ^\\infty F(\\xi) e^{2 \\pi i \\xi x} d\\xi\nWhere F(\\xi) represents a function in frequency space, \\xi represents a value in frequency space, f(x) represents a function in real space, and x represents a value in the real space.\nNote here that the only difference between the two exponential terms is a minus sign in the transformation to frequency space.\nAs I mentioned, this is not intuitive syntax, so please allow me to explain a bit.\nFirstly, what does the Fourier Transform do?\nIf we take a sum sinusoidal functions (like \\sin(\\omega t) or \\cos(\\omega t)), we might find a complicated mess of waves between \\pm 1.\nEach constituent wave can be described by only one value: \\omega.\nSo, instead of representing these curves as seen above, we could instead describe them as peaks in frequency space, as shown below.\n\n \n\n\nThis is what the Fourier Transform does!\nAfter performing the transform, it is now much, much easier to understand precisely which frequencies are in our waveform, which is essential to most areas of signal processing.\nNow, how does this relate to the transformations above?\nWell, the easiest way is to substitute in the Euler's formula:\ne^{2 \\pi i \\theta} = \\cos(2 \\pi \\theta) + i \\sin(2 \\pi \\theta)\nThis clearly turns our function in frequency space into:\nF(\\xi) = \\int_{-\\infty} ^\\infty f(x) (\\cos(-2 \\pi x \\xi) + i \\sin(-2 \\pi x \\xi))dx\nand our function in real space into:\nf(x) = \\int_{-\\infty} ^\\infty F(\\xi) (\\cos(2 \\pi \\xi x) + i \\sin(2 \\pi \\xi x)) d\\xi\nHere, the \\sin and \\cos functions are clearly written in the formulas, so it looks much friendlier, right?\nThis means that a point in real space is defined by the integral over all space of it's corresponding frequency function multiplied by sinusoidal oscillations.\nTruth be told, even after seeing this math, I still didn't understand Fourier Transforms.\nTruth be told, I didn't understand it fully until I discretized real and frequency space to create the Discrete Fourier Transform (DFT), which is the only way to implement Fourier Transforms in code.\nWhat is a Discrete Fourier Transform?\nIn principle, the Discrete Fourier Transform (DFT) is simply the Fourier transform with summations instead of integrals:\nX_k = \\sum_{n=0}^{N-1} x_n \\cdot e^{-2 \\pi i k n / N}\nand\nx_n = \\frac{1}{N} \\sum_{k=0}^{N-1} X_k \\cdot e^{2 \\pi i k n / N}\nWhere X_n and x_n are sequences of N numbers in frequency and real space, respectively.\nIn principle, this is no easier to understand than the previous case!\nFor some reason, though, putting code to this transformation really helped me figure out what was actually going on.\nfunction DFT(x)\n N = length(x)\n\n # We want two vectors here for real space (n) and frequency space (k)\n n = 0:N-1\n k = n'\n transform_matrix = exp.(-2im*pi*n*k/N)\n return transform_matrix*x\n\nend\n\nvoid dft(double complex *X, const size_t N) {\n double complex tmp[N];\n for (size_t i = 0; i \n(defn dft\n \"take a vector of real numbers and return a vector of frequency\n space\"\n [vx]\n (let [len (count vx)]\n (matrix-mult\n (partition len\n (for [n (range len)\n k (range len)]\n ;; expresion below is\n ;; e^(n*k*2*pi*(1/len)*(-i))\n (c/exp (c/* n k\n 2 Math/PI\n (/ len)\n (c/complex 0 -1)))))\n vx)))\n\ntemplate \nvoid dft(Iter X, Iter last) {\n const auto N = last - X;\n std::vector tmp(N);\n for (auto i = 0; i \ndft :: [Complex Double] -> [Complex Double]\ndft x = matMult dftMat x\n where\n n = length x\n w = exp $ (-2) * pi * (0 :+ 1) / fromIntegral n\n dftMat = [[w ^ (j * k) | j \ndef dft(X):\n N = len(X)\n temp = [0] * N\n for i in range(N):\n for k in range(N):\n temp[i] += X[k] * exp(-2.0j * pi * i * k / N)\n return temp\n\n# rdi - array ptr\n# rsi - array size\ndft:\n push rbx\n push r12\n push r13\n push r14\n push r15\n mov r12, rdi # Save parameters\n mov r13, rsi\n sub rsp, r13 # Make a double complex array\n xor r14, r14 # Set index to 0\ndft_loop_i:\n cmp r14, r13 # Check if index is equal to array size\n je dft_end_i\n lea rax, [rsp + r14] # Set tmp array to zero at r14\n mov QWORD PTR [rax], 0\n mov QWORD PTR [rax + 8], 0\n xor r15, r15 # Set second index to 0\ndft_loop_j:\n cmp r15, r13 # Check if the index is equal to array size\n je dft_end_j\n movsd xmm1, two_pi # Calculate xmm1 = -2pi * i * j / N\n mov rax, r14\n imul rax, r15\n shr rax, 4\n cvtsi2sdq xmm2, rax\n mulsd xmm1, xmm2\n cvtsi2sdq xmm2, r13\n divsd xmm1, xmm2\n pxor xmm0, xmm0 # Set xmm0 to 0\n call cexp\n lea rax, [r12 + r15] # Calculate X[i] * cexp(-2pi * i * j / N)\n movsd xmm2, QWORD PTR [rax]\n movsd xmm3, QWORD PTR [rax + 8]\n call __muldc3\n lea rax, [rsp + r14]\n movsd xmm6, QWORD PTR [rax] # Sum to tmp array\n movsd xmm7, QWORD PTR [rax + 8]\n addsd xmm6, xmm0\n addsd xmm7, xmm1\n movsd QWORD PTR [rax], xmm6 # Save to tmp array\n movsd QWORD PTR [rax + 8], xmm7\n add r15, 16\n jmp dft_loop_j\ndft_end_j:\n add r14, 16\n jmp dft_loop_i\ndft_end_i:\n mov rdi, r12 # Move tmp array to array ptr\n mov rsi, rsp\n mov rdx, r13\n call memcpy\n add rsp, r13\n pop r15\n pop r14\n pop r13\n pop r12\n pop rbx\n ret\n\nfunction dft(x) {\n const N = x.length;\n\n // Initialize an array with N elements, filled with 0s\n return Array(N)\n .fill(new Complex(0, 0))\n .map((temp, i) => {\n // Reduce x into the sum of x_k * exp(-2*sqrt(-1)*pi*i*k/N)\n return x.reduce((a, b, k) => {\n return a.add(b.mul(new Complex(0, (-2 * Math.PI * i * k) / N).exp()));\n }, new Complex(0, 0)); // Start accumulating from 0\n });\n}\n\nfn dft(x: &[Complex]) -> Vec> {\n let n = x.len();\n (0..n)\n .map(|i| {\n (0..n)\n .map(|k| {\n x[k] * (Complex::new(0.0_f64, -2.0_f64) * PI * (i as f64) * (k as f64)\n / (n as f64))\n .exp()\n })\n .sum()\n })\n .collect()\n}\n\n(defun coefficient (time-index freq-index dft-len)\n \"Calculates a single twiddle factor for the Fourier Transform.\"\n (exp (- (/ (* #c(0 1) 2.0 pi time-index freq-index)\n dft-len))))\n\n(defun dft (data)\n \"Performs the Discrete Fourier Transform\"\n (let ((dft-len (length data)))\n (loop for freq-index from 0 below dft-len collect\n (loop for time-index from 0 below dft-len sum\n (* (coefficient time-index freq-index dft-len) (elt data time-index))))))\n\n\n\nIn this function, we define n to be a set of integers from 0 \\rightarrow N-1 and arrange them to be a column.\nWe then set k to be the same thing, but in a row.\nThis means that when we multiply them together, we get a matrix, but not just any matrix!\nThis matrix is the heart to the transformation itself!\nM = [1.0+0.0im 1.0+0.0im 1.0+0.0im 1.0+0.0im;\n 1.0+0.0im 6.12323e-17-1.0im -1.0-1.22465e-16im -1.83697e-16+1.0im;\n 1.0+0.0im -1.0-1.22465e-16im 1.0+2.44929e-16im -1.0-3.67394e-16im;\n 1.0+0.0im -1.83697e-16+1.0im -1.0-3.67394e-16im 5.51091e-16-1.0im]\nIt was amazing to me when I saw the transform for what it truly was: an actual transformation matrix!\nThat said, the Discrete Fourier Transform is slow -- primarily because matrix multiplication is slow, and as mentioned before, slow code is not particularly useful.\nSo what was the trick that everyone used to go from a Discrete Fourier Transform to a Fast Fourier Transform?\nRecursion!\nThe Cooley-Tukey Algorithm\nThe problem with using a standard DFT is that it requires a large matrix multiplications and sums over all elements, which are prohibitively complex operations.\nThe Cooley-Tukey algorithm calculates the DFT directly with fewer summations and without matrix multiplications.\nIf necessary, DFTs can still be calculated directly at the early stages of the FFT calculation.\nThe trick to the Cooley-Tukey algorithm is recursion.\nIn particular, we split the matrix we wish to perform the FFT on into two parts: one for all elements with even indices and another for all odd indices.\nWe then proceed to split the array again and again until we have a manageable array size to perform a DFT (or similar FFT) on.\nWe can also perform a similar re-ordering by using a bit reversal scheme, where we output each array index's integer value in binary and flip it to find the new location of that element.\nWith recursion, we can reduce the complexity to \\sim \\mathcal{O}(n \\log n), which is a feasible operation.\nIn the end, the code looks like:\nfunction cooley_tukey(x)\n N = length(x)\n\n if (N > 2)\n x_odd = cooley_tukey(x[1:2:N])\n x_even = cooley_tukey(x[2:2:N])\n else\n x_odd = x[1]\n x_even = x[2]\n end\n n = 0:N-1\n half = div(N,2)\n factor = exp.(-2im*pi*n/N)\n return vcat(x_odd .+ x_even .* factor[1:half],\n x_odd .- x_even .* factor[1:half])\n\nend\n\nvoid cooley_tukey(double complex *X, const size_t N) {\n if (N >= 2) {\n double complex tmp [N / 2];\n for (size_t i = 0; i \n(defn fft [vx]\n (let [len (count vx)]\n (if (= len 1)\n vx\n ;;else\n (let [;; take values of vx in the even indices\n even-indices (keep-indexed #(if (even? %1) %2) vx)\n ;; take values in the odd indices\n odd-indices (keep-indexed #(if (odd? %1) %2) vx)\n ;; recursion\n even-fft (fft even-indices)\n odd-fft (fft odd-indices)\n ;; make a sequence of e^(-2pi*i*k/N) where N is the length\n ;; vx and k range from 0 to N/2\n omegas-half (map\n (comp c/exp\n (partial c/*\n (/ len)\n 2 Math/PI\n (c/complex 0 -1)))\n (range 0 (quot len 2)))\n ;; take the negative of the first sequence because\n ;; e^(-2pi*i*(k+N/2)/N=-e^(-2pi*i*k/N) where k ranges from\n ;; 0 to N/2 \n omegas-2half (map c/- omegas-half)\n mult-add (partial map #(c/+ %3 (c/* %1 %2)))]\n (concat (mult-add omegas-half odd-fft even-fft)\n (mult-add omegas-2half odd-fft even-fft))))))\n\ntemplate \nvoid cooley_tukey(Iter first, Iter last) {\n auto size = last - first;\n if (size >= 2) {\n // split the range, with even indices going in the first half,\n // and odd indices going in the last half.\n auto temp = std::vector(size / 2);\n for (int i = 0; i (size)));\n\n auto& bottom = first[k];\n auto& top = first[k + size / 2];\n top = bottom - w * top;\n bottom -= top - bottom;\n }\n }\n}\n\nfft :: [Complex Double] -> [Complex Double]\nfft x = fft' x\n where\n n = length x\n w0 = exp ((-2) * pi * (0 :+ 1) / fromIntegral n)\n w = M.fromList [(k % n, w0 ^ k) | k e + o * w ! (k %n)) e o [0 ..]\n x2 = zipWith3 (\\e o k -> e - o * w ! (k %n)) e o [0 ..]\n in x1 ++ x2\n\ndef cooley_tukey(X):\n N = len(X)\n if N \n# rdi - array ptr\n# rsi - array size\ncooley_tukey:\n cmp rsi, 16 # Check if size if greater then 1\n jle cooley_tukey_return\n push rbx\n push r12\n push r13\n push r14\n push r15\n mov r12, rdi # Save parameters\n mov r13, rsi\n mov r14, rsi # Save N / 2\n shr r14, 1\n sub rsp, r14 # Make a tmp array\n xor r15, r15\n mov rbx, r12\ncooley_tukey_spliting:\n cmp r15, r14\n je cooley_tukey_split\n lea rax, [r12 + 2 * r15] # Moving all odd entries to the front of the array\n movaps xmm0, XMMWORD PTR [rax + 16]\n movaps xmm1, XMMWORD PTR [rax]\n movaps XMMWORD PTR [rsp + r15], xmm0\n movaps XMMWORD PTR [rbx], xmm1\n add rbx, 16\n add r15, 16\n jmp cooley_tukey_spliting\ncooley_tukey_split:\n mov rax, rsp\n lea rdi, [r12 + r13]\ncooley_tukey_mov_data:\n cmp rbx, rdi\n je cooley_tukey_moved\n movaps xmm0, XMMWORD PTR [rax]\n movaps XMMWORD PTR [rbx], xmm0\n add rbx, 16\n add rax, 16\n jmp cooley_tukey_mov_data\ncooley_tukey_moved:\n add rsp, r14\n mov rdi, r12 # Makking a recursive call\n mov rsi, r14\n call cooley_tukey\n lea rdi, [r12 + r14] # Makking a recursive call\n mov rsi, r14\n call cooley_tukey\n lea rbx, [r12 + r14]\n mov r14, rbx\n mov r15, r12\ncooley_tukey_loop:\n cmp r15, rbx\n je cooley_tukey_end\n pxor xmm0, xmm0 # Calculate cexp(-2.0 * I * M_PI * i / N)\n movsd xmm1, two_pi\n mov rax, r14\n sub rax, rbx\n cvtsi2sdq xmm2, rax\n cvtsi2sdq xmm3, r13\n divsd xmm2, xmm3\n mulsd xmm1, xmm2\n call cexp\n movq xmm2, QWORD PTR [r14] # Calculating X[i] - cexp() * X[i + N / 2]\n movq xmm3, QWORD PTR [r14 + 8]\n call __muldc3\n movq xmm2, QWORD PTR [r15]\n movq xmm3, QWORD PTR [r15 + 8]\n subsd xmm2, xmm0\n subsd xmm3, xmm1\n movq QWORD PTR [r14], xmm2 # Save value in X[i + N / 2]\n movq QWORD PTR [r14 + 8], xmm3\n movq xmm0, QWORD PTR [r15] # Calculating X[i] -= X[i + N / 2] - X[i]\n movq xmm1, QWORD PTR [r15 + 8]\n subsd xmm2, xmm0\n subsd xmm3, xmm1\n subsd xmm0, xmm2\n subsd xmm1, xmm3\n movq QWORD PTR [r15], xmm0\n movq QWORD PTR [r15 + 8], xmm1\n add r14, 16\n add r15, 16\n jmp cooley_tukey_loop\ncooley_tukey_end:\n pop r15\n pop r14\n pop r13\n pop r12\n pop rbx\ncooley_tukey_return:\n ret\n\nfunction cooley_tukey(x) {\n const N = x.length;\n const half = Math.floor(N / 2);\n if (N !(idx % 2)));\n const odds = cooley_tukey(x.filter((_, idx) => idx % 2));\n\n // Fill an array with null values\n let temp = Array(N).fill(null);\n\n for (let i = 0; i \nfn cooley_tukey(x: &[Complex]) -> Vec> {\n let n = x.len();\n if n >());\n let odd = cooley_tukey(&x.iter().skip(1).step_by(2).cloned().collect::>());\n\n let mut temp = vec![Complex::new(0.0_f64, 0.0_f64); n];\n for k in 0..(n / 2) {\n temp[k] = even[k]\n + (Complex::new(0.0_f64, -2.0_f64) * PI * (k as f64) / (n as f64)).exp() * odd[k];\n temp[k + n / 2] = even[k]\n - (Complex::new(0.0_f64, -2.0_f64) * PI * (k as f64) / (n as f64)).exp() * odd[k];\n }\n temp\n}\n\n(defun merge-sub-ffts (evens odds)\n \"Combines the FFTs of the even and odd indices.\"\n (let* ((fft-length (+ (length evens) (length odds)))\n ;; Calculate coefficients for the odd indices.\n (twiddle-factors (loop for i from 0 below (length odds)\n collect (coefficient 1.0 i fft-length)))\n ;; Multiply values with coefficients.\n (odd-terms (mapcar #'* odds twiddle-factors)))\n ;; Combine the two FFTs.\n (concatenate 'list \n (mapcar #'+ evens odd-terms)\n (mapcar #'- evens odd-terms))))\n\n(defun cooley-tukey-rec (data)\n \"Performs the Fourier Transform using the recursive Cooley-Tukey method.\"\n (if (\n\n\nAs a side note, we are enforcing that the array must be a power of 2 for the operation to work.\nThis is a limitation of the fact that we are using recursion and dividing the array in 2 every time; however, if your array is not a power of 2, you can simply pad the leftover space with 0's until your array is a power of 2.\nThe above method is a perfectly valid FFT; however, it is missing the pictorial heart and soul of the Cooley-Tukey algorithm: Butterfly Diagrams.\nButterfly Diagrams\nButterfly Diagrams show where each element in the array goes before, during, and after the FFT.\nAs mentioned, the FFT must perform a DFT.\nThis means that even though we need to be careful about how we add elements together, we are still ultimately performing the following operation:\nX_k = \\sum_{n=0}^{N-1} x_n \\cdot e^{-2 \\pi i k n / N}\nHowever, after shuffling the initial array (by bit reversing or recursive subdivision), we perform the matrix multiplication of the e^{-2 \\pi k n / N} terms in pieces.\nBasically, we split the array into a series of omega values:\n\\omega_N^k = e^{-2 \\pi i k / N}\nAnd at each step, we use the appropriate term.\nFor example, imagine we need to perform an FFT of an array of only 2 elements.\nWe can represent this addition with the following (radix-2) butterfly:\n\n \n\n\nHere, the diagram means the following:\n\nb_0 = a_0 + \\omega_2^0 a_1 \\\\\n\nb_1 = a_0 + \\omega_2^1 a_1\n\nHowever, it turns out that the second half of our array of \\omega values is always the negative of the first half, so \\omega_2^0 = -\\omega_2^1, so we can use the following butterfly diagram:\n\n \n\n\nWith the following equations:\n\nb_0 = a_0 + \\omega_2^0 a_1 \\\\\n\nb_1 = a_0 - \\omega_2^0 a_1\n\nBy swapping out the second \\omega value in this way, we can save a good amount of space.\nNow imagine we need to combine more elements.\nIn this case, we start with simple butterflies, as shown above, and then sum butterflies of butterflies.\nFor example, if we have 8 elements, this might look like this:\n\n \n\n\nNote that we can perform a DFT directly before using any butterflies, if we so desire, but we need to be careful with how we shuffle our array if that's the case.\nIn the code snippet provided in the previous section, the subdivision was performed in the same function as the concatenation, so the ordering was always correct; however, if we were to re-order with bit-reversal, this might not be the case.\nFor example, take a look at the ordering of FFT (found on wikipedia) that performs the DFT shortcut:\n\n \n\n\nHere, the ordering of the array was simply divided into even and odd elements once, but they did not recursively divide the arrays of even and odd elements again because they knew they would perform a DFT soon thereafter.\nUltimately, that's all I want to say about Fourier Transforms for now, but this chapter still needs a good amount of work!\nI'll definitely come back to this at some point, so let me know what you liked and didn't like and we can go from there!\nBibliography\n1.Cooley, James W and Tukey, John W, An algorithm for the machine calculation of complex Fourier series, JSTOR, 1965.\nExample Code\nTo be clear, the example code this time will be complicated and requires the following functions:\n\nAn FFT library (either in-built or something like FFTW)\nAn approximation function to tell if two arrays are similar\n\nAs mentioned in the text, the Cooley-Tukey algorithm may be implemented either recursively or non-recursively, with the recursive method being much easier to implement.\nI would ask that you implement either the recursive or non-recursive methods (or both, if you feel so inclined).\nIf the language you want to write your implementation in is already used, please append your code to the already existing codebase.\nAs before, pull requests are favored.\nNote: I implemented this in Julia because the code seems more straightforward in Julia; however, if you wish to write better Julia code or better code in your own language, please feel free to do so!\nI do not claim that this is the most efficient way to implement the Cooley-Tukey method, so if you have a better way to do it, feel free to implement it that way!\nusing FFTW\n\n#simple DFT function\nfunction DFT(x)\n N = length(x)\n\n # We want two vectors here for real space (n) and frequency space (k)\n n = 0:N-1\n k = n'\n transform_matrix = exp.(-2im*pi*n*k/N)\n return transform_matrix*x\n\nend\n\n# Implementing the Cooley-Tukey Algorithm\nfunction cooley_tukey(x)\n N = length(x)\n\n if (N > 2)\n x_odd = cooley_tukey(x[1:2:N])\n x_even = cooley_tukey(x[2:2:N])\n else\n x_odd = x[1]\n x_even = x[2]\n end\n n = 0:N-1\n half = div(N,2)\n factor = exp.(-2im*pi*n/N)\n return vcat(x_odd .+ x_even .* factor[1:half],\n x_odd .- x_even .* factor[1:half])\n\nend\n\nfunction bitreverse(a::Array)\n # First, we need to find the necessary number of bits\n digits = convert(Int,ceil(log2(length(a))))\n\n indices = [i for i = 0:length(a)-1]\n\n bit_indices = []\n for i = 1:length(indices)\n push!(bit_indices, bitstring(indices[i]))\n end\n\n # Now stripping the unnecessary numbers\n for i = 1:length(bit_indices)\n bit_indices[i] = bit_indices[i][end-digits:end]\n end\n\n # Flipping the bits\n for i =1:length(bit_indices)\n bit_indices[i] = reverse(bit_indices[i])\n end\n\n # Replacing indices\n for i = 1:length(indices)\n indices[i] = 0\n for j = 1:digits\n indices[i] += 2^(j-1) * parse(Int, string(bit_indices[i][end-j]))\n end\n indices[i] += 1\n end\n\n b = [float(i) for i = 1:length(a)]\n for i = 1:length(indices)\n b[i] = a[indices[i]]\n end\n\n return b\nend\n\nfunction iterative_cooley_tukey(x)\n N = length(x)\n logN = convert(Int,ceil(log2(length(x))))\n bnum = div(N,2)\n stride = 0;\n\n x = bitreverse(x)\n\n z = [Complex(x[i]) for i = 1:length(x)]\n for i = 1:logN\n stride = div(N, bnum)\n for j = 0:bnum-1\n start_index = j*stride + 1\n y = butterfly(z[start_index:start_index + stride - 1])\n for k = 1:length(y)\n z[start_index+k-1] = y[k]\n end\n end\n bnum = div(bnum,2)\n end\n\n return z\nend\n\nfunction butterfly(x)\n N = length(x)\n half = div(N,2)\n n = [i for i = 0:N-1]\n half = div(N,2)\n factor = exp.(-2im*pi*n/N)\n\n y = [0 + 0.0im for i = 1:length(x)]\n\n for i = 1:half\n y[i] = x[i] + x[half+i]*factor[i]\n y[half+i] = x[i] - x[half+i]*factor[i]\n end\n\n return y\nend\n\nfunction main()\n x = rand(128)\n y = cooley_tukey(x)\n z = iterative_cooley_tukey(x)\n w = fft(x)\n if(isapprox(y, w))\n println(\"Recursive Cooley Tukey matches fft() from FFTW package.\")\n end\n if(isapprox(z, w))\n println(\"Iterative Cooley Tukey matches fft() from FFTW package.\")\n end\nend\n\nmain()\n\n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nvoid fft(double complex *x, size_t n) {\n double complex y[n];\n memset(y, 0, sizeof(y));\n fftw_plan p;\n\n p = fftw_plan_dft_1d((int)n, (fftw_complex*)x, (fftw_complex*)y,\n FFTW_FORWARD, FFTW_ESTIMATE);\n\n fftw_execute(p);\n fftw_destroy_plan(p);\n\n for (size_t i = 0; i = 2) {\n double complex tmp [N / 2];\n for (size_t i = 0; i >= 1;\n while (n > 0) {\n a = (a >= 1;\n }\n n = (a i) {\n double complex tmp = X[i];\n X[i] = X[n];\n X[n] = tmp;\n }\n }\n}\n\nvoid iterative_cooley_tukey(double complex *X, size_t N) {\n bit_reverse(X, N);\n\n for (int i = 1; i 1E-5) {\n printf(\"This is not approximate.\\n\");\n return;\n }\n }\n printf(\"This is approximate.\\n\");\n}\n\nint main() {\n srand((unsigned int)time(NULL));\n double complex x[64], y[64], z[64];\n for (size_t i = 0; i \n(ns fft.core\n (:require [complex.core :as c]))\n;; complex is a jar for complex numbers\n;; https://github.com/alanforr/complex\n;; add [complex \"0.1.11\"] to :dependencies in your project.clj\n;; and run lein repl or lein deps in the terminal\n(defn matrix-mult\n \"take a matrix m and a vector v which length is number of columns\n ,return a vector of applying dot-product between v and each row of\n m. the returned vector's length is the number of rows of m\"\n [m v]\n (mapv (comp (partial apply c/+)\n (partial map c/* v))\n m))\n(defn dft\n \"take a vector of real numbers and return a vector of frequency\n space\"\n [vx]\n (let [len (count vx)]\n (matrix-mult\n (partition len\n (for [n (range len)\n k (range len)]\n ;; expresion below is\n ;; e^(n*k*2*pi*(1/len)*(-i))\n (c/exp (c/* n k\n 2 Math/PI\n (/ len)\n (c/complex 0 -1)))))\n vx)))\n(defn fft [vx]\n (let [len (count vx)]\n (if (= len 1)\n vx\n ;;else\n (let [;; take values of vx in the even indices\n even-indices (keep-indexed #(if (even? %1) %2) vx)\n ;; take values in the odd indices\n odd-indices (keep-indexed #(if (odd? %1) %2) vx)\n ;; recursion\n even-fft (fft even-indices)\n odd-fft (fft odd-indices)\n ;; make a sequence of e^(-2pi*i*k/N) where N is the length\n ;; vx and k range from 0 to N/2\n omegas-half (map\n (comp c/exp\n (partial c/*\n (/ len)\n 2 Math/PI\n (c/complex 0 -1)))\n (range 0 (quot len 2)))\n ;; take the negative of the first sequence because\n ;; e^(-2pi*i*(k+N/2)/N=-e^(-2pi*i*k/N) where k ranges from\n ;; 0 to N/2 \n omegas-2half (map c/- omegas-half)\n mult-add (partial map #(c/+ %3 (c/* %1 %2)))]\n (concat (mult-add omegas-half odd-fft even-fft)\n (mult-add omegas-2half odd-fft even-fft))))))\n(defn -main [& args]\n (let [vx [0 1 2 3]\n len (count vx)\n ;; calculate the next power of 2 after len\n ;; the reason behind this is to fill them with zeros for fft\n next-len (->>\n [len 2]\n (map #(Math/log %))\n (apply /)\n Math/ceil\n (Math/pow 2)\n int)\n ;; add zeros at the end of vx\n complete-vx (into vx (repeat (- next-len len) 0))\n fft-cvx (fft complete-vx)\n dft-cvx (dft complete-vx)\n diffv (mapv c/- fft-cvx dft-cvx)]\n (println \"vx:\" vx)\n (println \"complete-vx:\" complete-vx)\n (println \"result from fft:\" (map c/stringify fft-cvx))\n (println \"result from dft:\" (map c/stringify dft-cvx))\n (println \"difference: \" (map c/stringify diffv))))\n\n// written by Gathros, modernized by Nicole Mazzuca.\n\n#include \n#include \n#include \n#include \n#include \n\n// These headers are for presentation not for the algorithm.\n#include \n#include \n#include \n\nusing std::begin;\nusing std::end;\nusing std::swap;\n\nusing std::size_t;\n\nusing complex = std::complex;\nstatic const double pi = 3.14159265358979323846264338327950288419716;\n\ntemplate \nvoid dft(Iter X, Iter last) {\n const auto N = last - X;\n std::vector tmp(N);\n for (auto i = 0; i \nvoid cooley_tukey(Iter first, Iter last) {\n auto size = last - first;\n if (size >= 2) {\n // split the range, with even indices going in the first half,\n // and odd indices going in the last half.\n auto temp = std::vector(size / 2);\n for (int i = 0; i (size)));\n\n auto& bottom = first[k];\n auto& top = first[k + size / 2];\n top = bottom - w * top;\n bottom -= top - bottom;\n }\n }\n}\n\n// note: (last - first) must be less than 2**32 - 1\ntemplate \nvoid sort_by_bit_reverse(Iter first, Iter last) {\n // sorts the range [first, last) in bit-reversed order,\n // by the method suggested by the FFT\n auto size = last - first;\n\n for (std::uint32_t i = 0; i > 1) | ((b & 0x55555555) > 2) | ((b & 0x33333333) > 4) | ((b & 0x0f0f0f0f) > 8) | ((b & 0x00ff00ff) > 16) | (b > (32 - std::uint32_t(log2(static_cast(size))));\n if (b > i) {\n swap(first[b], first[i]);\n }\n }\n}\n\n// `iterative_cooley_tukey` does the cooley-tukey algorithm iteratively\ntemplate \nvoid iterative_cooley_tukey(Iter first, Iter last) {\n sort_by_bit_reverse(first, last);\n\n // perform the butterfly on the range\n auto size = last - first;\n for (int stride = 2; stride distribution(0.0, 1.0);\n\n std::array initial;\n std::generate(\n begin(initial), end(initial), [&] { return distribution(rng); });\n\n auto recursive = initial;\n auto iterative = initial;\n\n // Preform an FFT on the arrays.\n cooley_tukey(begin(recursive), end(recursive));\n iterative_cooley_tukey(begin(iterative), end(iterative));\n\n // Check if the arrays are approximately equivalent\n std::cout \nimport Data.Complex\nimport Data.List (partition)\nimport Data.Map ((!))\nimport qualified Data.Map as M\nimport Data.Ratio\n\ndft :: [Complex Double] -> [Complex Double]\ndft x = matMult dftMat x\n where\n n = length x\n w = exp $ (-2) * pi * (0 :+ 1) / fromIntegral n\n dftMat = [[w ^ (j * k) | j [Complex Double]\nfft x = fft' x\n where\n n = length x\n w0 = exp ((-2) * pi * (0 :+ 1) / fromIntegral n)\n w = M.fromList [(k % n, w0 ^ k) | k e + o * w ! (k %n)) e o [0 ..]\n x2 = zipWith3 (\\e o k -> e - o * w ! (k %n)) e o [0 ..]\n in x1 ++ x2\n\nmain = do\n print $ dft [0, 1, 2, 3]\n print $ fft [0, 1, 2, 3]\n\nfrom random import random\nfrom cmath import exp, pi\nfrom math import log2\n\n\ndef dft(X):\n N = len(X)\n temp = [0] * N\n for i in range(N):\n for k in range(N):\n temp[i] += X[k] * exp(-2.0j * pi * i * k / N)\n return temp\n\n\ndef cooley_tukey(X):\n N = len(X)\n if N > i & 1)\n temp[k] = X[b]\n temp[b] = X[k]\n return temp\n\n\ndef iterative_cooley_tukey(X):\n N = len(X)\n\n X = bit_reverse(X)\n\n for i in range(1, int(log2(N)) + 1):\n stride = 2 ** i\n w = exp(-2.0j * pi / stride)\n for j in range(0, N, stride):\n v = 1\n for k in range(stride // 2):\n X[k + j + stride // 2] = X[k + j] - v * X[k + j + stride // 2]\n X[k + j] -= X[k + j + stride // 2] - X[k + j]\n v *= w\n return X\n\n\nX = []\n\nfor i in range(64):\n X.append(random())\n\nY = cooley_tukey(X)\nZ = iterative_cooley_tukey(X)\nT = dft(X)\n\nprint(all(abs([Y[i] - Z[i] for i in range(64)][j]) \n.intel_syntax noprefix\n\n.section .rodata\n two: .double 2.0\n one: .double 1.0\n two_pi: .double -6.28318530718\n rand_max: .long 4290772992\n .long 1105199103\n fmt: .string \"%g\\n\"\n\n.section .text\n .global main\n .extern printf, memset, memcpy, srand, rand, time, cexp, __muldc3, cabs, log2\n\n# rdi - array ptr\n# rsi - array size\ndft:\n push rbx\n push r12\n push r13\n push r14\n push r15\n mov r12, rdi # Save parameters\n mov r13, rsi\n sub rsp, r13 # Make a double complex array\n xor r14, r14 # Set index to 0\ndft_loop_i:\n cmp r14, r13 # Check if index is equal to array size\n je dft_end_i\n lea rax, [rsp + r14] # Set tmp array to zero at r14\n mov QWORD PTR [rax], 0\n mov QWORD PTR [rax + 8], 0\n xor r15, r15 # Set second index to 0\ndft_loop_j:\n cmp r15, r13 # Check if the index is equal to array size\n je dft_end_j\n movsd xmm1, two_pi # Calculate xmm1 = -2pi * i * j / N\n mov rax, r14\n imul rax, r15\n shr rax, 4\n cvtsi2sdq xmm2, rax\n mulsd xmm1, xmm2\n cvtsi2sdq xmm2, r13\n divsd xmm1, xmm2\n pxor xmm0, xmm0 # Set xmm0 to 0\n call cexp\n lea rax, [r12 + r15] # Calculate X[i] * cexp(-2pi * i * j / N)\n movsd xmm2, QWORD PTR [rax]\n movsd xmm3, QWORD PTR [rax + 8]\n call __muldc3\n lea rax, [rsp + r14]\n movsd xmm6, QWORD PTR [rax] # Sum to tmp array\n movsd xmm7, QWORD PTR [rax + 8]\n addsd xmm6, xmm0\n addsd xmm7, xmm1\n movsd QWORD PTR [rax], xmm6 # Save to tmp array\n movsd QWORD PTR [rax + 8], xmm7\n add r15, 16\n jmp dft_loop_j\ndft_end_j:\n add r14, 16\n jmp dft_loop_i\ndft_end_i:\n mov rdi, r12 # Move tmp array to array ptr\n mov rsi, rsp\n mov rdx, r13\n call memcpy\n add rsp, r13\n pop r15\n pop r14\n pop r13\n pop r12\n pop rbx\n ret\n\n# rdi - array ptr\n# rsi - array size\ncooley_tukey:\n cmp rsi, 16 # Check if size if greater then 1\n jle cooley_tukey_return\n push rbx\n push r12\n push r13\n push r14\n push r15\n mov r12, rdi # Save parameters\n mov r13, rsi\n mov r14, rsi # Save N / 2\n shr r14, 1\n sub rsp, r14 # Make a tmp array\n xor r15, r15\n mov rbx, r12\ncooley_tukey_spliting:\n cmp r15, r14\n je cooley_tukey_split\n lea rax, [r12 + 2 * r15] # Moving all odd entries to the front of the array\n movaps xmm0, XMMWORD PTR [rax + 16]\n movaps xmm1, XMMWORD PTR [rax]\n movaps XMMWORD PTR [rsp + r15], xmm0\n movaps XMMWORD PTR [rbx], xmm1\n add rbx, 16\n add r15, 16\n jmp cooley_tukey_spliting\ncooley_tukey_split:\n mov rax, rsp\n lea rdi, [r12 + r13]\ncooley_tukey_mov_data:\n cmp rbx, rdi\n je cooley_tukey_moved\n movaps xmm0, XMMWORD PTR [rax]\n movaps XMMWORD PTR [rbx], xmm0\n add rbx, 16\n add rax, 16\n jmp cooley_tukey_mov_data\ncooley_tukey_moved:\n add rsp, r14\n mov rdi, r12 # Makking a recursive call\n mov rsi, r14\n call cooley_tukey\n lea rdi, [r12 + r14] # Makking a recursive call\n mov rsi, r14\n call cooley_tukey\n lea rbx, [r12 + r14]\n mov r14, rbx\n mov r15, r12\ncooley_tukey_loop:\n cmp r15, rbx\n je cooley_tukey_end\n pxor xmm0, xmm0 # Calculate cexp(-2.0 * I * M_PI * i / N)\n movsd xmm1, two_pi\n mov rax, r14\n sub rax, rbx\n cvtsi2sdq xmm2, rax\n cvtsi2sdq xmm3, r13\n divsd xmm2, xmm3\n mulsd xmm1, xmm2\n call cexp\n movq xmm2, QWORD PTR [r14] # Calculating X[i] - cexp() * X[i + N / 2]\n movq xmm3, QWORD PTR [r14 + 8]\n call __muldc3\n movq xmm2, QWORD PTR [r15]\n movq xmm3, QWORD PTR [r15 + 8]\n subsd xmm2, xmm0\n subsd xmm3, xmm1\n movq QWORD PTR [r14], xmm2 # Save value in X[i + N / 2]\n movq QWORD PTR [r14 + 8], xmm3\n movq xmm0, QWORD PTR [r15] # Calculating X[i] -= X[i + N / 2] - X[i]\n movq xmm1, QWORD PTR [r15 + 8]\n subsd xmm2, xmm0\n subsd xmm3, xmm1\n subsd xmm0, xmm2\n subsd xmm1, xmm3\n movq QWORD PTR [r15], xmm0\n movq QWORD PTR [r15 + 8], xmm1\n add r14, 16\n add r15, 16\n jmp cooley_tukey_loop\ncooley_tukey_end:\n pop r15\n pop r14\n pop r13\n pop r12\n pop rbx\ncooley_tukey_return:\n ret\n\n# rdi - array ptr\n# rsi - array size\nbit_reverse:\n push rbx\n push r12\n push r13\n push r14\n push r15\n mov r12, rdi # Save parameters\n mov r13, rsi\n shr r13, 4\n xor r14, r14 # Loop through all entries\nbit_reverse_entries:\n cmp r14, r13\n je bit_reverse_return\n cvtsi2sdq xmm0, r13 # Calculating the number of bit in N\n call log2\n cvttsd2si rcx, xmm0\n mov rdi, 1 # Calculating (1 \nconst Complex = require(\"complex.js\");\n\nfunction dft(x) {\n const N = x.length;\n\n // Initialize an array with N elements, filled with 0s\n return Array(N)\n .fill(new Complex(0, 0))\n .map((temp, i) => {\n // Reduce x into the sum of x_k * exp(-2*sqrt(-1)*pi*i*k/N)\n return x.reduce((a, b, k) => {\n return a.add(b.mul(new Complex(0, (-2 * Math.PI * i * k) / N).exp()));\n }, new Complex(0, 0)); // Start accumulating from 0\n });\n}\n\nfunction cooley_tukey(x) {\n const N = x.length;\n const half = Math.floor(N / 2);\n if (N !(idx % 2)));\n const odds = cooley_tukey(x.filter((_, idx) => idx % 2));\n\n // Fill an array with null values\n let temp = Array(N).fill(null);\n\n for (let i = 0; i 2 * x);\n return twice.concat(twice.map(x => x + 1));\n }\n}\n\nfunction bit_reverse(x) {\n const N = x.length;\n const indexes = bit_reverse_idxs(Math.log2(N));\n return x.map((_, i) => x[indexes[i]]);\n}\n\n// Assumes log_2(N) is an integer\nfunction iterative_cooley_tukey(x) {\n const N = x.length;\n\n x = bit_reverse(x);\n\n for (let i = 1; i new Complex(Math.random(), 0));\nconst Y = cooley_tukey(X);\nconst Z = iterative_cooley_tukey(X);\nconst T = dft(X);\n\n// Check if the calculations are correct within a small tolerance\nconsole.log(\"Cooley tukey approximation is accurate: \", approx(Y, T));\nconsole.log(\"Iterative cooley tukey approximation is accurate: \", approx(Z, T));\n\nextern crate rand;\nextern crate rustfft;\n\nuse rand::prelude::*;\nuse rustfft::num_complex::Complex;\nuse rustfft::FFTplanner;\nuse std::f64::consts::PI;\n\n// This is based on the Python and C implementations.\n\nfn fft(x: &[Complex]) -> Vec> {\n let n = x.len();\n let mut new_x = x.to_vec();\n let mut y = vec![Complex::new(0.0_f64, 0.0_f64); n];\n\n let mut planner = FFTplanner::new(false);\n let this_fft = planner.plan_fft(n);\n this_fft.process(new_x.as_mut_slice(), y.as_mut_slice());\n\n // y.into_iter().map(|i| i / (n as f64).sqrt()).collect()\n y\n}\n\nfn dft(x: &[Complex]) -> Vec> {\n let n = x.len();\n (0..n)\n .map(|i| {\n (0..n)\n .map(|k| {\n x[k] * (Complex::new(0.0_f64, -2.0_f64) * PI * (i as f64) * (k as f64)\n / (n as f64))\n .exp()\n })\n .sum()\n })\n .collect()\n}\n\nfn cooley_tukey(x: &[Complex]) -> Vec> {\n let n = x.len();\n if n >());\n let odd = cooley_tukey(&x.iter().skip(1).step_by(2).cloned().collect::>());\n\n let mut temp = vec![Complex::new(0.0_f64, 0.0_f64); n];\n for k in 0..(n / 2) {\n temp[k] = even[k]\n + (Complex::new(0.0_f64, -2.0_f64) * PI * (k as f64) / (n as f64)).exp() * odd[k];\n temp[k + n / 2] = even[k]\n - (Complex::new(0.0_f64, -2.0_f64) * PI * (k as f64) / (n as f64)).exp() * odd[k];\n }\n temp\n}\n\nfn bit_reverse(x: &[Complex]) -> Vec> {\n let n = x.len();\n let mut temp = vec![Complex::new(0.0_f64, 0.0_f64); n];\n for k in 0..n {\n let b: usize = (0..((n as f64).log2() as usize))\n .filter(|i| k >> i & 1 != 0)\n .map(|i| 1 ]) -> Vec> {\n let n = x.len();\n\n let mut new_x = bit_reverse(x);\n\n for i in 1..=((n as f64).log2() as usize) {\n let stride = 2_u128.pow(i as u32);\n let w = (Complex::new(0.0_f64, -2.0_f64) * PI / (stride as f64)).exp();\n for j in (0..n).step_by(stride as usize) {\n let mut v = Complex::new(1.0_f64, 0.0_f64);\n for k in 0..((stride / 2) as usize) {\n new_x[k + j + ((stride / 2) as usize)] =\n new_x[k + j] - v * new_x[k + j + ((stride / 2) as usize)];\n new_x[k + j] =\n new_x[k + j] - (new_x[k + j + ((stride / 2) as usize)] - new_x[k + j]);\n v *= w;\n }\n }\n }\n\n new_x\n}\n\nfn main() {\n let mut x = Vec::with_capacity(64);\n let mut rng = thread_rng();\n for _i in 0..64 {\n let real = rng.gen_range(0.0_f64, 1.0_f64);\n x.push(Complex::new(real, 0.0_f64));\n }\n let v = fft(&x);\n let y = cooley_tukey(&x);\n let z = iterative_cooley_tukey(&x);\n let t = dft(&x);\n\n println!(\n \"{}\",\n v.iter().zip(y.iter()).all(|i| (i.0 - i.1).norm() \n\n(defun coefficient (time-index freq-index dft-len)\n \"Calculates a single twiddle factor for the Fourier Transform.\"\n (exp (- (/ (* #c(0 1) 2.0 pi time-index freq-index)\n dft-len))))\n\n(defun dft (data)\n \"Performs the Discrete Fourier Transform\"\n (let ((dft-len (length data)))\n (loop for freq-index from 0 below dft-len collect\n (loop for time-index from 0 below dft-len sum\n (* (coefficient time-index freq-index dft-len) (elt data time-index))))))\n\n(defun merge-sub-ffts (evens odds)\n \"Combines the FFTs of the even and odd indices.\"\n (let* ((fft-length (+ (length evens) (length odds)))\n ;; Calculate coefficients for the odd indices.\n (twiddle-factors (loop for i from 0 below (length odds)\n collect (coefficient 1.0 i fft-length)))\n ;; Multiply values with coefficients.\n (odd-terms (mapcar #'* odds twiddle-factors)))\n ;; Combine the two FFTs.\n (concatenate 'list \n (mapcar #'+ evens odd-terms)\n (mapcar #'- evens odd-terms))))\n\n(defun cooley-tukey-rec (data)\n \"Performs the Fourier Transform using the recursive Cooley-Tukey method.\"\n (if (\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"FTexample\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"radix2positive\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"radix2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"radix8\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"DIT-FFT-butterfly\" was created by Virens and is licensed under the Creative Commons Attribution 3.0 Unported License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/notation/notation.html":{"url":"contents/notation/notation.html","title":"Complexity Notation","keywords":"","body":"Complexity Notation\nAlgorithms are designed to solve problems.\nOver time, new algorithms are created to solve problems that old algorithms have already solved.\nIn some cases, the new algorithms are not intrinsically better than the older ones.\nIn other cases, these new algorithms breathe life into areas of research and engineering that could not exist without them.\nThe question is: what makes an algorithm \"better\" than another one?\nObviously, there is no good answer to this question.\nIf you write an algorithm to solve a problem, whatever you come up with will probably work just fine for small problems.\nThat said, if you need to use the algorithm for a larger system, you might find yourself waiting for longer and longer on your code to run.\nIn these cases, it's obvious that if you are working on a large system, you need an algorithm that scales well with a large size.\nIdeally, an algorithm that works well for a large system will also work with a smaller one; however, this is not always the case.\nIn order to determine the best algorithm for your system, it's often best to consult a tool computer scientists use to describe how algorithms scale with system size: complexity theory.\nHere's the idea: algorithms operate on data.\nComplexity theory uses different notations to describe how many operations an algorithm will need.\nIn this way, computational complexity measures runtime in terms of the number of operations an algorithm takes to complete its task.\nTo be clear, the notations used are not at all exact, but they roughly describe the run-time of code and can be used to estimate how long an algorithm should take to run.\nIn addition, there are many different notations depending on who you ask, but for now we'll focus on the big 3: O, \\Omega, and \\Theta.\nBig O assumes the worst, which is the often the most useful description of an algorithm.\nOn the other hand, \\Omega assumes the best and \\Theta is used when the best and worst cases are the same.\nIt may seems like strange that an algorithm can run in different time, but let me explain a while:\nfunction constant(a::UInt64, b::UInt64)\n println(b)\n for i=0:18446744073709551615\n if(a \nIf we calculates the big 3 in b, it will be \\Omega(1) and O(b), Obviously not the same.\nThe best-case runtime will be 1 println statement if a > b, the worst-case runtime will be b println statement if a = 1.\nSo that's the explanation, and let's move on.\nOf the three Big O is used the most, and is used in conversation to mean that the algorithm will take \"on the order of\" n operations.\nUnfortunately, at this point, these notations might be a little vague.\nIn fact, it was incredibly vague for me for a long time, and it wasn't until I saw the notations in action that it all started to make sense, so that's what this section is about: providing concrete examples to better understand computational complexity notation.\nIn algorithms below, let us consider that the slowest statement is println, and we always talk about all the println in the function.\nConstant Time\nLet's write some code that reads in an array of length n and runs with constant time:\nfunction constant(a::Array{Float64})\n println(a[1])\nend\n\nObviously, no matter how large a is, this function will not take any longer to run.\nBecause of this, we say it has a constant runtime and notate it with O(1) = \\Omega(1) = \\Theta(1).\nBasically, we are saying that this function will run with 1 operation total (a single print).\nThe best-case runtime will be 1 operation, the worst-case runtime will be 1 operation, and because they are both the same, we can use \\Theta to notate that.\nNow imagine the following function:\nfunction constant(a::Array{Float64})\n if (length(a) >= 3)\n println(a[1])\n println(a[2])\n println(a[3])\n end\nend\n\nThis function has 3 print statements, so it has 3 operations total.\nBecause of this, it's tempting to say that the runtime would be O(3) = \\Omega(3) = \\Theta(3), and you would not be wrong; however, complexity notations often make a big assumption: we don't care about constants!\nWhat does this mean? Well, it means that we get rid of all constants that are not 1!\nIn this case, that means we set O(3) = O(1).\nNow, I know what you are thinking, That's stupid! It's clear that the second function will take 3 times as long to run, shouldn't we notate that?\nYou're not wrong; however, complexity notation is mostly interested in how algorithms scale with larger and larger inputs.\nBecause we are talking about constant run-time, there is no scaling with larger inputs. No matter what array you read in to the above functions, they will always take a constant number of operations to finish.\nWhether that constant time is 1 operation or 3 operations doesn't really matter because different machines will have different runtimes anyway.\nNow, here's the thing: as we move on to more complicated examples, we will continue to ignore constants and extra terms to make the notation easier to understand.\nJust because this is common practice does not mean it's the best practice.\nI have run into several situation where knowing the constants has saved me hours of run-time, so keep in mind that all of these notations are somewhat vague and dependent on a number of auxiliary factors.\nStill, that doesn't mean the notation is completely useless. For now, let's keep moving forward with some more complicated (and useful) examples!\nLinear Time\nNow we are moving into interesting territory!\nLet's consider the following function:\nfunction linear(a::Array{Float64})\n for i = 1:length(a)\n println(a[i])\n end\nend\n\nHere, it's clear that if we increase a by one element, we will need to do another operation.\nThat is, with an array of size n, we will need to do n operations, which means that our complexity is O(n) = \\Omega(n) = \\Theta(n).\nAs before, adding more operations into the for loop will change the constant in front of n in our complexity notation, but we'll continue to ignore those constants.\nFor example:\nfunction linear(a::Array{Float64})\n println(\"The first element in our array is: \", a[1])\n\n println(\"The sum of all pairs of elements in our array are...\")\n for i = 1:length(a)/2\n println(\"a is: \", a[2*i])\n println(\"b is: \", a[2*i+1])\n println(\"The sum of a and b is: \", a[2*i] + a[2*i+1])\n end\n\n println(\"The last element in our array is: \", a[end])\nend\n\nTechnically has a complexity of \\Theta(\\frac{3n}{2} + 2), but we'll just call it \\Theta(n).\nRegardless of the notation, if you see something that is O(n), you know that at worst it will run at the speed of a for loop, which is pretty good!\nPolynomial Time\nA promise of O(n) is not bad in terms of run-time; however, it is unlikely that you will run into too many straightforward algorithms that are O(n).\nFor example, let's say you have a square, 2D image and want to iterate through all of its points.\nWell, to do this, we might write code that looks something like:\n# Here, size is the length of a single side of the image\nfunction access_image(img::Array{Float64}, size::Int64)\n for i = 1:size\n for j = 1:size\n index = j + i*size\n println(img[index])\n end\n end\nend\n\nThis is a simple case where a nested for loop is perfectly acceptable, and it's obvious geometrically that we need to access \\mathrm{size}\\times\\mathrm{size} number of elements (because we are working with a square).\nThis means that this example has \\Theta(n^2) complexity. This is not great.\nIf you have to access 3D space, this might require \\Theta(n^3), which is even worse! Don't even get me started on 4D!\nIntuitively, if you see anything that has a polynomial runtime, it's easy to think of it as a bunch of nested for loops.\nThat said, there have been several cases throughout the history of algorithms where polynomial runtimes have inhibited certain algorithms from being used entirely, simply because it takes too long to run!\nFor this reason, if you can avoid writing nested for loops, you certainly should!\nHowever, there are several cases where this cannot be avoided, so don't spend too much time worrying about it unless runtime becomes an issue!\nExponential and Logarithmic Time\nThese are two more cases that come up all the time and often require a common theme: recursion.\nGenerally speaking, logarithmic algorithms are some of the fastest algorithms out there, while exponential algorithms are some of the slowest.\nUnfortunately, this means that recursion can be either the most useful tool in existence for realizing certain algorithms or the most harmful one, depending on your problem.\nHere is a simple example of a function with exponential runtime:\n# Here, n is the number of iterations\nfunction exponential(value::Int64, n::Int64)\n println(value)\n if(n >= 0)\n value += 1\n exponential(value, n-1)\n exponential(value, n-1)\nend\n\nHere, we read in the maximum number n we are iterating through and recursively call the exponential function, decrementing the number of iterations left each time.\nBecause we are calling the exponential function twice, this has a complexity of \\Theta(2^n), which is not great, but if it's the only way to get a job done, it's the only way to get a job done.\nLogarithmic algorithms can be thought of as the opposite of exponential ones.\nInstead of taking a value and computing more and more values each time, a good example of a logarithmic algorithm is one that takes an array and recursively divides it up, like so:\n# Here, cutoff is an arbitrary variable to know when to stop recursing\nfunction logarithmic(a::Array{Float64}, cutoff::Int64)\n if (length(a) > cutoff)\n logarithmic(a[length(a)/2+1:end], cutoff)\n end\n println(length(a))\nend\n\nTo be honest, it is not obvious that the provided logarithmic function should operate in \\Theta(\\log(n)) time, where n is the size of a.\nThat said, I encourage you to think about an array of size 8.\nFirst, we split it in half and run the algorithm on one of them, creating an array of 4 elements.\nIf we split the new array and run it on 1 of them, we have an array of 2, and if we split it by two and run on 1 we have an array of 1 element each.\nThis is as far as we can go, and we ended up dividing the array 3 times to get to this point.\n3 = \\log_2(8), so this function runs with a logarithmic number of operations.\nPutting it all together\nWe've outlined the most common complexity cases of different algorithms here, but at this point things might still be unclear.\nWhich is better: O(n^2) or O(log(n))?\nWell, let's plot all the different cases out, and the answer should become obvious.\n\n \n\n\nHere, we see each of the complexity cases as n increases.\nClearly, linear time is not bad when compared to polynomial or exponential time; however, if you can manage something in logarithmic or constant time, do it!\nNow, there is a lot more to say about computational complexity and we'll definitely cover it at some point, but I can only move so fast!\nIn particular, I would love to have a discussion on the P=NP issue that has been rustling the jimmies of a few computer scientists for a while, but we'll get to that in due time.\nFinal Warning\nThis is a book about algorithms.\nIt would be nearly impossible to talk about most algorithms without touching on complexity theory and explaining why certain algorithms are faster than others.\nThat said, just because an algorithm runs in O(\\log n) does not mean it will always be faster than one that runs in O(n^2).\nBecause complexity notation often ignores constants, there could be a crazy constant that we are missing that actually makes a huge difference in runtime.\nIn addition, in order to use an algorithm that seems faster based on complexity notation, you may need to use a library that massively increases runtime due to a plethora of other reasons.\nBasically, take complexity notation with a grain of salt.\nIt is a useful descriptor of how fast algorithms should run in an ideal world; however, ideal worlds do not exist.\nWhen it comes to programming, there may be hundreds of other factors that need to be considered before implementing anything.\nThat said, complexity notation should not be ignored.\nIf you can easily implement an algorithm that is notationally faster with no repercussions, go for it!\nJust be sure you do not waste time trying to optimize code you haven't written yet.\nIn general, my advice would be the following:\nwrite code first and optimize what you can on the first run-through without going too far out of your way.\nIf the runtime is awful, go back and see about implementing algorithms that are faster based on complexity notation.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"Complexity Scaling\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/thomas_algorithm/thomas_algorithm.html":{"url":"contents/thomas_algorithm/thomas_algorithm.html","title":"Thomas Algorithm","keywords":"","body":"Thomas Algorithm\nAs alluded to in the Gaussian Elimination chapter, the Thomas Algorithm (or TDMA, Tri-Diagonal Matrix Algorithm) allows for programmers to massively cut the computational cost of their code from O(n^3) to O(n) in certain cases!\nThis is done by exploiting a particular case of Gaussian Elimination where the matrix looks like this:\n\n\\left[\n \\begin{array}{ccccc|c}\n b_0 & c_0 & & & & d_0 \\\\\n a_1 & b_1 & c_1 & & & d_1 \\\\\n & a_2 & \\ddots & & & \\vdots \\\\\n & & & & c_{n-1}& d_{n-1} \\\\\n & & & a_n & b_n & d_n\n \\end{array}\n\\right]\n\nThis matrix shape is called Tri-Diagonal (excluding the right-hand side of our system of equations, of course!).\nNow, at first, it might not be obvious how this helps. Well, firstly, it makes the system easier to encode: we may divide it into four separate vectors corresponding to a, b, c, and d (in some implementations, you will see the missing a_0 and c_n set to zero to get four vectors of the same size).\nSecondly, and most importantly, equations this short and regular are easy to solve analytically.\nWe'll start by applying mechanisms familiar to those who have read the Gaussian Elimination chapter.\nOur first goal is to eliminate the a_i terms and set the diagonal values b_i to 1. The c_i and d_i terms will be transformed into c'_i and d'_i.\nThe first row is particularly easy to transform since there is no a_0, we simply need to divide the row by b_0:\n\n\\left\\{\n\\begin{align}\nc'_0 &= \\frac{c_0}{b_0} \\\\\nd'_0 &= \\frac{d_0}{b_0}\n\\end{align}\n\\right.\n\nLet's assume that we found a way to transform the first i-1 rows. How would we transform the next one? We have\n\n\\begin{array}{ccccccc|c}\n & & \\ddots & & & & & \\\\\n(i-1) & & 0 & 1 & c'_{i-1} & & & d'_{i-1} \\\\\n(i) & & & a_i & b_i & c_i & & d_i \\\\\n & & & & & \\ddots & &\n\\end{array}\n\nLet's transform row (i) in two steps.\nStep one: eliminate a_i with the transformation (i)^* = (i) - a_i \\times (i-1):\n\n\\left\\{\n\\begin{align}\na^*_i &= 0 \\\\\nb^*_i &= b_i - a_i \\times c'_{i-1} \\\\\nc^*_i &= c_i \\\\\nd^*_i &= d_i - a_i \\times d'_{i-1}\n\\end{align}\n\\right.\n\nStep two: get b'_i=1 with the transformation (i)' = (i)^* / b^*_i :\n\n\\left\\{\n\\begin{align}\na'_i &= 0 \\\\\nb'_i &= 1 \\\\\nc'_i &= \\frac{c_i}{b_i - a_i \\times c'_{i-1}} \\\\\nd'_i &= \\frac{d_i - a_i \\times d'_{i-1}}{b_i - a_i \\times c'_{i-1}}\n\\end{align}\n\\right.\n\nBrilliant! With the last two formula, we can calculate all the c'_i and d'_i in a single pass, starting from row 1, since we already know the values of c'_0 and d'_0.\nOf course, what we really need are the solutions x_i. It's back substitution time!\nIf we express our system in terms of equations instead of a matrix, we get\n\nx_i + c'_i \\times x_{i+1} = d'_i\n\nplus the last row that is even simpler: x_n = d'_n. One solution for free!\nMaybe we can backtrack from the last solution? Let's (barely) transform the above equation:\n\nx_i = d'_i - c'_i \\times x_{i+1}\n\nand that's all there is to it. We can calculate all the x_i in a single pass starting from the end.\nOverall, we only need two passes, and that's why our algorithm is O(n)!\nThe transformations are quite easy too, isn't that neat?\nExample Code\nfunction thomas(a::Vector{Float64}, b::Vector{Float64}, c::Vector{Float64},\n d::Vector{Float64}, n::Int64)\n\n x = copy(d)\n c_prime = copy(c)\n\n # Setting initial elements\n c_prime[1] /= b[1]\n x[1] /= b[1]\n\n for i = 2:n\n # Scale factor is for c_prime and x\n scale = 1.0 / (b[i] - c_prime[i-1]*a[i])\n c_prime[i] *= scale\n x[i] = (x[i] - a[i] * x[i-1]) * scale\n end\n\n # Back-substitution\n for i = n-1:-1:1\n x[i] -= (c_prime[i] * x[i+1])\n end\n\n return x\n\nend\n\nfunction main()\n a = [0.0, 2.0, 3.0]\n b = [1.0, 3.0, 6.0]\n c = [4.0, 5.0, 0.0]\n d = [7.0, 5.0, 3.0]\n\n println(\n \"\"\"The system\n $(join((b[1], c[1], \"\", \"|\", d[1]), \"\\t\"))\n $(join((a[2], b[2], c[2], \"|\", d[2]), \"\\t\"))\n $(join((\"\", a[3], b[3], \"|\", d[3]), \"\\t\"))\n Has the solution:\"\"\"\n )\n\n soln = thomas(a, b, c, d, 3)\n\n println(soln)\nend\n\nmain()\n\n#include \n#include \n\nvoid thomas(double * const a, double * const b, double * const c,\n double * const x, const size_t size) {\n\n double y[size];\n memset(y, 0, size * sizeof(double));\n\n y[0] = c[0] / b[0];\n x[0] = x[0] / b[0];\n\n for (size_t i = 1; i \n# Author: gammison\n\n# note this example is inplace and destructive\ndef thomas(a, b, c, d):\n\n # set the initial elements\n c[0] = c[0] / b[0]\n d[0] = d[0] / b[0]\n\n n = len(d) # number of equations to solve\n for i in range(1, n):\n # scale factor for c and d\n scale = 1 / (b[i] - c[i-1] * a[i])\n\n c[i] *= scale\n d[i] = (d[i] - a[i] * d[i-1]) * scale\n\n\n # do the back substitution\n for i in range(n-2, -1, -1):\n d[i] -= c[i] * d[i+1]\n\n return d\n\ndef main():\n # example for matrix\n # [1 4 0][x] [7]\n # [2 3 5][y] = [5]\n # [0 3 6][z] [3]\n\n # [.8666]\n # soln will equal [1.533]\n # [-.266]\n # note we index a from 1 and c from 0\n a = [0, 2, 3]\n b = [1, 3, 6]\n c = [4, 5, 0]\n d = [7, 5, 3]\n\n soln = thomas(a, b, c, d)\n print(soln)\n\nif __name__ == '__main__':\n main()\n\nYou will find this algorithm implemented in this project.\n\n \npublic class Thomas {\n private static double[] thomasAlgorithm(double[] a, double[] b, double[] c, double[] x) {\n int size = a.length;\n double[] y = new double[size]; // This is needed so that we don't have to modify c\n double[] solution = new double[size];\n\n // Set initial elements\n y[0] = c[0] / b[0];\n solution[0] = x[0] / b[0];\n\n for (int i = 1; i = 0; --i) {\n solution[i] -= y[i] * solution[i + 1];\n }\n\n return solution;\n }\n\n public static void main(String[] args) {\n double[] a = {0.0, 2.0, 3.0};\n double[] b = {1.0, 3.0, 6.0};\n double[] c = {4.0, 5.0, 0.0};\n double[] x = {7.0, 5.0, 3.0};\n double[] solution = thomasAlgorithm(a, b, c, x);\n\n System.out.format(\"The system,\\n\");\n System.out.format(\"[%.1f, %.1f, %.1f][x] = [%.1f]\\n\", b[0], c[0], 0f, x[0]);\n System.out.format(\"[%.1f, %.1f, %.1f][y] = [%.1f]\\n\", a[1], b[1], c[1], x[1]);\n System.out.format(\"[%.1f, %.1f, %.1f][z] = [%.1f]\\n\", 0f, a[2], b[2], x[2]);\n System.out.format(\"has the solution:\\n\");\n\n for (int i = 0; i \nimport Data.List (zip4)\nimport Data.Ratio\n\nthomas :: Fractional a => [a] -> [a] -> [a] -> [a] -> [a]\nthomas a b c = init . scanr back 0 . tail . scanl forward (0, 0) . zip4 a b c\n where\n forward (c', d') (a, b, c, d) =\n let denominator = b - a * c'\n in (c / denominator, (d - a * d') / denominator)\n back (c, d) x = d - c * x\n\nmain :: IO ()\nmain = do\n let a = [0, 2, 3] :: [Ratio Int]\n b = [1, 3, 6]\n c = [4, 5, 0]\n d = [7, 5, 3]\n print $ thomas a b c d\n\npackage main\n\nimport \"fmt\"\n\nfunc thomas(a, b, c, d []float64) []float64 {\n c[0] = c[0] / b[0]\n d[0] = d[0] / b[0]\n\n for i := 1; i = 0; i-- {\n d[i] -= c[i] * d[i+1]\n }\n\n return d\n}\n\nfunc main() {\n a := []float64{0., 2., 3.}\n b := []float64{1., 3., 6.}\n c := []float64{4., 5., 0.}\n d := []float64{7., 5., 3.}\n\n fmt.Println(\"The system,\")\n fmt.Println(\"[1.0 4.0 0.0][x] = [7.0]\")\n fmt.Println(\"[2.0 3.0 5.0][y] = [5.0]\")\n fmt.Println(\"[0.0 3.0 6.0][z] = [3.0]\")\n fmt.Println(\"has the solution:\")\n solve := thomas(a, b, c, d)\n for _, i := range solve {\n fmt.Printf(\"[%f]\\n\", i)\n }\n}\n\nfn thomas(a []f32, b []f32, c []f32, d []f32) []f32 {\n mut new_c := c\n mut new_d := d\n new_c[0] = new_c[0] / b[0]\n new_d[0] = new_d[0] / b[0]\n\n for i := 1; i = 0; i-- {\n new_d[i] -= new_c[i] * new_d[i+1]\n }\n\n return new_d\n}\n\nfn main() {\n a := [0.0, 2.0, 3.0]\n b := [1.0, 3.0, 6.0]\n c := [4.0, 5.0, 0.0]\n d := [7.0, 5.0, 3.0]\n\n println(\"The system,\")\n println(\"[1.0 4.0 0.0][x] = [7.0]\")\n println(\"[2.0 3.0 5.0][y] = [5.0]\")\n println(\"[0.0 3.0 6.0][z] = [3.0]\")\n println(\"has the solution:\")\n solution := thomas(a, b, c, d)\n for i in solution {\n println(\"[$i]\")\n }\n}\n\nfunc thomas(a: [Double], b: [Double], c: [Double], d: [Double]) -> [Double] {\n var a = a\n var b = b\n var c = c\n var d = d\n\n // set the initial elements\n c[0] = c[0] / b[0]\n d[0] = d[0] / b[0]\n\n let n = d.count // number of equations to solve\n for i in 1..\n= 0; --$i)\n $x[$i] -= $y[$i] & $x[$i + 1];\n\n return $x;\n}\n\n\n$a = [0.0, 2.0, 3.0];\n$b = [1.0, 3.0, 6.0];\n$c = [4.0, 5.0, 0.0];\n$x = [7.0, 5.0, 3.0];\n\nprintf('The system,%s', PHP_EOL);\nprintf(' [%s, %s, %s][x] = [%s]%s', $b[0], $c[0], 0, $x[0], PHP_EOL);\nprintf(' [%s, %s, %s][y] = [%s]%s', $a[1], $b[1], $c[1], $x[1], PHP_EOL);\nprintf(' [%s, %s, %s][z] = [%s]%s', 0, $a[2], $b[2], $x[2], PHP_EOL);\nprintf('has the solution:%s', PHP_EOL);\n\n$solution = thomas_algorithm($a, $a, $c, $x, count($x));\nfor ($i = 0; $i \nproc thomas_algorithm(a, b, c_in, d_in: seq[float]): seq[float] = \n\n let n: int = len(d_in)\n\n var c: seq[float] = c_in\n var d: seq[float] = d_in\n\n c[0] /= b[0]\n d[0] /= b[0]\n\n for i in 1..n - 1:\n let scale: float = (1 / (b[i] - c[i - 1] * a[i]))\n\n c[i] *= scale\n d[i] = (d[i] - a[i] * d[i - 1]) * scale\n\n for i in countdown(n - 2,0):\n d[i] -= c[i] * d[i + 1]\n\n\n return d\n\n\nconst x: seq[float] = @[0.0, 2.0, 3.0]\nconst y: seq[float] = @[1.0, 3.0, 6.0]\nconst z: seq[float] = @[4.0, 5.0, 0.0]\nconst w: seq[float] = @[7.0, 5.0, 3.0] \n\necho \"The system,\"\necho \"[1.0 4.0 0.0][x] = [7.0]\"\necho \"[2.0 3.0 5.0][y] = [5.0]\"\necho \"[0.0 3.0 6.0][z] = [3.0]\"\n\necho \"has the solution:\"\n\nconst soln: seq[float] = thomas_algorithm(x, y, z, w)\n\nfor i in 0..len(w) - 1:\n echo soln[i]\n\n#include \n#include \n#include \n\nvoid thomas(\n std::vector const& a,\n std::vector const& b,\n std::vector const& c,\n std::vector& x) {\n auto y = std::vector(a.size(), 0.0);\n\n y[0] = c[0] / b[0];\n x[0] = x[0] / b[0];\n\n for (std::size_t i = 1; i a = {0.0, 2.0, 3.0};\n const std::vector b = {1.0, 3.0, 6.0};\n const std::vector c = {4.0, 5.0, 0.0};\n std::vector x = {7.0, 5.0, 3.0};\n\n std::cout \nlocal function thomas(a, b, c, d)\n\n -- Create tables and set initial elements\n local c_prime = {c[1] / b[1]}\n local result = {d[1] / b[1]}\n\n for i = 2, #a do\n -- Scale factor is for c_prime and result\n local scale = 1.0 / (b[i] - a[i] * c_prime[i - 1])\n c_prime[i] = c[i] * scale\n result[i] = (d[i] - a[i] * result[i - 1]) * scale\n end\n\n -- Back-substitution\n for i = #a-1, 1, -1 do\n result[i] = result[i] - (c_prime[i] * result [i + 1])\n end\n\n return result\nend\n\nlocal a = {0.0, 2.0, 3.0}\nlocal b = {1.0, 3.0, 6.0}\nlocal c = {4.0, 5.0, 0.0}\nlocal d = {7.0, 5.0, 3.0}\n\nprint(\"The system\")\nprint(b[1], c[1], \"\", \"|\", d[1])\nprint(a[2], b[2], c[2], \"|\", d[2])\nprint(\"\", a[3], b[3], \"|\", d[3])\nprint(\"Has the solution:\")\n\nlocal solution = thomas(a, b, c, d)\n\nprint(table.unpack(solution))\n\ndef thomas(a, b, c, d)\n c_prime = c.dup\n x = d.dup\n\n # Setting initial elements\n c_prime[0] /= b[0]\n x[0] /= b[0]\n\n 1.upto(a.size - 1) do |i|\n # Scale factor is for c_prime and x\n scale = 1.0 / (b[i] - c_prime[i - 1]*a[i])\n c_prime[i] *= scale\n x[i] = (x[i] - a[i] * x[i - 1]) * scale\n end\n\n # Back-substitution\n (a.size - 2).downto(0) do |i|\n x[i] -= (c_prime[i] * x[i + 1])\n end\n\n x\nend\n\ndef main\n a = [0.0, 2.0, 3.0]\n b = [1.0, 3.0, 6.0]\n c = [4.0, 5.0, 0.0]\n d = [7.0, 5.0, 3.0]\n\n puts \"The system\"\n puts [b[0], c[0], \"\", \"|\", d[0]].join(\"\\t\")\n puts [a[1], b[1], c[1], \"|\", d[1]].join(\"\\t\")\n puts [\"\", a[2], b[2], \"|\", d[2]].join(\"\\t\")\n puts \"Has the solution:\"\n\n soln = thomas(a, b, c, d)\n\n puts soln.join(\"\\t\")\nend\n\nmain\n\nprivate fun thomas(a: DoubleArray, b: DoubleArray, c: DoubleArray, d: DoubleArray): DoubleArray {\n val cPrime = c.clone()\n val x = d.clone()\n val size = a.size\n cPrime[0] /= b[0]\n x[0] /= b[0]\n for (i in 1 until size) {\n val scale = 1.0 / (b[i] - cPrime[i - 1] * a[i])\n cPrime[i] *= scale\n x[i] = (x[i] - a[i] * x[i - 1]) * scale\n }\n for (i in (size - 2) downTo 0) {\n x[i] -= cPrime[i] * x[i + 1]\n }\n return x\n}\n\nfun main(args: Array) {\n val a = doubleArrayOf(0.0, 2.0, 3.0)\n val b = doubleArrayOf(1.0, 3.0, 6.0)\n val c = doubleArrayOf(4.0, 5.0, 0.0)\n val x = doubleArrayOf(7.0, 5.0, 3.0)\n val solution = thomas(a, b, c, x)\n\n println(\"System:\")\n println(\"[%.1f, %.1f, %.1f][x] = [%.1f]\".format(b[0], c[0], 0f, x[0]))\n println(\"[%.1f, %.1f, %.1f][y] = [%.1f]\".format(a[1], b[1], c[1], x[1]))\n println(\"[%.1f, %.1f, %.1f][z] = [%.1f]\\n\".format(0f, a[2], b[2], x[2]))\n println(\"Solution:\")\n for (i in solution.indices) {\n println(\"[% .5f]\".format(solution[i]))\n }\n}\n\n;;;; Thomas algorithm implementation in Common Lisp\n\n(defmacro divf (place divisor)\n \"Divides the value at place by divisor\"\n `(setf ,place (/ ,place ,divisor)))\n\n(defun helper (v1 v2 v3 row)\n (- (svref v1 row) (* (svref v2 row) (svref v3 (1- row)))))\n\n(defun thomas (diagonal-a diagonal-b diagonal-c last-column)\n \"Returns the solutions to a tri-diagonal matrix non-destructively\"\n ;; We have to copy the inputs to ensure non-destructiveness\n (let ((a (copy-seq diagonal-a))\n (b (copy-seq diagonal-b))\n (c (copy-seq diagonal-c))\n (d (copy-seq last-column)))\n (divf (svref c 0) (svref b 0))\n (divf (svref d 0) (svref b 0))\n (loop\n for i from 1 upto (1- (length a)) do\n (divf (svref c i) (helper b a c i))\n (setf (svref d i) (/ (helper d a d i) (helper b a c i))))\n (loop\n for i from (- (length a) 2) downto 0 do\n (decf (svref d i) (* (svref c i) (svref d (1+ i)))))\n d))\n\n(defparameter diagonal-a #(0 2 3))\n(defparameter diagonal-b #(1 3 6))\n(defparameter diagonal-c #(4 5 0))\n(defparameter last-column #(7 5 3))\n\n;; should print 0.8666667 1.5333333 -0.26666668\n(format t \"~{~f ~}~%\" (coerce (thomas diagonal-a diagonal-b diagonal-c last-column) 'list))\n\n# note this example is inplace and destructive\ndef thomas(a, b, c, d)\n # set the initial elements\n c[0] = c[0] / b[0]\n d[0] = d[0] / b[0]\n\n n = d.length # number of equations to solve\n (1...n).each do |i|\n scale = 1 / (b[i] - c[i - 1] * a[i]) # scale factor for c and d\n c[i] *= scale\n d[i] = (d[i] - a[i] * d[i - 1]) * scale\n end\n\n # do the back substitution\n (n - 2).downto(0).each do |j|\n d[j] -= c[j] * d[j + 1]\n end\n\n d\nend\n\n# example for matrix\n# [1 4 0][x] [7]\n# [2 3 5][y] = [5]\n# [0 3 6][z] [3]\n\n# [.8666]\n# soln will equal [1.533]\n# [-.266]\n# note we index a from 1 and c from 0\n\na = [0.0, 2.0, 3.0]\nb = [1.0, 3.0, 6.0]\nc = [4.0, 5.0, 0.0]\nd = [7.0, 5.0, 3.0]\n\nsoln = thomas(a, b, c, d)\nputs soln\n\nfunction thomas(a, b, c, x) {\n const y = [];\n\n y[0] = c[0] / b[0];\n x[0] = x[0] / b[0];\n\n for (let i = 1; i = 0; i--)\n x[i] -= y[i] * x[i + 1];\n}\n\nlet a = [0.0, 2.0, 3.0];\nlet b = [1.0, 3.0, 6.0];\nlet c = [4.0, 5.0, 0.0];\nlet x = [7.0, 5.0, 3.0];\n\nconsole.log(\"The system,\");\nconsole.log(\"[1.0 4.0 0.0][x] = [7.0]\");\nconsole.log(\"[2.0 3.0 5.0][y] = [5.0]\");\nconsole.log(\"[0.0 3.0 6.0][z] = [3.0]\");\nconsole.log(\"has the solution:\\n\");\n\nthomas(a, b, c, x);\n\nfor (let i = 0; i \nfn thomas(a: &[f64], b: &[f64], c: &[f64], x: &[f64]) -> Vec {\n let size = a.len();\n let mut y = vec![0.0; size];\n let mut z = Vec::from(x);\n\n y[0] = c[0] / b[0];\n z[0] = x[0] / b[0];\n\n for i in 1..size {\n let scale = 1.0 / (b[i] - a[i] * y[i - 1]);\n y[i] = c[i] * scale;\n z[i] = (z[i] - a[i] * z[i - 1]) * scale;\n }\n\n for i in (0..(size - 1)).rev() {\n z[i] -= y[i] * z[i + 1];\n }\n\n z\n}\n\nfn main() {\n let a = vec![0.0, 2.0, 3.0];\n let b = vec![1.0, 3.0, 6.0];\n let c = vec![4.0, 5.0, 0.0];\n let x = vec![7.0, 5.0, 3.0];\n\n println!(\"The system\");\n println!(\"[{:?} {:?} {:?}][x] = [{:?}]\", a[0], b[0], c[0], &x[0]);\n println!(\"[{:?} {:?} {:?}][x] = [{:?}]\", a[1], b[1], c[1], &x[1]);\n println!(\"[{:?} {:?} {:?}][x] = [{:?}]\", a[2], b[2], c[2], &x[2]);\n println!(\"has the solution\");\n\n let y = thomas(&a, &b, &c, &x);\n\n y.iter()\n .for_each(|i| println!(\"[{:>19}]\", format!(\"{:18}\", format!(\"{:?}\", i))));\n}\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/IFS/IFS.html":{"url":"contents/IFS/IFS.html","title":"Iterated Function Systems","keywords":"","body":"Iterated Function Systems\nA few quick notes before we start:\n\nFor this chapter, we will be following the methodology set by the plotting chapter.\nThat is to say that the code presented in this chapter will output another file that can be easily plotted by an external plotter.\nIf you like to use a plotter provided by your language of choice, please modify the code provided to do so.\n\nThis chapter is currently a subsection to the plotting chapter, but we may extend the algorithm archive in the future with other fractal generation methods, which would require creating a new section on fractals, in particular.\nThis would include a chapter with more rigorous definitions on fractals, which is largely missing from the following discussion.\nPlease let us know if you are interested!\n\n\nIn this chapter, we will show you how to make one of the most famous fractals, the Sierpinski triangle, via Iterated Function Systems (IFSs).\nWe will also introduce a number of interesting concepts for further exploration, such as chaos games, Hutchinson operators, and attractors.\nThe Sierpinski Triangle\nTo begin the discussion of Iterated Function Systems (IFSs), we will first discuss what might be one of the most famous fractals currently known: the Sierpinski triangle (shown below):\n\nThis image is clearly a set of triangles embedded in a larger triangle in such a way that it can be continually cut into three identical pieces and still retain its internal structure.\nThis idea is known as self-similarity [1], and it is usually the first aspect of fractals to catch an audience's attention.\nIn fact, there are plenty of uses of fractals and their mathematical underpinnings, such as estimating the coastline of Britain [2], identifying fingerprints [3], and image compression [4][5].\nIn many more rigorous definitions, a fractal can be described as any system that has a non-integer Hausdorff dimension [6][7][8].\nThough this is an incredibly interesting concept, the discussion of this chapter will instead focus on methods to generate fractal patterns through iterated function systems.\nTo start, imagine creating a triangle from three points, A, B, and C.\nThese points can be arbitrarily chosen, but for this conversation, we will constrict them to the vertices of an equilateral triangle, as shown below:\n\nNow let's create three separate functions that can act on a 2-dimensional space:\n\n\\begin{align}\nf_1(P) &= \\frac{P + A}{2}\\\\\nf_2(P) &= \\frac{P + B}{2}\\\\\nf_3(P) &= \\frac{P + C}{2}\\\\\n\\end{align}\n\nEach function will read in a particular location in space (here, P \\in \\mathbb{R}^2) and output a new location that is the midpoint between the input location and A, B, or C for f_1, f_2, and f_3 respectively.\nThe union of all of these functions (the set of all possible functions available for use) is often notated as the Hutchinson operator [9][10], and for this case it would look like this:\n\nH(P) = \\bigcup_{i=1}^3f_i(P)\n\nBy iteratively using this operator, we can traverse through all possible movements in the set.\nFor example, let's generate 3 new points that are halfway between A and B, B and C, and A and C, which will be called D, E, and F respectively.\nThis is shown below:\n\nFrom here, each new point (D, E, and F) will spawn 3 children, and each child will move according to one of the three possible functions in the Hutchinson operator, as shown below:\n\n\n \n \n\n\n\nHere, all red children come from D, green children come from E and blue children come from F.\nAt this stage, the children will then spawn 3 more children, each of which will move according to a different function.\nThose children will then spawn more children, who act accordingly.\nAs this process continues on and on, we begin to see an interesting pattern form:\n\n\n \n \n\n\n\nThis is the Sierpinski triangle.\nAt first, it might seem like mathematical magic that a simple set of 3 functions can create such a pattern.\nAfter all, why aren't any of the children migrating to the empty spaces in the structure?\nThis will require some thought, but the simplest answer is that no function within the Hutchinson operator allows for children to enter those spaces; therefore, none of the children can enter them.\nWhat about a square?\nWhen I learned about how the Sierpinski triangle could be generated from 3 simple functions, I began to wonder about other shapes.\nCould we create fractal squares? Hexagons? Circles?\nSuch shapes seem like natural extensions to the triangular Hutchinson operator provided above, but there's a bit of a hitch...\nFirst, let's take 4 points, A, B, C, and D, this time located at the four vertices of a square, like so:\n\nIn a similar fashion, we'll create 4 functions with H(P) = \\bigcup_{i=1}^4f_i(P), and P \\in \\mathbb{R}^2 such that:\n\n\\begin{align}\nf_1(P) &= \\frac{P + A}{2}\\\\\nf_2(P) &= \\frac{P + B}{2}\\\\\nf_3(P) &= \\frac{P + C}{2}\\\\\nf_4(P) &= \\frac{P + D}{2}\\\\\n\\end{align}\n\nIf we then create 5 initial points located between all the vertices and allow these points to continually spawn children like before, something peculiar happens:\n\n\n \n \n\n\n\nWe essentially see a square of squares.\nWhat happened to the self-similar structure we were getting before?\nWhy isn't this more interesting?\nThe best answer I have for now is that some Hutchinson operators are interesting and some are not.\nStill, this square is a bit more interesting than it first appears, but to see why, we need to use the Hutchinson operator in a slightly different way.\nChaos games and attractors\nUntil now, our visualizations for both the Sierpinski triangle and the square have been computationally costly.\nEvery iteration, we generate 3 or 4 new children per child per step of the simulation.\nThis scales exponentially and means that we will quickly have millions of children to keep track of!\nIn fact, to deal with this, we developed our own method of counting through the tree to more efficiently keep track of everything, but that is a story for another day.\nThe question for now is whether there is a more computationally feasible way of iterating through our Hutchinson operator.\nAs it turns out, there is!\nRather than keeping track of every possible movement within the Hutchinson operator to draw out a shape, it's actually possible to randomly sample the function set instead through a process known as a chaos game [11][12]..\nHere, instead of tracking children of children, we track a single individual that chooses randomly between the Hutchinson functions, as shown here:\nfunction chaos_game(n::Int, shape_points)\n\n # Initializing the output array and the initial point\n output_points = zeros(n,2)\n point = [rand(), rand()]\n\n for i = 1:n\n output_points[i,:] .= point\n point = 0.5*(rand(shape_points) .+ point)\n end\n\n return output_points\n\nend\n\nchaosGame :: RandomGen g => g -> Int -> Array Int (Point -> Point) -> [Point]\nchaosGame g n hutchinson = take n points\n where\n (x, g') = random g\n (y, g'') = random g'\n choices = randomRs (bounds hutchinson) g''\n points = Point x y : zipWith (hutchinson !) choices points\n\n// This is a function to simulate a \"chaos game\"\nPointVector chaosGame(int numOutputPoints, const PointVector& inputPoints) {\n // Choose first point randomly\n Point curPoint = {drand(), drand()};\n\n // For each output point, compute midpoint to random input point\n PointVector outputPoints(numOutputPoints);\n for (auto& outPoint : outputPoints) {\n outPoint = curPoint;\n curPoint = 0.5 * (curPoint + choose(inputPoints));\n }\n\n return outputPoints;\n}\n\ndef chaos_game(n, shape_points):\n # Initialize the starting point\n point = [random(), random()]\n\n for _ in range(n):\n # Update the point position and yield the result\n point = [(p + s) / 2 for p, s in zip(point, choice(shape_points))]\n yield point\n\nvoid chaos_game(struct point *in, size_t in_n, struct point *out,\n size_t out_n) {\n\n struct point cur_point = {drand(), drand()};\n\n for (size_t i = 0; i \n(defun chaos-game (iterations shape-points)\n \"Plays a chaos game with a certain shape for a determined amount of iterations\"\n (loop\n repeat iterations\n for rand-point = (svref shape-points (random (length shape-points)))\n for point = (make-point (random 1.0) (random 1.0)) ; starting point\n then (make-point\n (* 0.5 (+ (point-x rand-point) (point-x point)))\n (* 0.5 (+ (point-y rand-point) (point-y point)))) ; every subsequent point\n collect point))\n\ndata point(x=0, y=0):\n def __add__(self, other):\n return point(self.x + other.x, self.y + other.y)\n\n def __rmul__(self, other):\n return point(self.x * other, self.y * other)\n\ndef chaos_game(n, shape_points):\n p = point(random(), random())\n\n for _ in range(n):\n p = (1/2) * (p + choice(shape_points))\n yield p\n\nfn chaos_game(iters: usize, shapes: Vec) -> Vec {\n let mut rng = rand::thread_rng();\n let mut p = Point{x: rng.gen(), y: rng.gen()};\n\n (0..iters).into_iter().map(|_| {\n let old_point = p;\n let tmp = shapes[rng.gen_range(0..shapes.len())];\n p.x = 0.5 * (p.x + tmp.x);\n p.y = 0.5 * (p.y + tmp.y);\n old_point\n }).collect()\n}\n\npublic static Point[] chaosGame(int n, Point[] shapePoints) {\n Random rng = new Random();\n\n // Initialize output vector\n Point[] outputPoints = new Point[n];\n\n // Choose first point randomly\n Point point = new Point(rng.nextDouble(), rng.nextDouble());\n\n for (int i = 0; i \nfunction Simulate-ChaosGame($n, $shapePoints) {\n $outputPoints = New-Object System.Collections.ArrayList\n\n # Initialize the starting point\n $point = @($(Get-Random -Minimum 0.0 -Maximum 1.0), $(Get-Random -Minimum 0.0 -Maximum 1.0))\n\n for ($i = 0; $i -lt $n; $i++) {\n $outputPoints.add($point) | Out-Null\n $temp = $shapePoints[$(Get-Random -Maximum $shapePoints.Count)]\n\n $point = @(\n 0.5 * ($point[0] + $temp[0])\n 0.5 * ($point[1] + $temp[1])\n )\n }\n\n return $outputPoints\n}\n\n\n\nIf we set the initial point to the on the equilateral triangle we saw before, we can see the Sierpinski triangle again after a few thousand iterations, as shown below:\n\n\n \n \n\n\n\nHere, we are plotting 200,000 point locations in sets of 1000, and every set becomes successively more blue as the visualization continues.\nAt first glance, this visualization seems bewildering.\nAfter all, it appears as if the entire triangle just magically comes into view in a few seconds.\nThe important thing to remember here is that each of these 200,000 dots is another location that our initial point decided to visit.\nThat said, there is something peculiar about the way the chaos game starts.\nWe are actually allowed to start the simulation off of the Sierpinski triangle.\nAs we mentioned earlier, none of the functions for the Sierpinski visualization allow children to enter the empty spaces of the triangle, so let's see what happens if we start the point off at the center of the triangle:\n\n\n \n \n\n\n\nHere, I have plotted the first 20 steps of the chaos game, and it is clear that the point gets closer and closer to the triangle each iteration.\nOnce it lands on the triangle, it can no longer escape and every movement from then on will be on the triangle.\nIn a sense, the wanderin point is attracted to the Sierpinski triangle with this set of functions, and that is actually the case!\nThe truth is that the word attractor is a very loaded term in the literature, but for the purposes of our discussion here, an attractor is any shape defined by the iteration through Hutchinson operator functions.\nSo let's go back to the example with the 4 points along the square and generate the attractor via a chaos game instead of going through every branch of the Hutchinson operator.\nIf we do this, we get what seems to be a random distribution of points:\n\nThis kinda boggled my mind a bit when I looked at it for the first time.\nWhat does a random distribution of points mean in this context?\nWell, firstly, it's only a random distribution between the square vertices of A, B, C, and D, but nothing exists outside of these points.\nThis means that it's not actually a random distribution of points, but instead an attractive plane that our lone wandering point can exist happily within.\nThis really helped me understand how attractors present themselves in different dimensions.\nThe Sierpinski triangle seems like a series of lines (one-dimensional objects) in two-dimensional space, but the square is a truly two-dimensional object.\nIn general, this means that an attractor embedded within \\mathbb{R}^N can be any shape of dimension N or lower.\nThe next obvious question is whether a square can create any more interesting fractally patterns, and the answer is \"yes, but only if we restrict the movement a bit.\"\nWhich brings us to another topic entirely: restricted chaos games.\nDiscussing restricted chaos games in more detail is a chapter in its own right, so I will forego the discussion here.\nIf you are interested, please let me know and I will be more than willing to add the chapter in the future!\nVideo Explanation\nHere is a video describing iterated function systems:\n\n\n\n\nExample Code\nFor the code in this chapter, we have decided to write it specifically for the Chaos game, not the hutchinson animations shown at the start of the chapter.\nThis is because that animation is slightly tricky to create and distracts from the overall purpose of this chapter.\nIn addition, we have written the chaos game code to take in a set of points so that it is not hard-coded for the Sierpinski triangle and can be easily extended to other shapes like the square or restricted chaos games, as we mentioned before!\nusing DelimitedFiles\n\n# This is a function to simulate a \"chaos game\"\nfunction chaos_game(n::Int, shape_points)\n\n # Initializing the output array and the initial point\n output_points = zeros(n,2)\n point = [rand(), rand()]\n\n for i = 1:n\n output_points[i,:] .= point\n point = 0.5*(rand(shape_points) .+ point)\n end\n\n return output_points\n\nend\n\n# This will generate a Sierpinski triangle with a chaos game of n points for an \n# initial triangle with three points on the vertices of an equilateral triangle:\n# A = (0.0, 0.0)\n# B = (0.5, sqrt(0.75))\n# C = (1.0, 0.0)\n# It will output the file sierpinski.dat, which can be plotted after\nshape_points = [[0.0, 0.0],\n [0.5, sqrt(0.75)],\n [1.0, 0.0]]\noutput_points = chaos_game(10000, shape_points)\nwritedlm(\"sierpinski.dat\", output_points)\n\nimport Data.Array ((!), Array, bounds, listArray)\nimport Data.List (intercalate)\nimport System.Random\n\ndata Point = Point Double Double\n\nchaosGame :: RandomGen g => g -> Int -> Array Int (Point -> Point) -> [Point]\nchaosGame g n hutchinson = take n points\n where\n (x, g') = random g\n (y, g'') = random g'\n choices = randomRs (bounds hutchinson) g''\n points = Point x y : zipWith (hutchinson !) choices points\n\nmain :: IO ()\nmain = do\n g \n#include \n#include \n#include \n#include \n\n// Simple X-Y point structure, along with some operators\nstruct Point {\n double x, y;\n};\n\nPoint operator+(Point lhs, Point rhs) { return {lhs.x + rhs.x, lhs.y + rhs.y}; }\nPoint operator*(double k, Point pt) { return {k * pt.x, k * pt.y}; }\nPoint operator*(Point pt, double k) { return k * pt; }\n\nusing PointVector = std::vector;\n\n// Returns a pseudo-random number generator\nstd::default_random_engine& rng() {\n // Initialize static pseudo-random engine with non-deterministic random seed\n static std::default_random_engine randEngine(std::random_device{}());\n return randEngine;\n}\n\n// Returns a random double in [0, 1)\ndouble drand() {\n return std::uniform_real_distribution(0.0, 1.0)(rng());\n}\n\n// Returns a random integer in [0, numElems-1]\nstd::size_t randrange(std::size_t numElems) {\n return std::uniform_int_distribution(0, numElems - 1)(rng());\n}\n\n// Return a random point from the non-empty PointVector\nPoint choose(const PointVector& points) {\n return points[randrange(points.size())];\n}\n\n// This is a function to simulate a \"chaos game\"\nPointVector chaosGame(int numOutputPoints, const PointVector& inputPoints) {\n // Choose first point randomly\n Point curPoint = {drand(), drand()};\n\n // For each output point, compute midpoint to random input point\n PointVector outputPoints(numOutputPoints);\n for (auto& outPoint : outputPoints) {\n outPoint = curPoint;\n curPoint = 0.5 * (curPoint + choose(inputPoints));\n }\n\n return outputPoints;\n}\n\nint main() {\n // This will generate a Sierpinski triangle with a chaos game of n points for\n // an initial triangle with three points on the vertices of an equilateral\n // triangle.\n PointVector inputPoints = {{0.0, 0.0}, {0.5, std::sqrt(0.75)}, {1.0, 0.0}};\n auto outputPoints = chaosGame(10000, inputPoints);\n\n // It will output the file sierpinski.dat, which can be plotted after\n std::ofstream ofs(\"sierpinski.dat\");\n for (auto pt : outputPoints)\n ofs \nfrom random import random, choice\nfrom math import sqrt\n\n# This generator simulates a \"chaos game\"\ndef chaos_game(n, shape_points):\n # Initialize the starting point\n point = [random(), random()]\n\n for _ in range(n):\n # Update the point position and yield the result\n point = [(p + s) / 2 for p, s in zip(point, choice(shape_points))]\n yield point\n\n# This will generate a Sierpinski triangle with a chaos game of n points for an\n# initial triangle with three points on the vertices of an equilateral triangle:\n# A = (0.0, 0.0)\n# B = (0.5, sqrt(0.75))\n# C = (1.0, 0.0)\n# It will output the file sierpinski.dat, which can be plotted after\nshape_points = [[0.0, 0.0],\n [0.5, sqrt(0.75)],\n [1.0, 0.0]]\nwith open(\"sierpinski.dat\", \"w\") as f:\n for point in chaos_game(10000, shape_points):\n f.write(\"{0}\\t{1}\\n\".format(*point))\n\n#include \n#include \n#include \n#include \n\nstruct point {\n double x, y;\n};\n\ndouble drand() {\n return ((double) rand() / (RAND_MAX));\n}\n\nstruct point random_element(struct point *array, size_t n) {\n return array[rand() % (int)n];\n}\n\nvoid chaos_game(struct point *in, size_t in_n, struct point *out,\n size_t out_n) {\n\n struct point cur_point = {drand(), drand()};\n\n for (size_t i = 0; i \n;;;; Iterated Function System implementation\n\n(defstruct (point (:constructor make-point (x y))) x y)\n\n(defun chaos-game (iterations shape-points)\n \"Plays a chaos game with a certain shape for a determined amount of iterations\"\n (loop\n repeat iterations\n for rand-point = (svref shape-points (random (length shape-points)))\n for point = (make-point (random 1.0) (random 1.0)) ; starting point\n then (make-point\n (* 0.5 (+ (point-x rand-point) (point-x point)))\n (* 0.5 (+ (point-y rand-point) (point-y point)))) ; every subsequent point\n collect point))\n\n(defparameter *shape-points*\n (map\n 'vector\n (lambda (e) (apply #'make-point e))\n ;; the backquote allows us to selectively evaluate (sqrt 0.75) with the comma\n `((0 0) (0.5 ,(sqrt 0.75)) (1 0))))\n\n;; output the data to the \"out.dat\" file\n(with-open-file (out \"sierpinski.dat\" :direction :output :if-exists :supersede)\n (flet ((format-point (p)\n ;; this is not very clean, but it's the simplest way to insert a tab into a string.\n (format nil \"~f~c~f\" (point-x p) #\\tab (point-y p))))\n (format out \"~{~a~%~}\" (map 'list #'format-point (chaos-game 10000 *shape-points*)))))\n\nfrom math import sqrt\nfrom random import random, choice\n\ndata point(x=0, y=0):\n def __add__(self, other):\n return point(self.x + other.x, self.y + other.y)\n\n def __rmul__(self, other):\n return point(self.x * other, self.y * other)\n\ndef chaos_game(n, shape_points):\n p = point(random(), random())\n\n for _ in range(n):\n p = (1/2) * (p + choice(shape_points))\n yield p\n\n\n# This will generate a Sierpinski triangle with a chaos game of n points for an\n# initial triangle with three points on the vertices of an equilateral triangle:\n# A = (0.0, 0.0)\n# B = (0.5, sqrt(0.75))\n# C = (1.0, 0.0)\n# It will output the file sierpinski.dat, which can be plotted after\nshape_points = [point(0.0, 0.0),\n point(0.5, sqrt(0.75)),\n point(1.0, 0.0)]\nwith open(\"sierpinski.dat\", \"w\") as f:\n for p in chaos_game(10000, shape_points):\n f.write(\"{0}\\t{1}\\n\".format(p.x, p.y))\n\nuse rand::*;\n\n#[derive(Clone, Copy)]\nstruct Point {\n x: f64,\n y: f64,\n}\n\nfn chaos_game(iters: usize, shapes: Vec) -> Vec {\n let mut rng = rand::thread_rng();\n let mut p = Point{x: rng.gen(), y: rng.gen()};\n\n (0..iters).into_iter().map(|_| {\n let old_point = p;\n let tmp = shapes[rng.gen_range(0..shapes.len())];\n p.x = 0.5 * (p.x + tmp.x);\n p.y = 0.5 * (p.y + tmp.y);\n old_point\n }).collect()\n}\n\nfn main() {\n let shapes = vec![\n Point{x: 0., y: 0.},\n Point{x: 0.5, y: 0.75_f64.sqrt()},\n Point{x: 1., y: 0.},\n ];\n\n let mut out = String::new();\n\n for point in chaos_game(10_000, shapes) {\n out += format!(\"{}\\t{}\\n\", point.x, point.y).as_str();\n }\n\n std::fs::write(\"./sierpinski.dat\", out).unwrap();\n}\n\nimport java.io.FileWriter;\nimport java.util.Random;\n\npublic class IFS {\n\n private static class Point {\n double x, y;\n\n public Point(double x, double y) {\n this.x = x;\n this.y = y;\n }\n }\n\n // This is a function to simulate a \"chaos game\"\n public static Point[] chaosGame(int n, Point[] shapePoints) {\n Random rng = new Random();\n\n // Initialize output vector\n Point[] outputPoints = new Point[n];\n\n // Choose first point randomly\n Point point = new Point(rng.nextDouble(), rng.nextDouble());\n\n for (int i = 0; i \n# This function simulates a \"chaos game\"\nfunction Simulate-ChaosGame($n, $shapePoints) {\n $outputPoints = New-Object System.Collections.ArrayList\n\n # Initialize the starting point\n $point = @($(Get-Random -Minimum 0.0 -Maximum 1.0), $(Get-Random -Minimum 0.0 -Maximum 1.0))\n\n for ($i = 0; $i -lt $n; $i++) {\n $outputPoints.add($point) | Out-Null\n $temp = $shapePoints[$(Get-Random -Maximum $shapePoints.Count)]\n\n $point = @(\n 0.5 * ($point[0] + $temp[0])\n 0.5 * ($point[1] + $temp[1])\n )\n }\n\n return $outputPoints\n}\n\n\n# This will generate a Sierpinski triangle with a chaos game of n points for an\n# initial triangle with three points on the vertices of an equilateral triangle:\n# A = (0.0, 0.0)\n# B = (0.5, sqrt(0.75))\n# C = (1.0, 0.0)\n# It will output the file sierpinski.dat, which can be plotted after\n$shapePoints = @(\n @(0.0, 0.0),\n @(0.5, [math]::sqrt(0.75)),\n @(1.0, 0.0)\n)\n\nSimulate-ChaosGame -n 10000 -shapePoints $shapePoints | % { \"$($_[0])`t$($_[1])\" } | Out-File -Path \"sierpinski.dat\"\n\n\n\nBibliography\n1.Wikipedia: Self-similarity, 2019.2.Mandelbrot, Benoit, How long is the coast of Britain? Statistical self-similarity and fractional dimension, American Association for the Advancement of Science, 1967.3.Jampour, Mahdi et al., A new fast technique for fingerprint identification with fractal and chaos game theory, World Scientific, 2010.4.Wikipedia: Fractal Compression, 2019.5.Saupe, Dietmar and Hamzaoui, Raouf, A review of the fractal image compression literature, ACM, 1994.6.Sanderson, G, 3blue1brown: Fractals are typically not self-similar, 2017.7.Wikipedia: Hausdorff dimension, 2019.8.Gneiting, Tilmann and Ševčíková, Hana and Percival, Donald B, Estimators of fractal dimension: Assessing the roughness of time series and spatial data, JSTOR, 2012.9.Wikipedia: Hutchinson Operator, 2019.10.Hutchinson, John E, Fractals and self similarity, JSTOR, 1981.11.Wikipedia: Chaos Game, 2019.12.Wolfram: Chaos Game, 2019.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"IFS triangle 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"IFS triangle 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"IFS triangle 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"IFS triangle 4\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"IFS triangle 5\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"IFS square 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"IFS square 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"IFS square 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Chaos 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Chaos 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"IFS triangle video 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"IFS triangle video 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"IFS square video 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Chaos video 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Chaos video 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n"},"contents/verlet_integration/verlet_integration.html":{"url":"contents/verlet_integration/verlet_integration.html","title":"Verlet Integration","keywords":"","body":"Verlet Integration\nVerlet integration is essentially a solution to the kinematic equation for the motion of any object,\n\nx = x_0 + v_0t + \\frac{1}{2}at^2 + \\frac{1}{6}bt^3 + \\cdots\n\nwhere x is the position, v is the velocity, a is the acceleration, b is the often forgotten jerk term, and t is time. This equation is a central equation to almost every Newtonian physics solver and brings up a class of algorithms known as force integrators. One of the first force integrators to work with is Verlet Integration.\nSo, let's say we want to solve for the next timestep in x. To a close approximation (actually performing a Taylor Series Expansion about x(t\\pm \\Delta t)), that might look like this:\n\nx(t+\\Delta t) = x(t) + v(t)\\Delta t + \\frac{1}{2}a(t)\\Delta t^2 + \\frac{1}{6}b(t) \\Delta t^3 + \\mathcal{O}(\\Delta t^4)\n\nThis means that if we need to find the next x, we need the current x, v, a, etc. However, because few people calculate the jerk term, our error is typically \\mathcal{O}(\\Delta t^3). That said, we can calculate x with less knowledge and higher accuracy if we play a trick! Let's say we want to calculate x of the previous timestep. Again, to a close approximation, that might look like this:\n\nx(t-\\Delta t) = x(t) - v(t)\\Delta t + \\frac{1}{2}a(t)\\Delta t^2 - \\frac{1}{6}b(t) \\Delta t^3 + \\mathcal{O}(\\Delta t^4)\n\nNow, we have two equations to solve for two different timesteps in x, one of which we already have. If we add the two equations together and solve for x(t+\\Delta t), we find that\n\nx(t+ \\Delta t) = 2x(t) - x(t-\\Delta t) + a(t)\\Delta t^2 + \\mathcal{O}(\\Delta t^4)\n\nSo, this means we can find our next x simply by knowing our current x, the x before that, and the acceleration! No velocity necessary! In addition, this drops the error to \\mathcal{O}(\\Delta t^4), which is great!\nHere is what it looks like in code:\nfunction verlet(pos::Float64, acc::Float64, dt::Float64)\n prev_pos = pos\n time = 0.0\n\n while (pos > 0)\n time += dt\n temp_pos = pos\n pos = pos * 2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n end\n\n return time\nend\n\ndouble verlet(double pos, double acc, double dt) {\n\n double prev_pos = pos;\n double time = 0;\n\n while (pos > 0) {\n time += dt;\n double next_pos = pos * 2 - prev_pos + acc * dt * dt;\n prev_pos = pos;\n pos = next_pos;\n }\n\n return time;\n}\n\nvoid verlet(double *time, double pos, double acc, double dt) {\n double prev_pos, temp_pos;\n prev_pos = pos;\n *time = 0.0;\n\n while (pos > 0) {\n *time += dt;\n temp_pos = pos;\n pos = pos * 2 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n }\n}\n\nstatic double verlet(double pos, double acc, double dt) {\n\n // Note that we are using a temp variable for the previous position\n double prev_pos, temp_pos, time;\n prev_pos = pos;\n time = 0;\n\n while (pos > 0) {\n time += dt;\n temp_pos = pos;\n pos = pos*2 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n }\n\n return time;\n}\n\ndef verlet(pos, acc, dt):\n prev_pos = pos\n time = 0\n\n while pos > 0:\n time += dt\n next_pos = pos * 2 - prev_pos + acc * dt * dt\n prev_pos, pos = pos, next_pos\n\n return time\n\ntype Method = Model -> Time -> Particle -> Particle -> Particle\n\nverlet :: Method\nverlet acc dt (xOld, _, _, _) (x, _, a, t) = (x', v', a', t + dt)\n where\n x' = 2 * x - xOld + a * dt ^ 2\n v' = 0\n a' = acc (x', v', a, t + dt)\n\nfunction verlet(pos, acc, dt) {\n let prevPos = pos;\n let time = 0;\n let tempPos;\n\n while (pos > 0) {\n time += dt;\n tempPos = pos;\n pos = pos * 2 - prevPos + acc * dt * dt;\n prevPos = tempPos;\n }\n\n return time;\n}\n\nfn verlet(mut pos: f64, acc: f64, dt: f64) -> f64 {\n let mut prev_pos = pos;\n let mut time = 0.0;\n\n while pos > 0.0 {\n time += dt;\n let temp_pos = pos;\n pos = pos * 2.0 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n }\n\n time\n}\n\nfunc verlet(pos: Double, acc: Double, dt: Double) -> Double {\n var pos = pos\n var temp_pos, time: Double\n var prev_pos = pos\n time = 0.0\n\n while (pos > 0) {\n time += dt\n temp_pos = pos\n pos = pos*2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n }\n\n return time\n}\n\nSUBROUTINE verlet(pos, acc, dt, time) \n IMPLICIT NONE\n REAL(8), INTENT(INOUT) :: pos, acc, dt, time\n REAL(8) :: prev_pos, next_pos\n\n\n prev_pos = pos\n time = 0d0\n\n DO\n IF (pos > 0d0) THEN\n time = time + dt\n next_pos = pos * 2d0 - prev_pos + acc * dt ** 2\n prev_pos = pos\n pos = next_pos\n ELSE\n EXIT\n END IF\n END DO\nEND SUBROUTINE verlet\n\ndef verlet(pos, acc, dt)\n\n prev_pos = pos\n time = 0\n while pos > 0 do\n time += dt\n temp_pos = pos\n pos = pos*2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n end\n\n return time\n\nend\n\nfunc verlet(pos, acc, dt float64) (time float64) {\n prevPos := pos\n time = 0\n\n for pos > 0 {\n time += dt\n nextPos := pos*2 - prevPos + acc*dt*dt\n prevPos, pos = pos, nextPos\n }\n\n return\n}\n\n# xmm0 - pos\n# xmm1 - acc\n# xmm2 - dt\n# RET xmm0 - time\nverlet:\n pxor xmm7, xmm7 # Holds 0 for comparisons\n pxor xmm3, xmm3 # Holds time value\n comisd xmm0, xmm7 # Check if pos is greater then 0.0\n jbe verlet_return\n movsd xmm6, xmm1 # xmm6 = acc * dt * dt\n mulsd xmm6, xmm2\n mulsd xmm6, xmm2\n movsd xmm5, xmm0 # Holds previous position\nverlet_loop:\n addsd xmm3, xmm2 # Adding dt to time\n movsd xmm4, xmm0 # Hold old value of posistion\n addsd xmm0, xmm0 # Calculating new position\n subsd xmm0, xmm5\n addsd xmm0, xmm6\n movsd xmm5, xmm4\n comisd xmm0, xmm7 # Check if position is greater then 0.0\n ja verlet_loop\nverlet_return:\n movsd xmm0, xmm3 # Saving time value\n ret\n\nfun verlet(_pos: Double, acc: Double, dt: Double): Double {\n var pos = _pos // Since function parameter are val and can't be modified\n var prevPos = pos\n var time = 0.0\n\n while (pos > 0) {\n time += dt\n val nextPos = pos * 2 - prevPos + acc * dt * dt\n prevPos = pos\n pos = nextPos\n }\n return time\n}\n\nfunc verlet(pos_in, acc, dt: float): float =\n var\n pos: float = pos_in\n prevPos: float = pos\n time: float = 0.0\n tempPos: float\n\n while pos > 0.0:\n time += dt\n tempPos = pos\n pos = pos * 2 - prevPos + acc * dt * dt\n prevPos = tempPos\n\n time\n\n(defun verlet (pos acc dt)\n \"Integrates Newton's equation for motion while pos > 0 using Verlet integration.\"\n (loop\n with prev-pos = pos\n for time = 0 then (incf time dt)\n while (> pos 0)\n ;; The starting speed is assumed to be zero.\n do (psetf\n pos (+ (* pos 2) (- prev-pos) (* acc dt dt))\n prev-pos pos)\n finally (return time)))\n\n\n\nNow, obviously this poses a problem; what if we want to calculate a term that requires velocity, like the kinetic energy, \\frac{1}{2}mv^2? In this case, we certainly cannot get rid of the velocity! Well, we can find the velocity to \\mathcal{O}(\\Delta t^2) accuracy by using the Stormer-Verlet method.\nWe have the equations for x(t+\\Delta t) and x(t-\\Delta t) above, so let's start there.\nIf we subtract the latter from the former, we get the following:\n\nx(t+\\Delta t) - x(t - \\Delta t) = 2v(t)\\Delta t + \\frac{1}{3}b(t)\\Delta t^3.\n\nWhen we solve for v(t), we get\n\n\\begin{align}\nv(t) &= \\frac{x(t+\\Delta t) - x(t-\\Delta t)}{2\\Delta t} + \\frac{b(t) \\Delta t^3}{3 \\Delta t} \\\\ \nv(t) &= \\frac{x(t+\\Delta t) - x(t-\\Delta t)}{2\\Delta t} + \\mathcal{O}(\\Delta t^2).\n\\end{align}\n\nNote that the 2 in the denominator makes sense because we are going over 2 timesteps. It's essentially solving v=\\frac{\\Delta x}{\\Delta t}. In addition, we can calculate the velocity of the next timestep like so\n\nv(t+\\Delta t) = \\frac{x(t+\\Delta t) - x(t)}{\\Delta t} + \\mathcal{O}(\\Delta t)\n\nHowever, the error for this is \\mathcal{O}(\\Delta t), which is quite poor, but it gets the job done in a pinch. Here's what it looks like in code:\nfunction stormer_verlet(pos::Float64, acc::Float64, dt::Float64)\n prev_pos = pos\n time = 0.0\n vel = 0.0\n\n while (pos > 0.0)\n time += dt\n temp_pos = pos\n pos = pos * 2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n\n # Because acceleration is constant, velocity is straightforward\n vel += acc * dt\n end\n\n return time, vel\nend\n\ntimestep stormer_verlet(double pos, double acc, double dt) {\n\n double prev_pos = pos;\n double time = 0;\n double vel = 0;\n while (pos > 0) {\n time += dt;\n double next_pos = pos * 2 - prev_pos + acc * dt * dt;\n prev_pos = pos;\n pos = next_pos;\n\n // The acceleration is constant, so the velocity is\n // straightforward\n vel += acc * dt;\n }\n\n return timestep { time, vel };\n}\n\nvoid stormer_verlet(double *time, double *vel,\n double pos, double acc, double dt) {\n double prev_pos, temp_pos;\n prev_pos = pos;\n *vel = 0.0;\n *time = 0.0;\n\n while (pos > 0) {\n *time += dt;\n temp_pos = pos;\n pos = pos * 2 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n\n *vel += acc * dt;\n }\n}\n\nstatic VerletValues stormer_verlet(double pos, double acc, double dt) {\n\n // Note that we are using a temp variable for the previous position\n double prev_pos, temp_pos, time, vel;\n prev_pos = pos;\n vel = 0;\n time = 0;\n while (pos > 0) {\n time += dt;\n temp_pos = pos;\n pos = pos*2 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n\n // The acceleration is constant, so the velocity is straightforward\n vel += acc*dt;\n }\n\n return new VerletValues(time, vel);\n}\n\ndef stormer_verlet(pos, acc, dt):\n prev_pos = pos\n time = 0\n vel = 0\n\n while pos > 0:\n time += dt\n next_pos = pos * 2 - prev_pos + acc * dt * dt\n prev_pos, pos = pos, next_pos\n vel += acc * dt\n\n return time, vel\n\nstormerVerlet :: Method\nstormerVerlet acc dt (xOld, _, _, _) (x, _, a, t) = (x', v', a', t + dt)\n where\n x' = 2 * x - xOld + a * dt ^ 2\n v' = (x' - x) / dt\n a' = acc (x', v', a, t + dt)\n\nfunction stormerVerlet(pos, acc, dt) {\n let prevPos = pos;\n let time = 0;\n let vel = 0;\n let tempPos;\n\n while (pos > 0) {\n time += dt;\n tempPos = pos;\n pos = pos * 2 - prevPos + acc * dt * dt;\n prevPos = tempPos;\n\n vel += acc * dt;\n }\n\n return { time, vel };\n}\n\nfn stormer_verlet(mut pos: f64, acc: f64, dt: f64) -> (f64, f64) {\n let mut prev_pos = pos;\n let mut time = 0.0;\n let mut vel = 0.0;\n\n while pos > 0.0 {\n time += dt;\n let temp_pos = pos;\n pos = pos * 2.0 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n\n // Because acceleration is constant, velocity is\n // straightforward\n vel += acc * dt;\n }\n\n (time, vel)\n}\n\nfunc stormerVerlet(pos: Double, acc: Double, dt: Double) -> (time: Double, vel: Double) {\n var pos = pos\n var temp_pos, time, vel: Double\n var prev_pos = pos\n vel = 0\n time = 0\n\n while (pos > 0) {\n time += dt\n temp_pos = pos\n pos = pos*2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n\n vel += acc*dt\n }\n\n return (time:time, vel:vel)\n}\n\nSUBROUTINE stormer_verlet(pos, acc, dt, time, vel) \n IMPLICIT NONE\n REAL(8), INTENT(INOUT) :: pos, acc, dt, time, vel\n REAL(8) :: prev_pos, next_pos\n\n prev_pos = pos \n time = 0d0\n vel = 0d0\n\n DO\n IF (pos > 0d0) THEN\n time = time + dt\n next_pos = pos * 2 - prev_pos + acc * dt ** 2\n prev_pos = pos\n pos = next_pos\n vel = vel + acc * dt\n ELSE\n EXIT\n END IF\n END DO\nEND SUBROUTINE stormer_verlet\n\ndef stormer_verlet(pos, acc, dt)\n\n prev_pos = pos\n vel = 0\n time = 0\n while pos > 0 do\n time += dt\n temp_pos = pos\n pos = pos*2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n\n vel += acc*dt\n end\n\n return time, vel\n\nend\n\nfunc stormerVerlet(pos, acc, dt float64) (time, vel float64) {\n prevPos := pos\n time, vel = 0, 0\n\n for pos > 0 {\n time += dt\n vel += acc * dt\n nextPos := pos*2 - prevPos + acc*dt*dt\n prevPos, pos = pos, nextPos\n }\n\n return\n}\n\n# xmm0 - pos\n# xmm1 - acc\n# xmm2 - dt\n# RET xmm0 - time\n# RET xmm1 - velocity\nstormer_verlet:\n pxor xmm7, xmm7 # Holds 0 for comparisons\n pxor xmm3, xmm3 # Holds time value\n comisd xmm0, xmm7 # Check if pos is greater then 0.0\n jbe stormer_verlet_return\n movsd xmm6, xmm1 # xmm6 = acc * dt * dt\n mulsd xmm6, xmm2\n mulsd xmm6, xmm2\n movsd xmm5, xmm0 # Holds previous position\nstormer_verlet_loop:\n addsd xmm3, xmm2 # Adding dt to time\n movsd xmm4, xmm0 # Hold old value of posistion\n addsd xmm0, xmm0 # Calculating new position\n subsd xmm0, xmm5\n addsd xmm0, xmm6\n movsd xmm5, xmm4\n comisd xmm0, xmm7 # Check if position is greater then 0.0\n ja stormer_verlet_loop\nstormer_verlet_return:\n movsd xmm0, xmm3 # Saving time and velocity\n mulsd xmm3, xmm1\n movsd xmm1, xmm3\n ret\n\nfun stormerVerlet(_pos: Double, acc: Double, dt: Double): VerletValues {\n var pos = _pos\n var prevPos = pos\n var time = 0.0\n var vel = 0.0\n while (pos > 0) {\n time += dt\n val nextPos = pos * 2 - prevPos + acc * dt * dt\n prevPos = pos\n pos = nextPos\n vel += acc * dt\n }\n return VerletValues(time, vel)\n}\n\nfunc stormerVerlet(pos_in, acc, dt: float): (float, float) =\n var\n pos: float = pos_in\n prevPos: float = pos\n time: float = 0.0\n vel: float = 0.0\n tempPos: float\n\n while pos > 0.0:\n time += dt\n tempPos = pos\n pos = pos * 2 - prevPos + acc * dt * dt\n prevPos = tempPos\n\n vel += acc * dt\n\n (time, vel)\n\n(defun stormer-verlet (pos acc dt)\n \"Integrates Newton's equation for motion while pos > 0 using the Stormer-Verlet method.\"\n (loop\n with prev-pos = pos\n for time = 0 then (incf time dt)\n for vel = 0 then (incf vel (* acc dt))\n while (> pos 0)\n ;; Variables are changed simultaneously by 'psetf', so there's no need for a temporary variable.\n do (psetf\n pos (+ (* pos 2) (- prev-pos) (* acc dt dt))\n prev-pos pos)\n finally (return (list time vel))))\n\n\n\n\nNow, let's say we actually need the velocity to calculate out next timestep. Well, in this case, we simply cannot use the above approximation and instead need to use the Velocity Verlet algorithm.\nVelocity Verlet\nIn some ways, this algorithm is even simpler than above. We can calculate everything like\n\n\\begin{align}\nx(t+\\Delta t) &=x(t) + v(t)\\Delta t + \\frac{1}{2}a(t)\\Delta t^2 \\\\\na(t+\\Delta t) &= f(x(t+\\Delta t)) \\\\\nv(t+\\Delta t) &= v(t) + \\frac{1}{2}(a(t) + a(t+\\Delta t))\\Delta t\n\\end{align}\n\nwhich is literally the kinematic equation above, solving for x, v, and a every timestep. You can also split up the equations like so\n\n\\begin{align}\nv(t+\\frac{1}{2}\\Delta t) &= v(t) + \\frac{1}{2}a(t)\\Delta t \\\\\nx(t+\\Delta t) &=x(t) + v(t+\\frac{1}{2}\\Delta t)\\Delta t \\\\\na(t+\\Delta t) &= f(x(t+\\Delta t)) \\\\\nv(t+\\Delta t) &= v(t+\\frac{1}{2}\\Delta t) + \\frac{1}{2}a(t+\\Delta t)\\Delta t\n\\end{align}\n\nHere is the velocity Verlet method in code:\nfunction velocity_verlet(pos::Float64, acc::Float64, dt::Float64)\n prev_pos = pos\n time = 0.0\n vel = 0.0\n\n while (pos > 0.0)\n time += dt\n pos += vel * dt + 0.5 * acc * dt * dt;\n vel += acc * dt;\n end\n\n return time, vel\nend\n\ntimestep velocity_verlet(double pos, double acc, double dt) {\n\n double time = 0;\n double vel = 0;\n while (pos > 0) {\n time += dt;\n pos += vel * dt + 0.5 * acc * dt * dt;\n vel += acc * dt;\n }\n\n return timestep { time, vel };\n}\n\nvoid velocity_verlet(double *time, double *vel,\n double pos, double acc, double dt) {\n *vel = 0.0;\n *time = 0.0;\n\n while (pos > 0) {\n *time += dt;\n pos += (*vel) * dt + 0.5 * acc * dt * dt;\n *vel += acc * dt;\n }\n}\n\nstatic VerletValues velocity_verlet(double pos, double acc, double dt) {\n\n // Note that we are using a temp variable for the previous position\n double time, vel;\n vel = 0;\n time = 0;\n while (pos > 0) {\n time += dt;\n pos += vel*dt + 0.5*acc * dt * dt;\n vel += acc*dt;\n }\n return new VerletValues(time, vel);\n}\n\ndef velocity_verlet(pos, acc, dt):\n time = 0\n vel = 0\n\n while pos > 0:\n time += dt\n pos += vel * dt + 0.5 * acc * dt * dt\n vel += acc * dt\n\n return time, vel\n\nvelocityVerlet :: Method\nvelocityVerlet acc dt (xOld, _, aOld, _) (x, v, a, t) = (x', v', a', t + dt)\n where\n x' = 2 * x - xOld + a * dt ^ 2\n v' = v + 0.5 * (aOld + a) * dt\n a' = acc (x', v', a, t + dt)\n\nfunction velocityVerlet(pos, acc, dt) {\n let time = 0;\n let vel = 0;\n\n while (pos > 0) {\n time += dt;\n pos += vel * dt + 0.5 * acc * dt * dt;\n vel += acc * dt;\n }\n\n return { time, vel };\n}\n\nfn velocity_verlet(mut pos: f64, acc: f64, dt: f64) -> (f64, f64) {\n let mut time = 0.0;\n let mut vel = 0.0;\n\n while pos > 0.0 {\n time += dt;\n pos += vel * dt + 0.5 * acc * dt * dt;\n vel += acc * dt;\n }\n\n (time, vel)\n}\n\nfunc velocityVerlet(pos: Double, acc: Double, dt: Double) -> (time: Double, vel: Double) {\n var pos = pos\n var time, vel : Double\n vel = 0\n time = 0\n\n while (pos > 0) {\n time += dt\n pos += vel*dt + 0.5*acc * dt * dt\n vel += acc*dt\n }\n\n return (time:time, vel:vel)\n}\n\nSUBROUTINE velocity_verlet(pos, acc, dt, time, vel) \n IMPLICIT NONE\n REAL(8), INTENT(INOUT) :: pos, acc, dt, time, vel\n\n time = 0d0\n vel = 0d0\n\n DO\n IF (pos > 0d0) THEN\n time = time + dt\n pos = pos + vel * dt + 0.5d0 * acc * dt ** 2 \n vel = vel + acc * dt\n ELSE\n EXIT\n END IF\n END DO\nEND SUBROUTINE velocity_verlet\n\ndef velocity_verlet(pos, acc, dt)\n\n vel = 0\n time = 0\n while pos > 0 do\n time += dt\n pos += vel*dt + 0.5*acc * dt * dt\n vel += acc*dt\n end\n\n return time, vel\n\nend\n\nfunc velocityVerlet(pos, acc, dt float64) (time, vel float64) {\n time, vel = 0, 0\n\n for pos > 0 {\n time += dt\n pos += vel*dt + .5*acc*dt*dt\n vel += acc * dt\n }\n\n return\n}\n\n# xmm0 - pos\n# xmm1 - acc\n# xmm2 - dt\n# RET xmm0 - time\n# RET xmm1 - velocity\nvelocity_verlet:\n pxor xmm7, xmm7 # Holds 0 for comparisons\n pxor xmm3, xmm3 # Holds the velocity value\n pxor xmm4, xmm4 # Holds the time value\n comisd xmm0, xmm7 # Check if pos is greater then 0.0\n jbe velocity_verlet_return\n movsd xmm5, half # xmm5 = 0.5 * dt * dt * acc\n mulsd xmm5, xmm2\n mulsd xmm5, xmm2\n mulsd xmm5, xmm1\nvelocity_verlet_loop:\n movsd xmm6, xmm3 # Move velocity into register\n mulsd xmm6, xmm2 # Calculate new position\n addsd xmm6, xmm5\n addsd xmm0, xmm6\n addsd xmm4, xmm2 # Incrementing time\n movsd xmm3, xmm4 # Updating velocity\n mulsd xmm3, xmm1\n comisd xmm0, xmm7\n ja velocity_verlet_loop\nvelocity_verlet_return:\n movsd xmm0, xmm4 # Saving time and velocity\n movsd xmm1, xmm3\n ret\n\nfun velocityVerlet(_pos: Double, acc: Double, dt: Double): VerletValues {\n var pos = _pos\n var time = 0.0\n var vel = 0.0\n while (pos > 0) {\n time += dt\n pos += vel * dt + 0.5 * acc * dt * dt\n vel += acc * dt\n }\n return VerletValues(time, vel)\n}\n\nfunc velocityVerlet(pos_in, acc, dt: float): (float, float) =\n var\n pos: float = pos_in\n time: float = 0.0\n vel: float = 0.0\n\n while pos > 0.0:\n time += dt\n pos += vel * dt + 0.5 * acc * dt * dt\n vel += acc * dt\n\n (time, vel)\n\n(defun velocity-verlet (pos acc dt)\n \"Integrates Newton's equation for motion while pos > 0 using the velocity in calculations.\"\n (loop\n for time = 0 then (incf time dt)\n for vel = 0 then (incf vel (* acc dt))\n for p = pos then (incf p (+ (* vel dt) (* 0.5 acc dt dt)))\n while (> p 0)\n finally (return (list time vel))))\n\n\n\nEven though this method is more widely used than the simple Verlet method mentioned above, it unfortunately has an error term of \\mathcal{O}(\\Delta t^2), which is two orders of magnitude worse. That said, if you want to have a simulation with many objects that depend on one another --- like a gravity simulation --- the Velocity Verlet algorithm is a handy choice; however, you may have to play further tricks to allow everything to scale appropriately. These types of simulations are sometimes called n-body simulations and one such trick is the Barnes-Hut algorithm, which cuts the complexity of n-body simulations from \\sim \\mathcal{O}(n^2) to \\sim \\mathcal{O}(n\\log(n)).\nVideo Explanation\nHere is a video describing Verlet integration:\n\n\n\n\nExample Code\nBoth of these methods work simply by iterating timestep-by-timestep and can be written straightforwardly in any language. For reference, here are snippets of code that use both the classic and velocity Verlet methods to find the time it takes for a ball to hit the ground after being dropped from a given height.\nfunction verlet(pos::Float64, acc::Float64, dt::Float64)\n prev_pos = pos\n time = 0.0\n\n while (pos > 0)\n time += dt\n temp_pos = pos\n pos = pos * 2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n end\n\n return time\nend\n\nfunction stormer_verlet(pos::Float64, acc::Float64, dt::Float64)\n prev_pos = pos\n time = 0.0\n vel = 0.0\n\n while (pos > 0.0)\n time += dt\n temp_pos = pos\n pos = pos * 2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n\n # Because acceleration is constant, velocity is straightforward\n vel += acc * dt\n end\n\n return time, vel\nend\n\nfunction velocity_verlet(pos::Float64, acc::Float64, dt::Float64)\n prev_pos = pos\n time = 0.0\n vel = 0.0\n\n while (pos > 0.0)\n time += dt\n pos += vel * dt + 0.5 * acc * dt * dt;\n vel += acc * dt;\n end\n\n return time, vel\nend\n\nfunction main()\n time = verlet(5.0, -10.0, 0.01);\n println(\"[#]\\nTime for Verlet integration is:\")\n println(\"$(time)\")\n\n time, vel = stormer_verlet(5.0, -10.0, 0.01);\n println(\"[#]\\nTime for Stormer Verlet integration is:\")\n println(\"$(time)\")\n println(\"[#]\\nVelocity for Stormer Verlet integration is:\")\n println(\"$(vel)\")\n\n time, vel = velocity_verlet(5.0, -10.0, 0.01);\n println(\"[#]\\nTime for velocity Verlet integration is:\")\n println(\"$(time)\")\n println(\"[#]\\nVelocity for velocity Verlet integration is:\")\n println(\"$(vel)\")\n\nend\n\nmain()\n\n#include \n#include \n\nstruct timestep {\n double time;\n double vel;\n};\n\ndouble verlet(double pos, double acc, double dt) {\n\n double prev_pos = pos;\n double time = 0;\n\n while (pos > 0) {\n time += dt;\n double next_pos = pos * 2 - prev_pos + acc * dt * dt;\n prev_pos = pos;\n pos = next_pos;\n }\n\n return time;\n}\n\ntimestep stormer_verlet(double pos, double acc, double dt) {\n\n double prev_pos = pos;\n double time = 0;\n double vel = 0;\n while (pos > 0) {\n time += dt;\n double next_pos = pos * 2 - prev_pos + acc * dt * dt;\n prev_pos = pos;\n pos = next_pos;\n\n // The acceleration is constant, so the velocity is\n // straightforward\n vel += acc * dt;\n }\n\n return timestep { time, vel };\n}\n\ntimestep velocity_verlet(double pos, double acc, double dt) {\n\n double time = 0;\n double vel = 0;\n while (pos > 0) {\n time += dt;\n pos += vel * dt + 0.5 * acc * dt * dt;\n vel += acc * dt;\n }\n\n return timestep { time, vel };\n}\n\nint main() {\n std::cout \n#include \n\nvoid verlet(double *time, double pos, double acc, double dt) {\n double prev_pos, temp_pos;\n prev_pos = pos;\n *time = 0.0;\n\n while (pos > 0) {\n *time += dt;\n temp_pos = pos;\n pos = pos * 2 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n }\n}\n\nvoid stormer_verlet(double *time, double *vel,\n double pos, double acc, double dt) {\n double prev_pos, temp_pos;\n prev_pos = pos;\n *vel = 0.0;\n *time = 0.0;\n\n while (pos > 0) {\n *time += dt;\n temp_pos = pos;\n pos = pos * 2 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n\n *vel += acc * dt;\n }\n}\n\nvoid velocity_verlet(double *time, double *vel,\n double pos, double acc, double dt) {\n *vel = 0.0;\n *time = 0.0;\n\n while (pos > 0) {\n *time += dt;\n pos += (*vel) * dt + 0.5 * acc * dt * dt;\n *vel += acc * dt;\n }\n}\n\nint main() {\n double time, vel;\n\n verlet(&time, 5.0, -10, 0.01);\n printf(\"[#]\\nTime for Verlet integration is:\\n\");\n printf(\"%lf\\n\", time);\n\n stormer_verlet(&time, &vel, 5.0, -10, 0.01);\n printf(\"[#]\\nTime for Stormer Verlet integration is:\\n\");\n printf(\"%lf\\n\", time);\n printf(\"[#]\\nVelocity for Stormer Verlet integration is:\\n\");\n printf(\"%lf\\n\", vel);\n\n velocity_verlet(&time, &vel, 5.0, -10, 0.01);\n printf(\"[#]\\nTime for velocity Verlet integration is:\\n\");\n printf(\"%lf\\n\", time);\n printf(\"[#]\\nVelocity for Stormer Verlet integration is:\\n\");\n printf(\"%lf\\n\", vel);\n\n return 0;\n}\n\npublic class Verlet {\n\n private static class VerletValues {\n public double time;\n public double vel;\n\n public VerletValues(double time, double vel) {\n this.time = time;\n this.vel = vel;\n }\n }\n\n\n static double verlet(double pos, double acc, double dt) {\n\n // Note that we are using a temp variable for the previous position\n double prev_pos, temp_pos, time;\n prev_pos = pos;\n time = 0;\n\n while (pos > 0) {\n time += dt;\n temp_pos = pos;\n pos = pos*2 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n }\n\n return time;\n }\n\n static VerletValues stormer_verlet(double pos, double acc, double dt) {\n\n // Note that we are using a temp variable for the previous position\n double prev_pos, temp_pos, time, vel;\n prev_pos = pos;\n vel = 0;\n time = 0;\n while (pos > 0) {\n time += dt;\n temp_pos = pos;\n pos = pos*2 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n\n // The acceleration is constant, so the velocity is straightforward\n vel += acc*dt;\n }\n\n return new VerletValues(time, vel);\n }\n\n static VerletValues velocity_verlet(double pos, double acc, double dt) {\n\n // Note that we are using a temp variable for the previous position\n double time, vel;\n vel = 0;\n time = 0;\n while (pos > 0) {\n time += dt;\n pos += vel*dt + 0.5*acc * dt * dt;\n vel += acc*dt;\n }\n return new VerletValues(time, vel);\n }\n\n public static void main(String[] args) {\n\n double verletTime = verlet(5.0, -10, 0.01);\n System.out.println(\"[#]\\nTime for Verlet integration is:\");\n System.out.println(verletTime);\n\n VerletValues stormerVerlet = stormer_verlet(5.0, -10, 0.01);\n System.out.println(\"[#]\\nTime for Stormer Verlet integration is:\");\n System.out.println(stormerVerlet.time);\n System.out.println(\"[#]\\nVelocity for Stormer Verlet integration is:\");\n System.out.println(stormerVerlet.vel);\n\n VerletValues velocityVerlet = velocity_verlet(5.0, -10, 0.01);\n System.out.println(\"[#]\\nTime for velocity Verlet integration is:\");\n System.out.println(velocityVerlet.time);\n System.out.println(\"[#]\\nVelocity for velocity Verlet integration is:\");\n System.out.println(velocityVerlet.vel);\n\n }\n}\n\ndef verlet(pos, acc, dt):\n prev_pos = pos\n time = 0\n\n while pos > 0:\n time += dt\n next_pos = pos * 2 - prev_pos + acc * dt * dt\n prev_pos, pos = pos, next_pos\n\n return time\n\ndef stormer_verlet(pos, acc, dt):\n prev_pos = pos\n time = 0\n vel = 0\n\n while pos > 0:\n time += dt\n next_pos = pos * 2 - prev_pos + acc * dt * dt\n prev_pos, pos = pos, next_pos\n vel += acc * dt\n\n return time, vel\n\ndef velocity_verlet(pos, acc, dt):\n time = 0\n vel = 0\n\n while pos > 0:\n time += dt\n pos += vel * dt + 0.5 * acc * dt * dt\n vel += acc * dt\n\n return time, vel\n\ndef main():\n time = verlet(5, -10, 0.01)\n print(\"[#]\\nTime for Verlet integration is:\")\n print(\"{:.10f}\".format(time))\n\n time, vel = stormer_verlet(5, -10, 0.01)\n print(\"[#]\\nTime for Stormer Verlet integration is:\")\n print(\"{:.10f}\".format(time))\n print(\"[#]\\nVelocity for Stormer Verlet integration is:\")\n print(\"{:.10f}\".format(vel))\n\n time, vel = velocity_verlet(5, -10, 0.01)\n print(\"[#]\\nTime for velocity Verlet integration is:\")\n print(\"{:.10f}\".format(time))\n print(\"[#]\\nVelocity for velocity Verlet integration is:\")\n print(\"{:.10f}\".format(vel))\n\n\nif __name__ == '__main__':\n main()\n\n-- submitted by Jie\ntype Time = Double\n\ntype Position = Double\n\ntype Speed = Double\n\ntype Acceleration = Double\n\ntype Particle = (Position, Speed, Acceleration, Time)\n\ntype Model = Particle -> Acceleration\n\ntype Method = Model -> Time -> Particle -> Particle -> Particle\n\nverlet :: Method\nverlet acc dt (xOld, _, _, _) (x, _, a, t) = (x', v', a', t + dt)\n where\n x' = 2 * x - xOld + a * dt ^ 2\n v' = 0\n a' = acc (x', v', a, t + dt)\n\nstormerVerlet :: Method\nstormerVerlet acc dt (xOld, _, _, _) (x, _, a, t) = (x', v', a', t + dt)\n where\n x' = 2 * x - xOld + a * dt ^ 2\n v' = (x' - x) / dt\n a' = acc (x', v', a, t + dt)\n\nvelocityVerlet :: Method\nvelocityVerlet acc dt (xOld, _, aOld, _) (x, v, a, t) = (x', v', a', t + dt)\n where\n x' = 2 * x - xOld + a * dt ^ 2\n v' = v + 0.5 * (aOld + a) * dt\n a' = acc (x', v', a, t + dt)\n\ntrajectory :: Method -> Model -> Time -> Particle -> [Particle]\ntrajectory method acc dt p0@(x, v, a, t0) = traj\n where\n traj = p0 : p1 : zipWith (method acc dt) traj (tail traj)\n p1 = (x', v', acc (x', v', a, t0 + dt), t0 + dt)\n x' = x + v * dt + 0.5 * a * dt ^ 2\n v' = v + a * dt\n\nmain :: IO ()\nmain = do\n let p0 = (5, 0, -10, 0)\n dt = 0.001\n freefall _ = -10\n aboveGround (x, _, _, _) = x > 0\n timeVelocity m =\n let (_, v, _, t) = last $ takeWhile aboveGround $ trajectory m freefall dt p0\n in (show t, show v)\n\n putStrLn \"[#]\\nTime for Verlet integration is:\"\n putStrLn $ fst $ timeVelocity verlet\n putStrLn \"[#]\\nTime for Stormer Verlet integration is:\"\n putStrLn $ fst $ timeVelocity stormerVerlet\n putStrLn \"[#]\\nVelocity for Stormer Verlet integration is:\"\n putStrLn $ snd $ timeVelocity stormerVerlet\n putStrLn \"[#]\\nTime for velocity Verlet integration is:\"\n putStrLn $ fst $ timeVelocity velocityVerlet\n putStrLn \"[#]\\nVelocity for velocity Verlet integration is:\"\n putStrLn $ snd $ timeVelocity velocityVerlet\n\nfunction verlet(pos, acc, dt) {\n let prevPos = pos;\n let time = 0;\n let tempPos;\n\n while (pos > 0) {\n time += dt;\n tempPos = pos;\n pos = pos * 2 - prevPos + acc * dt * dt;\n prevPos = tempPos;\n }\n\n return time;\n}\n\nfunction stormerVerlet(pos, acc, dt) {\n let prevPos = pos;\n let time = 0;\n let vel = 0;\n let tempPos;\n\n while (pos > 0) {\n time += dt;\n tempPos = pos;\n pos = pos * 2 - prevPos + acc * dt * dt;\n prevPos = tempPos;\n\n vel += acc * dt;\n }\n\n return { time, vel };\n}\n\nfunction velocityVerlet(pos, acc, dt) {\n let time = 0;\n let vel = 0;\n\n while (pos > 0) {\n time += dt;\n pos += vel * dt + 0.5 * acc * dt * dt;\n vel += acc * dt;\n }\n\n return { time, vel };\n}\n\nconst time = verlet(5, -10, 0.01);\nconsole.log(`[#]\\nTime for Verlet integration is:`);\nconsole.log(`${time}`);\n\nconst stormer = stormerVerlet(5, -10, 0.01);\nconsole.log(`[#]\\nTime for Stormer Verlet integration is:`);\nconsole.log(`${stormer.time}`);\nconsole.log(`[#]\\nVelocity for Stormer Verlet integration is:`);\nconsole.log(`${stormer.vel}`);\n\nconst velocity = velocityVerlet(5, -10, 0.01);\nconsole.log(`[#]\\nTime for velocity Verlet integration is:`);\nconsole.log(`${velocity.time}`);\nconsole.log(`[#]\\nVelocity for velocity Verlet integration is:`);\nconsole.log(`${velocity.vel}`);\n\nfn verlet(mut pos: f64, acc: f64, dt: f64) -> f64 {\n let mut prev_pos = pos;\n let mut time = 0.0;\n\n while pos > 0.0 {\n time += dt;\n let temp_pos = pos;\n pos = pos * 2.0 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n }\n\n time\n}\n\nfn stormer_verlet(mut pos: f64, acc: f64, dt: f64) -> (f64, f64) {\n let mut prev_pos = pos;\n let mut time = 0.0;\n let mut vel = 0.0;\n\n while pos > 0.0 {\n time += dt;\n let temp_pos = pos;\n pos = pos * 2.0 - prev_pos + acc * dt * dt;\n prev_pos = temp_pos;\n\n // Because acceleration is constant, velocity is\n // straightforward\n vel += acc * dt;\n }\n\n (time, vel)\n}\n\nfn velocity_verlet(mut pos: f64, acc: f64, dt: f64) -> (f64, f64) {\n let mut time = 0.0;\n let mut vel = 0.0;\n\n while pos > 0.0 {\n time += dt;\n pos += vel * dt + 0.5 * acc * dt * dt;\n vel += acc * dt;\n }\n\n (time, vel)\n}\n\nfn main() {\n let time_v = verlet(5.0, -10.0, 0.01);\n let (time_sv, vel_sv) = stormer_verlet(5.0, -10.0, 0.01);\n let (time_vv, vel_vv) = velocity_verlet(5.0, -10.0, 0.01);\n\n println!(\"[#]\\nTime for Verlet integration is:\");\n println!(\"{}\", time_v);\n\n println!(\"[#]\\nTime for Stormer Verlet integration is:\");\n println!(\"{}\", time_sv);\n println!(\"[#]\\nVelocity for Stormer Verlet integration is:\");\n println!(\"{}\", vel_sv);\n\n println!(\"[#]\\nTime for velocity Verlet integration is:\");\n println!(\"{}\", time_vv);\n println!(\"[#]\\nVelocity for velocity Verlet integration is:\");\n println!(\"{}\", vel_vv);\n}\n\nfunc verlet(pos: Double, acc: Double, dt: Double) -> Double {\n var pos = pos\n var temp_pos, time: Double\n var prev_pos = pos\n time = 0.0\n\n while (pos > 0) {\n time += dt\n temp_pos = pos\n pos = pos*2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n }\n\n return time\n}\n\nfunc stormerVerlet(pos: Double, acc: Double, dt: Double) -> (time: Double, vel: Double) {\n var pos = pos\n var temp_pos, time, vel: Double\n var prev_pos = pos\n vel = 0\n time = 0\n\n while (pos > 0) {\n time += dt\n temp_pos = pos\n pos = pos*2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n\n vel += acc*dt\n }\n\n return (time:time, vel:vel)\n}\n\nfunc velocityVerlet(pos: Double, acc: Double, dt: Double) -> (time: Double, vel: Double) {\n var pos = pos\n var time, vel : Double\n vel = 0\n time = 0\n\n while (pos > 0) {\n time += dt\n pos += vel*dt + 0.5*acc * dt * dt\n vel += acc*dt\n }\n\n return (time:time, vel:vel)\n}\n\nfunc main() {\n let verletTime = verlet(pos: 5.0, acc: -10.0, dt: 0.01)\n print(\"[#]\\nTime for Verlet integration is:\")\n print(\"\\(verletTime)\")\n\n let stormer = stormerVerlet(pos: 5.0, acc: -10.0, dt: 0.01);\n print(\"[#]\\nTime for Stormer Verlet integration is:\")\n print(\"\\(stormer.time)\")\n print(\"[#]\\nVelocity for Stormer Verlet integration is:\")\n print(\"\\(stormer.vel)\")\n\n let velVerlet = velocityVerlet(pos: 5.0, acc: -10, dt: 0.01)\n print(\"[#]\\nTime for velocity Verlet integration is:\")\n print(\"\\(velVerlet.time)\")\n print(\"[#]\\nVelocity for velocity Verlet integration is:\")\n print(\"\\(velVerlet.vel)\")\n}\n\nmain()\n\nSUBROUTINE verlet(pos, acc, dt, time) \n IMPLICIT NONE\n REAL(8), INTENT(INOUT) :: pos, acc, dt, time\n REAL(8) :: prev_pos, next_pos\n\n\n prev_pos = pos\n time = 0d0\n\n DO\n IF (pos > 0d0) THEN\n time = time + dt\n next_pos = pos * 2d0 - prev_pos + acc * dt ** 2\n prev_pos = pos\n pos = next_pos\n ELSE\n EXIT\n END IF\n END DO\nEND SUBROUTINE verlet\n\nSUBROUTINE stormer_verlet(pos, acc, dt, time, vel) \n IMPLICIT NONE\n REAL(8), INTENT(INOUT) :: pos, acc, dt, time, vel\n REAL(8) :: prev_pos, next_pos\n\n prev_pos = pos \n time = 0d0\n vel = 0d0\n\n DO\n IF (pos > 0d0) THEN\n time = time + dt\n next_pos = pos * 2 - prev_pos + acc * dt ** 2\n prev_pos = pos\n pos = next_pos\n vel = vel + acc * dt\n ELSE\n EXIT\n END IF\n END DO\nEND SUBROUTINE stormer_verlet \n\nSUBROUTINE velocity_verlet(pos, acc, dt, time, vel) \n IMPLICIT NONE\n REAL(8), INTENT(INOUT) :: pos, acc, dt, time, vel\n\n time = 0d0\n vel = 0d0\n\n DO\n IF (pos > 0d0) THEN\n time = time + dt\n pos = pos + vel * dt + 0.5d0 * acc * dt ** 2 \n vel = vel + acc * dt\n ELSE\n EXIT\n END IF\n END DO\nEND SUBROUTINE velocity_verlet \n\nPROGRAM verlet_integration\n\n IMPLICIT NONE \n REAL(8) :: pos,acc, dt, time, vel\n\n INTERFACE\n SUBROUTINE verlet(pos, acc, dt, time)\n REAL(8), INTENT(INOUT) :: pos, acc, dt, time\n REAL(8) :: prev_pos, next_pos\n END SUBROUTINE\n END INTERFACE \n\n INTERFACE \n SUBROUTINE stormer_verlet(pos, acc, dt, time, vel) \n REAL(8), INTENT(INOUT) :: pos, acc, dt, time, vel\n REAL(8) :: prev_pos, next_pos\n END SUBROUTINE \n END INTERFACE \n\n INTERFACE \n SUBROUTINE velocity_verlet(pos, acc, dt, time, vel) \n REAL(8), INTENT(INOUT) :: pos, acc, dt, time, vel\n REAL(8) :: prev_pos, next_pos \n END SUBROUTINE \n END INTERFACE \n\n pos = 5d0\n acc = -10d0\n dt = 0.01d0\n ! Verlet \n CALL verlet(pos, acc, dt, time)\n\n WRITE(*,*) '[#]'\n WRITE(*,*) 'Time for Verlet integration:'\n WRITE(*,*) time \n\n ! stormer Verlet \n pos = 5d0\n CALL stormer_verlet(pos, acc, dt, time, vel)\n\n WRITE(*,*) '[#]'\n WRITE(*,*) 'Time for Stormer Verlet integration:'\n WRITE(*,*) time\n WRITE(*,*) '[#]'\n WRITE(*,*) 'Velocity for Stormer Verlet integration:'\n WRITE(*,*) vel\n\n\n\n ! Velocity Verlet\n pos = 5d0\n CALL velocity_verlet(pos, acc, dt, time, vel)\n\n WRITE(*,*) '[#]'\n WRITE(*,*) 'Time for velocity Verlet integration:'\n WRITE(*,*) time\n WRITE(*,*) '[#]'\n WRITE(*,*) 'Velocity for velocity Verlet integration:'\n WRITE(*,*) vel\n\nEND PROGRAM verlet_integration\n\ndef verlet(pos, acc, dt)\n\n prev_pos = pos\n time = 0\n while pos > 0 do\n time += dt\n temp_pos = pos\n pos = pos*2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n end\n\n return time\n\nend\n\ndef stormer_verlet(pos, acc, dt)\n\n prev_pos = pos\n vel = 0\n time = 0\n while pos > 0 do\n time += dt\n temp_pos = pos\n pos = pos*2 - prev_pos + acc * dt * dt\n prev_pos = temp_pos\n\n vel += acc*dt\n end\n\n return time, vel\n\nend\n\ndef velocity_verlet(pos, acc, dt)\n\n vel = 0\n time = 0\n while pos > 0 do\n time += dt\n pos += vel*dt + 0.5*acc * dt * dt\n vel += acc*dt\n end\n\n return time, vel\n\nend\n\nputs \"[#]\\nTime for Verlet integration is:\"\np verlet(5.0, -10, 0.01)\n\ntime, vel = stormer_verlet(5.0, -10, 0.01)\nputs \"[#]\\nTime for Stormer Verlet integration is:\"\np time\nputs \"[#]\\nVelocity for Stormer Verlet integration is:\"\np vel\n\ntime, vel = velocity_verlet(5.0, -10, 0.01)\nputs \"[#]\\nTime for velocity Verlet integration is:\"\np time\nputs \"[#]\\nVelocity for velocity Verlet integration is:\"\np vel\n\npackage main\n\nimport \"fmt\"\n\nfunc verlet(pos, acc, dt float64) (time float64) {\n prevPos := pos\n time = 0\n\n for pos > 0 {\n time += dt\n nextPos := pos*2 - prevPos + acc*dt*dt\n prevPos, pos = pos, nextPos\n }\n\n return\n}\n\nfunc stormerVerlet(pos, acc, dt float64) (time, vel float64) {\n prevPos := pos\n time, vel = 0, 0\n\n for pos > 0 {\n time += dt\n vel += acc * dt\n nextPos := pos*2 - prevPos + acc*dt*dt\n prevPos, pos = pos, nextPos\n }\n\n return\n}\n\nfunc velocityVerlet(pos, acc, dt float64) (time, vel float64) {\n time, vel = 0, 0\n\n for pos > 0 {\n time += dt\n pos += vel*dt + .5*acc*dt*dt\n vel += acc * dt\n }\n\n return\n}\n\nfunc main() {\n time := verlet(5., -10., .01)\n fmt.Println(\"[#]\\nTime for Verlet integration is:\")\n fmt.Println(time)\n\n time, vel := stormerVerlet(5., -10., .01)\n fmt.Println(\"[#]\\nTime for Stormer Verlet integration is:\")\n fmt.Println(time)\n fmt.Println(\"[#]\\nVelocity for Stormer Verlet integration is:\")\n fmt.Println(vel)\n\n time, vel = velocityVerlet(5., -10., .01)\n fmt.Println(\"[#]\\nTime for velocity Verlet integration is:\")\n fmt.Println(time)\n fmt.Println(\"[#]\\nVelocity for velocity Verlet integration is:\")\n fmt.Println(vel)\n}\n\n.intel_syntax noprefix\n\n.section .rodata\n zero: .double 0.0\n two: .double 2.0\n half: .double 0.5\n verlet_fmt: .string \"[#]\\nTime for Verlet integration is:\\n%lf\\n\"\n stormer_fmt: .string \"[#]\\nTime for Stormer Verlet Integration is:\\n%lf\\n[#]\\nVelocity for Stormer Verlet Integration is:\\n%lf\\n\"\n velocity_fmt: .string \"[#]\\nTime for Velocity Verlet Integration is:\\n%lf\\n[#]\\nVelocity for Velocity Verlet Integration is:\\n%lf\\n\"\n pos: .double 5.0\n acc: .double -10.0\n dt: .double 0.01\n\n.section .text\n .global main\n .extern printf\n\n# xmm0 - pos\n# xmm1 - acc\n# xmm2 - dt\n# RET xmm0 - time\nverlet:\n pxor xmm7, xmm7 # Holds 0 for comparisons\n pxor xmm3, xmm3 # Holds time value\n comisd xmm0, xmm7 # Check if pos is greater then 0.0\n jbe verlet_return\n movsd xmm6, xmm1 # xmm6 = acc * dt * dt\n mulsd xmm6, xmm2\n mulsd xmm6, xmm2\n movsd xmm5, xmm0 # Holds previous position\nverlet_loop:\n addsd xmm3, xmm2 # Adding dt to time\n movsd xmm4, xmm0 # Hold old value of posistion\n addsd xmm0, xmm0 # Calculating new position\n subsd xmm0, xmm5\n addsd xmm0, xmm6\n movsd xmm5, xmm4\n comisd xmm0, xmm7 # Check if position is greater then 0.0\n ja verlet_loop\nverlet_return:\n movsd xmm0, xmm3 # Saving time value\n ret\n\n# xmm0 - pos\n# xmm1 - acc\n# xmm2 - dt\n# RET xmm0 - time\n# RET xmm1 - velocity\nstormer_verlet:\n pxor xmm7, xmm7 # Holds 0 for comparisons\n pxor xmm3, xmm3 # Holds time value\n comisd xmm0, xmm7 # Check if pos is greater then 0.0\n jbe stormer_verlet_return\n movsd xmm6, xmm1 # xmm6 = acc * dt * dt\n mulsd xmm6, xmm2\n mulsd xmm6, xmm2\n movsd xmm5, xmm0 # Holds previous position\nstormer_verlet_loop:\n addsd xmm3, xmm2 # Adding dt to time\n movsd xmm4, xmm0 # Hold old value of posistion\n addsd xmm0, xmm0 # Calculating new position\n subsd xmm0, xmm5\n addsd xmm0, xmm6\n movsd xmm5, xmm4\n comisd xmm0, xmm7 # Check if position is greater then 0.0\n ja stormer_verlet_loop\nstormer_verlet_return:\n movsd xmm0, xmm3 # Saving time and velocity\n mulsd xmm3, xmm1\n movsd xmm1, xmm3\n ret\n\n# xmm0 - pos\n# xmm1 - acc\n# xmm2 - dt\n# RET xmm0 - time\n# RET xmm1 - velocity\nvelocity_verlet:\n pxor xmm7, xmm7 # Holds 0 for comparisons\n pxor xmm3, xmm3 # Holds the velocity value\n pxor xmm4, xmm4 # Holds the time value\n comisd xmm0, xmm7 # Check if pos is greater then 0.0\n jbe velocity_verlet_return\n movsd xmm5, half # xmm5 = 0.5 * dt * dt * acc\n mulsd xmm5, xmm2\n mulsd xmm5, xmm2\n mulsd xmm5, xmm1\nvelocity_verlet_loop:\n movsd xmm6, xmm3 # Move velocity into register\n mulsd xmm6, xmm2 # Calculate new position\n addsd xmm6, xmm5\n addsd xmm0, xmm6\n addsd xmm4, xmm2 # Incrementing time\n movsd xmm3, xmm4 # Updating velocity\n mulsd xmm3, xmm1\n comisd xmm0, xmm7\n ja velocity_verlet_loop\nvelocity_verlet_return:\n movsd xmm0, xmm4 # Saving time and velocity\n movsd xmm1, xmm3\n ret\n\nmain:\n push rbp\n movsd xmm0, pos # Calling verlet\n movsd xmm1, acc\n movsd xmm2, dt\n call verlet\n mov rdi, OFFSET verlet_fmt # Print output\n mov rax, 1\n call printf\n movsd xmm0, pos # Calling stormer_verlet\n movsd xmm1, acc\n movsd xmm2, dt\n call stormer_verlet\n mov rdi, OFFSET stormer_fmt # Print output\n mov rax, 1\n call printf\n movsd xmm0, pos # Calling velocity_verlet\n movsd xmm1, acc\n movsd xmm2, dt\n call velocity_verlet\n mov rdi, OFFSET velocity_fmt # Print output\n mov rax, 1\n call printf\n pop rbp\n xor rax, rax # Set exit code to 0\n ret\n\ndata class VerletValues(val time: Double, val vel: Double)\n\nfun verlet(_pos: Double, acc: Double, dt: Double): Double {\n var pos = _pos // Since function parameter are val and can't be modified\n var prevPos = pos\n var time = 0.0\n\n while (pos > 0) {\n time += dt\n val nextPos = pos * 2 - prevPos + acc * dt * dt\n prevPos = pos\n pos = nextPos\n }\n return time\n}\n\nfun stormerVerlet(_pos: Double, acc: Double, dt: Double): VerletValues {\n var pos = _pos\n var prevPos = pos\n var time = 0.0\n var vel = 0.0\n while (pos > 0) {\n time += dt\n val nextPos = pos * 2 - prevPos + acc * dt * dt\n prevPos = pos\n pos = nextPos\n vel += acc * dt\n }\n return VerletValues(time, vel)\n}\n\nfun velocityVerlet(_pos: Double, acc: Double, dt: Double): VerletValues {\n var pos = _pos\n var time = 0.0\n var vel = 0.0\n while (pos > 0) {\n time += dt\n pos += vel * dt + 0.5 * acc * dt * dt\n vel += acc * dt\n }\n return VerletValues(time, vel)\n}\n\nfun main(args: Array) {\n val verletTime = verlet(5.0, -10.0, 0.01)\n println(\"[#]\\nTime for Verlet integration is:\")\n println(\"$verletTime\")\n\n val stormerVerlet = stormerVerlet(5.0, -10.0, 0.01)\n println(\"[#]\\nTime for Stormer Verlet integration is:\")\n println(\"${stormerVerlet.time}\")\n println(\"[#]\\nVelocity for Stormer Verlet integration is:\")\n println(\"${stormerVerlet.vel}\")\n\n val velocityVerlet = velocityVerlet(5.0, -10.0, 0.01)\n println(\"[#]\\nTime for Velocity Verlet integration is:\")\n println(\"${velocityVerlet.time}\")\n println(\"[#]\\nVelocity for Velocity Verlet integration is:\")\n println(\"${velocityVerlet.vel}\")\n}\n\nfunc verlet(pos_in, acc, dt: float): float =\n var\n pos: float = pos_in\n prevPos: float = pos\n time: float = 0.0\n tempPos: float\n\n while pos > 0.0:\n time += dt\n tempPos = pos\n pos = pos * 2 - prevPos + acc * dt * dt\n prevPos = tempPos\n\n time\n\nfunc stormerVerlet(pos_in, acc, dt: float): (float, float) =\n var\n pos: float = pos_in\n prevPos: float = pos\n time: float = 0.0\n vel: float = 0.0\n tempPos: float\n\n while pos > 0.0:\n time += dt\n tempPos = pos\n pos = pos * 2 - prevPos + acc * dt * dt\n prevPos = tempPos\n\n vel += acc * dt\n\n (time, vel)\n\nfunc velocityVerlet(pos_in, acc, dt: float): (float, float) =\n var\n pos: float = pos_in\n time: float = 0.0\n vel: float = 0.0\n\n while pos > 0.0:\n time += dt\n pos += vel * dt + 0.5 * acc * dt * dt\n vel += acc * dt\n\n (time, vel)\n\nwhen isMainModule:\n let timeV = verlet(5.0, -10.0, 0.01)\n echo \"[#]\\nTime for Verlet integration is:\"\n echo timeV\n\n let (timeSV, velSV) = stormerVerlet(5.0, -10.0, 0.01)\n echo \"[#]\\nTime for Stormer Verlet integration is:\"\n echo timeSV\n echo \"[#]\\nVelocity for Stormer Verlet integration is:\"\n echo velSV\n\n let (timeVV, velVV) = velocityVerlet(5.0, -10.0, 0.01)\n echo \"[#]\\nTime for velocity Verlet integration is:\"\n echo timeVV\n echo \"[#]\\nVelocity for velocity Verlet integration is:\"\n echo velVV\n\n;;;; Verlet integration implementation in Common Lisp\n\n(defun verlet (pos acc dt)\n \"Integrates Newton's equation for motion while pos > 0 using Verlet integration.\"\n (loop\n with prev-pos = pos\n for time = 0 then (incf time dt)\n while (> pos 0)\n ;; The starting speed is assumed to be zero.\n do (psetf\n pos (+ (* pos 2) (- prev-pos) (* acc dt dt))\n prev-pos pos)\n finally (return time)))\n\n(defun stormer-verlet (pos acc dt)\n \"Integrates Newton's equation for motion while pos > 0 using the Stormer-Verlet method.\"\n (loop\n with prev-pos = pos\n for time = 0 then (incf time dt)\n for vel = 0 then (incf vel (* acc dt))\n while (> pos 0)\n ;; Variables are changed simultaneously by 'psetf', so there's no need for a temporary variable.\n do (psetf\n pos (+ (* pos 2) (- prev-pos) (* acc dt dt))\n prev-pos pos)\n finally (return (list time vel))))\n\n(defun velocity-verlet (pos acc dt)\n \"Integrates Newton's equation for motion while pos > 0 using the velocity in calculations.\"\n (loop\n for time = 0 then (incf time dt)\n for vel = 0 then (incf vel (* acc dt))\n for p = pos then (incf p (+ (* vel dt) (* 0.5 acc dt dt)))\n while (> p 0)\n finally (return (list time vel))))\n\n(format T \"[#]~%Time for Verlet integration:~%\")\n(format T \"~d~%\" (verlet 5 -10 0.01))\n\n(defvar stormer-verlet-result (stormer-verlet 5 -10 0.01))\n(format T \"[#]~%Time for Stormer Verlet integration is:~%\")\n(format T \"~d~%\" (first stormer-verlet-result))\n(format T \"[#]~%Velocity for Stormer Verlet integration is:~%\")\n(format T \"~d~%\" (second stormer-verlet-result))\n\n(defvar velocity-verlet-result (velocity-verlet 5 -10 0.01))\n(format T \"[#]~%Time for velocity Verlet integration is:~%\")\n(format T \"~d~%\" (first velocity-verlet-result))\n(format T \"[#]~%Velocity for velocity Verlet integration is:~%\")\n(format T \"~d~%\" (second velocity-verlet-result))\n\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/split-operator_method/split-operator_method.html":{"url":"contents/split-operator_method/split-operator_method.html","title":"Split-Operator Method","keywords":"","body":"The Split-Operator Method\nThe Split-Operator Method (also called the Split-Step Method), was actually the primary method I used to solve the Schrödinger equation during my PhD.\nIt is one of the simplest and fastest methods for this purpose and is widely used throughout modern quantum research in the area, in particular when dealing with the Non-linear Schrödinger Equation (NLSE):\n\ni \\hbar \\frac{\\partial \\Psi(\\mathbf{r},t)}{\\partial t} = \\left[-\\frac{\\hbar^2}{2m}\\nabla^2 + V(\\mathbf{r}) + g|\\Psi(\\mathbf{r},t)|^2 \\right] \\Psi(\\mathbf{r},t),\n\nwhich follows from the notation provided in the quantum systems chapter: \\Psi(\\mathbf{r},t) is a quantum wave-function with spatial (\\mathbf{r}) and time (t) dependence, \\nabla^2 is a Laplacian, and V(\\mathbf{r}) is a potential of some sort (like \\omega x^2 or something).\nIn this case, we also add an interaction term g next to a nonlinear |\\Psi(\\mathbf{r},t)|^2 term.\nThis is the system I studied for most of my PhD (granted, we played a few tricks with parallelization and such, so it was slightly more complicated).\nAt its heart, the split-op method is nothing more than a pseudo-spectral differential equation solver... That is to say, it solves the Schrödinger equation with FFTs.\nIn fact, there is a large class of spectral and pseudo-spectral methods used to solve a number of different physical systems, and we'll definitely be covering those in the future.\nAs mentioned in the quantum systems section, we can represent a quantum wavefunction in momentum space, which is parameterized with the wavevector k.\nIn the Hamiltonian shown above, we can split our system into position space components, \\hat{H}_r = \\left[V(\\mathbf{r}) + g|\\Psi(\\mathbf{r},t)|^2 \\right] \\Psi(\\mathbf{r},t), and momentum space components, \\hat{H}_k = \\left[-\\frac{\\hbar^2}{2m}\\nabla^2 \\right]\\Psi(\\mathbf{r},t).\nI'll be honest, I didn't know what notation to use for \\hat H_r because p is used to describe momentum.\nI settled on r for real space, but that is somewhat notationally ambiguous.\nIn addition, k will indicate momentum space because it is a sum of all wavevectors, typically notated as k.\nBad notation aside, let's continue.\nIf we assume a somewhat general solution to our quantum system:\n\n\\Psi(\\mathbf{r},t + dt) = \\left[e^{-\\frac{i\\hat{H}dt}{\\hbar}}\\right]\\Psi(\\mathbf{r},t) = \\left[e^{-\\frac{i(\\hat{H}_r + \\hat{H}_k)dt}{\\hbar}}\\right]\\Psi(\\mathbf{r},t)\n\nand assume we are simulating our system by a series of small timesteps (dt), we can perform similar splitting by using the Baker-Campbell-Housdorff formula:\n\n\\Psi(\\mathbf{r},t+dt) = \\left[e^{-\\frac{i\\hat{H}_rdt}{\\hbar}}e^{-\\frac{i\\hat{H}_kdt}{\\hbar}}e^{-\\frac{[i\\hat{H}_r, i\\hat{H}_k]dt^2}{2}}\\right]\\Psi(\\mathbf{r},t)\n\nThis accrues a small amount of error (dt^2) related to the commutation of the real and momentum-space components of the Hamiltonian.\nThis is a relatively large error and that's not okay.\nIn order to change the dt^2 error to dt^3, we can split the system by performing a half-step in position space before doing a full-step in momentum space, through a process called Strang Splitting like so:\n\n\\Psi(\\mathbf{r},t+dt) = \\left[e^{-\\frac{i\\hat{H}_rdt}{2\\hbar}}e^{-\\frac{i\\hat{H}_kdt}{\\hbar}}e^{-\\frac{i\\hat{H}_rdt}{2\\hbar}} \\right]\\Psi(\\mathbf{r},t) + \\mathcal{O}(dt^3)\n\nWe can then address each part of this solution in chunks, first in position space, then in momentum space, then in position space again by using Fourier Transforms.\nWhich looks something like this:\n\n\\Psi(\\mathcal{r}, t+dt) = \\left[\\hat{U}_r\\left(\\frac{dt}{2}\\right)\\mathcal{F}^{-1}\\left[\\hat{U}_k(dt) \\mathcal{F} \\left[\\hat{U}_r\\left(\\frac{dt}{2}\\right) \\Psi(\\mathbf{r},t) \\right] \\right] \\right] + \\mathcal{O}(dt^3)\n\nwhere \\hat{U}_r = e^{-\\frac{i\\hat{H}_rdt}{\\hbar}}, \\hat{U}_k = e^{-\\frac{i\\hat{H}_kdt}{\\hbar}}, and \\mathcal{F} and \\mathcal{F}^{-1} indicate forward and inverse Fourier Transforms.\nHere's a flowchart of what we are looking for every timestep:\n\n \n\n\n\nFor the most part, that's it:\n\nMultiply the wavefunction in real space with the real-space operator.\nFlip to momentum space with a Fourier transform.\nMultiply the momentum-space wavefunction by the momentum-space operator.\nFlip to position space with an inverse Fourier transform.\nRepeat 1-4 until satisfied.\n\nIf we guess that our initial wavefunction is Gaussian-like and is slightly offset from the center or the trap, this should allow us to see our wavefunction \"sloshing\" back and forth in our trap, like so:\n\n \n\n\nAs a small concession, using this method enforces periodic boundary conditions, where the wavefunction will simply slide from one side of your simulation box to the other, but that's fine for most cases.\nIn fact, for many cases (such as large-scale turbulence models) it's ideal.\nThat said, there is more to the story.\nAs we mentioned in the quantum systems section, many simulations of quantum systems desire to find the ground state of our system.\nThe split-operator method can be used for that too!\nIf we run this simulation in imaginary time, by simply setting \\tau = it and stepping through \\tau instead of t, we will no longer see an \"real-world\" example of how the atoms should behave, but will instead see an exponential decay of higher-energy states.\nIf we run the simulation for long enough with a small enough timestep, all higher energy states will vanish.\nThis means that we can find the ground state of our system by running the simulation in imaginary time, which is an incredibly useful feature!\nIf we run the same simulation as above in imaginary time, we should see our wavefunction smoothly move to the center of our trap (the lowest energy position), like so:\n\n \n\n\n\nThe Algorithm\nLuckily, the code in this case is pretty straightforward.\nAs a note before starting, we will be using normalized units in this simulation where \\hbar = c = 1.\nThese units are often called natural units.\nMany of you (cough experimentalists cough) will probably think that these units are completely unphysical, and they are; however, they allow us to output fractions and whole numbers.\nFor example, if we are trying to find the energy of the ground state of atoms in a simple harmonic oscillator, we know it should be \\frac{1}{2}\\hbar \\omega, where \\omega is the coefficient in front of the x^2 term known as the frequency of the trap.\nIf we were to calculate the energy in real units, our simulation would output 5.272859 \\times 10^{-35}, which is hard to interpret.\nBy instead using natural units, we get precisely \\frac{1}{2} and we know that those are in units of \\hbar\\omega.\nThere is no doubt that it makes the simulation easier to understand (albeit a little misleading in the end).\nRegardless, we first need to set all the initial parameters, including the initial grids in real and momentum space:\nstruct Param\n xmax::Float64\n res::Int64\n dt::Float64\n timesteps::Int64\n dx::Float64\n x::Vector{Float64}\n dk::Float64\n k::Vector{Float64}\n im_time::Bool\n\n Param() = new(10.0, 512, 0.05, 1000, 2 * 10.0/512,\n Vector{Float64}(-10.0 + 10.0/512 : 20.0/512 : 10.0),\n pi / 10.0,\n Vector{Float64}(vcat(0:512/2 - 1, -512/2 : -1) * pi/10.0),\n false)\n Param(xmax::Float64, res::Int64, dt::Float64, timesteps::Int64,\n im_val::Bool) = new(\n xmax, res, dt, timesteps,\n 2*xmax/res, Vector{Float64}(-xmax+xmax/res:2*xmax/res:xmax),\n pi/xmax, Vector{Float64}(vcat(0:res/2-1, -res/2:-1)*pi/(xmax)),\n im_val\n )\nend\n\nstruct params {\n double xmax;\n unsigned int res;\n double dt;\n unsigned int timesteps;\n double dx;\n double *x;\n double dk;\n double *k;\n bool im_time;\n};\n\nvoid init_params(struct params *par, double xmax, unsigned int res, double dt,\n unsigned int timesteps, bool im) {\n\n par->xmax = xmax;\n par->res = res;\n par->dt = dt;\n par->timesteps = timesteps;\n par->dx = 2.0 * xmax / res;\n par->x = malloc(sizeof(double) * res);\n par->dk = M_PI / xmax;\n par->k = malloc(sizeof(double) * res);\n par->im_time = im;\n\n for (size_t i = 0; i x[i] = xmax / res - xmax + (double)i * (2.0 * xmax / res);\n if (i k[i] = (double)i * M_PI / xmax;\n } else {\n par->k[i] = ((double)i - res) * M_PI / xmax;\n }\n }\n}\n\nusing complex = std::complex;\nusing vector_real = std::vector;\nusing vector_complex = std::vector;\n\nstruct Params {\n Params(double _xmax, unsigned int _res, double _dt, unsigned int _timesteps, bool im) {\n xmax = _xmax;\n res = _res;\n dt = _dt;\n timesteps = _timesteps;\n dx = 2.0 * xmax / res;\n x.reserve(res);\n dk = M_PI / xmax;\n k.reserve(res);\n im_time = im;\n\n for (size_t i = 0; i (i) * (2.0 * xmax / res));\n if (i (i) * M_PI / xmax);\n } else {\n k.push_back((static_cast(i) - res) * M_PI / xmax);\n }\n }\n }\n\n double xmax;\n unsigned int res;\n double dt;\n unsigned int timesteps;\n double dx;\n vector_real x;\n double dk;\n vector_real k;\n bool im_time;\n};\n\nclass Param:\n \"\"\"Container for holding all simulation parameters.\"\"\"\n def __init__(self,\n xmax: float,\n res: int,\n dt: float,\n timesteps: int,\n im_time: bool) -> None:\n\n self.xmax = xmax\n self.res = res\n self.dt = dt\n self.timesteps = timesteps\n self.im_time = im_time\n\n self.dx = 2 * xmax / res\n self.x = np.arange(-xmax + xmax / res, xmax, self.dx)\n self.dk = pi / xmax\n self.k = np.concatenate((np.arange(0, res / 2),\n np.arange(-res / 2, 0))) * self.dk\n\ndata Parameters = Parameters\n { xmax :: Double\n , res :: Int\n , dt :: Double\n , timesteps :: Int\n , dx :: Double\n , x :: Vector\n , dk :: Double\n , ks :: Vector\n , imTime :: Bool\n }\n\ndefaultParameters :: Parameters\ndefaultParameters = makeParameters 10 512 0.01 1000 True\n\nmakeParameters :: Double -> Int -> Double -> Int -> Bool -> Parameters\nmakeParameters xmax res dt timesteps imTime =\n let fi = fromIntegral\n rng = (0, res - 1)\n ks = [0 .. div res 2 - 1] ++ [-div res 2 .. -1]\n in Parameters\n xmax\n res\n dt\n timesteps\n (2 * xmax / fi res)\n (listArray rng $\n map (\\n -> xmax * (-1 + 2 * fi n / fi res) :+ 0) [1 .. res])\n (pi / xmax)\n (listArray rng $ map ((:+ 0) . (pi / xmax *) . fi) ks)\n imTime\n\n xmax: f64,\n res: usize,\n dt: f64,\n timesteps: usize,\n dx: f64,\n x: Vec,\n dk: f64,\n k: Vec,\n im_time: bool,\n}\n\nimpl Parameters {\n pub fn new(xmax: f64, res: usize, dt: f64, timesteps: usize, im_time: bool) -> Parameters {\n let dx = 2.0_f64 * xmax / (res as f64);\n let mut x: Vec = Vec::with_capacity(res);\n let dk = PI / xmax;\n let mut k: Vec = Vec::with_capacity(res);\n for i in 0..res {\n x.push(xmax / (res as f64) - xmax + (i as f64) * dx);\n match i {\n i if (i k.push((i as f64) * PI / xmax),\n _ => k.push(((i as f64) - (res as f64)) * PI / xmax),\n }\n }\n Parameters {\n xmax,\n res,\n dt,\n timesteps,\n im_time,\n dx,\n x,\n dk,\n k,\n }\n }\n}\n\n\n\nAs a note, when we generate our grid in momentum space k, we need to split the grid into two lines, one that is going from 0 to -kmax and is then discontinuous and goes from kmax to 0.\nThis is simply because the FFT will naturally assume that the 0 in our grid is at the left side of the simulation, so we shift k-space to match this expectation.\nAlso, for this code we will be using notation to what we used above: opr.R will be the real space operators and opr.K will be the momentum space operators.\nThere is another Boolean value here called im_time, which is for imaginary time evolution.\nAfterwards, we turn them into operators:\nmutable struct Operators\n V::Vector{Complex{Float64}}\n R::Vector{Complex{Float64}}\n K::Vector{Complex{Float64}}\n wfc::Vector{Complex{Float64}}\n\n Operators(res) = new(zeros(res),\n zeros(res),\n zeros(res),\n zeros(res))\nend\n\n# Function to initialize the wfc and potential\nfunction init(par::Param, voffset::Float64, wfcoffset::Float64)\n opr = Operators(length(par.x))\n opr.V = 0.5 * (par.x .- voffset).^2\n opr.wfc = exp.(-(par.x .- wfcoffset).^2/2)\n if (par.im_time)\n opr.K = exp.(-0.5*par.k.^2*par.dt)\n opr.R = exp.(-0.5*opr.V*par.dt)\n else\n opr.K = exp.(-im*0.5*par.k.^2*par.dt)\n opr.R = exp.(-im*0.5*opr.V*par.dt)\n end\n\n return opr\nend\n\nstruct operators {\n size_t size;\n double complex *v;\n double complex *pe;\n double complex *ke;\n double complex *wfc;\n};\n\nvoid init_operators(struct operators *opr, struct params par, double voffset,\n double wfcoffset) {\n\n opr->size = par.res;\n opr->v = malloc(sizeof(double complex) * par.res);\n opr->pe = malloc(sizeof(double complex) * par.res);\n opr->ke = malloc(sizeof(double complex) * par.res);\n opr->wfc = malloc(sizeof(double complex) * par.res);\n\n for (size_t i = 0; i v[i] = 0.5 * cpow(par.x[i] - voffset, 2);\n opr->wfc[i] = cexp(-cpow(par.x[i] - wfcoffset, 2) / 2.0);\n\n if (par.im_time) {\n opr->ke[i] = cexp(-0.5 * par.dt * cpow(par.k[i], 2));\n opr->pe[i] = cexp(-0.5 * par.dt * opr->v[i]);\n } else {\n opr->ke[i] = cexp(-0.5 * par.dt * cpow(par.k[i], 2) * I);\n opr->pe[i] = cexp(-0.5 * par.dt * opr->v[i] * I);\n }\n }\n}\n\nstruct Operators {\npublic:\n Operators(Params &par, double voffset,\n double wfcoffset) {\n size = par.res;\n v.reserve(size);\n pe.reserve(size);\n ke.reserve(size);\n wfc.reserve(size);\n\n for (size_t i = 0; i \nclass Operators:\n \"\"\"Container for holding operators and wavefunction coefficients.\"\"\"\n def __init__(self, res: int) -> None:\n\n self.V = np.empty(res, dtype=complex)\n self.R = np.empty(res, dtype=complex)\n self.K = np.empty(res, dtype=complex)\n self.wfc = np.empty(res, dtype=complex)\n\n\ndef init(par: Param, voffset: float, wfcoffset: float) -> Operators:\n \"\"\"Initialize the wavefunction coefficients and the potential.\"\"\"\n opr = Operators(len(par.x))\n opr.V = 0.5 * (par.x - voffset) ** 2\n opr.wfc = np.exp(-((par.x - wfcoffset) ** 2) / 2, dtype=complex)\n if par.im_time:\n opr.K = np.exp(-0.5 * (par.k ** 2) * par.dt)\n opr.R = np.exp(-0.5 * opr.V * par.dt)\n else:\n opr.K = np.exp(-0.5 * (par.k ** 2) * par.dt * 1j)\n opr.R = np.exp(-0.5 * opr.V * par.dt * 1j)\n return opr\n\ndata Operators = Operators\n { v :: Vector\n , rStep :: Vector\n , kStep :: Vector\n , wfc :: Vector\n }\n\nmakeOperators :: Parameters -> Complex Double -> Complex Double -> Operators\nmakeOperators param v0 wfc0 =\n let rng = (0, res param - 1)\n time\n | imTime param = dt param :+ 0\n | otherwise = 0 :+ dt param\n v = liftArray (\\x -> 0.5 * (x - v0) ^ 2) (x param)\n rStep = liftArray (\\x -> exp (-0.5 * time * x)) v\n kStep = liftArray (\\k -> exp (-0.5 * time * k ^ 2)) (ks param)\n wfc = liftArray (\\x -> exp (-(x - wfc0) ^ 2 / 2)) (x param)\n in Operators v rStep kStep (normalize (dx param) wfc)\n\n v: Vec>,\n pe: Vec>,\n ke: Vec>,\n wfc: Vec>,\n}\n\nimpl Operators {\n pub fn new(par: &Parameters, v_offset: f64, wfc_offset: f64) -> Operators {\n let mut v: Vec> = Vec::with_capacity(par.res);\n let mut pe: Vec> = Vec::with_capacity(par.res);\n let mut ke: Vec> = Vec::with_capacity(par.res);\n let mut wfc: Vec> = Vec::with_capacity(par.res);\n\n for i in 0..par.res {\n v.push(Complex::new(\n 0.5_f64 * (par.x[i] - v_offset).powi(2),\n 0.0_f64,\n ));\n wfc.push(Complex::new(\n (-((par.x[i] - wfc_offset).powi(2)) / 2.0_f64).exp(),\n 0.0_f64,\n ));\n if par.im_time {\n ke.push(Complex::new(\n (-0.5_f64 * par.dt * par.k[i].powi(2)).exp(),\n 0.0_f64,\n ));\n pe.push(Complex::new((-0.5_f64 * par.dt * v[i].re).exp(), 0.0_f64));\n } else {\n ke.push(Complex::new(\n 0.0_f64,\n (-0.5_f64 * par.dt * par.k[i].powi(2)).exp(),\n ));\n pe.push(Complex::new(0.0_f64, (-0.5_f64 * par.dt * v[i].re).exp()));\n }\n }\n Operators { v, pe, ke, wfc }\n }\n}\n\n\n\nHere, we use a standard harmonic potential for the atoms to sit in and a Gaussian distribution for an initial guess for the probability distribution.\nIf we give either the trap or the atoms a slight offset (so the Gaussian distribution of atoms does not quite rest at the bottom of the x^2 potential, we can see the atoms moving back and forth in the potential as we move the simulation forward in time.\nThis means that we can easily see the dynamics of our quantum system!\nIf we run the simulation in imaginary time, we will see the Gaussian distribution of atoms move towards the center of the potential, which is the location with the lowest energy.\nBoth of these have been shown in the figures above.\nThe final step is to do the iteration, itself.\nfunction split_op!(par::Param, opr::Operators)\n\n for i = 1:par.timesteps\n # Half-step in real space\n opr.wfc = opr.wfc .* opr.R\n\n # fft to momentum space\n opr.wfc = fft(opr.wfc)\n\n # Full step in momentum space\n opr.wfc = opr.wfc .* opr.K\n\n # ifft back\n opr.wfc = ifft(opr.wfc)\n\n # final half-step in real space\n opr.wfc = opr.wfc .* opr.R\n\n # density for plotting and potential\n density = abs2.(opr.wfc)\n\n # renormalizing for imaginary time\n if (par.im_time)\n renorm_factor = sum(density) * par.dx\n\n for j = 1:length(opr.wfc)\n opr.wfc[j] /= sqrt(renorm_factor)\n end\n end\n\n # Outputting data to file. Plotting can also be done in a similar way\n # This is set to output exactly 100 files, no matter how many timesteps\n if ((i-1) % div(par.timesteps, 100) == 0)\n outfile = open(\"output\" * string(lpad(string(i-1), 5, string(0)))\n * \".dat\",\"w\")\n\n # Outputting for gnuplot. Any plotter will do.\n for j = 1:length(density)\n write(outfile, string(par.x[j]) * \"\\t\"\n * string(density[j]) * \"\\t\"\n * string(real(opr.V[j])) * \"\\n\")\n end\n\n close(outfile)\n println(\"Outputting step: \", i)\n end\n end\nend\n\nvoid split_op(struct params par, struct operators opr) {\n double density[opr.size];\n\n for (size_t i = 0; i \nvoid split_op(Params &par, Operators &opr) {\n auto density = std::vector(opr.size, 0);\n\n for (size_t i = 0; i \ndef split_op(par: Param, opr: Operators) -> None:\n\n for i in range(par.timesteps):\n\n # Half-step in real space\n opr.wfc *= opr.R\n\n # FFT to momentum space\n opr.wfc = np.fft.fft(opr.wfc)\n\n # Full step in momentum space\n opr.wfc *= opr.K\n\n # iFFT back\n opr.wfc = np.fft.ifft(opr.wfc)\n\n # Final half-step in real space\n opr.wfc *= opr.R\n\n # Density for plotting and potential\n density = np.abs(opr.wfc) ** 2\n\n # Renormalizing for imaginary time\n if par.im_time:\n renorm_factor = sum(density) * par.dx\n opr.wfc /= sqrt(renorm_factor)\n\n # Outputting data to file. Plotting can also be done in a\n # similar way. This is set to output exactly 100 files, no\n # matter how many timesteps were specified.\n if i % (par.timesteps // 100) == 0:\n filename = \"output{}.dat\".format(str(i).rjust(5, str(0)))\n with open(filename, \"w\") as outfile:\n # Outputting for gnuplot. Any plotter will do.\n for j in range(len(density)):\n template = \"{}\\t{}\\t{}\\n\".format\n line = template(par.x[j], density[j].real, opr.V[j].real)\n outfile.write(line)\n print(\"Outputting step: \", i + 1)\n\nevolve :: Parameters -> Operators -> [Operators]\nevolve param op@(Operators _ rStep kStep _) = iterate splitop op\n where\n splitop op = op {wfc = wfc' op}\n wfc' = norm . (rStep .*) . idft . (kStep .*) . dft . (rStep .*) . wfc\n norm = if imTime param then normalize (dx param) else id\n\n let mut density: Vec;\n\n for i in 0..par.timesteps {\n for j in 0..par.res {\n opr.wfc[j] *= opr.pe[j];\n }\n\n fft(&mut opr.wfc, false);\n\n for j in 0..par.res {\n opr.wfc[j] *= opr.ke[j];\n }\n\n fft(&mut opr.wfc, true);\n\n for j in 0..par.res {\n opr.wfc[j] *= opr.pe[j];\n }\n\n density = opr.wfc.iter().map(|x| x.norm().powi(2)).collect();\n\n if par.im_time {\n let sum = density.iter().sum::() * par.dx;\n\n for j in 0..par.res {\n opr.wfc[j] /= sum.sqrt();\n }\n }\n\n // Writing data into a file in the format of:\n // index, density, real potential.\n let path_name = format!(\"output{}.dat\", i);\n let path = Path::new(&path_name);\n let display = path.display();\n\n let mut file = match File::create(&path) {\n Err(why) => panic!(\"Couldn't create {}: {}\", display, why),\n Ok(good) => good,\n };\n\n for j in 0..par.res {\n if let Err(why) = writeln!(file, \"{}\\t{}\\t{}\", j, density[j], opr.v[j].re) {\n panic!(\"Couldn't write to {}: {}\", display, why)\n }\n if let Err(why) = file.flush() {\n panic!(\"Couldn't flush {}: {}\", display, why)\n }\n }\n }\n}\n\n\n\nAnd that's it.\nThere is something a bit odd about the simulation in imaginary time, though.\nBasically, in imaginary time, we see an exponential decay of all the higher energy states, which means we are technically losing a large amount of our wavefunction density every timestep!\nTo solve this issue, we renormalize by enforcing that \\int_{-\\infty}^{+\\infty}\\Psi^\\ast\\Psi dx = 1.\nAs you can see from the code, this involves summing the density, multiplying that sum by dx, and then dividing each element in the wavefunction by the sqrt() of that value.\nThe Split-Operator method is one of the most commonly used quantum simulation algorithms because of how straightforward it is to code and how quickly you can start really digging into the physics of the simulation results!\nVideo Explanation\nHere is a video describing the split-operator method:\n\n\n\n\nExample Code\nThis example code is a simulation of a Gaussian distribution of atoms slightly offset in a harmonic trap in imaginary time.\nSo long as the code is written appropriately, this means that the atoms should move towards the center of the trap and the energy should decay to \\frac{1}{2}\\hbar\\omega, which will be simply \\frac{1}{2} in this simulation.\nChecking to make sure your code can output the correct energy for a harmonic trap is a good test to make sure it is all working under-the-hood before simulating systems with more complicated Hamiltonians.\n#------------split_op.jl-------------------------------------------------------#\n#\n# Plotting: to plot individual timesteps, use gnuplot like so:\n# p \"output00000.dat\" u 1:2 w l\n# rep \"output00000.dat\" u 1:3 w l\n#\n#------------------------------------------------------------------------------#\n\nusing FFTW\n\nstruct Param\n xmax::Float64\n res::Int64\n dt::Float64\n timesteps::Int64\n dx::Float64\n x::Vector{Float64}\n dk::Float64\n k::Vector{Float64}\n im_time::Bool\n\n Param() = new(10.0, 512, 0.05, 1000, 2 * 10.0/512,\n Vector{Float64}(-10.0 + 10.0/512 : 20.0/512 : 10.0),\n pi / 10.0,\n Vector{Float64}(vcat(0:512/2 - 1, -512/2 : -1) * pi/10.0),\n false)\n Param(xmax::Float64, res::Int64, dt::Float64, timesteps::Int64,\n im_val::Bool) = new(\n xmax, res, dt, timesteps,\n 2*xmax/res, Vector{Float64}(-xmax+xmax/res:2*xmax/res:xmax),\n pi/xmax, Vector{Float64}(vcat(0:res/2-1, -res/2:-1)*pi/(xmax)),\n im_val\n )\nend\n\nmutable struct Operators\n V::Vector{Complex{Float64}}\n R::Vector{Complex{Float64}}\n K::Vector{Complex{Float64}}\n wfc::Vector{Complex{Float64}}\n\n Operators(res) = new(zeros(res),\n zeros(res),\n zeros(res),\n zeros(res))\nend\n\n# Function to initialize the wfc and potential\nfunction init(par::Param, voffset::Float64, wfcoffset::Float64)\n opr = Operators(length(par.x))\n opr.V = 0.5 * (par.x .- voffset).^2\n opr.wfc = exp.(-(par.x .- wfcoffset).^2/2)\n if (par.im_time)\n opr.K = exp.(-0.5*par.k.^2*par.dt)\n opr.R = exp.(-0.5*opr.V*par.dt)\n else\n opr.K = exp.(-im*0.5*par.k.^2*par.dt)\n opr.R = exp.(-im*0.5*opr.V*par.dt)\n end\n\n return opr\nend\n\n# Function for the split-operator loop\nfunction split_op!(par::Param, opr::Operators)\n\n for i = 1:par.timesteps\n # Half-step in real space\n opr.wfc = opr.wfc .* opr.R\n\n # fft to momentum space\n opr.wfc = fft(opr.wfc)\n\n # Full step in momentum space\n opr.wfc = opr.wfc .* opr.K\n\n # ifft back\n opr.wfc = ifft(opr.wfc)\n\n # final half-step in real space\n opr.wfc = opr.wfc .* opr.R\n\n # density for plotting and potential\n density = abs2.(opr.wfc)\n\n # renormalizing for imaginary time\n if (par.im_time)\n renorm_factor = sum(density) * par.dx\n\n for j = 1:length(opr.wfc)\n opr.wfc[j] /= sqrt(renorm_factor)\n end\n end\n\n # Outputting data to file. Plotting can also be done in a similar way\n # This is set to output exactly 100 files, no matter how many timesteps\n if ((i-1) % div(par.timesteps, 100) == 0)\n outfile = open(\"output\" * string(lpad(string(i-1), 5, string(0)))\n * \".dat\",\"w\")\n\n # Outputting for gnuplot. Any plotter will do.\n for j = 1:length(density)\n write(outfile, string(par.x[j]) * \"\\t\"\n * string(density[j]) * \"\\t\"\n * string(real(opr.V[j])) * \"\\n\")\n end\n\n close(outfile)\n println(\"Outputting step: \", i)\n end\n end\nend\n\n# We are calculating the energy to check \nfunction calculate_energy(par, opr)\n # Creating real, momentum, and conjugate wavefunctions\n wfc_r = opr.wfc\n wfc_k = fft(wfc_r)\n wfc_c = conj(wfc_r)\n\n # Finding the momentum and real-space energy terms\n energy_k = 0.5*wfc_c.*ifft((par.k.^2) .* wfc_k)\n energy_r = wfc_c.*opr.V .* wfc_r\n\n # Integrating over all space\n energy_final = 0\n for i = 1:length(energy_k)\n energy_final += real(energy_k[i] + energy_r[i])\n end\n\n return energy_final*par.dx\nend\n\n# main function\nfunction main()\n par = Param(5.0, 256, 0.05, 100, true)\n\n # Starting wavefunction slightly offset so we can see it change\n opr = init(par, 0.0, -1.00)\n split_op!(par, opr)\n\n energy = calculate_energy(par, opr)\n println(\"Energy is: \", energy)\nend\n\nmain()\n\n#include \n#include \n#include \n#include \n#include \n#include \n\n// Using fftw3 library.\n#include \n\nstruct params {\n double xmax;\n unsigned int res;\n double dt;\n unsigned int timesteps;\n double dx;\n double *x;\n double dk;\n double *k;\n bool im_time;\n};\n\nstruct operators {\n size_t size;\n double complex *v;\n double complex *pe;\n double complex *ke;\n double complex *wfc;\n};\n\nvoid fft(double complex *x, size_t n, bool inverse) {\n double complex y[n];\n memset(y, 0, sizeof(y));\n fftw_plan p;\n\n if (inverse) {\n p = fftw_plan_dft_1d((int)n, (fftw_complex*)x, (fftw_complex*)y,\n FFTW_BACKWARD, FFTW_ESTIMATE);\n } else {\n p = fftw_plan_dft_1d((int)n, (fftw_complex*)x, (fftw_complex*)y,\n FFTW_FORWARD, FFTW_ESTIMATE);\n }\n\n fftw_execute(p);\n fftw_destroy_plan(p);\n\n for (size_t i = 0; i xmax = xmax;\n par->res = res;\n par->dt = dt;\n par->timesteps = timesteps;\n par->dx = 2.0 * xmax / res;\n par->x = malloc(sizeof(double) * res);\n par->dk = M_PI / xmax;\n par->k = malloc(sizeof(double) * res);\n par->im_time = im;\n\n for (size_t i = 0; i x[i] = xmax / res - xmax + (double)i * (2.0 * xmax / res);\n if (i k[i] = (double)i * M_PI / xmax;\n } else {\n par->k[i] = ((double)i - res) * M_PI / xmax;\n }\n }\n}\n\nvoid init_operators(struct operators *opr, struct params par, double voffset,\n double wfcoffset) {\n\n opr->size = par.res;\n opr->v = malloc(sizeof(double complex) * par.res);\n opr->pe = malloc(sizeof(double complex) * par.res);\n opr->ke = malloc(sizeof(double complex) * par.res);\n opr->wfc = malloc(sizeof(double complex) * par.res);\n\n for (size_t i = 0; i v[i] = 0.5 * cpow(par.x[i] - voffset, 2);\n opr->wfc[i] = cexp(-cpow(par.x[i] - wfcoffset, 2) / 2.0);\n\n if (par.im_time) {\n opr->ke[i] = cexp(-0.5 * par.dt * cpow(par.k[i], 2));\n opr->pe[i] = cexp(-0.5 * par.dt * opr->v[i]);\n } else {\n opr->ke[i] = cexp(-0.5 * par.dt * cpow(par.k[i], 2) * I);\n opr->pe[i] = cexp(-0.5 * par.dt * opr->v[i] * I);\n }\n }\n}\n\nvoid split_op(struct params par, struct operators opr) {\n double density[opr.size];\n\n for (size_t i = 0; i \n#include \n#include \n#include \n#include \n#include \n\n// Using fftw3 library.\n#include \n\n#ifndef M_PI\n#define M_PI 3.14159265358979323846\n#endif\n\nusing complex = std::complex;\nusing vector_real = std::vector;\nusing vector_complex = std::vector;\n\nstruct Params {\n Params(double _xmax, unsigned int _res, double _dt, unsigned int _timesteps, bool im) {\n xmax = _xmax;\n res = _res;\n dt = _dt;\n timesteps = _timesteps;\n dx = 2.0 * xmax / res;\n x.reserve(res);\n dk = M_PI / xmax;\n k.reserve(res);\n im_time = im;\n\n for (size_t i = 0; i (i) * (2.0 * xmax / res));\n if (i (i) * M_PI / xmax);\n } else {\n k.push_back((static_cast(i) - res) * M_PI / xmax);\n }\n }\n }\n\n double xmax;\n unsigned int res;\n double dt;\n unsigned int timesteps;\n double dx;\n vector_real x;\n double dk;\n vector_real k;\n bool im_time;\n};\n\nstruct Operators {\npublic:\n Operators(Params &par, double voffset,\n double wfcoffset) {\n size = par.res;\n v.reserve(size);\n pe.reserve(size);\n ke.reserve(size);\n wfc.reserve(size);\n\n for (size_t i = 0; i > y(x.size(), std::complex(0.0, 0.0));\n fftw_plan p;\n\n fftw_complex *in = reinterpret_cast(x.data());\n fftw_complex *out = reinterpret_cast(y.data());\n p = fftw_plan_dft_1d(static_cast(x.size()), in, out,\n (inverse ? FFTW_BACKWARD : FFTW_FORWARD), FFTW_ESTIMATE);\n\n fftw_execute(p);\n fftw_destroy_plan(p);\n\n for (size_t i = 0; i (x.size()));\n }\n}\n\nvoid split_op(Params &par, Operators &opr) {\n auto density = std::vector(opr.size, 0);\n\n for (size_t i = 0; i \nfrom math import pi\nfrom math import sqrt\n\nimport numpy as np\n\n\nclass Param:\n \"\"\"Container for holding all simulation parameters.\"\"\"\n def __init__(self,\n xmax: float,\n res: int,\n dt: float,\n timesteps: int,\n im_time: bool) -> None:\n\n self.xmax = xmax\n self.res = res\n self.dt = dt\n self.timesteps = timesteps\n self.im_time = im_time\n\n self.dx = 2 * xmax / res\n self.x = np.arange(-xmax + xmax / res, xmax, self.dx)\n self.dk = pi / xmax\n self.k = np.concatenate((np.arange(0, res / 2),\n np.arange(-res / 2, 0))) * self.dk\n\n\nclass Operators:\n \"\"\"Container for holding operators and wavefunction coefficients.\"\"\"\n def __init__(self, res: int) -> None:\n\n self.V = np.empty(res, dtype=complex)\n self.R = np.empty(res, dtype=complex)\n self.K = np.empty(res, dtype=complex)\n self.wfc = np.empty(res, dtype=complex)\n\n\ndef init(par: Param, voffset: float, wfcoffset: float) -> Operators:\n \"\"\"Initialize the wavefunction coefficients and the potential.\"\"\"\n opr = Operators(len(par.x))\n opr.V = 0.5 * (par.x - voffset) ** 2\n opr.wfc = np.exp(-((par.x - wfcoffset) ** 2) / 2, dtype=complex)\n if par.im_time:\n opr.K = np.exp(-0.5 * (par.k ** 2) * par.dt)\n opr.R = np.exp(-0.5 * opr.V * par.dt)\n else:\n opr.K = np.exp(-0.5 * (par.k ** 2) * par.dt * 1j)\n opr.R = np.exp(-0.5 * opr.V * par.dt * 1j)\n return opr\n\n\ndef split_op(par: Param, opr: Operators) -> None:\n\n for i in range(par.timesteps):\n\n # Half-step in real space\n opr.wfc *= opr.R\n\n # FFT to momentum space\n opr.wfc = np.fft.fft(opr.wfc)\n\n # Full step in momentum space\n opr.wfc *= opr.K\n\n # iFFT back\n opr.wfc = np.fft.ifft(opr.wfc)\n\n # Final half-step in real space\n opr.wfc *= opr.R\n\n # Density for plotting and potential\n density = np.abs(opr.wfc) ** 2\n\n # Renormalizing for imaginary time\n if par.im_time:\n renorm_factor = sum(density) * par.dx\n opr.wfc /= sqrt(renorm_factor)\n\n # Outputting data to file. Plotting can also be done in a\n # similar way. This is set to output exactly 100 files, no\n # matter how many timesteps were specified.\n if i % (par.timesteps // 100) == 0:\n filename = \"output{}.dat\".format(str(i).rjust(5, str(0)))\n with open(filename, \"w\") as outfile:\n # Outputting for gnuplot. Any plotter will do.\n for j in range(len(density)):\n template = \"{}\\t{}\\t{}\\n\".format\n line = template(par.x[j], density[j].real, opr.V[j].real)\n outfile.write(line)\n print(\"Outputting step: \", i + 1)\n\n\ndef calculate_energy(par: Param, opr: Operators) -> float:\n \"\"\"Calculate the energy .\"\"\"\n # Creating real, momentum, and conjugate wavefunctions.\n wfc_r = opr.wfc\n wfc_k = np.fft.fft(wfc_r)\n wfc_c = np.conj(wfc_r)\n\n # Finding the momentum and real-space energy terms\n energy_k = 0.5 * wfc_c * np.fft.ifft((par.k ** 2) * wfc_k)\n energy_r = wfc_c * opr.V * wfc_r\n\n # Integrating over all space\n energy_final = sum(energy_k + energy_r).real\n\n return energy_final * par.dx\n\n\ndef main() -> None:\n par = Param(5.0, 256, 0.05, 100, True)\n\n # Starting wavefunction slightly offset so we can see it change\n opr = init(par, 0.0, -1.00)\n split_op(par, opr)\n\n energy = calculate_energy(par, opr)\n print(\"Energy is: \", energy)\n\n\nif __name__ == \"__main__\":\n main()\n\nimport Data.Array.CArray\nimport Data.Complex\nimport Data.List (intercalate, transpose)\nimport Math.FFT (dft, idft)\n\ntype Vector = CArray Int (Complex Double)\n\n(.*), (.+) :: Vector -> Vector -> Vector\na .* b = liftArray2 (*) a b\na .+ b = liftArray2 (+) a b\n\nnormalize :: Double -> Vector -> Vector\nnormalize dx v =\n let factor = 1 / sqrt dx / norm2 v :+ 0\n in liftArray (factor *) v\n\ndata Parameters = Parameters\n { xmax :: Double\n , res :: Int\n , dt :: Double\n , timesteps :: Int\n , dx :: Double\n , x :: Vector\n , dk :: Double\n , ks :: Vector\n , imTime :: Bool\n }\n\ndefaultParameters :: Parameters\ndefaultParameters = makeParameters 10 512 0.01 1000 True\n\nmakeParameters :: Double -> Int -> Double -> Int -> Bool -> Parameters\nmakeParameters xmax res dt timesteps imTime =\n let fi = fromIntegral\n rng = (0, res - 1)\n ks = [0 .. div res 2 - 1] ++ [-div res 2 .. -1]\n in Parameters\n xmax\n res\n dt\n timesteps\n (2 * xmax / fi res)\n (listArray rng $\n map (\\n -> xmax * (-1 + 2 * fi n / fi res) :+ 0) [1 .. res])\n (pi / xmax)\n (listArray rng $ map ((:+ 0) . (pi / xmax *) . fi) ks)\n imTime\n\ndata Operators = Operators\n { v :: Vector\n , rStep :: Vector\n , kStep :: Vector\n , wfc :: Vector\n }\n\nmakeOperators :: Parameters -> Complex Double -> Complex Double -> Operators\nmakeOperators param v0 wfc0 =\n let rng = (0, res param - 1)\n time\n | imTime param = dt param :+ 0\n | otherwise = 0 :+ dt param\n v = liftArray (\\x -> 0.5 * (x - v0) ^ 2) (x param)\n rStep = liftArray (\\x -> exp (-0.5 * time * x)) v\n kStep = liftArray (\\k -> exp (-0.5 * time * k ^ 2)) (ks param)\n wfc = liftArray (\\x -> exp (-(x - wfc0) ^ 2 / 2)) (x param)\n in Operators v rStep kStep (normalize (dx param) wfc)\n\nevolve :: Parameters -> Operators -> [Operators]\nevolve param op@(Operators _ rStep kStep _) = iterate splitop op\n where\n splitop op = op {wfc = wfc' op}\n wfc' = norm . (rStep .*) . idft . (kStep .*) . dft . (rStep .*) . wfc\n norm = if imTime param then normalize (dx param) else id\n\ncalculateEnergy :: Parameters -> Operators -> Double\ncalculateEnergy param ops = (* dx param) . sum . map realPart $ elems totalE\n where\n totalE = potentialE .+ kineticE\n potentialE = wfcConj .* v ops .* wfc ops\n kineticOp = liftArray ((/ 2) . (^ 2)) (ks param)\n kineticE = wfcConj .* idft (kineticOp .* dft (wfc ops))\n wfcConj = liftArray conjugate $ wfc ops\n\n-- Use gnuplot to make an animated GIF using ../gnuplot/plot_output.plt\n-- $ gnuplot -e \"folder='../haskell'\" plot_output.plt\nprintEvolution :: Parameters -> [Operators] -> IO ()\nprintEvolution param =\n mapM_ (export . (format )) . zip [0 ..] . take 100 . skip\n where\n skip (x:xs) = x : skip (drop (div (timesteps param) 100 - 1) xs)\n format (Operators v _ _ wfc) =\n let density = liftArray ((^ 2) . abs) wfc\n values = map (map (show . realPart) . elems) [x param, density, v]\n in intercalate \"\\n\" $ map (intercalate \"\\t\") $ transpose values\n export (i, f) = writeFile (\"output\" ++ pad (show i) ++ \".dat\") f\n pad n = replicate (5 - length n) '0' ++ n\n\nmain :: IO ()\nmain = do\n let p = defaultParameters\n o = makeOperators p 0 4\n evol = evolve p o\n print $ calculateEnergy p (evol !! timesteps p)\n printEvolution p evol\n\nextern crate rustfft;\n\nuse rustfft::num_complex::Complex;\nuse rustfft::FFTplanner;\nuse std::f64::consts::PI;\nuse std::fs::File;\nuse std::io::Write;\nuse std::path::Path;\n\n// This implementation is based on the C and C++ implementations.\n\n#[derive(Clone)]\nstruct Parameters {\n xmax: f64,\n res: usize,\n dt: f64,\n timesteps: usize,\n dx: f64,\n x: Vec,\n dk: f64,\n k: Vec,\n im_time: bool,\n}\n\nimpl Parameters {\n pub fn new(xmax: f64, res: usize, dt: f64, timesteps: usize, im_time: bool) -> Parameters {\n let dx = 2.0_f64 * xmax / (res as f64);\n let mut x: Vec = Vec::with_capacity(res);\n let dk = PI / xmax;\n let mut k: Vec = Vec::with_capacity(res);\n for i in 0..res {\n x.push(xmax / (res as f64) - xmax + (i as f64) * dx);\n match i {\n i if (i k.push((i as f64) * PI / xmax),\n _ => k.push(((i as f64) - (res as f64)) * PI / xmax),\n }\n }\n Parameters {\n xmax,\n res,\n dt,\n timesteps,\n im_time,\n dx,\n x,\n dk,\n k,\n }\n }\n}\n\nstruct Operators {\n v: Vec>,\n pe: Vec>,\n ke: Vec>,\n wfc: Vec>,\n}\n\nimpl Operators {\n pub fn new(par: &Parameters, v_offset: f64, wfc_offset: f64) -> Operators {\n let mut v: Vec> = Vec::with_capacity(par.res);\n let mut pe: Vec> = Vec::with_capacity(par.res);\n let mut ke: Vec> = Vec::with_capacity(par.res);\n let mut wfc: Vec> = Vec::with_capacity(par.res);\n\n for i in 0..par.res {\n v.push(Complex::new(\n 0.5_f64 * (par.x[i] - v_offset).powi(2),\n 0.0_f64,\n ));\n wfc.push(Complex::new(\n (-((par.x[i] - wfc_offset).powi(2)) / 2.0_f64).exp(),\n 0.0_f64,\n ));\n if par.im_time {\n ke.push(Complex::new(\n (-0.5_f64 * par.dt * par.k[i].powi(2)).exp(),\n 0.0_f64,\n ));\n pe.push(Complex::new((-0.5_f64 * par.dt * v[i].re).exp(), 0.0_f64));\n } else {\n ke.push(Complex::new(\n 0.0_f64,\n (-0.5_f64 * par.dt * par.k[i].powi(2)).exp(),\n ));\n pe.push(Complex::new(0.0_f64, (-0.5_f64 * par.dt * v[i].re).exp()));\n }\n }\n Operators { v, pe, ke, wfc }\n }\n}\n\nfn fft(x: &mut Vec>, inverse: bool) {\n let mut y = vec![Complex::new(0.0_f64, 0.0_f64); x.len()];\n let mut p = FFTplanner::new(inverse);\n let fft = p.plan_fft(x.len());\n fft.process(x.as_mut_slice(), y.as_mut_slice());\n\n for i in 0..x.len() {\n x[i] = y[i] / (x.len() as f64).sqrt();\n }\n}\n\nfn split_op(par: &Parameters, opr: &mut Operators) {\n let mut density: Vec;\n\n for i in 0..par.timesteps {\n for j in 0..par.res {\n opr.wfc[j] *= opr.pe[j];\n }\n\n fft(&mut opr.wfc, false);\n\n for j in 0..par.res {\n opr.wfc[j] *= opr.ke[j];\n }\n\n fft(&mut opr.wfc, true);\n\n for j in 0..par.res {\n opr.wfc[j] *= opr.pe[j];\n }\n\n density = opr.wfc.iter().map(|x| x.norm().powi(2)).collect();\n\n if par.im_time {\n let sum = density.iter().sum::() * par.dx;\n\n for j in 0..par.res {\n opr.wfc[j] /= sum.sqrt();\n }\n }\n\n // Writing data into a file in the format of:\n // index, density, real potential.\n let path_name = format!(\"output{}.dat\", i);\n let path = Path::new(&path_name);\n let display = path.display();\n\n let mut file = match File::create(&path) {\n Err(why) => panic!(\"Couldn't create {}: {}\", display, why),\n Ok(good) => good,\n };\n\n for j in 0..par.res {\n if let Err(why) = writeln!(file, \"{}\\t{}\\t{}\", j, density[j], opr.v[j].re) {\n panic!(\"Couldn't write to {}: {}\", display, why)\n }\n if let Err(why) = file.flush() {\n panic!(\"Couldn't flush {}: {}\", display, why)\n }\n }\n }\n}\n\nfn calculate_energy(par: &Parameters, opr: &Operators) -> f64 {\n let wfc_r = opr.wfc.clone();\n let mut wfc_k = opr.wfc.clone();\n let mut wfc_c = vec![Complex::new(0.0_f64, 0.0_f64); par.res];\n\n fft(&mut wfc_k, false);\n\n for i in 0..par.res {\n wfc_c[i] = wfc_r[i].conj();\n }\n\n let mut energy_k = vec![Complex::new(0.0_f64, 0.0_f64); par.res];\n let mut energy_r = vec![Complex::new(0.0_f64, 0.0_f64); par.res];\n\n for i in 0..par.res {\n energy_k[i] = wfc_k[i] * Complex::new(par.k[i], 0.0_f64).powi(2);\n }\n\n fft(&mut energy_k, true);\n\n for i in 0..par.res {\n energy_k[i] *= wfc_c[i].scale(0.5_f64);\n energy_r[i] = wfc_c[i] * opr.v[i] * wfc_r[i];\n }\n\n let energy_final = energy_k\n .into_iter()\n .zip(energy_r.into_iter())\n .fold(0.0_f64, |acc, x| acc + (x.0 + x.1).re);\n\n energy_final * par.dx\n}\n\nfn main() {\n let par = Parameters::new(5.0, 256, 0.05, 100, true);\n let mut opr = Operators::new(&par, 0.0, -1.0);\n\n split_op(&par, &mut opr);\n\n println!(\"The energy is {}\", calculate_energy(&par, &opr));\n}\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"split_op_method\" was created by Julian Schacher and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe animation \"realsplitop\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe animation \"imaginarysplitop\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/domain_coloring/domain_coloring.html":{"url":"contents/domain_coloring/domain_coloring.html","title":"Domain Coloring","keywords":"","body":"Domain coloring\nDomain coloring is a much more complicated plotting technique than those outlined in the plotting chapter and is used to plot complex functions where both the input and output have imaginary and real components.\nFor the code in this chapter, we will focus on languages that are easily able to plot two-dimensional images or heat maps, instead of languages meant for number-crunching.\nThat is to say that this chapter will certainly have a code implementation in gnuplot, but it will not likely have an implementation in C, Fortran, or Java because these languages do not have plotting capabilities in-built.\nTo start, imagine the following function: f(z) = z^2.\nIn this case, we could create a plot that looks like this:\n\n \n\n\nThis indicates that for various input values along z, we have different function outputs from f(z).\nFor this function, z\\in\\mathbb{R} is purely in real space and because of this, the output is also in real space.\nNow let's imagine another function with complex input (z \\in \\mathbb{C}), but a purely real output (f(z) \\in \\mathbb{R}):\n\nf(z) = |z|\n\nIn this case, this can be plotted as a two-dimensional dataset like so:\n\n \n\n\nHere, the x-axis and y-axis represent the imaginary and real components of the input variable, respectively.\nThe color bar represents the output of f(z).\nAt this point, we can start to see the problem.\nIf the output of f(z) also requires plotting of real and imaginary components, then we would need four dimensions to appropriately represent the full function space, one axis for the real component and another for the imaginary component of both the input (z) and the output of f(z)!\nUnfortunately, feeble human minds are incapable of understanding four spatial dimensions without projecting onto lower dimensionality, so we need to improvise.\nWe do this by assuming the complex output can be represented in the following form:\n\nz = re^{i \\theta} = r(\\cos(\\theta) + i\\sin(\\theta))\n\nwhere, r is a complex magnitude and \\theta is a complex phase.\nThis is the formula for a circle in the complex plane and we can easily find r and \\theta like so:\n\n\\begin{align}\n r &= \\sqrt{\\text{Re}(z)^2 + \\text{Im}(z)^2} \\\\ \n \\theta &= \\text{atan}\\left(\\frac{\\text{Im}(z)}{\\text{Re}(z)}\\right)\n\\end{align}\n\nOnce we have our complex function output in this form, we then color the output domain according to a color space with at least 2 independent dimensions, like RGB (Red, Green, Blue), or HSV (Hue, Saturation, Value) [1].\nThe choice of color space is completely dependent on what the users feel is most visually intuitive.\nIn any case, one dimension of the color system will be used to represent the complex magnitude and another dimension of the color system will be used to represent the complex phase of the output.\nThe xy grid will be representing the real and imaginary inputs to these functions.\nThat is to say, we plug every value in the 2D complex plane into the function and then color each pixel based on the function output.\nAs an example, let's look at the simplest function we can f(z) = z, but in this case z \\in \\mathbb{C}.\nIf we use an RGB color scheme, where red represents \\theta and blue represents r, we can generate the following image:\n\n \n\n\nAs a note here, there is a clear phase discontinuity along the horizontal axis, which is a consequence of the fact that\nthe complex phase wraps around the origin, ranging from 0 (clear) to 2\\pi (red).\nIn addition, the edges of the plot are blue because the function's magnitude increases linearly as we move from the origin.\nIf we instead look at the function f(z) = z^2, we can generate a similar plot:\n\n \n\n\nHere, it is clear that the complex phase wraps around the origin twice, creating two separate phase discontinuities on top of each other.\nThis indicates a 4\\pi phase winding.\nFor some purposes, such as vortex tracking for inviscid fluids, this visualization is ideal, because a vortex is located precisely at the center of the phase discontinuity [2] [3].\nFor other purposes, the discontinuity is visually distracting, and for this reason, many people use an HSV scheme for plotting complex functions [4] [5] [6].\nSo here is the same function \\left(f(z)=z^2\\right), but using hue to represent the complex phase and saturation to represent the magnitude:\n\n \n\n\nIn this plot, the Value for HSV was always set to 1.\nWhen looking at the edges of the plot, the hue changes rapidly, but each color is mirrored on the opposite edge.\nThis indicates the 4\\pi phase winding we saw in the RGB plot.\nAlso, because the complex magnitude increases as we move further from the center of the plot, the saturation also increases.\nThus the center of the plot is completely washed out!\nWe need to fix this in subsequent plots to make them more representative of the actual data.\nOne easy way to show the increasing complex magnitude without sacrificing phase information is by using contours.\nEssentially, at ever integer value of the magnitude, we want to draw some kind of line.\nThere are a number of ways to generate these lines, and one simple way is by using an alternative shading function like so:\n\ng(r) = r-\\lfloor r \\rfloor.\n\nThis will create the following image:\n\n \n\n\nThis function will essentially create a smooth gradient, but because of the floor operation \\left(\\lfloor \\cdot \\rfloor \\right), the saturation will go from 0 to 1 between each integer value of the magnitude.\nHere, it is clear that the magnitude is increasing as z^2 from the origin; however, because the saturation is fluctuating so much, it is difficult to see the phase pattern next to each contour.\nThis can be fixed simply by adding an offset to the shading function such that,\n\ng(r) = \\frac{1}{2} + \\frac{1}{2}\\left(r-\\lfloor r \\rfloor \\right).\n\nWhich will produce the following image:\n\n \n\n\nThis means that the saturation will fluctuate from \\frac12 to 1 instead of from 0 to 1, which makes it way easier to see phase information next to contours.\nAgain, there are a lot of different ways to play with these equations, so feel free to use whatever function you want!\nAs long as some sort of rounding operation is used to establish some form of integer value for the magnitude, it should be possible to create contours of various types.\nAt this point, changing the saturation shows changes in the complex magnitude, and changing the hue shows changes in the complex phase.\nUnfortunately, neither the magnitude nor the phase directly show what is happening in real or imaginary space with the output.\nTo show this, we might want to draw grid lines that color our pixels black whenever the imaginary or real components of the output function are integer values.\nFor example, let's go back to a simpler function f(z) = z.\nIf we draw lines on this plot, corresponding to integer values in the output, we get a simple grid\n\n \n\n\nLike before, the choice of which function to use in order to create the grid lines is somewhat arbitrary.\nIt is important to choose a function that sharply drops to 0 or peaks at 1 for all integer values, and then we simply plug values of f(z) into this function.\nFor the purposes of this chapter, we chose the following function\n\nh(z) = |\\sin(\\pi\\times\\text{Re}(f(z)))^t|\\times|\\sin(\\pi\\times\\text{Im}(f(z)))^t|,\n\nwhere t is some threshold value, and was set to be 0.1 in our plot.\nA plot of h(z) for f(z) = z where z\\in\\mathbb{R} is shown below:\n\n \n\n\nSo, putting it all together and returning to the function of f(z) = z^2, we find the following image.\n\n \n\n\nHere, the diagonal lines through the center represent integer values along the imaginary axis for f(z) and the vertical and horizontal lines represent integer values of the real axis for f(z).\nAn easy way to determine which lines correspond to which integer values is by plugging in certain values for z into f(z).\nFor example, there is a black line at z = 1 + 1i where f(z) = 2i, this means that all values along that contour correspond to values that are constrained to having an imaginary component of precisely 2.\nOverall, there are plenty of interesting ways to plot complex functions and make really compelling and beautiful images!\nWe will be using domain coloring in other contexts throughout this text when describing methods that heavily use complex space.\nVideo Explanation\nHere is a video describing domain coloring:\n\n\n\n\nExample Code\nHere is the full script to generate a domain colored output of f(z)=z^2.\n# setting output to file of size 800 x 800\nset terminal pngcairo size 1000, 1000 \nset output 'domain.png'\n\n# sets title for full plot\nset title 'f(z)=z^2'\n\n# removes legend\nunset key\n\n# projects image onto 2D plane\nset view map\n\n# sets aspect ratio of plot to be square \nset size square\n\n# sets x and y range and labels\nset xrange[-2:2]\nset yrange[-2:2]\n\nset xlabel \"Re(z)\"\nset ylabel \"Im(z)\"\n\n# scaling the x, y, and colorbar tics to zero so they are not seen in the plot\nset xtics border scale 0,0\nset ytics border scale 0,0\nset cbtics border scale 0,0\n\n# sets tics in color bar at 0 and 2pi\nset cbtics (\"0\" -3.14159, '2pi' 3.14159)\n\nset cblabel \"Phase Angle\" \nset cbrange [ -3.14159 : 3.14159 ]\n\n# use hsv for colorbar and set palette to use full hsv space\nset palette model HSV\nset palette defined ( 0 0 1 1, 1 1 1 1 )\n\n# setting isosamples for output grid and samples for input grid\nset isosamples 2000, 2000\nset samples 2000, 2000\n\n# setting functions necessary for domain coloring\n# setting threshold for gridlines. Smaller threshold will make smaller lines\nthresh = 0.1\nf(z) = z**2\n\n# atan2 returns a range from -pi to pi, so we need to add pi, but this offsets\n# the value by 180 degrees, so we also imput (-y, -x) for another 180 degrees\n# to invert rotation\nangle(x,y) = (pi + atan2(-y,-x)) / (2*pi)\n\n# complex magnitude\nr(x,y) = sqrt(x*x + y*y)\n\n# complex phase and magnitude\ntheta(x,y) = atan2(y,x)\nz(x,y) = r(x,y)*exp(theta(x,y)*sqrt(-1))\n\n# imaginary and real output functions\nimaginary_f(z) = imag(f(z))\nreal_f(z) = real(f(z))\n\n# magnitude contours\nmagnitude_shading(x,y) = 0.5 + 0.5*(abs(f(z(x,y)))-floor(abs(f(z(x,y)))))\n\n# gridlines\ngridlines(x,y) = (abs(sin(real_f(z(x,y))*pi)**thresh) \\\n * abs(sin(imaginary_f(z(x,y))*pi))**thresh)\n\n# overall coloring function\ncolor(x,y) = hsv2rgb(angle(real_f(z(x,y)), imaginary_f(z(x,y))), \\\n magnitude_shading(x,y), \\\n gridlines(x,y))\n\nsave_encoding = \"utf8\"\n\n# Last datafile plotted: \"++\"\n# In this case, it means, \"plot the data file created with the\n# samples and isosamples\"\nsplot '++' using 1:2:(color($1,$2)) with pm3d lc rgb variable nocontour\n\n\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport matplotlib.colors\nfrom matplotlib.cm import ScalarMappable\n\n\ndef f(z):\n return z**2\n\n\ndef magnitude_shading(f_val):\n f_val_abs = np.abs(f_val)\n return 0.5 + 0.5 * (f_val_abs - np.floor(f_val_abs))\n\n\ndef gridlines(f_val, threshold):\n return (np.abs(np.sin(np.pi * np.real(f_val))) ** threshold\n * np.abs(np.sin(np.pi * np.imag(f_val))) ** threshold)\n\n\ndef color(f_val, threshold):\n hue = (np.pi - np.angle(f_val)) / (2.0 * np.pi)\n saturation = magnitude_shading(f_val)\n value = gridlines(f_val, threshold)\n\n # Currently we have a tuple of 2D-arrays (hue, saturation, value).\n # This makes it a 2D-array of tuples, which the conversion function requires.\n hsv = np.moveaxis((hue, saturation, value), 0, -1)\n return matplotlib.colors.hsv_to_rgb(hsv)\n\n\nif __name__ == \"__main__\":\n # Create a new figure containing a single plot\n fig, axes = plt.subplots(1, 1)\n\n # Set the title for the plot\n axes.set_title(\"$f(x)=z^2$\")\n\n # Create color bar\n cbar = fig.colorbar(\n ScalarMappable(matplotlib.colors.Normalize(0.0, 2.0 * np.pi), \"hsv\"),\n ax=axes,\n label=\"Phase Angle\")\n\n # Set x and y labels\n axes.set_xlabel(\"$Re(z)$\")\n axes.set_ylabel(\"$Im(z)$\")\n\n # Set color bar tick locations and labels\n cbar.set_ticks([0.0, np.pi, 2.0 * np.pi])\n cbar.set_ticklabels([\"$0.0$\", \"$\\pi$\", \"$2\\pi$\"])\n\n # Hide x and y ticks\n for tick in axes.get_xticklines():\n tick.set_visible(False)\n\n for tick in axes.get_yticklines():\n tick.set_visible(False)\n\n # Create a 500x500 input grid\n coords = np.linspace(-2.0, 2.0, 500)\n z_real, z_imag = np.meshgrid(coords, coords)\n z = z_real + 1j * z_imag\n\n # Calculate function values\n f_val = f(z)\n\n # Map function values to colors\n colors = color(f_val, 0.1)\n\n # Plot the colors\n # extent=(-2.0, 2.0, -2.0, 2.0) sets the x and y ranges\n # origin=\"lower\" places index (0,0) of the color array in the lower-left corner\n # aspect=\"equal\" ensures that the plot is square\n axes.imshow(\n colors,\n extent=(-2.0, 2.0, -2.0, 2.0),\n origin=\"lower\",\n aspect=\"equal\")\n\n # Save output\n fig.savefig(\"domain.png\")\n\n\n\nBibliography\n1.Wikipedia: HSL and HSV, 2020.2.Schloss, James, Massively parallel split-step Fourier techniques for simulating quantum systems on graphics processing units, 2019.3.Pethick, Christopher J and Smith, Henrik, Bose--Einstein condensation in dilute gases, Cambridge university press, 2008.4.Wegert, Elias, Visual complex functions: an introduction with phase portraits, Springer Science \\& Business Media, 2012.5.Poelke, Konstantin and Polthier, Konrad, Domain Coloring of Complex Functions.6.Lundmark, Hans, Visualizing complex analytic functions using domain coloring, 2004.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"z2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"absz\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"rgb1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"rgb2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"hsv1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"hsv2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"hsv3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"hsv4\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"shade\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"hsv5\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nThe following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/barnsley/barnsley.html":{"url":"contents/barnsley/barnsley.html","title":"The Barnsley Fern","keywords":"","body":"The Barnsley Fern\nAt the end of the chapter on Iterated Function Systems, we introduced two separate attractors: the Sierpinski triangle, and a uniform two-dimensional square, shown below with their corresponding Hutchinson operator.\n\n\n\nHutchinson Operator\nAttractor\n\n\n\n\n\\begin{align} f_1(P) &= \\frac{P+A}{2} \\\\ f_2(P) &= \\frac{P+B}{2} \\\\ f_3(P) &= \\frac{P+C}{2} \\end{align}\n\n\n\n\\begin{align} f_1(P) &= \\frac{P+A}{2} \\\\ f_2(P) &= \\frac{P+B}{2} \\\\ f_3(P) &= \\frac{P+C}{2} \\\\ f_4(P) &= \\frac{P+D}{2} \\end{align}\n\n\n\n\nAs a reminder, the Hutchinson operator is a set of functions that act on a point in space, P, and return another another point at a new location.\nThese functions are meant to be used over and over again in some fashion, and as you continually iterate through them, some shape will eventually be drawn.\nThis shape is known as an attractor, and the entire system is called an iterated function system due to the iterative nature of drawing the attractor.\nIn these cases, each function will move the point to be halfway between its original position and the position of A, B, C, and D for f_1, f_2, f_3, and f_4, respectively.\nEven though f_1, f_2, and f_3 are the same for both attractors, the addition of f_4 drastically changes the final result!\nIt is surprising that two seemingly identical sets of functions can look so different in the end, and this leads us to a somewhat challenging question: given a set of functions, is there any way to predict what the attractor will be without iterating through the functions?\nIn general, the answer is no.\nYou must sample the function set in some fashion to get find the resulting attractor.\nThis feels somewhat unsettling to me.\nAfter all, each individual function is simple, so why is the result so difficult to predict?\nIn this chapter, I hope to provide a slightly more satisfying answer by introducing another iterated function system with beautiful attractor, known as the Barnsley fern [1]:\n\n\n\nHutchinson Operator\nAttractor\n\n\n\n\n\\begin{align} f_1(P) &= \\begin{bmatrix} 0 &0 \\\\ 0 &0.16 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix} \\\\ f_2(P) &= \\begin{bmatrix} 0.85 &0.04 \\\\ -0.04 &0.85 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 1.6 \\end{bmatrix} \\\\ f_3(P) &= \\begin{bmatrix} 0.2 &-0.26 \\\\ 0.23 &0.22 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 1.6 \\end{bmatrix} \\\\ f_4(P) &= \\begin{bmatrix} -0.15 &0.28 \\\\ 0.26 &0.24 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 0.44 \\end{bmatrix} \\end{align}\n\n\n\n\nAt first glance, this set of functions looks like an incomprehensible mess of magic numbers to create a specific result, and in a sense, that is precisely correct.\nThat said, we will go through each function and explain how it works, while also providing a simple chaos game implementation in code.\nBy the end of this chapter, we do not hope to provide a general strategy for understanding all iterated function systems, but we hope to at least make this one set of functions a bit more understandable.\nIndividual affine transforms\nThe first thing to note about the Barnsley set of functions is that each one is an affine transformation.\nThough it is not a hard rule, most iterated function systems use affine transforms, so this notation is common.\nIn fact, the Sierpinski operators can also be written in an affine form:\n\n\n\nNon-affine\nAffine\n\n\n\n\n\\begin{align} f_1(P) &= \\frac{P+A}{2} \\\\ f_2(P) &= \\frac{P+B}{2} \\\\ f_3(P) &= \\frac{P+C}{2} \\end{align}\n\\begin{align} f_1(P) &= \\begin{bmatrix} 0.5 &0 \\\\ 0 &0.5 \\end{bmatrix}P + \\frac{A}{2} \\\\ f_2(P) &= \\begin{bmatrix} 0.5 &0 \\\\ 0 &0.5 \\end{bmatrix}P + \\frac{B}{2} \\\\ f_3(P) &= \\begin{bmatrix} 0.5 &0 \\\\ 0 &0.5 \\end{bmatrix}P + \\frac{C}{2} \\end{align}\n\n\n\nThe affine variant performs the same operation by scaling the x and y component of P by 0.5 and then adding half of either A, B, or C for f_1, f_2, or f_3, respectively.\nEach of these transforms involves some linear component (scaling or shearing) with an additional translation.\nAs an important side-note: in both the Barnsley and Sierpinski function systems, the coefficients of the transformation matrix are all less than 1.\nThis property is known as contractivity, and an iterated function system can only have an attractor if the system is contractive.\nUpon reflection, this makes sense.\nIf the matrix elements were greater than 1, the point could tend towards infinity after successive iterations of the function.\nNow let's hop into disecting the Barnsley fern by seeing how each transform affects a random distribution of points:\n\n\n\nFunction\nOperation\n\n\n\n\nf_1(P) = \\begin{bmatrix} 0 &0 \\\\ 0 &0.16 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix} This operation moves every point to a single line.\n Your browser does not support the video tag. \n\n\nf_2(P) = \\begin{bmatrix} 0.85 &0.04 \\\\ -0.04 &0.85 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 1.6 \\end{bmatrix} This operation moves every point up and to the right.\n Your browser does not support the video tag. \n\n\nf_3(P) = \\begin{bmatrix} 0.2 &-0.26 \\\\ 0.23 &0.22 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 1.6 \\end{bmatrix} This operation rotates every point to the left.\n Your browser does not support the video tag. \n\n\nf_4(P) = \\begin{bmatrix} -0.15 &0.28 \\\\ 0.26 &0.24 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 0.44 \\end{bmatrix} This operation flips every point and rotates to the right.\n Your browser does not support the video tag. \n\n\n\nAt this stage, it might be clear what is going on, but it's not exactly obvious.\nEssentially, each operation corresponds to another part of the fern:\n\nf_1 creates the stem.\nf_2 creates successively smaller ferns moving up and to the right.\nf_3 creates the leaves on the right.\nf_4 creates the leaves on the left.\n\nThe easiest way to make sense of this is to show the operations on the Barnsley fern, itself, instead of a random distribution of points.\n\n\n\nFunction\nOperation\n\n\n\n\nf_1(P) = \\begin{bmatrix} 0 &0 \\\\ 0 &0.16 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix}\n Your browser does not support the video tag. \n\n\nf_2(P) = \\begin{bmatrix} 0.85 &0.04 \\\\ -0.04 &0.85 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 1.6 \\end{bmatrix}\n Your browser does not support the video tag. \n\n\nf_3(P) = \\begin{bmatrix} 0.2 &-0.26 \\\\ 0.23 &0.22 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 1.6 \\end{bmatrix}\n Your browser does not support the video tag. \n\n\nf_4(P) = \\begin{bmatrix} -0.15 &0.28 \\\\ 0.26 &0.24 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 0.44 \\end{bmatrix}\n Your browser does not support the video tag. \n\n\n\nHere, the self-similar nature of the fern becomes apparent.\nEach operation is effectively moving a point on one part of the fern to a point on another part of the fern.\nIn the final construction, it is clear that fewer points are necessary on some parts than others.\nThe stem, for example, does not need many points at all.\nMeanwhile, the bulk of the fern seems to be generated by f_2, so we probably want the majority of the points to choose that function when iterating through he set.\nTo account for this, each function is also given a probability of being chosen:\n\n\n\nFunction\nProbability\n\n\n\n\nf_1(P) = \\begin{bmatrix} 0 &0 \\\\ 0 &0.16 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix}\n0.01\n\n\nf_2(P) = \\begin{bmatrix} 0.85 &0.04 \\\\ -0.04 &0.85 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 1.6 \\end{bmatrix}\n0.85\n\n\nf_3(P) = \\begin{bmatrix} 0.2 &-0.26 \\\\ 0.23 &0.22 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 1.6 \\end{bmatrix}\n0.07\n\n\nf_4(P) = \\begin{bmatrix} -0.15 &0.28 \\\\ 0.26 &0.24 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 0.44 \\end{bmatrix}\n0.07\n\n\n\nPlaying around a bit...\nOne big advantage of using affine transformations to construct an attractor is that mathematicians and programmers can leverage their knowledge of how these transformations work to also modify the resulting image.\nHere are a few examples of ferns that can be generated by modifying constituent functions:\n\n\n\nFunction\nOperation\n\n\n\n\nf_1(P) = \\begin{bmatrix} \\tau &0 \\\\ 0 &0.16 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix} where -0.5 Turning stems to leaves\n Your browser does not support the video tag. \n\n\nf_2(P) = \\begin{bmatrix} 0.85 & \\tau \\\\ -0.04 &0.85 \\end{bmatrix}P + \\begin{bmatrix} 0 \\\\ 1.6 \\end{bmatrix} where -0.01 Changing fern tilt\n Your browser does not support the video tag. \n\n\nf_3(P) = \\begin{bmatrix} 0.2 &-0.26 \\\\ 0.23 &0.22 \\end{bmatrix}P + \\begin{bmatrix} \\tau \\\\ 1.6 \\end{bmatrix} where -0.5 Plucking left leaves\n Your browser does not support the video tag. \n\n\nf_4(P) = \\begin{bmatrix} -0.15 &0.28 \\\\ 0.26 &0.24 \\end{bmatrix}P + \\begin{bmatrix} \\tau \\\\ 0.44 \\end{bmatrix} where -0.5 Plucking right leaves\n Your browser does not support the video tag. \n\n\n\nAs an important note: the idea of modifying a resulting image by twiddling the knobs of an affine transform is the heart of many interesting methods, including fractal image compression where a low resolution version of an image is stored along with a reconstructing function set to generate high-quality images on-the-fly [2][3].\nIf this seems mystifying, don't worry!\nWe'll definitely come back to this soon, I just wanted to briefly mention it now so it's on everyone's mind as we move forward.\nVideo Explanation\nHere is a video describing the Barnsley fern:\n\n\n\n\nExample Code\nSimilar to the chapter on iterated function systems, the example code here will show a chaos game for the construction of an attractor;\nhowever, in this case the attractor will be the Barnsley fern instead of the Sierpinski triangle.\nThe biggest differences between the two code implementations is that the Barnsley implementation must take into account the varying probabilities for choosing each function path and that we will be choosing an initial point that is on the attractor this time (namely (0,0)).\nusing DelimitedFiles\n\n# This is a function that reads in the Hutchinson operator and corresponding\n# probabilities and outputs a randomly selected transform\n# This works by choosing a random number and then iterating through all \n# probabilities until it finds an appropriate bin\nfunction select_array(hutchinson_op, probabilities)\n\n # random number to be binned\n rnd = rand()\n\n # This checks to see if a random number is in a bin, if not, that \n # probability is subtracted from the random number and we check the\n # next bin in the list\n for i = 1:length(probabilities)\n if (rnd \nuse rand::prelude::*;\n#[derive(Clone, Copy)]\nstruct Point2 {\n x: f64,\n y: f64,\n}\n\n#[derive(Clone, Copy)]\nstruct Point3 {\n x: f64,\n y: f64,\n z: f64,\n}\n\nimpl Point3 {\n fn new(x: f64, y: f64, z: f64) -> Self {\n Self { x, y, z }\n }\n\n fn matrix_mul(self, rhs: Vec) -> Self {\n let x = rhs[0].x * self.x + rhs[0].y * self.y + rhs[0].z * self.z;\n let y = rhs[1].x * self.x + rhs[1].y * self.y + rhs[1].z * self.z;\n let z = rhs[2].x * self.x + rhs[2].y * self.y + rhs[2].z * self.z;\n Self::new(x, y, z)\n }\n}\n\nfn select_array(hutchinson_op: &[Vec], probabilities: &[f64]) -> Vec {\n let mut rng = rand::thread_rng();\n let mut rnd = rng.gen::();\n\n for (i, probability) in probabilities.iter().enumerate() {\n if rnd ],\n probabilities: &[f64],\n) -> Vec {\n let mut point = Point3 {\n x: initial_location.x,\n y: initial_location.y,\n z: 1.0,\n };\n (0..iters)\n .into_iter()\n .map(|_| {\n let old_point = point;\n let operation = select_array(hutchinson_op, probabilities);\n point = point.matrix_mul(operation);\n Point2 {\n x: old_point.x,\n y: old_point.y,\n }\n })\n .collect()\n}\n\nfn main() {\n let barnsley_hutchinson = vec![\n vec![\n Point3::new(0.0, 0.0, 0.0),\n Point3::new(0.0, 0.16, 0.0),\n Point3::new(0.0, 0.0, 1.0),\n ],\n vec![\n Point3::new(0.85, 0.04, 0.0),\n Point3::new(-0.04, 0.85, 1.60),\n Point3::new(0.0, 0.0, 1.0),\n ],\n vec![\n Point3::new(0.20, -0.26, 0.0),\n Point3::new(0.23, 0.22, 1.60),\n Point3::new(0.0, 0.0, 1.0),\n ],\n vec![\n Point3::new(-0.15, 0.28, 0.0),\n Point3::new(0.26, 0.24, 0.44),\n Point3::new(0.0, 0.0, 1.0),\n ],\n ];\n\n let barnsley_probabilities = vec![0.01, 0.85, 0.07, 0.07];\n\n let mut out = String::new();\n\n for point in chaos_game(\n 10_000,\n Point2 { x: 0.0, y: 0.0 },\n &barnsley_hutchinson,\n &barnsley_probabilities,\n ) {\n out += format!(\"{}\\t{}\\n\", point.x, point.y).as_str();\n }\n\n std::fs::write(\"./out.dat\", out).unwrap();\n}\n\n// The code bellow uses C++-17 features, compile it with C++-17 flags, e.g.:\n// clang++ -Wall -Wextra -Wshadow -Wnon-virtual-dtor -Wold-style-cast -Wcast-align -Wunused -Woverloaded-virtual -Wpedantic -Wconversion -Wsign-conversion -Wnull-dereference -Wdouble-promotion -Wformat=2 -gdwarf-3 -D_GLIBCXX_DEBUG -std=c++17 -O3 -c ./barnsley.cpp barnsley\n\n#include \n#include \n#include \n#include \n\nusing Vec2 = std::array;\nusing Vec3 = std::array;\nusing Row = std::array;\nusing Op = std::array;\n\nconstexpr auto OpN = 4U;\n\ntemplate \nauto operator+(std::array x, std::array y) {\n for (auto i = 0U; i \nauto operator*(double k, std::array v) {\n for (auto i = 0U; i \nauto operator*(std::array v, double k) {\n return k * v;\n}\n\nauto operator*(const Op& x, const Vec3& y) {\n auto ret = Vec3{};\n for (auto i = 0U; i (0.0, 1.0)(rng());\n}\n\n// This is a function that reads in the Hutchinson operator and\n// corresponding\n// probabilities and outputs a randomly selected transform\n// This works by choosing a random number and then iterating through all\n// probabilities until it finds an appropriate bin\nauto select_array(\n const std::array& hutchinson_op,\n const std::array& probabilities) {\n\n // random number to be binned\n auto rnd = drand();\n\n // This checks to see if a random number is in a bin, if not, that\n // probability is subtracted from the random number and we check the\n // next bin in the list\n for (auto i = 0U; i (\"check if probabilities adding up to 1\"));\n return hutchinson_op[0];\n}\n\n// This is a general function to simulate a chaos game\n// n is the number of iterations\n// initial_location is the the starting point of the chaos game\n// hutchinson_op is the set of functions to iterate through\n// probabilities is the set of probabilities corresponding to the likelihood\n// of choosing their corresponding function in hutchinson_op\nauto chaos_game(\n size_t n,\n Vec2 initial_location,\n const std::array& hutchinson_op,\n const std::array& probabilities) {\n\n // Initializing the output array and the initial point\n auto output_points = std::vector{};\n\n // extending point to 3D for affine transform\n auto point = Vec3{initial_location[0], initial_location[1], 1};\n\n for (auto i = 0U; i \n#include \n#include \n\nstruct matrix {\n double xx, xy, xz,\n yx, yy, yz,\n zx, zy, zz;\n};\n\nstruct point2d {\n double x, y;\n};\n\nstruct point3d {\n double x, y, z;\n};\n\nstruct point3d matmul(struct matrix mat, struct point3d point)\n{\n struct point3d out = {\n mat.xx * point.x + mat.xy * point.y + mat.xz * point.z,\n mat.yx * point.x + mat.yy * point.y + mat.yz * point.z,\n mat.zx * point.x + mat.zy * point.y + mat.zz * point.z\n };\n return out;\n}\n\n// This function reads in the Hutchinson operator and corresponding\n// probabilities and returns a randomly selected transform\n// This works by choosing a random number and then iterating through all\n// probabilities until it finds an appropriate bin\nstruct matrix select_array(struct matrix *hutchinson_op, double *probabilities,\n size_t num_op)\n{\n // random number to be binned\n double rnd = (double)rand() / RAND_MAX;\n\n // This checks to see if a random number is in a bin, if not, that\n // probability is subtracted from the random number and we check the next\n // bin in the list\n for (size_t i = 0; i \nimport java.io.FileWriter;\nimport java.io.IOException;\nimport java.util.Random;\n\npublic class Barnsley {\n\n private static class Point {\n public double x, y, z;\n\n public Point(double x, double y, double z) {\n this.x = x;\n this.y = y;\n this.z = z;\n }\n\n public Point(double[] coordinates) {\n this.x = coordinates[0];\n this.y = coordinates[1];\n this.z = coordinates[2];\n }\n\n public Point matrixMultiplication(double[][] matrix) {\n double[] results = new double[3];\n for (int i = 0; i \nfrom random import choices\nimport numpy as np\n\ndata Point(x=0, y=0):\n def __rmatmul__(self, mat: np.array):\n point_array = np.array([self.x, self.y, 1])\n x, y, *_ = tuple(*(mat @ point_array))\n return Point(x, y)\n\n\ndef chaos_game(initial_location is Point, hutchinson_op, probabilities):\n point = initial_location\n while True:\n yield (point := choices(hutchinson_op, probabilities) @ point)\n\nbarnsley_hutchinson = [\n np.array([\n [0., 0., 0.],\n [0., 0.16, 0.],\n [0., 0., 1.],\n ]),\n np.array([\n [0.85, 0.04, 0.],\n [-0.04, 0.85, 1.6],\n [0., 0., 1.],\n ]),\n np.array([\n [0.2, -0.26, 0.],\n [0.23, 0.22, 1.6],\n [0., 0., 1.],\n ]),\n np.array([\n [-0.15, 0.28, 0.],\n [0.26, 0.24, 0.44],\n [0., 0., 1.],\n ]),\n]\n\nbarnsley_probabilities = [0.01, 0.85, 0.07, 0.07]\n\nif __name__ == '__main__':\n output_gen = chaos_game(Point(0, 0), barnsley_hutchinson, barnsley_probabilities)\n output_points = np.array([*output_gen$[:10000]])\n np.savetxt(\"out.dat\", output_points)\n\nimport Data.Array (Array, bounds, elems, listArray, (!))\nimport Data.List (intercalate)\nimport System.Random\n\ndata Point = Point Double Double\n\nchaosGame :: RandomGen g => g -> Int -> Array Int (Double, (Point -> Point)) -> [Point]\nchaosGame g n hutchinson = take n points\n where\n (x, g') = random g\n (y, g'') = random g'\n\n cumulProbabilities = scanl1 (+) $ map fst $ elems hutchinson\n to_choice x = length $ takeWhile (x >) cumulProbabilities\n\n picks = map to_choice $ randomRs (0, 1) g''\n step = fmap snd hutchinson\n\n points = Point x y : zipWith (step !) picks points\n\naffine :: (Double, Double, Double, Double) -> (Double, Double) -> Point -> Point\naffine (xx, xy, yx, yy) (a, b) (Point x y) = Point (a + xx * x + xy * y) (b + yx * x + yy * y)\n\nshowPoint :: Point -> String\nshowPoint (Point x y) = show x ++ \"\\t\" ++ show y\n\nmain :: IO ()\nmain = do\n g \n\n\nBibliography\n1.Barnsley, Michael F, Fractals everywhere, Academic press, 2014.2.Wikipedia: Fractal Compression, 2019.3.Saupe, Dietmar and Hamzaoui, Raouf, A review of the fractal image compression literature, ACM, 1994.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"IFS triangle 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"IFS square 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Simple Barnsley fern\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine random transform 0\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine random transform 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine random transform 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine random transform 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine fern transform 0\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine fern transform 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine fern transform 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine fern transform 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Fern twiddle 0\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Fern twiddle 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Fern twiddle 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Fern twiddle 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n"},"contents/box_muller/box_muller.html":{"url":"contents/box_muller/box_muller.html","title":"Box Muller Transform","keywords":"","body":"The Box—Muller Transform\nThe Box—Muller transform holds a special place in my heart as it was the first method I ever had to implement for my own research.\nThe purpose of this transformation is simple.\nIt takes a uniform (probably random) distribution and turns it into a Gaussian one.\n\n \n\n\nThat's it.\nIt was originally developed by George Box (yes, Box is his last name) and Mervin Muller in 1958 and is one of the most common methods to create a random, Gaussian distribution of points [1].\nIt's particularly useful when initializing a set of particles for a physical, N-body simulation.\nThis chapter will be divided into a few subsections:\n\nHow to initialize the Box—Muller transform\nHow to use the Box—Muller transform in Cartesian coordinates [2].\nHow to use the Box—Muller transform in Polar Coordinates, also called the Marsaglia transform [3].\n\nOf course, there will be full code examples at the bottom.\nSo, let's get to it!\nHow to initialize the Box—Muller transform\nThe main thing to mention here is that the Box—Muller transform requires some form of uniform distribution as its input.\nOne obvious way to initialize a random distribution of points is to start with a grid, like so:\n\nfunction create_grid(n, endpoints)\n\n grid_extents = endpoints[2] - endpoints[1]\n\n # number of points along any given axis\n # For 2D, we take the sqrt(n) and then round up\n axis_num = ceil(Int, sqrt(n))\n\n # we are now rounding n up to the nearest square if it was not already one\n if sqrt(n) != axis_num\n n = axis_num^2\n end \n\n # Distance between each point\n dx = grid_extents / (axis_num)\n\n # Initializing the array, particles along the column, dimensions along rows\n a = zeros(n, 2)\n\n # This loops over the relevant dimensions\n for i = 1:axis_num\n for j = 1:axis_num\n a[(i - 1) * axis_num + j, :] .=\n [(i - 0.5) * dx + endpoints[1],\n (j - 0.5) * dx + endpoints[1]]\n end\n end\n\n return a\n\n\n\nThis will create the following set of points for n=100:\n\n \n\n\nTo be honest, there are a bunch of ways to generate this exact same distribution.\nHere, we simply walked backwards half of the grid size, determined the step size, and then placed a particle at each step.\nNote that there is an inherent limitation with this method in that it only works for a square numbers.\nBecause of this, we decided to round n up to the nearest square to make a nice grid.\nIt's not the cleanest implementation, but the grid will mainly be used for debugging anyway, so it's OK to be a little messy here.\nThe real star of the show is the uniform random distribution, which can be generated like this:\n\nfunction create_rand_dist(n, endpoints)\n grid_extents = endpoints[2] - endpoints[1]\n return(rand(n,2) * grid_extents .+ endpoints[1])\n\n\n\nThis will create the following set of points for n=100:\n\n \n\n\nOK, but how do we know this is uniform?\nGood question!\nThe easiest way is to plot a histogram of a super large number of points.\nIf the random distribution is uniform, then all the bins should be roughly the same value.\nThe more points we have, the smaller the percent difference between the bins will be.\nHere is a set of images generated by rand() for n=100, 1,000, and 10,000 all in one dimension:\n\n\n\n100\n1,000\n10,000\n\n\n\n\n\n\n\n\n\n\nIt is clear that the 10,000 case looks the most uniform.\nNote that for two dimensions, the same logic applies, but we need to create separate histograms for the x and y coordinates.\nOnce this test is complete, we can be fairly sure that the function we are using to generate the initial distribution is uniform and ready for the next step of the process: actually using the Box—Muller transform!\nHow to use the Box—Muller transform in Cartesian coordinates\nThe two dimensional Cartesian version of the Box—Muller transform starts with two random input values (u_1 and u_2), both of which come from their own uniform distributions that are between 0 and 1.\nIt then creates two output points (z_1 and z_2).\nFor this, u_1 is used to create a Gaussian distribution along some radial value r, and u_2 is used to spin that around a circle with some angular component \\theta, such that \n\n\\begin{align}\nr &= \\sqrt{-2\\ln(u_1)} \\\\\n\\theta &= 2\\pi u_2.\n\\end{align}\n\nLooking at these equations, \\theta seems to make a decent amount of sense.\nAfter all, angles typically vary from 0 \\rightarrow 2\\pi, and our input distribution varies from 0 \\rightarrow 1, so we can get some value between 0 and 2\\pi by multiplying 2\\pi by one of our input values.\nSo what about r?\nWell, remember that if we want u to be in a Gaussian form, then we might say something like, u = e^{-\\frac{r^2}{2}}, so if we solve this for r, we get r=\\sqrt{-2\\ln(u)}.\nFrom these values, we can calculate our new x,y points as,\n\n\\begin{align}\nx &= r\\cos(\\theta) \\\\\ny &= r\\sin(\\theta).\n\\end{align}\n\nFinally, in order to specify the size and shape of the generated Gaussian distribution, we can use the standard deviation, \\sigma, and the mean, \\mu, like so:\n\n\\begin{align}\nz_1 &= x\\sigma + \\mu \\\\\nz_2 &= y\\sigma + \\mu.\n\\end{align}\n\nIn general, this can be written in code like so:\n# Box--Muller transform\nfunction cartesian_box_muller(input_pts, sigma, mu)\n r = sqrt(-2 * log(input_pts[1]))\n theta = 2 * pi * input_pts[2]\n\n return [sigma * r * cos(theta) + mu[1],\n sigma * r * sin(theta) + mu[2]]\n\nend\n\n\n\nWhich produces the following output\n\n \n \n\n\nNote that we have written the code to work on a single set of input values, but it could also be written to read in the entire distribution of points all at once.\nAs this particular technique is usually implemented in parallel, it's up to you to decided which is the fastest for your own individual use-case.\nAt this stage, we have a good idea of how the transform works, but some people shy away from the Cartesian method in practice and instead opt for the polar form, which will be discussed next!\nHow to use the Box—Muller transform in polar coordinates\nThe Cartesian form of the Box—Muller transform is relatively intuitive.\nThe polar method is essentially the same, but without the costly \\sin and \\cos operations.\nIn this case, we use the input values to create an initial radial point (to be scaled later):\n\nr_0 = \\sqrt{u_1^2 + u_2^2}.\n\nThis means that we are essentially trying to transform our set of u values into a new input value r_0.\nTo do this, we need to start with a uniformly distributed circle, so we must reject any values for u_1 and u_2 where r is either 0 or \\gt 1.\nThis also means that the initial distributions of u_1 and u_2 must range from -1 \\rightarrow +1.\nFrom here, we can use basic trigonometric identities to redefine the \\sin and \\cos to be\n\n\\begin{align}\n\\cos(\\theta) &= u_1/\\sqrt{r_0} \\\\\n\\sin(\\theta) &= u_2/\\sqrt{r_0}.\n\\end{align}\n\nThis changes the output equations to be\n\n\\begin{align}\nx &= r\\cos(\\theta) = \\sqrt{-2\\ln(r_0)}\\left(\\frac{u_1}{\\sqrt{r_0}}\\right) = u_1 \\sqrt{\\frac{-2\\ln(r_0)}{r_0}} \\\\\ny &= r\\sin(\\theta) = \\sqrt{-2\\ln(r_0)}\\left(\\frac{u_2}{\\sqrt{r_0}}\\right) = u_2 \\sqrt{\\frac{-2\\ln(r_0)}{r_0}}.\n\\end{align}\n\nAgain, the final values are:\n\n\\begin{align}\nz_1 &= \\sigma x + \\mu \\\\\nz_2 &= \\sigma y + \\mu.\n\\end{align}\n\nIn code, it might look like this:\n# Box--Muller transform\nfunction polar_box_muller(input_pts, sigma, mu)\n r_0 = input_pts[1]^2 + input_pts[2]^2\n\n # this method is only valid for points within the unit circle\n if r_0 == 0 || r_0 > 1\n return [NaN, NaN]\n end\n\n return [sigma * input_pts[1] * sqrt(-2 * log(r_0) / r_0) + mu[1],\n sigma * input_pts[2] * sqrt(-2 * log(r_0) / r_0) + mu[2]]\n\n\n\nThis will produce the following output:\n\n \n \n\n\nAgain, this is ultimately the same as the Cartesian method, except that it:\n\nRejects points in the initial distribution that are outside of the unit circle (also called rejection sampling)\nAvoids costly \\sin and \\cos operations\n\nPoint 2 means that the polar method should be way faster than the Cartesian one, but rejection sampling is somewhat interesting in it's own right, which we have discussed in a separate chapter\nExample Code\nThe example code here is straightforward: we start with a uniform distribution of points (both on a grid and a uniform random distribution) and then we preform the Box—Muller transform to see how far off it is from the Gaussian we expect.\nusing DelimitedFiles, LinearAlgebra\nusing Test\n\nfunction create_grid(n, endpoints)\n\n grid_extents = endpoints[2] - endpoints[1]\n\n # number of points along any given axis\n # For 2D, we take the sqrt(n) and then round up\n axis_num = ceil(Int, sqrt(n))\n\n # we are now rounding n up to the nearest square if it was not already one\n if sqrt(n) != axis_num\n n = axis_num^2\n end \n\n # Distance between each point\n dx = grid_extents / (axis_num)\n\n # Initializing the array, particles along the column, dimensions along rows\n a = zeros(n, 2)\n\n # This loops over the relevant dimensions\n for i = 1:axis_num\n for j = 1:axis_num\n a[(i - 1) * axis_num + j, :] .=\n [(i - 0.5) * dx + endpoints[1],\n (j - 0.5) * dx + endpoints[1]]\n end\n end\n\n return a\nend\n\nfunction create_rand_dist(n, endpoints)\n grid_extents = endpoints[2] - endpoints[1]\n return(rand(n,2) * grid_extents .+ endpoints[1]) \nend\n\n# This function reads in a pair of input points and performs the Cartesian\n# Box--Muller transform\nfunction cartesian_box_muller(input_pts, sigma, mu)\n r = sqrt(-2 * log(input_pts[1]))\n theta = 2 * pi * input_pts[2]\n\n return [sigma * r * cos(theta) + mu[1],\n sigma * r * sin(theta) + mu[2]]\n\nend\n\n# This function reads in a pair of input points and performs the Cartesian\n# Box--Muller transform\nfunction polar_box_muller(input_pts, sigma, mu)\n r_0 = input_pts[1]^2 + input_pts[2]^2\n\n # this method is only valid for points within the unit circle\n if r_0 == 0 || r_0 > 1\n return [NaN, NaN]\n end\n\n return [sigma * input_pts[1] * sqrt(-2 * log(r_0) / r_0) + mu[1],\n sigma * input_pts[2] * sqrt(-2 * log(r_0) / r_0) + mu[2]]\n\nend\n\nfunction is_gaussian(input_pts; bounds = [-1 1; -1 1], dx = 0.1,\n sigma = 1, mu = [0,0], threshold = 0.1)\n histogram = zeros(ceil(Int,(bounds[1,2]-bounds[1,1])/dx),\n ceil(Int,(bounds[2,2]-bounds[2,1])/dx))\n\n for i = 1:size(input_pts)[1]\n input_x = input_pts[i, 1]\n input_y = input_pts[i, 2]\n if !(isnan(input_x) || isnan(input_y))\n\n bin = CartesianIndex(ceil(Int, (input_x - bounds[1,1]) / dx),\n ceil(Int, (input_y - bounds[2,1]) / dx))\n\n if bin[1] 0 &&\n bin[2] 0\n histogram[bin] += 1\n end\n end\n end\n\n n = sum(histogram)\n normalize!(histogram)\n\n rms = 0\n for i = 1:size(histogram)[1]\n x = bounds[1,1] + i*dx\n for j = 1:size(histogram)[2]\n y = bounds[2,1] + j*dx\n gaussian_value = exp(-(((x+mu[1])^2)/(2*sigma^2) +\n ((y+mu[2])^2)/(2*sigma^2)))\n rms += (gaussian_value - histogram[i,j])^2\n end\n end\n\n return sqrt(rms/n) \n\n\nBibliography\n1.Box, George EP, A note on the generation of random normal deviates, 1958.2.Wikipedia: Box-Muller Transform, 2022.3.Wikipedia: Marsaglia Transform, 2022.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"IFS triangle 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"IFS square 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Simple Barnsley fern\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine random transform 0\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine random transform 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine random transform 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine random transform 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine fern transform 0\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine fern transform 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine fern transform 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Affine fern transform 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Fern twiddle 0\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Fern twiddle 1\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Fern twiddle 2\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Fern twiddle 3\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n"},"contents/computus/computus.html":{"url":"contents/computus/computus.html","title":"Computus","keywords":"","body":"The Easter Algorithm (Computus)\nThough the word Computus can technically describe any sort of computation [1] or else a set of medieval tables for calculating various astrological events [2], it is also one of the most common historical names for the calculation of the Christian holiday of Easter every year.\nNominally, Easter happens the Sunday after the first full moon after the spring equinox (roughly March 21st).\nThis particular full moon is known by a number of names, such as the Pink (Strawberry) Moon, Hunter's Moon, or the Snow Moon, along with several others.\nThe most common name for it is the paschal full moon, which translates to \"Passover\" in Greek and signifies an important Jewish festival.\nFor the first few centuries, the date of Easter each year was dictated by the Pope; however, after the church grew, it was no longer straightforward to communicate this date to all of Christendom.\nAs such, the church did what it could to algorithmically generate tables for clergy to determine the date of Easter each year.\nTo this day, the calculation of Easter still poses a problem, with western and eastern (orthodox) churches celebrating on different dates approximately 50% of the time.\nI'll be honest, there is a lot of good, Christian drama surrounding the calculation of this event and it's remarkably interesting to read about [3].\nSuffice it to say that the date of Easter bamboozled many historical scholars, with at least one algorithm appearing in the early archives of the now famous scientific journal of Nature [4].\nThe calculation was so complicated that even Frederick Gauss had to try his hand at it (and failed before being corrected by one of his students).\nEssentially, the date of Easter depends on both the lunar and solar cycles\nThe date of the paschal full moon, for example, is static in the lunar calendar, but it is not in the solar calendar.\nIn this way, computus is the act of mapping a lunar cycle onto the Gregorian (solar) calendar everyone knows and loves.\nBecause many different calendar systems have existed throughout history, there was a natural question as to which calendar system would be used to calculate the precise date of Easter.\nThe western churches chose the Gregorian calendar and the eastern churches chosethe Julian one, and this is one reason why western and eastern churches sometimes celebrate on different dates.\nThat said, the Gregorian calendar more accurately represents the true date of the paschal full moon, so the western church's approach ended up being more precise.\nThough there are many methods to calculate Easter, for now, we will focus only on Gauss's algorithm; however, we mayl certainly come back (in subsequent years) to incorporate other Easter algorithms if there is demand.\nThese algorithms are some of my favorite gems in the history of algorithm design because of all the drama surrounding the calculation of something that seems trivial!\nAfter all, how hard could it be to calculate Easter?\nGauss's Easter algorithm history\nGauss is known for a lot of things: Gaussian elimination, the Cooley-Tukey method before Cooley or Tukey even existed, Gauss's Law for electromagnetism, etc.\nOne thing he is not particularly well known for is an algorithm he devised in 1800, which was later corrected by his student Peter Paul Tittle in 1816.\nIn fact, there were a series of publications from Gauss in this era all relating to the precise date of Easter.\nThe legend goes that Gauss actually did not know his real birthday in the Gregorian calendar and used this same algorithm to determine it.\nApparently, his mother only told him that he was born on a Wednesday 8 days before Ascension Day in 1777, which corresponds to April 30th [3].\nHonestly, Gauss's Easter algorithm was the 19th century equivalent of undocumented code.\nI could imagine Gauss grumpily \"patching\" his method when users complained that it did not work on dates past 4200 or even certain dates within his own era!\nWhen some of his compatriots (such as Johann Lambert and Jean Joseph Delambre) expressed their concern over the method's performance, Gauss replied by saying,\n\nThe investigation by which the formula [...] is found is based on higher arithmetic, for which I presumably cannot refer to any publication.\n\nWhich was the 19th century equivalent of saying, \"you are too dumb to understand my genius.\"\nI have definitely met a few fledgling programmers who feel the same, but none of them were anywhere near as prolific as Gauss.\nOne of the most important fans of Gauss's work was Servois, who created a calendar based on Gauss's 1800 publication, shown below:\n\nThis calendar shows the date the paschal full moon, indicating that Easter will be the following Sunday [5].\nIn this table, a value greater than 22 indicates the full moon will be on the presented number (date) in March and a value less than 22 indicates the full moon will be on that date in April.\nThe y-axis of this table indicates the decade and the x-axis indicates the precise year.\nAdmittedly, the notation is a bit funky, but it was 1813.\nTimes were different then.\nThe task for this chapter will be to explain (to the best of my abilities) how one would go about using Gauss's Easter algorithm to calculate the date of Easter for any given year (within the limitations of the algorithm).\nBackground\nBecause Easter is the Sunday following the paschal full moon, which is the first full moon of spring, Gauss's algorithm is tasked at finding a way to map the lunar calendar to the Gregorian (solar) calendar.\nFor this reason, before discussing the algorithm, itself, we must first introduce both calendar systems.\nThe Gregorian (solar) calendar has been created to mark Earth's full revolution around the Sun, which is approximately 365.2425 days.\nUnfortunately, days are based on the Earth's rotation about its axis, not its revolution around the Sun, so the number of days in a year is not an integer number (such as 365).\nThis discrepancy has actually lead to a large number of calendar systems, including one invented by Gauss, himself [6].\nBefore the Gregorian calendar, there was another correction made from an old Roman calendar to set the days in a year to be 365.25 days.\nThis was called the Julian calendar.\nFrom there, the Julian calendar was further corrected to the Gregorian calendar with 365.2425 days.\nThough there is only a small change necessary to use Gauss's Easter algorithm for the Julian calendar, this will not be covered here; however, if you want to see this, we can add it in upon request.\nTo account for the non-integer nature of the Gregorian year, a leap day is celebrated on February 29th every 4 years, with exception of when the year is a multiple of 100, where no leap-day is observed; if the year is divisible by 400, however, a leap day is still observed.\nThis means that every 400 years, there are 97 leap days.\nThis is why a leap day was celebrated in 2020 and 2000, but was not in 1900.\nIf at this point, you feel like your favorite calendar system is held together by duct tape and string, you would be right.\nIn addition to the solar year, Gauss's Easter algorithm also needs to keep the lunar year into account.\nA lunar month corresponds to the time it takes the Moon to complete one full revolution around the Earth.\nIn most cases, this is approximately 27.5 days [7].\nThat said, space is complicated and the Moon is not the only revolving body.\nLunar phases are related to the time it takes for the Moon to return to its location in relation to the line connecting the Sun and Earth, as shown below:\n\nThis is called the synodic month and will be the approximation used for this chapter.\nBelow, we also show a snapshot of this simulation after 6 synodic months:\n\nHere, we show an outline of the Earth and Moon in an arbitrary initial position, each with an angle of -\\frac{\\pi}{4} from the horizontal axis.\nIn addition, we show the location of the Moon and Earth again after 6 synodic months and additional outlines for each intermediate synodic month.\nRed lines are drawn from the center of the sun to the moon to indicate the positioning of the moon in relation to the sun and earth.\nIn all positions, the Moon is hidden behind the Earth, creating the full moon phase.\nIn this way, the synodic month is the time between two consecutive phases, which is slightly longer than the time it takes to revolve around the Earth and return to the same angle (here \\frac{\\pi}{4}).\nEach synodic month is approximately 29.5 days, so a synodic year of 12 lunar months is 354 days, which is 11 days shorter than the normal 365 days in a Gregorian year.\nThe following is a pictorial representation of offset between a solar and lunar year:\n\nHere, we see the Sun at the center, with the Earth and Moon starting the year at an angle of -\\frac{\\pi}{4} from the horizontal axis.\nThe initial location of the Earth and Moon are shown as an outline with the letter \"A\" at their center.\nAfter a full synodic lunar year (12 lunar months), another outline of the Earth and Moon are shown at position B, and after a full Gregorian year, they are shown in position C.\nAn arc is then drawn showing the difference of 11 days between the Earth's position after a synodic year, and another arc is drawn to show the difference between the Moon's position after a full Gregorian year.\nBecause the synodic month and the solar year are not synchronized, the phase of the Moon will be different on the same day of the Gregorian year.\nThat said, the lunar and solar calendars will re-synchronize roughly every 19 years.\nFor example, if there is a new moon on January 1st, 2020, there will not be a new moon on January 1st, 2021; however, there will be a new moon on January 1st, 2039.\nThis 19-year cycle where the Moon and Sun are waiting to re-synchronize is known as the Metonic cycle and has been studied for centuries.\nThis cycle allows us to somewhat easily transition between solar and lunar calendars.\nIf we imagine any Gregorian date (let's say January 1st again for clarity), the moon could be in one of 19 different phases, as shown below:\n\nHere, we show each possible phase of the moon as an outline, but the actual phase as a grey circle.\nEssentially, by knowing what year we are on in the Metonic cycle, we can single out which phase of the moon we will see on any given date.\nThis is powerful and will allow us to find the next full moon by looking ahead a few days.\nAs a final note, there is a small offset in the Metonic cycle of 1 hour and 45 minutes every 19 years, so in 2500 years, it will be 8 days off, but that's a problem for people in 2500.\nFor now, we should be able to start discussing the algorithm, itself.\nThe algorithm\nAs alluded to in Gauss's quote above, the Easter algorithm is closer to a set of formulas than a method used to compute anything on a modern computer.\nThis is partially because of bad software engineering by Gauss and partially because computers did not really exist at that point.\nConsidering this method was literally called Computus, there probably was not much to compute at all at the time.\nNowadays, you could more easily find the date of Easter with loops and conditions, but this is the Arcane Algorithm Archive, and this is definitely an arcane algorithm, so let's go!\nFor this section, we will be following similar notation to Gauss's original 1800 work, which is a bit terse and hard to follow; however, each term is significantly meaningful.\nIf you are reading this and think you have a better way to present anything, please let us know (with an issue or pull request on github) and we can correct the text!\nThis method can be split into 2 parts:\n\nCalculating the days from March 21st to the next full moon\nCalculating the days from the full moon to the next Sunday\n\nIn the following sections, we will discuss both individually.\nCalculating the date of the next full moon\nTo start, we will be calculating d, which is the number of days until the next full moon from March 21st (the first day of spring according to the pope).\nTo calculate this, we need to first calculate a number of auxiliary variables, starting with the current year's location on the Metonic calendar,\n\na = \\text{year}~\\%~19,\n\nwhere \\% is the modulo operator and 19 is the length of the Metonic calendar in years.\nFrom here, we also need to calculate an offset to a, and for this we need the century index,\n\nk = \\left\\lfloor\\frac{\\text{year}}{100}\\right\\rfloor,\n\nwhere \\lfloor\\cdot\\rfloor is the flooring operation of rounding the value down to the nearest integer.\nWith this, we can calculate the shift in the Metonic cycle to be,\n\np = \\left\\lfloor\\frac{13+8k}{25}\\right\\rfloor.\n\nThis expression represents the fact that the Metonic cycle will be 8 days off every 2500 years and adds an additional offset of 13 to ensure the Metonic cycle aligns with empirical observation.\nAt this point, we know what year we are at on the Metonic calendar and have calculated an offset accordingly; however, we have yet to take into account leap years.\nAs stated above, there are 97 leap days every 400 years, and the calculation of p above requires correction for the 3 leap days missed.\nIf one adds 25 leap days per century and subtracts k, they will find 96 leap days every 400 years instead, which is a close approximation, but off by one.\nThis accounts for the fact that leap days are not celebrated on years that are multiples of 100.\nThere is, however, an exception made for years that are multiples of 400, which is why Gauss calculated an additional variable,\n\nq = \\left\\lfloor\\frac{k}{4}\\right\\rfloor.\n\nThis means that 100-k-q will provide the appropriate number of leap days every 400 years.\nAfter this is found, we then calculate a sum of all offsets within a lunar month.\n\nM = (15-p+k-q)~\\%~30\n\nwhere 15 is an offset indicating that the full moon on year 0 is 15 days from March 21st, p is the number of days we are off from the Metonic cycle, and k-q are non-observed leap days.\nThe values of p, k, and q all provide century offsets, which means that the value of M will provide the correct starting point for each century.\nThe \\%30 (modulo 30 arithmetic) constricts our calculation to be within a single synodic lunar month of approximately 30 days.\nWith all this information, we can finally calculate the number of days from March 21st until the first full moon, as\n\nd = (19a+M)~\\%~30\n\nAgain, the \\%~30 operation makes sense here because there is no way the next full moon could occur over 30 days (a synodic lunar month) from March 21st.\nAt first glance, this is simply a calculation of a (where we are on the Metonic cycle) with some offset, M.\nThis is true, but there is an additional multiplicative factor of 19.\nOne might be tempted to wave this away by saying, \"19 is the number of years in the Metonic cycle, so this makes sense!\"\nThe truth is that that 19 is a bit more complicated.\nThis calculation is a calculation of days, not years.\nEvery 12 lunar months is roughly 354 days, which is 11 days shorter than 365.\nThis means that every year in the Metonic cycle, the lunar phase will be 11 days behind.\nIt just so happens that -11~\\%~30 = 19.\nThus, 19a is a combination of this 11 day offset and the fact that we are using modulo 30 arithmetic.\nAfter 19 years, the lunar calendar will be a full 365 days off in the solar calendar, but again, we only care about day offsets in this calculation.\nNo one really keeps track of lunar years, just solar ones.\nRegardless, we now have d, the number of days until the next full moon.\nInterestingly, this is all the information necessary to replicate Servois's table above.\nFrom here, we simply need to create a two-dimensional array with the decade on the y axis and year on the x axis and set within it the value of (21+d)~\\%~31, where the 21 represents the 21st of March, and the \\%~31 comes from the fact that there are 31 days in March.\nFor example, if we were to do this computation for the years from 2000 to 2099, we would find the following table:\n\nWhich shows that the date of the paschal full moon for 2020 is April 9th.\nNow we can move on to finding the precise date of Easter, which should be the following Sunday\nCalculating the next Sunday\nThis calculation will take a few variables from the previous section, namely k-q (the number of non-observed leap days), and d (the number of days since March 21st to the next full moon).\nFor the last calculation, we synchronized the number of days in a lunar month with the Gregorian (solar) calendar.\nFor this computation, we do similar operations, but for the weekly calendar of 7 days, this value will be stored in e.\nThe first step is calculating the correct offset each century based on the fact that Jan 1st, in year 1 was a Friday and then accounting for all the non-observed leap days (k-q),\n\nN = (4+k-q)~\\%~7.\n\nFrom here, things get a little tricky.\nThere are 52 weeks in a year, but 52\\times7=364, meaning we are essentially one day off every year, with exception of leap years where we are two days off.\nAs an example, look at the following table\n\n\n\nJanuary 1st\nDay of the week\nSpecial considerations\n\n\n\n\n2017\nSunday\nNone\n\n\n2018\nMonday\nNone\n\n\n2019\nTuesday\nNone\n\n\n2020\nWednesday\nLeap Year\n\n\n2021\nFriday\nNone\n\n\n\nSimply put, every year we should subtract one day of the week, but on leap years, we should subtract 2.\nTo keep tabs on this, we need two separate counts,\n\nb = \\text{year}~\\%~4,\n\nand\n\nc = \\text{year}~\\%~7,\n\nwhere b keeps track of leap years, and c simply increments by 1 every year.\nThrough a bit of mathematical magic, we can find the expression 2b+4c, which will be -1 in modulo 7 arithmetic for every year, except leap years where it will be -2.\nWith all these terms put together, we can finally calculate the offset from the full moon to Easter Sunday as\n\ne = (2b+4c+6d+N)~\\%~7.\n\nHere, all terms are described as above and the multiplicative factor of 6 to d will provide an offset to Sunday without correcting for leap days.\nWrapping up\nAt this point, we can calculate the days from March 21st to Easter Sunday to be d+e.\nIn particular\n\n\\text{Easter} = \\left\\{\n \\begin{align}\n d+e+22\\text{ March}& \\qquad \\text{if } 22+d+e\\leq31 \\\\\n d+e-9\\text{ April}& \\qquad \\text{if } 22+d+e>31 \\\\\n \\end{align}\n\\right.\n\nRemember that March 22nd would be the first possible day to celebrate Easter because March 21st would be the first possible full moon of spring.\nAll said, there are a few exceptions that are somewhat tricky to understand, namely:\n\ne = \\left\\{\n \\begin{align}\n &e \\\\\n &-1, \\qquad \\text{if } d=29 \\text{ and } e=6 \\text{ or } d=28, e=6, \\text{ and } a>10\n \\end{align}\n\\right.\n\nThese conditionals are placed on the output of d and correspond to when Easter falls on April 26th (if d = 29) or April 25th (if d = 28).\nIn both of these cases, we are setting e=-1, which has the effect of removing a week from the date of Easter.\nFor example, an Easter that would be celebrated on the 26th would instead be celebrated on the 19th.\nMany say that these conditionals are placed on the output for historical reasons, but between you and me, I feel there is a more mathematical reason that I do not fully understand.\nAfter all, why is the correction for d=28 only placed on the Easter date output on the second half of the Metonic cycle (if a > 10)?\nIf you think you might have a better idea as to why these dates are corrected as such, please let us know!\nAs mentioned, this particular algorithm does not make use of any standard computational techniques.\nThere are no loops, conditionals, stacks, or queues.\nHowever, there can be no doubt that Gauss was a master of his craft.\nThe sheer complexity of this calculation both baffles and astounds me -- especially because this was done hundreds of years before computational thinking became common-place.\nSure, this can be done straightforwardly with a calculator, but it is no doubt an algorithm worth discussing and celebrating for its ingenuity at the time of creation.\nVideo Explanation\nHere is a video describing key elements of Gauss's Easter Algorithm:\n\n\n\n\nExample Code\nUnlike many other chapters in the Algorithm Archive, this particular method can be described almost entirely by mathematical expressions.\nAs such, it should be relatively straightforward to implement in a number of different languages, and I heartily encourage you to do so!\nFor now, we have the code outputting a tuple of d and e, so users can use this to calculate either the date of Easter or Servois's table, depending on their use-case; however, please modify the code however you wish!\nfunction computus(year; servois=false)\n\n # Year's position on the 19 year metonic cycle\n a = mod(year, 19)\n\n # Century index\n k = fld(year, 100)\n\n # Shift of metonic cycle, add a day offset every 300 years\n p = fld(13 + 8 * k, 25)\n\n # Correction for non-observed leap days\n q = fld(k, 4)\n\n # Correction to starting point of calculation each century\n M = mod(15 - p + k - q, 30)\n\n # Number of days from March 21st until the full moon\n d = mod(19 * a + M, 30)\n\n # Returning if user wants value for Servois' table\n if servois\n return string(mod(21 + d,31))\n end\n\n # Finding the next Sunday\n # Century-based offset in weekly calculation\n N = mod(4 + k - q, 7)\n\n # Correction for leap days\n b = mod(year, 4)\n c = mod(year, 7)\n\n # Days from d to next Sunday\n e = mod(2 * b + 4 * c + 6 * d + N, 7)\n\n # Historical corrections for April 26 and 25\n if (d == 29 && e == 6) || (d == 28 && e == 6 && a > 10)\n e = -1\n end\n\n # Determination of the correct month for Easter\n if(22 + d + e > 31)\n return \"April \" * string(d + e - 9)\n else\n return \"March \" * string(22 + d + e)\n end\nend\n\n# Here, we will output the date of the Paschal full moon\n# (using Servois notation), and Easter for 2020-2030\n\na = collect(2020:2030)\nservois_numbers = computus.(a; servois=true)\neaster_dates = computus.(a)\n\nprintln(\"The following are the dates of the Paschal full moon (using Servois \" *\n \"notation) and the date of Easter for 2020-2030 AD:\")\nprintln(\"Year\\tServois number\\tEaster\")\nfor i = 1:length(a)\n println(\"$(a[i])\\t$(servois_numbers[i])\\t\\t$(easter_dates[i])\")\nend\n\ndata Mode = Servois | Easter\n\ncomputus :: Mode -> Int -> String\ncomputus mode year =\n case mode of\n Servois ->\n -- Value for Servois' table\n show $ (21 + d) `mod` 31\n Easter ->\n -- Determination of the correct month for Easter\n if 22 + d + f > 31\n then \"April \" ++ show (d + f - 9)\n else \"March \" ++ show (22 + d + f)\n where\n a, b, c, d, e, f, k, m, n, p, q :: Int\n -- Year's position on the 19 year metonic cycle\n a = year `mod` 19\n -- Century index\n k = year `div` 100\n -- Shift of metonic cycle, add a day offset every 300 years\n p = (13 + 8 * k) `div` 25\n -- Correction for non-observed leap days\n q = k `div` 4\n -- Correction to starting point of calculation each century\n m = (15 - p + k - q) `mod` 30\n -- Number of days from March 21st until the full moon\n d = (19 * a + m) `mod` 30\n -- Finding the next Sunday\n -- Century-based offset in weekly calculation\n n = (4 + k - q) `mod` 7\n -- Correction for leap days\n b = year `mod` 4\n c = year `mod` 7\n -- Days from d to next Sunday\n e = (2 * b + 4 * c + 6 * d + n) `mod` 7\n -- Historical corrections for April 26 and 25\n f =\n if (d == 29 && e == 6) || (d == 28 && e == 6 && a > 10)\n then -1\n else e\n\n-- Here, we will output the date of the Paschal full moon\n-- (using Servois notation), and Easter for 2020-2030\nmain :: IO ()\nmain = do\n let years :: [Int]\n years = [2020 .. 2030]\n servoisNumbers, easterDates :: [String]\n servoisNumbers = map (computus Servois) years\n easterDates = map (computus Easter) years\n putStrLn \"The following are the dates of the Paschal full moon (using Servois notation) and the date of Easter for 2020-2030 AD:\"\n putStrLn \"Year\\tServois number\\tEaster\"\n let conc :: Int -> String -> String -> String\n conc y s e = show y ++ \"\\t\" ++ s ++ \"\\t\\t\" ++ e\n mapM_ putStrLn $ zipWith3 conc years servoisNumbers easterDates\n\ndef computus(year, servois=False):\n # Year's position on the 19-year metonic cycle\n a = year % 19\n\n # Century index\n k = year // 100\n\n # Shift of metonic cycle, add a day offset every 300 years\n p = (13 + 8 * k) // 25\n\n # Correction for non-observed leap days\n q = k // 4\n\n # Correction to starting point of calculation each century\n M = (15 - p + k - q) % 30\n\n # Number of days from March 21st until the full moon\n d = (19 * a + M) % 30\n\n # Returning if user wants value for Servois' table\n if servois:\n return str((21 + d) % 31)\n\n # Finding the next Sunday\n # Century-based offset in weekly calculation\n N = (4 + k - q) % 7\n\n # Correction for leap days\n b = year % 4\n c = year % 7\n\n # Days from d to next Sunday\n e = (2 * b + 4 * c + 6 * d + N) % 7\n\n # Historical corrections for April 26 and 25\n if (d == 29 and e == 6) or (d == 28 and e == 6 and a > 10):\n e = -1\n\n # Determination of the correct month for Easter\n if 22 + d + e > 31:\n return \"April \" + str(d + e - 9)\n else:\n return \"March \" + str(22 + d + e)\n\n\n# Here, we will output the date of the Paschal full moon\n# (using Servois notation), and Easter for 2020-2030\n\nprint(\n \"The following are the dates of the Paschal full moon (using Servois\",\n \"notation) and the date of Easter for 2020-2030 AD:\",\n)\nprint(\"Year\\tServois number\\tEaster\")\nfor year in range(2020, 2031):\n print(f\"{year}\\t{computus(year, servois=True)}\\t\\t{computus(year)}\")\n\ndef computus(year, servois = false)\n # Year's position on the 19 year metonic cycle\n a = year % 19\n\n # Century index\n k = year // 100\n\n # Shift of metonic cycle, add a day offset every 300 years\n p = (13 + 8 * k) // 25\n\n # Correction for non-observed leap days\n q = k // 4\n\n # Correction to starting point of calculation each century\n m = (15 - p + k - q) % 30\n\n # Number of days from March 21st until the full moon\n d = (19 * a + m) % 30\n\n # Returning if user wants value for Servois' table\n if servois\n return ((21 + d) % 31).to_s\n end\n\n # Finding the next Sunday\n # Century-based offset in weekly calculation\n n = (4 + k - q) % 7\n\n # Correction for leap days\n b = year % 4\n c = year % 7\n\n # Days from d to next Sunday\n e = (2 * b + 4 * c + 6 * d + n) % 7\n\n # Historical corrections for April 26 and 25\n if (d == 29 && e == 6) || (d == 28 && e == 6 && a > 10)\n e = -1\n end\n\n # Determination of the correct month for Easter\n if (22 + d + e > 31)\n return \"April \" + (d + e - 9).to_s\n else\n return \"March \" + (22 + d + e).to_s\n end\nend\n\n# Here, we will output the date of the Paschal full moon\n# (using Servois notation), and Easter for 2020-2030\ndef main\n a = (2020..2030).to_a\n servois_numbers = a.map { |y| computus(y, servois = true) }\n easter_dates = a.map { |y| computus(y) }\n\n puts \"The following are the dates of the Paschal full moon (using Servois \" +\n \"notation) and the date of Easter for 2020-2030 AD:\"\n puts \"Year\\tServois number\\tEaster\"\n a.each_index { |i|\n puts \"#{a[i]}\\t#{servois_numbers[i]}\\t\\t#{easter_dates[i]}\"\n }\nend\n\nmain\n\nfn computus(year: usize, servois: bool) -> String {\n // Year's position on the 19 year metonic cycle\n let a = year % 19;\n\n // Century index\n let k = year / 100; // NOTE: dividing integers always truncates the result\n\n // Shift of metonic cycle, add a day offset every 300 years\n let p = (13 + 8 * k) / 25;\n\n // Correction for non-observed leap days\n let q = k / 4;\n\n // Correction to starting point of calculation each century\n let m = (15 - p + k - q) % 30;\n\n // Number of days from March 21st until the full moon\n let d = (19 * a + m) % 30;\n\n if servois {\n return ((21 + d) % 31).to_string();\n }\n\n // Finding the next Sunday\n // Century-based offset in weekly calculation\n let n = (4 + k - q) % 7;\n\n // Correction for leap days\n let b = year % 4;\n let c = year % 7;\n\n // Days from d to next Sunday\n let temp_e = ((2 * b + 4 * c + 6 * d + n) % 7) as isize;\n\n // Historical corrections for April 26 and 25\n let e = if (d == 29 && temp_e == 6) || (d == 28 && temp_e == 6 && a > 10) {\n -1\n } else {\n temp_e\n };\n\n // Determination of the correct month for Easter\n if (22 + d) as isize + e > 31 {\n format!(\"April {}\", d as isize + e - 9)\n } else {\n format!(\"March {}\", 22 + d as isize + e)\n }\n}\n\nfn main() {\n // Here, we will output the date of the Paschal full moon\n // (using Servois notation), and Easter for 2020-2030\n\n let years = 2020..=2030;\n\n println!(\n \"The following are the dates of the Paschal full moon (using \\\n Servois notation) and the date of Easter for 2020-2030 AD:\"\n );\n println!(\"Year\\tServois number\\tEaster\");\n years.for_each(|year| {\n println!(\n \"{}\\t{:\nfunction Calculate-Computus([int]$Year, [switch]$Servois) {\n\n # Year's position on the 19 year metonic cycle\n $a = $Year % 19\n\n # Century index\n $k = [Math]::Floor($Year / 100)\n\n # Shift of metonic cycle, add a day offset every 300 years\n $p = [Math]::Floor((13 + 8 * $k) / 25)\n\n # Correction for non-observed leap days\n $q = [Math]::Floor($k / 4)\n\n # Correction to starting point of calculation each century\n $M = (15 - $p + $k - $q) % 30\n\n # Number of days from March 21st until the full moon\n $d = (19 * $a + $M) % 30\n\n # Returning if user wants value for Servois' table\n if($Servois) {\n return ((21 + $d) % 31).ToString()\n }\n\n # Finding the next Sunday\n # Century-based offset in weekly calculation\n $N = (4 + $k - $q) % 7\n\n # Correction for leap days\n $b = $Year % 4\n $c = $Year % 7\n\n # Days from d to next Sunday\n $e = (2 * $b + 4 * $c + 6 * $d + $N) % 7\n\n # Historical corrections for April 26 and 25\n if(($d -eq 29 -and $e -eq 6) -or ($d -eq 28 -and $e -eq 6 -and $a -gt 10)) {\n $e = -1\n }\n\n # Determination of the correct month for Easter\n if(22 + $d + $e -gt 31) {\n return \"April \" + ($d + $e - 9)\n }\n else {\n return \"March \" + (22 + $d + $e)\n }\n}\n\n\n# Here, we will output the date of the Paschal full moon\n# (using Servois notation), and Easter for 2020-2030\n\nWrite-Host \"The following are the dates of the Paschal full moon (using Servois\",\n \"notation) and the date of Easter for 2020-2030 AD:\"\nWrite-Host \"Year`tServois number`tEaster\"\nforeach($year in 2020..2030) {\n Write-Host \"$year`t$(Calculate-Computus $year -Servois)`t`t$(Calculate-Computus $year)\"\n}\n\n#include \n\nchar *computus(int year, int servois, char *out, size_t out_size) {\n // Year's position on the 19 year metonic cycle\n int a = year % 19;\n\n // Century index\n int k = year / 100;\n\n //Shift of metonic cycle, add a day offset every 300 years\n int p = (13 + 8 * k) / 25;\n\n // Correction for non-observed leap days\n int q = k / 4;\n\n // Correction to starting point of calculation each century\n int M = (15 - p + k - q) % 30;\n\n // Number of days from March 21st until the full moon\n int d = (19 * a + M) % 30;\n\n // Returning if user wants value for Servois' table\n if (servois) {\n snprintf(out, out_size, \"%d\",(21 + d) % 31);\n return out;\n }\n\n // Finding the next Sunday\n // Century-based offset in weekly calculation\n int N = (4 + k - q) % 7;\n\n // Correction for leap days\n int b = year % 4;\n int c = year % 7;\n\n // Days from d to next Sunday\n int e = (2 * b + 4 * c + 6 * d + N) % 7;\n\n // Historical corrections for April 26 and 25\n if ((d == 29 && e == 6) || (d == 28 && e == 6 && a > 10)) {\n e = -1;\n }\n\n if ((22 + d + e) > 31) {\n snprintf(out, out_size, \"April %d\", d + e - 9);\n } else {\n snprintf(out, out_size, \"March %d\", 22 + d + e);\n }\n\n return out;\n}\n\nint main() {\n char tmp1[9], tmp2[9];\n\n printf(\"The following are the dates of the Paschal full moon (using \"\n \"Servois notation) and the date of Easter for 2020-2030 AD:\\n\");\n\n printf(\"Year\\tServois number\\tEaster\\n\");\n\n for (int year = 2020; year \n#include \n#include \n\nstd::string computus(int year, bool servois = false) {\n // Year's position on the 19 year metonic cycle\n int a = year % 19;\n\n // Century index\n int k = year / 100;\n\n // Shift of metonic cycle, add a day offset every 300 years\n int p = (13 + 8 * k) / 25;\n\n // Correction for non-observed leap days\n int q = k / 4;\n\n // Correction to starting point of calculation each century\n int M = (15 - p + k - q) % 30;\n\n // Number of days from March 21st until the full moon\n int d = (19 * a + M) % 30;\n\n // Returning if user wants value for Servois' table\n if (servois) {\n return std::to_string((21 + d) % 31);\n }\n\n // Finding the next Sunday\n // Century-based offset in weekly calculation\n int N = (4 + k - q) % 7;\n\n // Correction for leap days\n int b = year % 4;\n int c = year % 7;\n\n // Days from d to next Sunday\n int e = (2 * b + 4 * c + 6 * d + N) % 7;\n\n // Historical corrections for April 26 and 25\n if ((d == 29 && e == 6) || (d == 28 && e == 6 && a > 10)) {\n e = -1;\n }\n\n // Determination of the correct month for Easter\n return 22 + d + e > 31 ? \"April \" + std::to_string(d + e - 9)\n : \"March \" + std::to_string(22 + d + e);\n}\n\n// Here, we will output the date of the Paschal full moon (using Servois\n// notation), and Easter for 2020-2030\nint main() {\n std::cout \n;;;; Gauss's Easter algorithm implementation\n\n(defun computus (year &optional (servois nil))\n \"Calculates the day of Easter for a given year and optionally its Servois number\"\n (let*\n ((a (mod year 19)) ; year's position on the 19 year metonic cycle\n (k (floor year 100)) ; century index\n (p (floor (+ 13 (* 8 k)) 25)) ; shift of metonic cycle, add a day offset every 300 years\n (q (floor k 4)) ; correction for non-observed leap days\n (m (mod (+ 15 (- p) k (- q)) 30)) ; correction to starting point of calculation each century\n (d (mod (+ (* 19 a) m) 30)) ; number of days from March 21st until the full moon\n (n (mod (+ 4 k (- q)) 7)) ; century-based offset in weekly calculation\n (b (mod year 4)) ; correction for leap days\n (c (mod year 7)) ; also a correction for leap days\n ;; days from d to next Sunday\n (e (mod (+ (* 2 b) (* 4 c) (* 6 d) n) 7)))\n ;; historical corrections for April 26 and 25\n (when (or (and (eql d 29) (eql e 6)) (and (eql d 28) (eql e 6) (> a 10)))\n (setf e -1))\n (values\n ;; determination of the correct month for Easter\n (if (> (+ 22 d e) 31)\n (format nil \"April ~a\" (+ d e -9))\n (format nil \"March ~a\" (+ 22 d e)))\n ;; optionally return a value for the Servois' table\n (if servois (mod (+ 21 d) 31)))))\n\n(format t \"~{~a~%~}\"\n '(\"The following are the dates of the Paschal full moon (using Servois\"\n \"notation) and the date of Easter for 2020-2030 AD:~%\"\n \"Year Servois number Easter\"))\n(loop for year from 2020 to 2030 do\n (multiple-value-bind (easter servois) (computus year t)\n (format t \"~8a~18a~a~%\" year servois easter)))\n\nimport strformat\n\nfunc computus(year: int, servois: bool = false): string =\n let\n # Year's position on the 19 year metonic cycle\n a = year mod 19\n # Century index\n k = year div 100\n # Shift of metonic cycle, add a day offset every 300 years\n p = (13 + 8 * k) div 25\n # Correction for non-observed leap days\n q = k div 4\n # Correction to starting point of calculation each century\n m = (15 - p + k - q) mod 30\n # Number of days from March 21st until the full moon\n d = (19 * a + m) mod 30\n # Returning of user wants value for Servois' table\n if servois:\n return $((21 + d) mod 31)\n let\n # Find the next Sunday\n # Century-based offset in weekly calculation\n n = (4 + k - q) mod 7\n # Correction for leap days\n b = year mod 4\n c = year mod 7\n # Days from d to next Sunday\n temp_e = (2 * b + 4 * c + 6 * d + n) mod 7\n # Historical corrections for April 26 and 25\n e = if (d == 29 and temp_e == 6) or (d == 28 and temp_e == 6 and a > 10):\n -1\n else:\n temp_e\n # Determination of the correct month for Easter\n if (22 + d + e) > 31:\n result = \"April {d + e - 9}\".fmt\n else:\n result = \"March {22 + d + e}\".fmt\n\nwhen isMainModule:\n echo \"The following are the dates of the Paschal full moon (using Servois \"\n echo \"notation) and the date of Easter for 2020-2030 AD:\"\n echo \"Year Servois number Easter\"\n for year in 2020..2030:\n echo \"{year} {computus(year, true):14} {computus(year, false):6}\".fmt\n\nobject GaussEaster {\n def computus(year : Int, servois: Boolean = false): String = {\n\n // Year's position on the 19 year metonic cycle\n val a = year % 19\n\n // Century index\n val k = (year / 100).toInt\n\n // Shift of metonic cycle, add a day offset every 300 years\n val p = ((13 + 8 * k) / 25).toInt\n\n // Correction for non-observed leap days\n val q = (k / 4).toInt\n\n // Correction to starting point of calculation each century\n val M = (15 - p + k - q) % 30\n\n // Number of days from March 21st until the full moon\n val d = (19 * a + M) % 30\n\n // Returning if user wants value for Servois' table\n if (servois) \n return s\"${(21 + d) % 31}\"\n\n // Finding the next Sunday\n // Century-based offset in weekly calculation\n val N = (4 + k - q) % 7\n\n // Correction for leap days\n val b = year % 4\n val c = year % 7\n\n // Days from d to next Sunday\n var e = (2 * b + 4 * c + 6 * d + N) % 7\n\n // Historical corrections for April 26 and 25\n if ((d == 29 && e == 6) || (d == 28 && e == 6 && a > 10)) {\n e = -1\n }\n\n // Determination of the correct month for Easter\n if (22 + d + e > 31) \n s\"April ${d + e - 9}\"\n else \n s\"March ${22 + d + e}\"\n }\n\n def main(args: Array[String]): Unit = {\n println(\"The following are the dates of the Paschal full moon (using \" + \n \"Servois notation) and the date of Easter for 2020-2030 AD:\\n\" +\n \"Year\\tServois number\\tEaster\\n\")\n\n for( year \nString computus(int year, {bool servois = false}) {\n // Year's position in metonic cycle\n final a = year % 19;\n\n // Century index\n final k = (year / 100).floor();\n\n // Shift of metonic cycle, add a day offset every 300 years\n final p = ((13 + 8 * k) / 25).floor();\n\n // Correction for non-observed leap days\n final q = (k / 4).floor();\n\n // Correction to starting point of calculation each century\n final M = (15 - p + k - q) % 30;\n\n // Number of days from March 21st until the full moon\n final d = (19 * a + M) % 30;\n\n // Returning if user wants value for Servois' table\n if (servois) {\n return ((21 + d) % 31).toString();\n }\n\n // Finding the next Sunday\n // Century-based offset in weekly calculation\n final N = (4 + k - q) % 7;\n\n // Correction for leap days\n final b = year % 4;\n final c = year % 7;\n\n // Days from d to next Sunday\n var e = (2 * b + 4 * c + 6 * d + N) % 7;\n\n // Historical corrections for April 26 and 25\n if (e == 6) {\n if (d == 29 || (d == 28 && a > 10)) {\n e = -1;\n }\n }\n\n // Determination of the correct month for Easter\n if (22 + d + e > 31) {\n return 'April ${d + e - 9}';\n } else {\n return 'March ${22 + d + e}';\n }\n}\n\nvoid main() {\n print(\"The following are the dates of the Paschal full moon (using Servois \" +\n \"notation) and the date of Easter for 2020-2030 AD:\");\n\n print(\"Year\\tServois number\\tEaster\");\n\n for (var year = 2020; year \n/**\n * In this code, the modulus operator is used.\n * However, this operator in javascript/typescript doesn't support negative numbers.\n * So, where there may be negative numbers, the function mod is used.\n * This function gives the modulo of any relative number a\n */\n\n/**\n * @param {number} a\n * @param {number} b\n * @returns {number}\n */\nfunction mod(a, b) {\n if (a 10)) {\n e = -1;\n }\n }\n\n // Determination of the correct month for Easter\n if (22 + d + e > 31) {\n return `April ${d + e - 9}`;\n } else {\n return `March ${22 + d + e}`;\n }\n}\n\nconsole.log(\n \"The following are the dates of the Paschal full moon (using Servois \" +\n \"notation) and the date of Easter for 2020-2030 AD:\"\n);\n\nconst values = [];\n\nfor (let year = 2020; year \n/**\n * In this code, the modulus operator is used.\n * However, this operator in javascript/typescript doesn't support negative numbers.\n * So, where there may be negative numbers, the function mod is used.\n * This function gives the modulo of any relative number a\n */\n\nfunction mod(a: number, b: number): number {\n if (a 10)) {\n e = -1;\n }\n }\n\n // Determination of the correct month for Easter\n if (22 + d + e > 31) {\n return `April ${d + e - 9}`;\n } else {\n return `March ${22 + d + e}`;\n }\n}\n\nconsole.log(\n \"The following are the dates of the Paschal full moon (using Servois \" +\n \"notation) and the date of Easter for 2020-2030 AD:\"\n);\n\n// Type of a line in the output table\ninterface IOutputLine {\n \"servois number\": number;\n easter: string;\n}\n\nconst values: IOutputLine[] = [];\n\nfor (let year = 2020; year \n\n\n\nBibliography\n1.Venerabilis, Beda and others, Bede, the Reckoning of Time, Liverpool University Press, 1999.2.Dictionary.com definition of computus, 2020.3.Bien, Reinhold, Gauss and beyond: The making of Easter algorithms, Springer, 2004.4.unknown, To find Easter: a new York correspondent sends us the following, 1876.5.Servois, M, 84 Calendrier, Annales de Mathématiques pures et appliquées.6.Standish, EM, The astronomical unit now, Cambridge University Press, 2004.7.Wikipedia: Lunar Month, 2020.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"Servois 1800 Colored Table\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Relative Orbits\" was created by Xadisten and was provided during a discussion on Twitch. It is licensed under the Creative Commons Attribution 4.0 International License.\nThe image \"Synodic Half Year\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Metonic shadows\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Full Year Orbit\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Servois 2000 Colored Table\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n"},"contents/gaussian_elimination/gaussian_elimination.html":{"url":"contents/gaussian_elimination/gaussian_elimination.html","title":"Gaussian Elimination","keywords":"","body":"Gaussian Elimination\nLet's say we have a system of equations,\n\n\\begin{align}\n2x + 3y + 4z &= 6 \\\\\nx + 2y + 3z &= 4 \\\\\n3x - 4y &= 10\n\\end{align}\n\nand we want to solve for x, y, and z.\nWell, one way to do this is with Gaussian Elimination, which you may have encountered before in a math class or two.\nThe first step is to transform the system of equations into a matrix by using the coefficients in front of each variable, where each row corresponds to another equation and each column corresponds to an independent variable like x, y, or z.\nFor the previous system of equations, this might look like this:\n\n\\left[\n\\begin{array}{ccc}\n2 & 3 & 4\\\\\n1 & 2 & 3\\\\\n3 & -4 & 0\n\\end{array}\n\\right]\n\\left[\n\\begin{array}{c}\nx \\\\\ny \\\\\nz\n\\end{array}\n\\right]\n=\n\\left[\n\\begin{array}{c}\n6 \\\\\n4 \\\\\n10\n\\end{array}\n\\right]\n\nOr more simply:\n\n\\left[\n\\begin{array}{ccc|c}\n2 & 3 & 4 & 6 \\\\\n1 & 2 & 3 & 4 \\\\\n3 & -4 & 0 & 10\n\\end{array}\n\\right]\n\nAt first, translating the set of equations into a matrix like this doesn't seem to help with anything, so let's think of this in another way.\nRow Echelon Form\nInstead of the complicated mess of equations shown above, imagine if the system looked like this:\n\n\\begin{align}\n2x + 3y + 4z &= 6 \\\\\ny + 2z &= 2 \\\\\n11z &= 18\n\\end{align}\n\nThen we could just solve for z and plug that value in to the top two equations to solve for x and y through a process known as back-substitution.\nIn matrix form, this set of equations would look like this:\n\n\\left[\n\\begin{array}{ccc|c}\n2 & 3 & 4 & 6 \\\\\n0 & 1 & 2 & 2 \\\\\n0 & 0 & 11 & 18\n\\end{array}\n\\right]\n\nThis matrix form has a particular name: Row Echelon Form.\nBasically, any matrix can be considered in row echelon form if the leading coefficient or pivot (the first non-zero element in every row when reading from left to right) is right of the pivot of the row above it.\nThis creates a matrix that sometimes resembles an upper-triangular matrix; however, that doesn't mean that all row-echelon matrices are upper-triangular.\nFor example, all of the following matrices are in row echelon form:\n\n\\left[\n\\begin{array}{ccc|c}\n2 & 3 & 4 & 6 \\\\\n0 & 1 & 2 & 2 \\\\\n0 & 0 & 11 & 18\n\\end{array}\n\\right]\n\\;,\\;\n\\left[\n\\begin{array}{ccc|c}\n5 & 4 & 0 & 10 \\\\\n0 & 0 & 5 & 7 \\\\\n0 & 0 & 0 & 1\n\\end{array}\n\\right]\n\\;,\\;\n\\left[\n\\begin{array}{ccccc}\n1 & -3 & 4 & 1 & 6 \\\\\n0 & 3 & 3 & 5 & 0 \\\\\n0 & 0 & 0 & 2 & 0\n\\end{array}\n\\right]\n\\;,\\;\n\\left[\n\\begin{array}{cc}\n1 & 2 \\\\\n2 & 0 \\\\\n0 & 0\n\\end{array}\n\\right]\n\nThe first two of these have the right dimensions to find a solution to a system of equations; however, the last two matrices are respectively under- and over-constrained, meaning they do not provide an appropriate solution to a system of equations.\nThat said, this doesn't mean that every matrix in the correct form can be solved either.\nFor example, if you translate the second matrix into a system of equations again, the last row translates into 0x+0y+0z=1, which is a contradiction.\nThis is due to the fact that the matrix is singular, and there are no solutions to this particular system.\nNevertheless, all of these matrices are in row echelon form.\nReduced Row Echelon Form\nRow echelon form is nice, but wouldn't it be even better if our system of equations looked simply like this:\n\n\\begin{align}\nx &= \\frac{18}{11} \\\\\ny &= \\frac{-14}{11} \\\\\nz &= \\frac{18}{11}\n\\end{align}\n\nThen we would know exactly what x, y, and z are without any fuss! In matrix form, it looks like this:\n\n\\left[\n\\begin{array}{ccc|c}\n1 & 0 & 0 & \\frac{18}{11} \\\\\n0 & 1 & 0 & \\frac{-14}{11} \\\\\n0 & 0 & 1 & \\frac{18}{11}\n\\end{array}\n\\right]\n\nThis introduces yet another matrix configuration: Reduced Row Echelon Form.\nA matrix is in reduced row echelon form if it satisfies the following conditions:\n\nIt is in row echelon form.\nEvery pivot is 1 and is the only nonzero entry in its column.\n\nAll the following examples are in the reduced row echelon form:\n\n\\left[\n\\begin{array}{ccc|c}\n1 & 0 & 0 & 8 \\\\\n0 & 1 & 0 & -3 \\\\\n0 & 0 & 1 & 9\n\\end{array}\n\\right]\n\\;,\\;\n\\left[\n\\begin{array}{ccc|c}\n1 & 4 & 0 & 9 \\\\\n0 & 0 & 1 & 7 \\\\\n0 & 0 & 0 & 1\n\\end{array}\n\\right]\n\\;,\\;\n\\left[\n\\begin{array}{cc}\n0 & 0 \\\\\n0 & 0 \\\\\n0 & 0\n\\end{array}\n\\right]\n\nAgain, only the first of these (the one that looks like an identity matrix) is desirable in the context of solving a system of equations, but transforming any matrix in this form gives us an immediate and definitive answer at the question: can I solve my system of equations?\nBeyond solving a system of equations, reshaping a matrix in this form makes it very easy to deduce other properties of the matrix, such as its rank — the maximum number of linearly independent columns.\nIn reduced row echelon form, the rank is simply the number of pivots.\nFor now, I hope the motivation is clear: we want to convert a matrix into row echelon and then reduced row echelon form to make large systems of equations trivial to solve, so we need some method to do that.\nIn general, the term Gaussian Elimination refers to the process of transforming a matrix into row echelon form, and the process of transforming a row echelon matrix into reduced row echelon form is called Gauss-Jordan Elimination.\nThat said, the notation here is sometimes inconsistent.\nSeveral authors use the term Gaussian Elimination to include Gauss-Jordan elimination as well.\nIn addition, the process of Gauss-Jordan elimination is sometimes called Back-substitution, which is also confusing because the term can also be used to mean solving a system of equations from row echelon form, without simplifying to reduced row echelon form.\nFor this reason, we will be using the following definitions in this chapter:\n\nGaussian Elimination: The process of transforming a matrix into row echelon form\nGauss-Jordan Elimination: The process of transforming a row echelon matrix into reduced row echelon form\nBack-substitution: The process of directly solving a row echelon matrix, without transforming into reduced row echelon form\n\nThe Analytical Method\nGaussian elimination is inherently analytical and can be done by hand for small systems of equations; however, for large systems, this (of course) become tedious and we will need to find an appropriate numerical solution.\nFor this reason, I have split this section into two parts. One will cover the analytical framework, and the other will cover an algorithm you can write in your favorite programming language.\nIn the end, reducing large systems of equations boils down to a game you play on a seemingly random matrix with 3 possible moves. You can:\n\nSwap any two rows.\nMultiply any row by a non-zero scale value.\nAdd any row to a multiple of any other row.\n\nThat's it.\nBefore continuing, I suggest you try to recreate the row echelon matrix we made above.\nThat is, do the following:\n\n\\left[\n\\begin{array}{ccc|c}\n2 & 3 & 4 & 6 \\\\\n1 & 2 & 3 & 4 \\\\\n3 & -4 & 0 & 10\n\\end{array}\n\\right]\n\\quad \\rightarrow \\quad\n\\left[\n\\begin{array}{ccc|c}\n2 & 3 & 4 & 6 \\\\\n0 & 1 & 2 & 2 \\\\\n0 & 0 & 11 & 18\n\\end{array}\n\\right]\n\nThere are plenty of different strategies you could use to do this, and no one strategy is better than the rest.\nOne method is to subtract a multiple of the top row from subsequent rows below it such that all values beneath the pivot value are zero.\nThis process might be easier if you swap some rows around first and can be performed for each pivot.\nAfter you get a row echelon matrix, the next step is to find the reduced row echelon form. In other words, we do the following:\n\n\\left[\n\\begin{array}{ccc|c}\n2 & 3 & 4 & 6 \\\\\n0 & 1 & 2 & 2 \\\\\n0 & 0 & 11 & 18\n\\end{array}\n\\right]\n\\quad \\rightarrow \\quad\n\\left[\n\\begin{array}{ccc|c}\n1 & 0 & 0 & \\frac{18}{11} \\\\\n0 & 1 & 0 & \\frac{-14}{11} \\\\\n0 & 0 & 1 & \\frac{18}{11}\n\\end{array}\n\\right]\n\nHere, the idea is similar to above and the same rules apply.\nIn this case, we might start from the right-most column and subtracts upwards instead of downwards.\nThe Computational Method\nThe analytical method for Gaussian Elimination may seem straightforward, but the computational method does not obviously follow from the \"game\" we were playing before.\nUltimately, the computational method boils down to two separate steps and has a complexity of \\mathcal{O}(n^3).\nAs a note, this process iterates through all the rows in the provided matrix.\nWhen we say \"current row\" (curr_row), we mean the specific row iteration number we are on at that time, and as before, the \"pivot\" corresponds to the first non-zero element in that row.\nStep 1\nFor each element in the pivot column under the current row, find the highest value and switch the row with the highest value with the current row.\nThe pivot is then considered to be the first element in the highest swapped row.\nFor example, in this case the highest value is 3:\n\n\\left[\n\\begin{array}{ccc|c}\n2 & 3 & 4 & 6 \\\\\n1 & 2 & 3 & 4 \\\\\n\\mathbf{3} & -4 & 0 & 10\n\\end{array}\n\\right]\n\nAfter finding this value, we simply switch the row with the 3 to the current row:\n\n\\left[\n\\begin{array}{ccc|c}\n\\mathbf{2} & \\mathbf{3} & \\mathbf{4} & \\mathbf{6} \\\\\n1 & 2 & 3 & 4 \\\\\n\\mathbf{3} & \\mathbf{-4} & \\mathbf{0} & \\mathbf{10}\n\\end{array}\n\\right]\n\\rightarrow\n\\left[\n\\begin{array}{ccc|c}\n\\mathbf{3} & \\mathbf{-4} & \\mathbf{0} & \\mathbf{10} \\\\\n1 & 2 & 3 & 4 \\\\\n\\mathbf{2} & \\mathbf{3} & \\mathbf{4} & \\mathbf{6}\n\\end{array}\n\\right]\n\nIn this case, the new pivot is 3.\nIn code, this process might look like this:\n# finding the maximum element for each column\nmax_index = argmax(abs.(A[row:end,col])) + row-1\n\n# Check to make sure matrix is good!\nif (A[max_index, col] == 0)\n println(\"matrix is singular!\")\n continue\nend\n\n# swap row with highest value for that column to the top\ntemp_vector = A[max_index, :]\nA[max_index, :] = A[row, :]\nA[row, :] = temp_vector\n\n// finding the maximum element\nfor (int i = row + 1; i Math.abs(a[pivot][col])) {\n pivot = i;\n }\n}\n\nif (a[pivot][col] == 0) {\n System.err.println(\"The matrix is singular\");\n continue;\n}\n\nif (row != pivot) {\n // Swap the row with the highest valued element\n // with the current row\n swapRow(a, col, pivot);\n}\n\nvoid swap_rows(double *a, const size_t i, const size_t pivot,\n const size_t cols) {\n\n for (size_t j = 0; j \nsize_t pivot = row;\n\nfor (size_t i = row + 1; i fabs(a[pivot * cols + col])) {\n pivot = i;\n }\n}\n\nif (a[pivot * cols + col] == 0) {\n printf(\"The matrix is singular.\\n\");\n continue;\n}\n\nif (col != pivot) {\n swap_rows(a, col, pivot, cols);\n}\n\n std::size_t pivot = i;\n\nfor (std::size_t j = i + 1; j fabs(eqns[pivot][i])) pivot = j;\n}\n\nif (eqns[pivot][i] == 0.0)\n continue; // But continuing to simplify the matrix as much as possible\n\nif (i != pivot) // Swapping the rows if new row with higher maxVals is found\n std::swap(eqns[pivot], eqns[i]); // C++ swap function\n\nswapRows :: Int -> Int -> Matrix a -> Matrix a\nswapRows r1 r2 m\n | r1 == r2 = m\n | otherwise =\n m //\n concat [[((r2, c), m ! (r1, c)), ((r1, c), m ! (r2, c))] | c \n(target, pivot) =\n maximumBy (compare `on` abs . snd) [(k, m ! (k, c)) | k \nlet pivot = row;\nfor (let i = row + 1; i Math.abs(a[pivot][col])) {\n pivot = i;\n }\n}\n\nif (a[pivot][col] === 0) {\n console.log(\"The matrix is singular.\");\n continue;\n}\n\nif (col !== pivot) {\n const t = a[col];\n a[col] = a[pivot];\n a[pivot] = t;\n}\n\n// 1. find highest value in column below row to be pivot\np, highest := r, 0.\nfor i, row := range a[r:] {\n if abs := math.Abs(row[c]); abs > highest {\n p = r + i\n highest = abs\n }\n}\nhighest = a[p][c] // correct sign\n\nif highest == 0. {\n if !singular {\n singular = true\n fmt.Println(\"This matrix is singular.\")\n }\n continue\n}\n\ntemp = A[pivot_row, :].copy()\nA[pivot_row, :] = A[max_i, :]\nA[max_i, :] = temp\n\n# Skip on singular matrix, not actually a pivot\nif A[pivot_row, pivot_col] == 0:\n continue\n\n // find the maximum element for this column\n let mut max_row = k;\n let mut max_value = a[(k, k)].abs();\n for row in (k + 1)..a.rows {\n if max_value \n\n\nAs a note, if the highest value is 0, the matrix is singular and the system has no single solution.\nThis makes sense because if the highest value in a column is 0, the entire column must be 0, thus there can be no unique solution when we read the matrix as a set of equations.\nThat said, Gaussian elimination is more general and allows us to continue, even if the matrix is not necessarily solvable as a set of equations.\nFeel free to exit after finding a 0 if your end-goal is to solve a system of equations.\nStep 2\nFor the row beneath the current pivot row and within the pivot column, find a fraction that corresponds to the ratio of the value in that column to the pivot, itself.\nAfter this, subtract the current pivot row multiplied by the fraction from each corresponding row element.\nThis process essentially subtracts an optimal multiple of the current row from each row underneath (similar to Step 3 from the above game).\nIdeally, this should always create a 0 under the current row's pivot value.\nFor example, in this matrix, the next row is 1 and the pivot value is 3, so the fraction is \\frac{1}{3}.\n\n\\rightarrow\n\\left[\n\\begin{array}{ccc|c}\n3 & -4 & 0 & 10 \\\\\n\\mathbf{1} & 2 & 3 & 4 \\\\\n2 & 3 & 4 & 6\n\\end{array}\n\\right] \\\\\n\\begin{align}\n f &= A(\\text{curr_row}, \\text{pivot}_{\\text{col}}) / A(\\text{pivot}_{\\text{row}}, \\text{pivot}_{\\text{col}}) \\\\\n &= \\frac{1}{3}\n\\end{align}\n\nAfter finding the fraction, we simply subtract \\text{current_row} - \\frac{1}{3}\\times \\text{pivot_row}, like so:\n\n\\left[\n\\begin{array}{ccc|c}\n3 & -4 & 0 & 10 \\\\\n\\mathbf{1} & \\mathbf{2} & \\mathbf{3} & \\mathbf{4} \\\\\n2 & 3 & 4 & 6\n\\end{array}\n\\right]\n\\rightarrow\n\\left[\n\\begin{array}{ccc|c}\n3 & -4 & 0 & 10 \\\\\n0 & \\mathbf{\\frac{10}{3}} & \\mathbf{3} & \\mathbf{\\frac{2}{3}}\n\\\\\n2 & 3 & 4 & 6\n\\end{array}\n\\right]\n\nAfter this, repeat the process for all other rows.\nHere is what it might look like in code:\n# Loop for all remaining rows\nfor i = (row+1):rows\n\n # finding fraction\n fraction = A[i,col]/A[row,col]\n\n # loop through all columns for that row\n for j = (col+1):cols\n\n # re-evaluate each element\n A[i,j] -= A[row,j]*fraction\n\n end\n\nfor (int i = row + 1; i \nfor (size_t i = row + 1; i \nfor (std::size_t j = i + 1; j \nsubRows ::\n Fractional a\n => (Int, Int) -- pivot location\n -> (Int, Int) -- rows to cover\n -> (Int, Int) -- columns to cover\n -> Matrix a\n -> Matrix a\nsubRows (r, c) (r1, rn) (c1, cn) m =\n accum\n (-)\n m\n [ ((i, j), m ! (i, c) * m ! (r, j) / m ! (r, c))\n | i \n| otherwise = go (r + 1, c + 1) $ subRows (r, c) (r + 1, rn) (c, cn) m'\n\nfor (let i = row + 1; i \nfor _, row := range a[r+1:] {\n // 3. find fraction from pivot value\n frac := row[c] / highest\n\n // 4. subtract row to set rest of column to zero\n for j := range row {\n row[j] -= frac * a[r][j]\n }\n\n // 5. ensure col goes to zero (no float rounding)\n row[c] = 0.\n}\n\n# Zero out elements below pivot\nfor r in range(pivot_row + 1, A.shape[0]):\n # Get fraction\n frac = -A[r, pivot_col] / A[pivot_row, pivot_col]\n # Add rows\n A[r, :] += frac * A[pivot_row, :]\n\n// Loop over all remaining rows\nfor i in k + 1..a.rows {\n // find the fraction\n let fraction = a[(i, k)] / a[(k, k)];\n\n // Loop through all columns for that row\n for j in (k + 1)..a.cols {\n // re-evaluate each element\n a[(i, j)] -= a[(k, j)] * fraction;\n }\n\n // set lower elements to 0\n a[(i, k)] = 0.0;\n}\n\n\n\nAll together\nWhen we put everything together, it looks like this:\nfunction gaussian_elimination!(A::Array{Float64,2})\n\n rows = size(A,1)\n cols = size(A,2)\n\n # Row index\n row = 1\n\n # Main loop going through all columns\n for col = 1:(cols-1)\n\n # finding the maximum element for each column\n max_index = argmax(abs.(A[row:end,col])) + row-1\n\n # Check to make sure matrix is good!\n if (A[max_index, col] == 0)\n println(\"matrix is singular!\")\n continue\n end\n\n # swap row with highest value for that column to the top\n temp_vector = A[max_index, :]\n A[max_index, :] = A[row, :]\n A[row, :] = temp_vector\n\n # Loop for all remaining rows\n for i = (row+1):rows\n\n # finding fraction\n fraction = A[i,col]/A[row,col]\n\n # loop through all columns for that row\n for j = (col+1):cols\n\n # re-evaluate each element\n A[i,j] -= A[row,j]*fraction\n\n end\n\n # Set lower elements to 0\n A[i,col] = 0\n end\n row += 1\n end\nend\n\nvoid gaussian_elimination(double *a, const size_t rows, const size_t cols) {\n size_t row = 0;\n\n for (size_t col = 0; col fabs(a[pivot * cols + col])) {\n pivot = i;\n }\n }\n\n if (a[pivot * cols + col] == 0) {\n printf(\"The matrix is singular.\\n\");\n continue;\n }\n\n if (col != pivot) {\n swap_rows(a, col, pivot, cols);\n }\n\n for (size_t i = row + 1; i \nvoid gaussianElimination(std::vector > &eqns) {\n // 'eqns' is the matrix, 'rows' is no. of vars\n std::size_t rows = eqns.size(), cols = eqns[0].size();\n\n for (std::size_t i = 0; i fabs(eqns[pivot][i])) pivot = j;\n }\n\n if (eqns[pivot][i] == 0.0)\n continue; // But continuing to simplify the matrix as much as possible\n\n if (i != pivot) // Swapping the rows if new row with higher maxVals is found\n std::swap(eqns[pivot], eqns[i]); // C++ swap function\n\n for (std::size_t j = i + 1; j \nswapRows :: Int -> Int -> Matrix a -> Matrix a\nswapRows r1 r2 m\n | r1 == r2 = m\n | otherwise =\n m //\n concat [[((r2, c), m ! (r1, c)), ((r1, c), m ! (r2, c))] | c (Int, Int) -- pivot location\n -> (Int, Int) -- rows to cover\n -> (Int, Int) -- columns to cover\n -> Matrix a\n -> Matrix a\nsubRows (r, c) (r1, rn) (c1, cn) m =\n accum\n (-)\n m\n [ ((i, j), m ! (i, c) * m ! (r, j) / m ! (r, c))\n | i Matrix a -> Matrix a\ngaussianElimination mat = go (r1, c1) mat\n\ndef gaussian_elimination(A):\n\n pivot_row = 0\n\n # Go by column\n for pivot_col in range(min(A.shape[0], A.shape[1])):\n\n # Swap row with highest element in col\n max_i = np.argmax(abs(A[pivot_row:, pivot_col])) + pivot_row\n\n temp = A[pivot_row, :].copy()\n A[pivot_row, :] = A[max_i, :]\n A[max_i, :] = temp\n\n # Skip on singular matrix, not actually a pivot\n if A[pivot_row, pivot_col] == 0:\n continue\n\n # Zero out elements below pivot\n for r in range(pivot_row + 1, A.shape[0]):\n # Get fraction\n frac = -A[r, pivot_col] / A[pivot_row, pivot_col]\n # Add rows\n A[r, :] += frac * A[pivot_row, :]\n\n pivot_row += 1\n\nstatic void gaussianElimination(double[][] a) {\n int row = 0;\n\n int rows = a.length;\n int cols = a[0].length;\n\n for (int col = 0; col Math.abs(a[pivot][col])) {\n pivot = i;\n }\n }\n\n if (a[pivot][col] == 0) {\n System.err.println(\"The matrix is singular\");\n continue;\n }\n\n if (row != pivot) {\n // Swap the row with the highest valued element\n // with the current row\n swapRow(a, col, pivot);\n }\n\n for (int i = row + 1; i \nfunction gaussianElimination(a) {\n const rows = a.length\n const cols = a[0].length\n let row = 0;\n for (let col = 0; col Math.abs(a[pivot][col])) {\n pivot = i;\n }\n }\n\n if (a[pivot][col] === 0) {\n console.log(\"The matrix is singular.\");\n continue;\n }\n\n if (col !== pivot) {\n const t = a[col];\n a[col] = a[pivot];\n a[pivot] = t;\n }\n\n for (let i = row + 1; i \nfunc gaussianElimination(a [][]float64) {\n singular := false\n rows := len(a)\n cols := len(a[0])\n\n for c, r := 0, 0; c highest {\n p = r + i\n highest = abs\n }\n }\n highest = a[p][c] // correct sign\n\n if highest == 0. {\n if !singular {\n singular = true\n fmt.Println(\"This matrix is singular.\")\n }\n continue\n }\n\n // 2. swap pivot with current row\n if p != r {\n a[r], a[p] = a[p], a[r]\n }\n\n for _, row := range a[r+1:] {\n // 3. find fraction from pivot value\n frac := row[c] / highest\n\n // 4. subtract row to set rest of column to zero\n for j := range row {\n row[j] -= frac * a[r][j]\n }\n\n // 5. ensure col goes to zero (no float rounding)\n row[c] = 0.\n }\n\n r++\n }\n}\n\nfn gaussian_elimination(a: &mut Matrix) {\n for k in 0..min(a.cols, a.rows) {\n // find the maximum element for this column\n let mut max_row = k;\n let mut max_value = a[(k, k)].abs();\n for row in (k + 1)..a.rows {\n if max_value \n\n\nTo be clear: if the matrix is found to be singular during this process, the system of equations is either over- or under-determined and no general solution exists.\nFor this reason, many implementations of this method will stop the moment the matrix is found to have no unique solutions.\nIn this implementation, we allowed for the more general case and opted to simply output when the matrix is singular instead.\nIf you intend to solve a system of equations, then it makes sense to stop the method the moment you know there is no unique solution, so some small modification of this code might be necessary!\nSo what do we do from here?\nWell, we continue reducing the matrix; however, there are two ways to do this:\n\nReduce the matrix further into reduced row echelon form with Gauss-Jordan elimination\nSolve the system directly with back-substitution if the matrix allows for such solutions\n\nLet's start with Gauss-Jordan Elimination and then back-substitution\nGauss-Jordan Elimination\nGauss-Jordan Elimination is precisely what we said above; however, in this case, we often work from the bottom-up instead of the top-down.\nWe basically need to find the pivot of every row and set that value to 1 by dividing the entire row by the pivot value.\nAfterwards, we subtract upwards until all values above the pivot are 0 before moving on to the next column from right to left (instead of left to right, like before).\nHere it is in code:\nfunction gauss_jordan_elimination!(A::Array{Float64,2})\n\n rows = size(A,1)\n cols = size(A,2)\n\n\n # After this, we know what row to start on (r-1)\n # to go back through the matrix\n row = 1\n for col = 1:cols-1\n if (A[row, col] != 0)\n\n # divide row by pivot and leaving pivot as 1\n for i = cols:-1:col\n A[row,i] /= A[row,col]\n end\n\n # subtract value from above row and set values above pivot to 0\n for i = 1:row-1\n for j = cols:-1:col\n A[i,j] -= A[i,col]*A[row,j]\n end\n end\n row += 1\n end\n end\nend\n\nvoid gauss_jordan(double *a, const size_t cols) {\n size_t row = 0;\n\n for (size_t col = 0; col col - 1; --i) {\n a[row * cols + i] /= a[row * cols + col];\n }\n\n for (size_t i = 0; i col - 1; --j) {\n a[i * cols + j] -= a[i * cols + col] * a[row * cols + j];\n }\n }\n\n row++;\n }\n }\n}\n\nvoid gaussJordan(std::vector > &eqns) {\n // 'eqns' is the (Row-echelon) matrix, 'rows' is no. of vars\n std::size_t rows = eqns.size();\n\n for (std::size_t i = rows - 1; i \n((r1, c1), (rn, cn)) = bounds mat\ngo (r, c) m\n | c == cn = m\n | pivot == 0 = go (r, c + 1) m\n | otherwise = go (r + 1, c + 1) $ subRows (r, c) (r + 1, rn) (c, cn) m'\n where\n (target, pivot) =\n maximumBy (compare `on` abs . snd) [(k, m ! (k, c)) | k \n# Assumes A is already row echelon form\ndef gauss_jordan_elimination(A):\n\n col = 0\n\n # Scan for pivots\n for row in range(A.shape[0]):\n while col = A.shape[1]:\n continue\n\n # Set each pivot to one via row scaling\n A[row, :] /= A[row, col]\n\n # Zero out elements above pivot\n for r in range(row):\n A[r, :] -= A[r, col] * A[row, :]\n\nstatic void gaussJordan(double[][] a) {\n int row = 0;\n\n int cols = a[0].length;\n\n for (int col = 0; col col - 1; i--) {\n // divide row by pivot so the pivot is set to 1\n a[row][i] /= a[row][col];\n }\n\n // subtract the value form above row and set values above pivot to 0\n for (int i = 0; i col - 1; j--) {\n a[i][j] -= a[i][col] * a[row][j];\n }\n }\n row++;\n }\n }\n}\n\nfunction gaussJordan(a) {\n const cols = a[0].length;\n let row = 0;\n\n for (let col = 0; col col - 1; --i) {\n a[row][i] /= a[row][col];\n }\n\n for (let i = 0; i col - 1; --j) {\n a[i][j] -= a[i][col] * a[row][j];\n }\n }\n\n ++row;\n }\n }\n}\n\nfunc gaussJordan(a [][]float64) {\n for r := len(a) - 1; r >= 0; r-- {\n // Find pivot col\n p := -1\n for c, cell := range a[r] {\n if cell != 0. {\n p = c\n break\n }\n }\n if p \nfn gauss_jordan(a: &mut Matrix) {\n let mut row = 0;\n for k in 0..(a.cols - 1) {\n if a[(row, k)] != 0.0 {\n for i in (k..a.cols).rev() {\n a[(row, i)] /= a[(row, k)];\n }\n\n for i in 0..row {\n for j in (k..a.cols).rev() {\n a[(i, j)] -= a[(i, k)] * a[(row, j)];\n }\n }\n\n row += 1;\n }\n }\n}\n\n\n\nAs a note: Gauss-Jordan elimination can also be used to find the inverse of a matrix by following the same procedure to generate a reduced row echelon matrix, but with an identity matrix on the other side instead of the right-hand side of each equation.\nThis process is straightforward but will not be covered here, simply because there are much faster numerical methods to find an inverse matrix; however, if you would like to see this, let me know and I can add it in for completeness.\nBack-substitution\nThe idea of back-substitution is straightforward: we create a matrix of solutions and iteratively solve for each variable by plugging in all variables before it.\nFor example, if our matrix looks like this:\n\n\\left[\n\\begin{array}{ccc|c}\n2 & 3 & 4 & 6 \\\\\n0 & 1 & 2 & 2 \\\\\n0 & 0 & 11 & 18\n\\end{array}\n\\right]\n\nWe can quickly solve 11z = 18 for z, and then use that to solve y + 2z = 2 for y by plugging in for z.\nAfter that, we simply need to solve 2x + 3y + 4z = 6 for x in a similar fashion.\nIn code, this involves keeping a rolling sum of all the values we substitute, subtracting that sum from the solution column and then dividing by the coefficient variable.\nIn code, it looks like this:\nfunction back_substitution(A::Array{Float64,2})\n\n rows = size(A,1)\n cols = size(A,2)\n\n # Creating the solution Vector\n soln = zeros(rows)\n\n for i = rows:-1:1\n sum = 0.0\n for j = rows:-1:i\n sum += soln[j]*A[i,j]\n end\n soln[i] = (A[i, cols] - sum) / A[i, i]\n end\n\n return soln\nend\n\nvoid back_substitution(const double *a, double *x, const int rows,\n const int cols) {\n\n for (int i = rows - 1; i >= 0; --i) {\n double sum = 0.0;\n\n for (int j = cols - 2; j > i; --j) {\n sum += x[j] * a[i * cols + j];\n }\n\n x[i] = (a[i * cols + cols - 1] - sum) / a[i * cols + i];\n }\n}\n\nstd::vector backSubs(const std::vector > &eqns) {\n // 'eqns' is matrix, 'rows' is no. of variables\n std::size_t rows = eqns.size();\n\n std::vector ans(rows);\n for (std::size_t i = rows - 1; i (0);\n }\n return ans;\n}\n\nfn back_substitution(a: &Matrix) -> Vec {\n let mut soln = vec![0.0; a.rows];\n\n soln[a.rows - 1] = a[(a.rows - 1, a.cols - 1)] / a[(a.rows - 1, a.cols - 2)];\n\n for i in (0..a.rows - 1).rev() {\n let mut sum = 0.0;\n for j in (i..a.rows).rev() {\n sum += soln[j] * a[(i, j)];\n }\n soln[i] = (a[(i, a.cols - 1)] - sum) / a[(i, i)];\n }\n\n soln\n}\n\ngaussJordan :: (Fractional a, Eq a) => Matrix a -> Matrix a\ngaussJordan mat = go (r1, c1) mat\n where\n ((r1, c1), (rn, cn)) = bounds mat\n go (r, c) m\n | c == cn = m\n\n# Assumes A has a unique solution and A in row echelon form\ndef back_substitution(A):\n\n sol = np.zeros(A.shape[0]).T\n\n # Go by pivots along diagonal\n for pivot_i in range(A.shape[0] - 1, -1, -1):\n s = 0\n for col in range(pivot_i + 1, A.shape[1] - 1):\n s += A[pivot_i, col] * sol[col]\n sol[pivot_i] = (A[pivot_i, A.shape[1] - 1] - s) / A[pivot_i, pivot_i]\n\n return sol\n\nstatic double[] backSubstitution(double[][] a) {\n int rows = a.length;\n int cols = a[0].length;\n\n double[] solution = new double[rows];\n\n for (int i = rows - 1; i >= 0; i--) {\n double sum = 0;\n\n for (int j = cols - 2; j > i; j--) {\n sum += solution[j] * a[i][j];\n }\n solution[i] = (a[i][cols - 1] - sum) / a[i][i];\n }\n return solution;\n}\n\nfunction backSubstitution(a) {\n const rows = a.length;\n const cols = a[0].length;\n const sol = [];\n\n for (let i = rows - 1; i >= 0; --i) {\n\n let sum = 0;\n for (let j = cols - 2; j > i; --j) {\n sum += sol[j] * a[i][j];\n }\n\n sol[i] = (a[i][cols - 1] - sum) / a[i][i];\n }\n return sol;\n}\n\nfunc backSubstitution(a [][]float64) []float64 {\n rows := len(a)\n cols := len(a[0])\n x := make([]float64, rows)\n for r := rows - 1; r >= 0; r-- {\n sum := 0.\n\n for c := cols - 2; c > r; c-- {\n sum += x[c] * a[r][c]\n }\n\n x[r] = (a[r][cols-1] - sum) / a[r][r]\n }\n return x\n}\n\n\n\nVisual Representation\nWe have thus far used Gaussian elimination as a method to solve a system of equations; however, there is often a much easier way to find a similar solution simply by plotting each row in our matrix.\nFor the case of 2 equations and 2 unknowns, we would plot the two lines corresponding to each equation and the (x, y) location of their point of intersection would be the solution for x and y.\nSimilarly, for the case of 3 equations and 3 unknowns, we would plot 3 planes and the (x, y, z) location of their point of intersection would be the solution for x, y, and z.\nWhat, then, is the point of Gaussian elimination if we can simply plot our set of equations to find a solution?\nWell, this analogy breaks down quickly when we start moving beyond 3D, so it is obvious we need some method to deal with higher-dimensional systems.\nThat said, it is particularly interesting to see what happens as we plot our matrix during Gaussian elimination for the 3D case.\n\n\n \nYour browser does not support the video tag.\n\n\n\nAs we can see in the above visualization, the planes wobble about in 3D until they reach row echelon form, where one plane is parallel to the x and y axes.\nAt this point, it's trivial to find the z-coordinate for the solution because it's simply the z intercept of the parallel plane.\nFrom there, the matrices become even easier to interpret as they move to the reduced row echelon form.\nIn this form, the solution is simply the x, y, and z intercepts of the appropriate planes.\nThis visualization might have been obvious for some readers, but I found it particularly enlightening at first.\nBy performing Gaussian elimination, we are manipulating our planes such that they can be interpreted at a glance -- which is precisely the same thing we are doing with the matrix interpretation!\nConclusions\nAnd with that, we have two possible ways to reduce our system of equations and find a solution.\nIf we are sure our matrix is not singular and that a solution exists, it's fastest to use back-substitution to find our solution.\nIf no solution exists or we are trying to find a reduced row echelon matrix, then Gauss-Jordan elimination is best.\nAs we said at the start, the notation for Gaussian Elimination is rather ambiguous in the literature, so we are hoping that the definitions provided here are clear and consistent enough to cover all the bases.\nAs for what's next... Well, we are in for a treat!\nThe above algorithm clearly has 3 for loops and has a complexity of \\sim O(n^3), which is abysmal!\nIf we can reduce the matrix to a specifically tridiagonal matrix, we can actually solve the system in \\sim O(n)!\nHow? Well, we can use an algorithm known as the Tri-Diagonal Matrix Algorithm (TDMA) also known as the Thomas Algorithm.\nThere are also plenty of other solvers that do similar things that we will get to in due time.\nVideo Explanation\nHere's a video describing Gaussian elimination:\n\n\n\n\nExample Code\nfunction gaussian_elimination!(A::Array{Float64,2})\n\n rows = size(A,1)\n cols = size(A,2)\n\n # Row index\n row = 1\n\n # Main loop going through all columns\n for col = 1:(cols-1)\n\n # finding the maximum element for each column\n max_index = argmax(abs.(A[row:end,col])) + row-1\n\n # Check to make sure matrix is good!\n if (A[max_index, col] == 0)\n println(\"matrix is singular!\")\n continue\n end\n\n # swap row with highest value for that column to the top\n temp_vector = A[max_index, :]\n A[max_index, :] = A[row, :]\n A[row, :] = temp_vector\n\n # Loop for all remaining rows\n for i = (row+1):rows\n\n # finding fraction\n fraction = A[i,col]/A[row,col]\n\n # loop through all columns for that row\n for j = (col+1):cols\n\n # re-evaluate each element\n A[i,j] -= A[row,j]*fraction\n\n end\n\n # Set lower elements to 0\n A[i,col] = 0\n end\n row += 1\n end\nend\n\nfunction back_substitution(A::Array{Float64,2})\n\n rows = size(A,1)\n cols = size(A,2)\n\n # Creating the solution Vector\n soln = zeros(rows)\n\n for i = rows:-1:1\n sum = 0.0\n for j = rows:-1:i\n sum += soln[j]*A[i,j]\n end\n soln[i] = (A[i, cols] - sum) / A[i, i]\n end\n\n return soln\nend\n\n\nfunction gauss_jordan_elimination!(A::Array{Float64,2})\n\n rows = size(A,1)\n cols = size(A,2)\n\n\n # After this, we know what row to start on (r-1)\n # to go back through the matrix\n row = 1\n for col = 1:cols-1\n if (A[row, col] != 0)\n\n # divide row by pivot and leaving pivot as 1\n for i = cols:-1:col\n A[row,i] /= A[row,col]\n end\n\n # subtract value from above row and set values above pivot to 0\n for i = 1:row-1\n for j = cols:-1:col\n A[i,j] -= A[i,col]*A[row,j]\n end\n end\n row += 1\n end\n end\nend\n\nfunction main()\n A = [2. 3 4 6;\n 1 2 3 4;\n 3 -4 0 10]\n\n gaussian_elimination!(A)\n println(A)\n\n gauss_jordan_elimination!(A)\n println(A)\n\n soln = back_substitution(A)\n println(soln)\n\nend\n\nmain()\n\n#include \n#include \n#include \n\nvoid swap_rows(double *a, const size_t i, const size_t pivot,\n const size_t cols) {\n\n for (size_t j = 0; j fabs(a[pivot * cols + col])) {\n pivot = i;\n }\n }\n\n if (a[pivot * cols + col] == 0) {\n printf(\"The matrix is singular.\\n\");\n continue;\n }\n\n if (col != pivot) {\n swap_rows(a, col, pivot, cols);\n }\n\n for (size_t i = row + 1; i = 0; --i) {\n double sum = 0.0;\n\n for (int j = cols - 2; j > i; --j) {\n sum += x[j] * a[i * cols + j];\n }\n\n x[i] = (a[i * cols + cols - 1] - sum) / a[i * cols + i];\n }\n}\n\nvoid gauss_jordan(double *a, const size_t cols) {\n size_t row = 0;\n\n for (size_t col = 0; col col - 1; --i) {\n a[row * cols + i] /= a[row * cols + col];\n }\n\n for (size_t i = 0; i col - 1; --j) {\n a[i * cols + j] -= a[i * cols + col] * a[row * cols + j];\n }\n }\n\n row++;\n }\n }\n}\n\nint main() {\n double a[3][4] = {{3.0, 2.0, -4.0, 3.0},\n {2.0, 3.0, 3.0, 15.0},\n {5.0, -3.0, 1.0, 14.0}};\n\n gaussian_elimination((double *)a, 3, 4);\n\n printf(\"Gaussian elimination:\\n\");\n for (size_t i = 0; i \n#include \n#include \n#include \n#include \n#include \n\n\nvoid gaussianElimination(std::vector > &eqns) {\n // 'eqns' is the matrix, 'rows' is no. of vars\n std::size_t rows = eqns.size(), cols = eqns[0].size();\n\n for (std::size_t i = 0; i fabs(eqns[pivot][i])) pivot = j;\n }\n\n if (eqns[pivot][i] == 0.0)\n continue; // But continuing to simplify the matrix as much as possible\n\n if (i != pivot) // Swapping the rows if new row with higher maxVals is found\n std::swap(eqns[pivot], eqns[i]); // C++ swap function\n\n for (std::size_t j = i + 1; j > &eqns) {\n // 'eqns' is the (Row-echelon) matrix, 'rows' is no. of vars\n std::size_t rows = eqns.size();\n\n for (std::size_t i = rows - 1; i backSubs(const std::vector > &eqns) {\n // 'eqns' is matrix, 'rows' is no. of variables\n std::size_t rows = eqns.size();\n\n std::vector ans(rows);\n for (std::size_t i = rows - 1; i (0);\n }\n return ans;\n}\n\n\nvoid printMatrix(const std::vector > &matrix) {\n for (std::size_t row = 0; row > equations{\n {2, 3, 4, 6},\n {1, 2, 3, 4},\n {3, -4, 0, 10}};\n\n std::cout ans = backSubs(equations);\n std::cout \n// submitted by jess 3jane\n\nuse std::cmp::min;\nuse std::ops::{Index, IndexMut};\n\npub struct Matrix {\n rows: usize,\n cols: usize,\n data: Vec,\n}\n\nimpl Matrix {\n fn new(rows: usize, cols: usize, data: &[f64]) -> Matrix {\n Matrix {\n rows,\n cols,\n data: data.to_vec(),\n }\n }\n\n fn swap_rows(&mut self, a: usize, b: usize) {\n for col in 0..self.cols {\n self.data.swap(a * self.cols + col, b * self.cols + col);\n }\n }\n}\n\nimpl Index for Matrix {\n type Output = f64;\n fn index(&self, (row, col): (usize, usize)) -> &f64 {\n &self.data[row * self.cols + col]\n }\n}\n\nimpl IndexMut for Matrix {\n fn index_mut(&mut self, (row, col): (usize, usize)) -> &mut f64 {\n &mut self.data[row * self.cols + col]\n }\n}\n\nfn gaussian_elimination(a: &mut Matrix) {\n for k in 0..min(a.cols, a.rows) {\n // find the maximum element for this column\n let mut max_row = k;\n let mut max_value = a[(k, k)].abs();\n for row in (k + 1)..a.rows {\n if max_value Vec {\n let mut soln = vec![0.0; a.rows];\n\n soln[a.rows - 1] = a[(a.rows - 1, a.cols - 1)] / a[(a.rows - 1, a.cols - 2)];\n\n for i in (0..a.rows - 1).rev() {\n let mut sum = 0.0;\n for j in (i..a.rows).rev() {\n sum += soln[j] * a[(i, j)];\n }\n soln[i] = (a[(i, a.cols - 1)] - sum) / a[(i, i)];\n }\n\n soln\n}\n\nfn main() {\n // The example matrix from the text\n let mut a = Matrix::new(\n 3,\n 4,\n &vec![2.0, 3.0, 4.0, 6.0, 1.0, 2.0, 3.0, 4.0, 3.0, -4.0, 0.0, 10.0],\n );\n\n gaussian_elimination(&mut a);\n gauss_jordan(&mut a);\n let soln = back_substitution(&a);\n println!(\"Solution: {:?}\", soln);\n}\n\nimport Data.Array\nimport Data.Function (on)\nimport Data.List (intercalate, maximumBy)\nimport Data.Ratio\n\ntype Matrix a = Array (Int, Int) a\n\ntype Vector a = Array Int a\n\nswapRows :: Int -> Int -> Matrix a -> Matrix a\nswapRows r1 r2 m\n | r1 == r2 = m\n | otherwise =\n m //\n concat [[((r2, c), m ! (r1, c)), ((r1, c), m ! (r2, c))] | c (Int, Int) -- pivot location\n -> (Int, Int) -- rows to cover\n -> (Int, Int) -- columns to cover\n -> Matrix a\n -> Matrix a\nsubRows (r, c) (r1, rn) (c1, cn) m =\n accum\n (-)\n m\n [ ((i, j), m ! (i, c) * m ! (r, j) / m ! (r, c))\n | i Matrix a -> Matrix a\ngaussianElimination mat = go (r1, c1) mat\n where\n ((r1, c1), (rn, cn)) = bounds mat\n go (r, c) m\n | c == cn = m\n | pivot == 0 = go (r, c + 1) m\n | otherwise = go (r + 1, c + 1) $ subRows (r, c) (r + 1, rn) (c, cn) m'\n where\n (target, pivot) =\n maximumBy (compare `on` abs . snd) [(k, m ! (k, c)) | k Matrix a -> Matrix a\ngaussJordan mat = go (r1, c1) mat\n where\n ((r1, c1), (rn, cn)) = bounds mat\n go (r, c) m\n | c == cn = m\n | m ! (r, c) == 0 = go (r, c + 1) m\n | otherwise = go (r + 1, c + 1) $ subRows (r, c) (r1, r - 1) (c, cn) m'\n where\n m' = accum (/) m [((r, j), m ! (r, c)) | j Matrix a -> Vector a\nbackSubstitution m = sol\n where\n ((r1, _), (rn, cn)) = bounds m\n sol =\n listArray (r1, rn) [(m ! (r, cn) - sum' r) / m ! (r, r) | r Matrix a -> String\nprintM m =\n let ((r1, c1), (rn, cn)) = bounds m\n in unlines\n [ intercalate \"\\t\" [show $ m ! (r, c) | c Vector a -> String\nprintV = unlines . map show . elems\n\nmain :: IO ()\nmain = do\n let mat = [2, 3, 4, 6, 1, 2, 3, 4, 3, -4, 0, 10] :: [Ratio Int]\n m = listArray ((1, 1), (3, 4)) mat\n putStrLn \"Original Matrix:\"\n putStrLn $ printM m\n putStrLn \"Echelon form\"\n putStrLn $ printM $ gaussianElimination m\n putStrLn \"Reduced echelon form\"\n putStrLn $ printM $ gaussJordan $ gaussianElimination m\n putStrLn \"Solution from back substitution\"\n putStrLn $ printV $ backSubstitution $ gaussianElimination m\n\nimport numpy as np\n\ndef gaussian_elimination(A):\n\n pivot_row = 0\n\n # Go by column\n for pivot_col in range(min(A.shape[0], A.shape[1])):\n\n # Swap row with highest element in col\n max_i = np.argmax(abs(A[pivot_row:, pivot_col])) + pivot_row\n\n temp = A[pivot_row, :].copy()\n A[pivot_row, :] = A[max_i, :]\n A[max_i, :] = temp\n\n # Skip on singular matrix, not actually a pivot\n if A[pivot_row, pivot_col] == 0:\n continue\n\n # Zero out elements below pivot\n for r in range(pivot_row + 1, A.shape[0]):\n # Get fraction\n frac = -A[r, pivot_col] / A[pivot_row, pivot_col]\n # Add rows\n A[r, :] += frac * A[pivot_row, :]\n\n pivot_row += 1\n\n\n# Assumes A is already row echelon form\ndef gauss_jordan_elimination(A):\n\n col = 0\n\n # Scan for pivots\n for row in range(A.shape[0]):\n while col = A.shape[1]:\n continue\n\n # Set each pivot to one via row scaling\n A[row, :] /= A[row, col]\n\n # Zero out elements above pivot\n for r in range(row):\n A[r, :] -= A[r, col] * A[row, :]\n\n\n# Assumes A has a unique solution and A in row echelon form\ndef back_substitution(A):\n\n sol = np.zeros(A.shape[0]).T\n\n # Go by pivots along diagonal\n for pivot_i in range(A.shape[0] - 1, -1, -1):\n s = 0\n for col in range(pivot_i + 1, A.shape[1] - 1):\n s += A[pivot_i, col] * sol[col]\n sol[pivot_i] = (A[pivot_i, A.shape[1] - 1] - s) / A[pivot_i, pivot_i]\n\n return sol\n\n\ndef main():\n A = np.array([[2, 3, 4, 6],\n [1, 2, 3, 4,],\n [3, -4, 0, 10]], dtype=float)\n\n print(\"Original\")\n print(A, \"\\n\")\n\n gaussian_elimination(A)\n print(\"Gaussian elimination\")\n print(A, \"\\n\")\n\n print(\"Back subsitution\")\n print(back_substitution(A), \"\\n\")\n\n gauss_jordan_elimination(A)\n print(\"Gauss-Jordan\")\n print(A, \"\\n\")\n\n\nif __name__ == \"__main__\":\n main()\n\nimport java.util.Arrays;\n\npublic class GaussianElimination {\n\n static void gaussianElimination(double[][] a) {\n int row = 0;\n\n int rows = a.length;\n int cols = a[0].length;\n\n for (int col = 0; col Math.abs(a[pivot][col])) {\n pivot = i;\n }\n }\n\n if (a[pivot][col] == 0) {\n System.err.println(\"The matrix is singular\");\n continue;\n }\n\n if (row != pivot) {\n // Swap the row with the highest valued element\n // with the current row\n swapRow(a, col, pivot);\n }\n\n for (int i = row + 1; i col - 1; i--) {\n // divide row by pivot so the pivot is set to 1\n a[row][i] /= a[row][col];\n }\n\n // subtract the value form above row and set values above pivot to 0\n for (int i = 0; i col - 1; j--) {\n a[i][j] -= a[i][col] * a[row][j];\n }\n }\n row++;\n }\n }\n }\n\n static double[] backSubstitution(double[][] a) {\n int rows = a.length;\n int cols = a[0].length;\n\n double[] solution = new double[rows];\n\n for (int i = rows - 1; i >= 0; i--) {\n double sum = 0;\n\n for (int j = cols - 2; j > i; j--) {\n sum += solution[j] * a[i][j];\n }\n solution[i] = (a[i][cols - 1] - sum) / a[i][i];\n }\n return solution;\n }\n\n static void swapRow(double[][] a, int rowA, int rowB) {\n double[] temp = a[rowA];\n a[rowA] = a[rowB];\n a[rowB] = temp;\n }\n\n public static void main(String[] args) {\n double[][] a = {\n { 3, 2, -4, 3 },\n { 2, 3, 3, 15 },\n { 5, -3, 1, 14 }\n };\n\n gaussianElimination(a);\n System.out.println(\"Gaussian elimination:\");\n Arrays.stream(a).forEach(x -> System.out.println(Arrays.toString(x)));\n\n gaussJordan(a);\n System.out.println(\"\\nGauss-Jordan:\");\n Arrays.stream(a).forEach(x -> System.out.println(Arrays.toString(x)));\n\n System.out.println(\"\\nSolutions:\");\n System.out.println(Arrays.toString(backSubstitution(a)));\n }\n}\n\nfunction gaussianElimination(a) {\n const rows = a.length\n const cols = a[0].length\n let row = 0;\n for (let col = 0; col Math.abs(a[pivot][col])) {\n pivot = i;\n }\n }\n\n if (a[pivot][col] === 0) {\n console.log(\"The matrix is singular.\");\n continue;\n }\n\n if (col !== pivot) {\n const t = a[col];\n a[col] = a[pivot];\n a[pivot] = t;\n }\n\n for (let i = row + 1; i = 0; --i) {\n\n let sum = 0;\n for (let j = cols - 2; j > i; --j) {\n sum += sol[j] * a[i][j];\n }\n\n sol[i] = (a[i][cols - 1] - sum) / a[i][i];\n }\n return sol;\n}\n\nfunction gaussJordan(a) {\n const cols = a[0].length;\n let row = 0;\n\n for (let col = 0; col col - 1; --i) {\n a[row][i] /= a[row][col];\n }\n\n for (let i = 0; i col - 1; --j) {\n a[i][j] -= a[i][col] * a[row][j];\n }\n }\n\n ++row;\n }\n }\n}\n\nfunction printMatrixRow(row) {\n const text = row\n .map(v => (v \n// Package demonstrates Gaussian Elimination\npackage main\n\nimport (\n \"fmt\"\n \"math\"\n)\n\nfunc gaussianElimination(a [][]float64) {\n singular := false\n rows := len(a)\n cols := len(a[0])\n\n for c, r := 0, 0; c highest {\n p = r + i\n highest = abs\n }\n }\n highest = a[p][c] // correct sign\n\n if highest == 0. {\n if !singular {\n singular = true\n fmt.Println(\"This matrix is singular.\")\n }\n continue\n }\n\n // 2. swap pivot with current row\n if p != r {\n a[r], a[p] = a[p], a[r]\n }\n\n for _, row := range a[r+1:] {\n // 3. find fraction from pivot value\n frac := row[c] / highest\n\n // 4. subtract row to set rest of column to zero\n for j := range row {\n row[j] -= frac * a[r][j]\n }\n\n // 5. ensure col goes to zero (no float rounding)\n row[c] = 0.\n }\n\n r++\n }\n}\n\nfunc gaussJordan(a [][]float64) {\n for r := len(a) - 1; r >= 0; r-- {\n // Find pivot col\n p := -1\n for c, cell := range a[r] {\n if cell != 0. {\n p = c\n break\n }\n }\n if p = 0; r-- {\n sum := 0.\n\n for c := cols - 2; c > r; c-- {\n sum += x[c] * a[r][c]\n }\n\n x[r] = (a[r][cols-1] - sum) / a[r][r]\n }\n return x\n}\n\nfunc printMatrixRow(row []float64) {\n fmt.Print(\"[\")\n for _, cell := range row {\n fmt.Printf(\"%9.4f \", cell)\n }\n fmt.Println(\"]\")\n}\n\nfunc printMatrix(a [][]float64) {\n for _, row := range a {\n printMatrixRow(row)\n }\n fmt.Println()\n}\n\nfunc main() {\n a := [][]float64{\n {2, 3, 4, 6},\n {1, 2, 3, 4},\n {3, -4, 0, 10},\n }\n fmt.Println(\"Original Matrix:\")\n printMatrix(a)\n\n fmt.Println(\"Gaussian elimination:\")\n gaussianElimination(a)\n printMatrix(a)\n\n gaussJordan(a)\n fmt.Println(\"Gauss-Jordan:\")\n printMatrix(a)\n\n fmt.Println(\"Solutions are:\")\n x := backSubstitution(a)\n printMatrixRow(x)\n}\n\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe animation \"GEvis\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/quantum_systems/quantum_systems.html":{"url":"contents/quantum_systems/quantum_systems.html","title":"Quantum Systems","keywords":"","body":"Quantum Systems\nAs I am sure you have heard, the quantum world is weird.\nAs you deal with progressively smaller and smaller systems, at some point, it becomes less accurate to describe objects as particles.\nInstead, it is better to describe objects as probability densities.\nThese densities are easiest to understand in terms of wavefunctions, which are complex functions characterizing a quantum system's behavior.\nAgain, this is pretty common knowledge; however, there is a distinct lack of readable literature on how to simulate quantum systems, even though there are numerous methods for exactly that!\nThis section will deal with the computation of quantum states with classical machines.\nNow, I know what you are thinking, \"Wait. Why are we simulating quantum systems on classical computers? Why not simulate it with some sort of experiment or with quantum computers?\"\nWell, here's where the notation gets really sticky.\nThere is a clear difference between quantum computers and quantum simulators.\nA quantum computer is the quantum analog to a classical computer, replacing bits with qubits by using quantum information theory.\nQuantum computers are usually thought of as a way to use quantum mechanics to eventually solve real-world problems with new quantum algorithms.\nBoth Grover's and Shor's algorithms are good examples of cases where quantum computation could greatly change the landscape of modern computation as we know it!\nQuantum simulators on the other hand are quantum systems used to better understand quantum mechanics.\nThese will often come in the form of experimental quantum systems that express quantum behavior and allow us to better understand other areas of quantum systems.\nIn other words, quantum simulators are general techniques to study quantum systems on quantum hardware; however, quantum computers are quantum hardware used for the explicit purpose of quantum computation with qubits.\nBecause supercomputers are not great at performing quantum computations, certain quantum simulators exist as a building block for quantum computation.\nA universal quantum simulator is often called a quantum computer for this reason.\nThe truth is that quantum simulators are hard to make in laboratories, so simulating quantum systems on classical hardware is as good as we can do in most cases.\nThis section is devoted to all the different methods currently used to solve complex quantum systems, so let's start with the Schrödinger Equation, which has many different formulations.\nHere is the easiest one to explain:\n\ni \\hbar \\frac{\\partial \\Psi(\\mathbf{r},t)}{\\partial t} = \\left[-\\frac{\\hbar^2}{2m} \\nabla^2 + V(\\mathbf{r},t) \\right] \\Psi(\\mathbf{r},t)\n\nWhere \\Psi(\\mathbf{r},t) is a quantum wavefunction, V(\\mathbf{r},t) is a trapping potential, \\nabla^2 is a Laplacian, \\mathbf{r} is some sort of spatial component, and t is time.\nThere is a lot to take in here; however, it's ultimately just some time derivative on the left-hand side and a spatial derivative (with some extra steps) on the right-hand side.\nIn this way, it isn't too different from the diffusion (heat) equation:\n\n\\frac{\\partial\\phi(\\mathbf{r},t)}{\\partial t} = D \\nabla^2 \\phi(\\mathbf{r},t)\n\nwhere D is some positive definite matrix and \\phi(\\mathbf{r},t) is the density (or temperature) of the system.\nIn fact, this is why one of the most common types of quantum simulation is sometimes called diffusion Monte Carlo.\nThere really isn't that much of a difference between the two systems in terms of how they are simulated on classical hardware... but we are getting ahead of ourselves.\nFor now, let's talk about how quantum mechanics differs from classical mechanics and how we can use this to our advantage.\nProbability Density\nQuantum mechanics works fundamentally differently than classical mechanics in physics.\nThe wavefunction can be thought of as a set of all possible states for an object to be in, where there is some probability for the particle to be found in each state.\nThis means that it is not possible to say that a particle is at a particular location, and instead we often say that it could be at any location with probability, as shown in the probability density:\n\nP(\\mathbf{r}, t) = |\\Psi(\\mathbf{r},t)|^2 = \\Psi(\\mathbf{r},t)^{*}\\Psi(\\mathbf{r},t)\n\nHere, there are 2 things to note:\n\nThe absolute value squared of a complex parameter \\Psi(\\mathbf{r},t) is a dot product (inner product) between a complex function and it's Hermitian conjugate. This means the value will always be real, while the wavefunction, itself, might not be.\nAs you have probably heard, once a wavefunction is observed it collapses onto a single state. This can be simply interpreted as absolute knowledge of the particle's location. A probability density doesn't make sense if we know where the particle is!\n\nNow, to be clear: the probabilities must all sum to 1, or (more formally):\n\n\\int_{-\\infty}^{+\\infty}|\\Psi(\\mathbf{r},t)|^2 d\\mathbf{r} = 1\n\nThis simply means that the probability of finding our quantum particle somewhere in real space is 1.\nIn other words, our particle must exist somewhere in the known universe.\nAs another note: Just like position space can be parameterized by a position vector \\textbf{x}, wavefunctions can also be parameterized by a wave vector \\textbf{k} in frequency space.\nAny wavevector \\textbf{k} has the same units as reciprocal space and is thus analogous to angular frequency \\omega.\nOften times, the wavevector space is called momentum space, which makes sense when considering the de Broglie formula:\n\np = \\frac{h}{\\lambda} = \\frac{2 \\pi h}{2 \\pi \\lambda} = \\hbar k\n\nwhere h is Planck's constant and \\lambda is the wavelength.\nThis means that we can ultimately move between position and momentum space by using Fourier Transforms, which is incredibly useful in a number of cases!\nEven though the relation between position and momentum space is an essential cornerstone of understanding modern quantum mechanics, it is difficult to understand at a fundamental level.\nPosition space and momentum space are related by a Fourier transform; however, the rather hand-wavey argument above might not have been convincing enough and it does not offer any intuitive description of why the Fourier transform comes into this discussion at all.\nThe easiest way to understand this might be to look at the Heisenberg uncertainty principle, which is a fundamental relation between position and momentum space.\nHeisenberg Uncertainty Principle\nSimply put, the Heisenberg uncertainty principle states that we cannot definitely know both the position and momentum of a quantum particle.\nIn particular, it says:\n\n\\sigma_x \\sigma_p \\geq \\frac{\\hbar}{2}\n\nwhere \\hbar is Planck's constant and \\sigma_q = \\sqrt{\\frac{1}{N}\\sum_{i=1}^{N}(q_i-\\mu)^2}.\nIn this case, \\sigma is the standard deviation, \\mu is the statistical mean of your distribution, N is the number of points sampled, q_i is the value for each point i, and q stands for r or p.\nUltimately, this means that if we have a higher precision in position space, we will have a lower precision in momentum space.\nThe converse is also true: a higher precision in momentum space will lead to a lower precision in position space.\nThis makes the most sense if we imagine having a Gaussian-like probability density (|\\Psi(x)|^2) in position space, which will provide a Gaussian-like density when in momentum space.\nHere, we see that if we have a broader distribution in one space, we must have a thinner distribution in the opposite space, as shown here:\n\n \n\n\n\nBecause the density can be interpreted as \"the probability of finding a quantum particle at any provided location in position (x_i) or momentum (k_i) space, the interpretation is clear: the more we understand about a particle's position, the less we understand about it's momentum.\nThis is a powerful statement and should be given some thought.\nTo me, the most interesting part of this description is not the physical interpretation, but the fact that this act of transforming between larger and smaller Gaussians is precisely what Fourier transforms do!\nThis further strengthens our argument from before.\nPosition and momentum space are related by the Fourier transform!\nThis is the heart of several algorithms for simulating quantum systems, including the Split-operator method.\nAt least for me, I found this description to be intuitive, but not complete.\nThere is still something missing from the picture that should be described in more depth, and to do that, we need to dive deeper into the heart of quantum mechanics and into Hamiltonians.\nHamiltonian\nHere is the Schrödinger equation again:\n\ni \\hbar \\frac{\\partial \\Psi(\\mathbf{r},t)}{\\partial t} = \\left[-\\frac{\\hbar^2}{2m} \\nabla^2 + V(\\mathbf{r},t) \\right] \\Psi(\\mathbf{r},t)\n\nWe described it in the initial section of this chapter.\nFor the most part, when we are trying to solve this equation the left-hand side does not change.\nIt's always i \\hbar \\frac{\\partial \\Psi(\\mathbf{r},t)}{\\partial t}.\nOn the other hand, the right-hand side can change a lot depending on the situation.\nThat is to say that we can easily simplify the Schrödinger equation by using a mathematical formalism known as the Hamiltonian.\nTo be clear, Hamiltonian mechanics is not a quantum-specific idea.\nIt's everywhere in statistical physics and is often taught in classical physics courses as an analogue to another notational form known as Lagrangian mechanics.\nFor simplicity, we will restrict our discussion here to interpreting Hamiltonians physically.\nWe can basically say that the Hamiltonian is a measure of the energy of our quantum system.\nMore specifically, we can say that the Hamiltonian is a set of energy operators that act on our wavefunction.\nIn the case of a 1D particle in a harmonic trap, we might use the following definitions:\n\n\\begin{align}\n\\hat H &= \\hat T + \\hat V \\\\\n\\hat T &= \\frac{p^2}{2m} \\\\\n\\hat V &= \\frac{1}{2}\\omega x^2\n\\end{align}\n\nwhere p = -i\\hbar \\nabla is the momentum operator and \\omega is the trapping frequency indicating how confined our quantum system will be.\nIn this case, \\hat T is an operator that works on our wavefunction in momentum space, while \\hat V acts in position space.\nBoth of these are operators.\nThat is to say that they operate on our quantum system by transforming it in some way.\nUltimately, this means that the operators are not meant to be interpreted on their own without acting on some other object, in this case, the wavefunction \\Psi(x).\nIn the end, we can update our Schrödinger equation to be\n\ni \\hbar \\frac{\\partial \\Psi(\\mathbf{r},t)}{\\partial t} = \\hat H \\Psi(\\mathbf{r},t)\n\nWhich is a lot cleaner and more general.\nNow, the Schrödinger equation can solve any quantum system so long as it can be written in terms of Hamiltonian mechanics!\nWhen looking at the operators, it is clear that the \\hat V operator is in position space.\nWe can clearly see that it operates as a function of x.\nThat said, it is not immediately obvious why the \\hat T is in momentum space.\nThis is not an easy question to answer, but it is definitely important and will be covered in more depth when we discuss spectral methods.\nFor now, we will blanketly say\n\n\\frac{\\partial f}{\\partial x} = \\mathcal{F}^{-1}\\left( 2\\pi i k \\mathcal{F}\\left( f \\right)\\right)\n\nIn other words, we can derive a function by performing a Fourier transform on the function, multiplying by some momentum-space grid, and then inverse-transforming it back.\nBecause this operation inherently involves a transform into momentum space before transformation, it is a momentum-space operator.\nThis is the most intuitive reasoning I can find; however, I am sure there are more intuitive explanations of why the derivatives are always momentum-space operations.\nThis section will be updated further when we discuss spectral methods, but if you have better descriptions, please let me know!\nBra Ket Notation\nUnfortunately, the interpretation of quantum simulation is rather tricky and is sometimes easier to understand with slightly different notation.\nThis notation is called braket notation, where a ket looks like this:\n\n\\lvert A \\rangle\n\nand basically describes A as a column vector.\nThe bra represents the Hermitian conjugate of the ket and looks like this:\n\n\\langle B \\rvert\n\nThe ket is often represented as a row vector for B.\nBecause of this, \\langle B \\rvert A \\rangle represents the inner product of the two vectors and \\lvert A \\rangle \\langle B \\rvert represents the outer product.\nNow, to this point, the braket notation does not have any particularly quantum-like features; however, it becomes useful when describing actual quantum phenomenon.\nFor example, if we want to indicate the probability of a wavefunction \\psi collapsing onto state \\phi, we might write: \\langle \\phi \\rvert \\psi \\rangle, which is precisely the same as the probability density defined above.\nNow that we have a basic understanding of the notation, we should go through several other important quantum mechanical ideas and properties.\nEigenstates\nAs mentioned, the wavefunction \\Psi(x) is complex and has both real and imaginary parts; however, there are certain states that are exclusively real.\nThese states are eigenstates of the system, and are often described as the constituent states that make up all other possible wavefunctions.\nIn other words,\n\n\\lvert \\Psi(x)\\rangle = \\sum_i c_i \\lvert \\Psi_i \\rangle\n\nWhere c_i is some constant describing how much of a given eigenstate i is in the full wavefunction.\nAs you might expect, all of the c_i's should sum to 1.\nEnergy Calculations\nWhen it comes to quantum systems, there is no quantity more important than energy.\nBasically, every eigenstate of the system has a different energy associated with it, and you can find this energy with a simple calculation:\n\nE = \\langle \\Psi \\lvert \\hat H \\lvert \\Psi \\rangle\n\nWhich can be done rather trivially in code by finding the conjugate of the wavefunction and multiplying it with another wavefunction after operation in position and momentum space.\nThis ultimately looks like this:\n# We are calculating the energy to check \nfunction calculate_energy(par, opr)\n # Creating real, momentum, and conjugate wavefunctions\n wfc_r = opr.wfc\n wfc_k = fft(wfc_r)\n wfc_c = conj(wfc_r)\n\n # Finding the momentum and real-space energy terms\n energy_k = 0.5*wfc_c.*ifft((par.k.^2) .* wfc_k)\n energy_r = wfc_c.*opr.V .* wfc_r\n\n # Integrating over all space\n energy_final = 0\n for i = 1:length(energy_k)\n energy_final += real(energy_k[i] + energy_r[i])\n end\n\n return energy_final*par.dx\nend\n\ncalculateEnergy :: Parameters -> Operators -> Double\ncalculateEnergy param ops = (* dx param) . sum . map realPart $ elems totalE\n where\n totalE = potentialE .+ kineticE\n potentialE = wfcConj .* v ops .* wfc ops\n kineticOp = liftArray ((/ 2) . (^ 2)) (ks param)\n kineticE = wfcConj .* idft (kineticOp .* dft (wfc ops))\n wfcConj = liftArray conjugate $ wfc ops\n\ndouble calculate_energy(struct params par, struct operators opr) {\n double complex wfc_r[opr.size];\n double complex wfc_k[opr.size];\n double complex wfc_c[opr.size];\n memcpy(wfc_r, opr.wfc, sizeof(wfc_r));\n\n memcpy(wfc_k, opr.wfc, sizeof(wfc_k));\n fft(wfc_k, opr.size, false);\n\n for (size_t i = 0; i \ndouble calculate_energy(Params &par, Operators &opr) {\n vector_complex wfc_r(opr.wfc);\n vector_complex wfc_k(opr.wfc);\n vector_complex wfc_c(opr.size);\n fft(wfc_k, false);\n\n for (size_t i = 0; i \ndef calculate_energy(par: Param, opr: Operators) -> float:\n \"\"\"Calculate the energy .\"\"\"\n # Creating real, momentum, and conjugate wavefunctions.\n wfc_r = opr.wfc\n wfc_k = np.fft.fft(wfc_r)\n wfc_c = np.conj(wfc_r)\n\n # Finding the momentum and real-space energy terms\n energy_k = 0.5 * wfc_c * np.fft.ifft((par.k ** 2) * wfc_k)\n energy_r = wfc_c * opr.V * wfc_r\n\n # Integrating over all space\n energy_final = sum(energy_k + energy_r).real\n\n return energy_final * par.dx\n\n\n\nThis calculation will be used in many different simulations of quantum systems to check our results.\nIn the end, many quantum simulations are focused on the ground state, which is the lowest energy state (\\Psi_0); however, sometimes higher energy states are desired.\nThe Future\nAs we proceed to add new algorithms to simulate quantum systems, I will add more and more notation to this section; however, there are already huge textbooks out there related to understanding and studying quantum systems.\nWe don't want to re-invent the wheel here.\nInstead, we want to focus on an area that is often not considered with too much detail: algorithms and methods researchers use to ascertain new knowledge about quantum mechanics, like the split-operator method, DMRG, quantum Monte Carlo, exact diagonalization, and many more.\nQuantum mechanics is one of those areas of physics that really does push the boundary of human knowledge in a number of different areas and computing is one of those areas.\nIn fact, quantum information theory is currently set to be the next innovation to radically change the landscape of modern computation as we know it!\nOf course, because of the large-scale effects that this will likely have on the industry, it deserved it's own section.\nAs always, if there is something that you feel is missing from this section, please feel free to contact me or create an issue on GitHub and we'll get to it as soon as we can!\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe animation \"FTgaussian\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/affine_transformations/affine_transformations.html":{"url":"contents/affine_transformations/affine_transformations.html","title":"Affine Transformations","keywords":"","body":"Affine Transformations\nAffine transformations are a class of mathematical operations that encompass rotation, scaling, translation, shearing, and several similar transformations that are regularly used for various applications in mathematics and computer graphics.\nTo start, we will draw a distinct (yet thin) line between affine and linear transformations before discussing the augmented matrix formalism typically used in practice.\nA quick intro to affine (and linear) transforms\nLet us start with a provided point, (x,y), on a two-dimensional plane.\nIf we treat this point as a 1 \\times 2 vector, we can transform it into another 1 \\times 2 vector by multiplying it with a 2 \\times 2 transformation matrix.\nSimilarly, a three-dimensional point could be seen as a 1\\times 3 vector and would need a 3 \\times 3 transformation matrix.\nThese types of operations are known as linear transformations and are often notated as,\n\n\\mathbf{v} = \\mathbf{A}\\mathbf{v}_0.\n\nHere, \\mathbf{A} is an n\\times n transformation matrix, where n is the length of the input and output vectors, \\mathbf{v_0} and \\mathbf{v}, respectively.\nThough these transformations are powerful, all of them are centered about the origin.\nAffine transformations extend linear transformations beyond this limitation and allow us to also translate our initial vector locations such that\n\n\\textbf{v} = \\mathbf{A}\\mathbf{v}_0 + \\ell.\n\nHere, \\ell is an n\\times 1 translation vector.\nTo understand the power of these transformations, it is important to see them in practice:\n\n\n\nDescription\nTransform\n\n\n\n\nScaling along x\n Your browser does not support the video tag. \n\n\nScaling along y\n Your browser does not support the video tag. \n\n\nShearing along x\n Your browser does not support the video tag. \n\n\nShearing along y\n Your browser does not support the video tag. \n\n\nTranslation along x\n Your browser does not support the video tag. \n\n\nTranslation along y\n Your browser does not support the video tag. \n\n\n\nFor all of these visualizations, we show a set of 4 points that are assigned to the vertices of a square.\nInitially, \\mathbf{A} is set to be the identity matrix and \\ell = [0,0], such that there is no transformation or translation to the input vectors.\nFrom there, each element of \\mathbf{A} and \\ell are modified individually and the resulting transformation can be seen on the left.\nThe amount by which each element has been modified is shown numerically in the matrix representation and also as small dials underneath.\nThe hope is that these visualizations show that each element within \\mathbf{A} and \\ell are simply dials that can be manipulated to perform a specified transformation on the set of input vectors.\nOf course, it is entirely possible to move more than one dial at a time, which is why it is worth diving into an example that everyone loves: rotation.\nRotation: a special side-note\nI will be honest, when I initially learned how to perform rotation with a linear transformation, I did not really understand how it worked.\nFor this reason, I think it is important to delve a bit deeper into this topic, hopefully providing an intuitive explanation for those who are new (and potentially those who already use the rotation matrix regularly, but do not fully understand it).\nIf someone were to take the set of dials shown above and mix them to create a rotational effect, they might start by shearing in one direction along x and then another direction along y which will create a \"pseudo-rotation\" effect.\nThis is definitely a step in the right direction, but if the shearing components are modified while the other components remain 1, the points will also move further away from the origin.\nFor this reason, an additional scaling along x and y is necessary.\nThis is shown in the following animation:\n\n\n \nYour browser does not support the video tag.\n\n\n\nHere, we see that (at least for angles less than \\pi/2), rotation is simply a matter of shearing in opposite directions and scaling accordingly.\nNow the only question is, \"How do we know the amount we need to shear and scale?\"\nWell, the answer is not particularly surprising.\nIf we want to rotate our points, we probably are already imagining this rotation along a circle with some angle \\theta.\nWe know that the identity matrix should correspond to a non-rotated object with \\theta = 0.\nFor this reason, we know that two elements should start at 1 (note: \\cos(0) = 1) and the other two should start at 0 (note: \\sin(0) = 0).\nWe also know that the shearing should happen in opposite directions, so we might guess that the rotation matrix would be:\n\n\\mathbf{A}_{\\text{rot}} = \\begin{bmatrix}\n\\cos(\\theta) & -\\sin(\\theta) \\\\\n\\sin(\\theta) & \\cos(\\theta) \\\\\n\\end{bmatrix}\n\nIn this case, the amount we want to shear should start at 0 when \\theta = 0 and then go to \\pm 1 when \\theta = \\pm \\pi/2.\nMeanwhile, the scale factor should start at 1 when \\theta = 0 and go to 0 when \\theta = \\pi/2.\nThis seems right, but it is worth dwelling on this a bit more.\nIf the scale factor is 0 at \\pi/2, surely this means that all points on the square are also at 0, right?\nAfter all, anything scaled by 0 should be 0!\nWell, not exactly.\nIn this case,\n\n\\mathbf{A} = \\begin{bmatrix}\n1 & 0 \\\\\n0 & 1 \\\\\n\\end{bmatrix}\n\\rightarrow\n\\begin{bmatrix}\n0 & -1 \\\\\n1 & 0 \\\\\n\\end{bmatrix}\n\nThis means that even though the scaling components are 0, the shear components are \\pm 1.\nThis might still be a little confusing so let us multiply the vector [1,2] with both of these matrices:\n\n\\begin{align}\n\\begin{bmatrix}\n1 & 0 \\\\\n0 & 1 \\\\\n\\end{bmatrix}\n\\begin{bmatrix}\n1 \\\\\n2 \\\\\n\\end{bmatrix}\n&=\n\\begin{bmatrix}\n1 \\\\\n2 \\\\\n\\end{bmatrix},\\\\\n\n\n\\begin{bmatrix}\n0 & -1 \\\\\n1 & 0 \\\\\n\\end{bmatrix}\n\\begin{bmatrix}\n1 \\\\\n2 \\\\\n\\end{bmatrix}\n&=\n\\begin{bmatrix}\n-2 \\\\ \n1 \\\\\n\\end{bmatrix}.\n\n\\end{align}\n\nHere, we see that when multiplying by the identity matrix, the vector remains the same, but when multiplying by the second matrix, the x and y components flip.\nEssentially, all of the vector magnitude moved into the \"shear\" component, while none of it remains in the \"scale\" component.\nMy point is that even though it is useful to think of two of our dials as scale factors along x and y, it does not necessarily paint the whole picture and it is important to consider how these different components work together.\nBefore continuing to show what the \\mathbf{A}_{\\text{rot}} matrix does when applied to a square, it is worth considering two somewhat related matrices where the identity matrix is modified with only the \\sin(\\theta) or \\cos(\\theta) components.\n\n\n\nDescription\nTransform\n\n\n\n\nJust sines\n Your browser does not support the video tag. \n\n\nJust cosines\n Your browser does not support the video tag. \n\n\n\nHere, we see two completely different behaviors:\n\nIn the sine-only case, we see that as \\theta wraps around from 0 \\rightarrow 2\\pi, the square seems to grow and rotate like expected, but at \\pi/2, it somewhat abruptly decides to move in the other direction.\nIn cosine-only case, we see the square flip around entirely at \\pi/2.\n\nBefore watching the next video, it is important to think for a little bit about how these two different interactions will work together in practice.\nWhen you are ready, go ahead and click the play button:\n\n\n \nYour browser does not support the video tag.\n\n\n\nAt least for me, it took some thinking to figure out why the two animations above create rotation when put together.\nWhen thinking about it, it makes sense that at \\pi/2, the sine component will start to encourage the square to slowly oscillate back towards the original position, but will be tugged in the opposite direction by the cosine component that has turned negative at the same time.\nThis \"coincidence\" is what creates a rotational effect.\nOverall, the rotation matrix is a fun and interesting application to linear transformations that really helped me understand how the entire class of operations can be used to create more complicated movements.\nGuarantees of affine transformations\nAt this stage, we have discussed what affine transforms are from a functional perspective; however, (as always) there is a lot more to discuss.\nThis particular chapter is meant to provide an intuitive feel for the transformations for those who might need to use them for whatever application they need, so I am hesitant to dive too deeply into more rigorous definitions; however, it is important to talk about certain properties of affine transforms that make them suitable for a wide variety of applications.\nNamely, affine transformations preserve the following:\n\ncollinearity between points. This means that any points that are on the same line before an affine transform must be on that same line after the transformation. The line can still change in slope or position.\nparallelism between lines. Any lines parallel before the transform must also be parallel after.\nratios of the lengths of parallel line segments. This means if you have two different line segments, one of which is parameterized by p_1 and p_2, while the other is parameterized by p_3 and p_4, then \\frac{\\vec{p_1 p_2}}{\\vec{p_3 p_4}} must be the same before and after transformation.\nconvexity of any transformed shape. If a shape does not have any concave component (a point that points in towards its center), then it cannot have a concave component after the transformation.\nbarycenters of the collection of points. The barycenter is the collective center of mass of the system, like the balancing point for a plate. Essentially, there is an equal amount of \"stuff\" on either side of the barycenter. This location must remain at the same location relative to each point after transformation.\n\nAgain, there is a lot more we could talk about, but I feel we will leave more rigorous discussions for later if we need them for subsequent algorithms.\nInstead, I believe it is useful to move on to a relatively common implementation of affine transformations: the augmented matrix formalism.\nAugmented matrix implementation\nAs stated before, affine transformations are basically a mix of a transformation matrix and translation.\nFor two-dimensional input vectors, the augmented matrix formalism combines both of these into a large 3 \\times 3 transformation matrix.\nIf you are like me, this might be a bit confusing.\nAfter all, if the two-dimensional vector is described by a 1 \\times 2 array, then how do you do a matrix multiplication with a 3 \\times 3 array?\nTo be honest, the answer feels like a bit of a hack: we simply append a 1 to the end of the input, output, and translation vectors, such that:\n\n\\begin{bmatrix}\n\\mathbf{v} \\\\\n1 \\\\\n\\end{bmatrix}\n=\n\\left[\\begin{array}{@{}ccc|c@{}}\n & \\mathbf{A} & & \\ell \\\\\n0 & \\cdots & 0 & 1 \\\\\n\\end{array}\\right]\n\\begin{bmatrix}\n\\mathbf{v}_0 \\\\\n1\n\\end{bmatrix}\n\nSo, using \n\n\\begin{align}\n\\mathbf{v}_0 &= \\begin{bmatrix}\n1 \\\\ \n2 \\\\\n\\end{bmatrix} \\\\\n\\mathbf{A} &= \\begin{bmatrix}\n0 & -1 \\\\\n1 & 0 \\\\\n\\end{bmatrix} \\\\\n\\ell &= \\begin{bmatrix}\n0 \\\\ \n0 \\\\\n\\end{bmatrix}\n\\end{align},\n\nwe would perform the following computation:\n\n\\begin{bmatrix}\n\\mathbf{v} \\\\\n1 \\\\\n\\end{bmatrix}\n=\n\\left[\\begin{array}{@{}cc|c@{}}\n0 & -1 & 0 \\\\\n1 & 0 & 0 \\\\\n0 & 0 & 1 \\\\\n\\end{array}\\right]\n\\begin{bmatrix}\n1 \\\\\n2 \\\\\n1\n\\end{bmatrix}\n\nDoing this, we find that \\mathbf{v} = [-2,1], just as we found in the previous example.\nOk, now we need to talk about why this works.\nAppending the 1 to the end of the two-dimensional vectors essentially turn them into three-dimensional vectors, with the z dimension simply set to be 1.\nThe easiest way to visualize this is by thinking of the top plane on a larger cube, so here are the same vector operations as before on that cube:\n\n\n\nDescription\nTransform\n\n\n\n\nScaling along x\n Your browser does not support the video tag. \n\n\nScaling along y\n Your browser does not support the video tag. \n\n\nShearing along x\n Your browser does not support the video tag. \n\n\nShearing along y\n Your browser does not support the video tag. \n\n\nTranslation along x\n Your browser does not support the video tag. \n\n\nTranslation along y\n Your browser does not support the video tag. \n\n\n\nThe shear and scaling operations seem about the same as before; however, the translation operations are now clearly a shear along the entire cube!\nThe only reason this acts as translation for two dimensions is because we only care about the slice through the cube at z=1.\nNow, the reason I always feel this implementation is a bit hacky is because there is a little magic that everyone keeps quiet about: the last row in the matrix.\nWith all of the operations shown above, it was simply set to [0,0,1] and never touched again...\nBut that is terribly unsatisfying!\nWhat would happen if we actually moved those dials and modified the bottom row?\nWell...\n\n\n\nDescription\nTransform\n\n\n\n\nShearing along z and x\n Your browser does not support the video tag. \n\n\nShearing along z and y\n Your browser does not support the video tag. \n\n\nScaling along z\n Your browser does not support the video tag. \n\n\n\nIn this case, the first two components are shearing along z and x and z and y, while the last component is a scale along z.\nIf someone was taking a picture from above, none of these transformations would be visible.\nBecause we are hyper-focused on the top-down view for affine transformations, none of these operations are technically affine; however, they are still linear, and it is still nice to show all possible linear transforms for the cube as well.\nFinally, let us go back to the rotation example:\n\n\n \nYour browser does not support the video tag.\n\n\n\nHere, we see that we can embed just about any affine transformation into three dimensional space and still see the same results as in the two dimensional case.\nI think that is a nice note to end on: affine transformations are linear transformations in an n+1 dimensional space.\nVideo Explanation\nHere is a video describing affine transformations:\n\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe video \"A11 square\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A22 square\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A12 square\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A21 square\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A13 square\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A23 square\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Semi Rotate\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Sines\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Cosines\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Rotate Square\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A11 cube\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A22 cube\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A12 cube\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A21 cube\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A13 cube\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A23 cube\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A31 cube\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A32 cube\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"A33 cube\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe video \"Rotation cube\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n"},"contents/approximate_counting/approximate_counting.html":{"url":"contents/approximate_counting/approximate_counting.html","title":"Approximate Counting Algorithm","keywords":"","body":"The Approximate Counting Algorithm\nThis might seem like a straightforward question, but how high can you count on your fingers?\nThis depends on how many fingers you have, but in general the answer has to be 10, right?\nWell, not exactly, it can actually go much, much higher with a few simple abstractions.\nThe first strategy is to think of your fingers as binary registers, like so [1]:\n\n \n\n\nIf your fingers are out, they count as a 1 for that register.\nIf they are not, they count as a 0.\nThis means that after you have decided on the appropriate finger configuration, you have created a bitstring that can be read from left to right, where each number represents a power of 2.\nFor this example, we would have a bitstring of 1110010101, which reads to 917:\n\n1 \\cdot 2^9 + 1 \\cdot 2^8 + 1 \\cdot 2^7 + 0 \\cdot 2^6 + 0 \\cdot 2^5 + 1 \\cdot 2^4 + 0 \\cdot 2^3 + 1 \\cdot 2^2 + 0 \\cdot 2^1 + 1 \\cdot 2^0\n\n\n=\n\n\n512 + 256 + 128 + 16 + 4 + 1 = 917\n\nBecause you have 10 fingers and each one represents a power of 2, you can count up to a maximum of 2^{10}-1 or 1023, which is about 100 times higher than simple finger counting!\nFor those who might be wondering why you can count to 2^{10}-1 instead of 2^{10} exactly, remember that each finger represents a power of 2.\nThe right thumb counts as 2^0 = 1 and the left thumb is 2^9 = 512.\nWith all fingers out, we have counted to \\sum_{n=0}^9 2^n = 1023 = 2^{10}-1.\nSo what if we wanted to go beyond 1023?\nWell, we could start counting with our fingers as trits where 0 is closed, 1 is half-up, and 2 is fully up.\nThere are actually a huge variety of different ways we could move our hands about to count in odd ways, but we are interested in a more concrete problem: how high can we count with only 10 bits?\nThis is almost exactly the problem that Morris encountered in Bell Labs around 1977 [2].\nThere, he was given an 8-bit register and asked to count much higher than 2^8 - 1= 255.\nHis solution was to invent a new method known as the approximate counting algorithm.\nWith this method, he could count to about 130,000 with a relatively low error (standard deviation, \\sigma \\approx 17,000).\nUsing 10 registers (fingers), he could count to about 1.1\\times 10^{16} with similar parameters, which is undoubtedly impressive!\nThe approximate counting algorithm is an early predecessor to streaming algorithms where information must be roughly processed in real-time.\nAs we dive into those methods later, this chapter will certainly be updated.\nFor now, we will not be showing any proofs (though those might come later as well), but a rigorous mathematical description of this method can be found in a follow-up paper by Philippe Flajolet [3].\nIn addition, there are several blogs and resources online that cover the method to varying degrees of accessibility [4] [5].\nHere, we hope to provide a basic understanding of the method, along with code implementations for anyone who might want to try something similar in the future.\nA Simple Example\nIf we need to count more than 255 items with 8 bits, there is one somewhat simple strategy: count every other item.\nThis means that we will increment our counter with 2, 4, 6, 8... items, effectively doubling the number of items we can count to 511!\n(Note: that \"!\" is out of excitement and is not a factorial.)\nSimilarly, if we need to count above 511, we can increment our counter every 3 or 4 items; however, the obvious drawback to this method is that if we only count every other item, there is no way to represent odd numbers.\nSimilarly, if we count every 3rd or 4th item, we would miss out on any numbers that are not multiples of our increment number.\nThe most important thing to take away from this line of reasoning is that counting can be done somewhat approximately by splitting the process into two distinct actions: incrementing the counter and storing the count, itself.\nFor example, every time a sheep walks by, you could lift a finger.\nIn this case, the act of seeing a sheep is a trigger for incrementing your counter, which is stored on your hand.\nAs mentioned, you could also lift a finger every time 2 or 3 sheep go by to count higher on your hand.\nIn code, bits are obviously preferred to hands for long-term storage.\nTaking this example a bit further, imagine counting 1,000,000 sheep.\nIf we wanted to save all of them on 8 bits (maximum size of 255), we could increment our counter every \\sim 4000 sheep.\nBy counting in this way, we would first need to count around 4000 sheep before incrementing the main counter by 1.\nAfter all the sheep have gone by, we would have counted up to 250 on our counter, and also counted up to 4000 on a separate counter 250 times.\nThis has a few important consequences:\n\nIf the final number of sheep is not a multiple of 4000, then we will have an error associated with the total count of up to 4000 (0.4%).\nThere is no way to determine the final number of sheep if it is not a multiple of 4000.\nWe now need some way to count up to 4000 before incrementing the main counter.\nThis means we need a second counter!\n\nIn a sense, 4000 would be a type of \"counting resolution\" for our system.\nOverall, a 0.4% error is not bad, but it is possible to ensure that the approximate count is more accurate (but potentially less precise) by using randomness to our advantage.\nThat is to say, instead of incrementing out counter every 4000th sheep, we could instead give each item a 1/4000 = 0.025\\% chance of incrementing our main counter.\nThis averages out to be roughly 1 count every 4000 sheep, but the expectation value of a large number of counting experiments should be the correct number.\nThis means that even though we need to count all the sheep multiple times to get the right expectation value, we no longer need to keep a separate counter for the counting resolution of 4000.\nBecause multiple counting trials are necessary to ensure the correct result, each counting experiment will have some associated error (sometimes much higher than 0.4%).\nTo quantify this error, let's actually perform multiple the experiment, as shown below:\n\n \n\n\nIn this image, we have counted 1,000,000 sheep (items) 10,000 different times.\nIn each run, we have given each item a 0.025% chance to flip our primary counter and have given each increment in our primary counter a weight of 4000 items.\nWe have plotted 10 of the 10,000 runs (chosen at random), and each upward tick of the lines represents one of the items winning a game of chance and adding 1 to the primary counter and thus adding 4000 to the approximate count.\nWe have also shaded the maximum and minimum approximate count for each true count of the 10,000 trials in gray, thereby highlighting the range of possible outputs.\nOn top of the plot, we have shown the distribution of all 10,000 runs for the approximate count at 10,000, 500,000, and 1,000,000 items.\nThere's a lot to unpack here, so let's start with the upward trending lines.\nHere, it seems like the approximate counts are roughly following the line of y=x (dotted black line), which would indicate simple counting (without any randomness or approximation).\nThis makes sense because in a perfect world, the approximate count would always be exactly equal to the true number of items being counted.\nUnfortunately, none of the lines shown here exactly follow y=x.\nIn fact, it would be impossible for any of the approximations to do so because we are always increasing the approximation in steps of 4000 while the true count increments by 1 with each new item.\nThat said, the average of all these counts together is a really good approximation for the true number of items.\nThis is where the 3 additional plots come in:\n\n \n\n\nEach of these is a histogram of the approximate count for all 10,000 runs at 10,000 (left), 500,000 (middle), and 1,000,000 (left) items.\nAll three (especially the approximation for 1,000,000) look Gaussian, and the peak of the Gaussian seems to be the correct count.\nIn fact, the expectation value for our approximate counting scheme will always be correct.\nIn practice, this means that we can approximate any count on a small number of bits by doing a large number of counting trials and averaging their results.\nThere is still a little catch that becomes more evident as we look at the approximation for 10,000 items.\nIn this case, even though the expectation value for the Gaussian distribution looks correct, it's kinda hard to tell exactly because there are only 8 (or so) possible values for each individual experiment.\nEssentially, we are trying to count to 10,000 in steps of 4,000.\nClearly the closest we can get on any individual run is either 8,000 or 12,000, as these are multiples of 4,000.\nSimply put: we cannot resolve 10,000 items with this method!\nDoes this mean that this counting method is less useful for a small number of items?\nIn a sense, yes.\nHere is a table for the true count, approximate count, and percent error for 10,000, 500,000, and 1,000,000 for the case where we do 10,000 counting experiments:\n\n\n\nTrue Count\nApproximate Count\nPercent Error\n\n\n\n\n10,000\n9,958.0\n0.42\n\n\n500,000\n499,813.2\n0.037\n\n\n1,000,000\n999,466.0\n0.053\n\n\n\nHere, it seems that the percent error is 10 times higher when we count 10,000 items; however,\nwith these numbers, I could imagine some people reading this are thinking that we are splitting hairs.\nA 0.42% error is still really good, right?\nRight.\nIt's definitely not bad, but this was with 10,000 counting experiments.\nHere a new table where we only did 10:\n\n\n\nTrue Count\nApproximate Count\nPercent Error\n\n\n\n\n10,000\n8,000.0\n20.0\n\n\n500,000\n483,200.0\n3.36\n\n\n1,000,000\n961,600.0\n3.84\n\n\n\nThis time, there is a 20% error when counting to 10,000.\nThat's unacceptably high!\nTo solve this problem, we need to find some way to for the value of each increment on the actual counter to be more meaningful for lower counts.\nThis is precisely the job for a logarithm, which is what we will be looking at in the next section.\nFor now, it's important to look at another anomaly: why are the percent errors for the 500,000 and 1,000,000 cases so close?\nI gotta be honest, I don't know the correct answer here, but I would guess that it has something to do with the fact that both 500,000 and 1,000,000 are multiples of 4000 so our counting scheme can resolve both of them with roughly equal precision.\nOn top of that, both values are significantly higher than 4,000 so the counting resolution does not have as significant of an impact on the measured count.\nSimply put, 4000 is a big step size when counting to 10,000, but a smaller one when counting to 500,000 or 1,000,000.\nAs an important note, each approximate count shown in the tables above was the expectation value for a Gaussian probability distribution of different counting experiments all providing a guess at what the count could be.\nBecause we are no longer counting with integer increments but instead with probability distributions, we now need to quantify our error with the tools of probability, namely standard deviations.\nIn the next section, we will tackle both issues brought up here:\n\nIn order to better approximate different scales of counting, it makes sense to use a logarithmic scale.\nBecause we are counting by using the expectation value of a Gaussian probability distribution from a set of counting experiments, it makes sense to quantify error with the tools we learned from probability and statistics.\n\nSo I guess we should hop to it!\nAdding a logarithm\nAt this stage, I feel it's important to use terminology that more closely matches Morris's original paper [2], so we will begin to talk about events, which are a general abstraction to the previous item / sheep analogy.\nWe will also introduce three different values:\n\nn: the number of events that have occurred.\nv: the number we have stored in our bitstring.\nn_v: the approximate number of events that have occurred.\n\nIt's important to stop here and think about what's actually going on.\nWe have a certain number of events (n) that have occurred and have stored that number on a binary register as v.\nTraditionally, the number stored on the binary register would be exactly equal to the number of events, but because we do not have enough space on the register, we end up settling for an approximation of the number of events, n_v.\nThis is precisely what we did in the previous example, where v = \\frac{n}{4000} and n_v = 4000*v.\nAs mentioned, using a constant scaling value (4000) for our approximate counting scheme means that the approximation is not ideal for a smaller number of events.\nFor this reason, it might be more appropriate to create a new method of storing the number of events by using a logarithmic scale, such that\n\nv = \\log_2(1+n),\n\nwhich would mean that the approximate count would be\n\nn_v = 2^v-1.\n\nIn this case, we are adding 1 to the argument of the logarithm for v because \\log_2(1) = 0 and we start counting at 1; therefore, we need some way to represent the value of 0.\nAlso, for this we can use any base logarithm (like e), but because we are dealing with bits, it makes sense to use base 2.\nWe'll talk about different bases next.\nTo be clear, here is a table of several values that could be stored in a bitstring along with their corresponding approximate counts:\n\n\n\nv(n)\nn_v\n\n\n\n\n00000000 = 0\n0\n\n\n00000001 = 1\n1\n\n\n00000010 = 2\n3\n\n\n00000100 = 4\n15\n\n\n00010000 = 16\n65535\n\n\n01000000 = 64\n1.85 \\times 10^{19}\n\n\n10000000 = 128\n3.40 \\times 10^{38}\n\n\n11111111 = 255\n5.79 \\times 10^{76}\n\n\n\nThis means that we can hold from 0 to 2^{255} - 1 \\approx 5.79 \\times 10^{76} with 8 bits using this new method.\nSo let's now think about what happens every time a new event occurs.\nTo do this, Morris calculated a new value:\n\n\\Delta = \\frac{1}{n_{v+1} - n_{v}}\n\nwhere n_{v+1} is the approximate count for the next possible value v stored in the register.\nIn this case, \\Delta will always be between 0 and 1, so we can consider it to be the probability of whether we should increment our stored count or not.\nFor example, if we have a stored value of 2 (v=2), then\n\n\\Delta = \\frac{1}{n_3 - n_2} = \\frac{1}{(2^3-1)-(2^2-1)} \\approx \\frac{1}{7-3} \\approx 0.25.\n\nThis indicates that there will be a 25% chance to increment v from 2 to 3.\nIn practice, this means that we need to create another random variable r and set our counter such that\n\n\\begin{align}\n\\text{if } & r \\Delta, \\qquad v = v.\n\\end{align}\n\nAgain, \\Delta is essentially the probability that we will increment our counter with each object, and as we count higher, the probability decreases exponentially.\n\n \n\n\nNote: the y-axis to this figure is in logscale, which is why it looks like a straight line.\nBefore leaving this section, it's important to note that the highest anyone can count with this method in base 2 using an 8-bit register is 5.79 \\times 10^{76}.\nThat's great!\nWay, way better than 255, but we can still go higher with a different base of logarithm.\nFor example, if we use e as our base, we can get up to e^{255}-1 = 5.56 \\times 10^{110}.\nIn addition, by choosing smaller bases, we can also find a more accurate approximate count for lower values.\nIn practice, we want to select a base that allows us to count to a value of the same order (or one order higher) than the number of events we are expected to have.\nIn the next section, we will consider how to generalize this logarithmic method to take arbitrary bases into account.\nA slightly more general logarithm\nLet's start by considering the differences between base 2 and base e.\nFor base e,\n\n\\begin{align}\nn_v &= e^v - 1 \\\\\nv &= \\log_e(1+n).\n\\end{align}\n\nIf we were to update our count and wanted to keep the value in the counter as accurate as possible, then the new value in the register with every new event would be\n\nv = \\log_e(1+e^v).\n\nThis is generally not an integer value, but v must be an integer value (unless we want to try and store floating-point values (which we definitely don't have space for)), so what do we do in this situation?\nWell, let's look at the very first event where we need to increment our count from 0 to 1.\nWith base e, there would only be a 58% chance of counting the first event (\\Delta = \\frac{1}{1.72-0} = 0.58), and if the event is counted, the value in the register would be \\approx 1.71 \\neq 1.\nAgain, the expectation value for a bunch of trials is correct, but we did not have this issue with base 2, because\n\nv = \\frac{\\log_e(n+1)}{\\log_e(2)} = 1\n\nwhen n=1.\nAs a reminder, the above formula is a way to convert any logarithm from a given base (in this case e) to another base (in this case 2).\nGoing one step further, we need to chose a specific base to a logarithm that will at least ensure that the first count is correct, and for this reason, Morris studied a specific solution:\n\n\\begin{align}\n v &= \\frac{\\log(1+n/a)}{\\log(1+1/a)}. \\\\\n n_v &= a\\left(\\left(1+\\frac{1}{a}\\right)^v-1\\right).\n\\end{align}\n\nHere, a is an effective tuning parameter and sets the maximum count allowed by the bitstring and the expected error.\nThe expression 1+1/a acts as a base for the logarithm and exponents and ensures that the first count of n=1 will also set the value v=1.\nAs an example, if the bitstring can be a maximum of 255 (for 8 bits) and we arbitrarily set\na=30, then the highest possible count with this approach will be \\approx 130,000, which was the number reported in Morris's paper.\nIf we perform a few counting experiments, we find that this formula more closely tracks smaller numbers than before (when we were not using the logarithm):\n\n \n\n\nNow, let's pause for a second and look back at the case where our counting resolution was a constant 4000:\n\n \n\n\nIt would seem that for higher counts, the previous method (with a constant counting resolution) is actually better!\nRemember that in the case of a constant counting resolution, the step size is really small for higher counts, so we get a higher resolution probability distribution for when we count 500,000 and 1,000,000 items.\nWith the logarithmic scale, this is not the case, as the counting resolution now changes with the count, itself.\nThis is also why all three probability distributions for the logarithmic scaling have a similar distance between each bar.\nIn fact, it is probably worthwhile to look at each case more specifically:\n\n\n\nConstant Counting Resolution\nLogarithmic Counting Resolution\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nIn the case where we count only to 10,000, we see a moderate increase in the resolution of the probability distribution, but in the 500,000 and 1,000,000 cases, we do not.\nIt's also important to notice that the logarithmic plots are a bit skewed to the left and are only Gaussian on logarithmic scales along x.\nOn the one hand, the logarithmic plots are nice in that they have the same relative error for all scales, but on the other hand, the error is relatively high.\nHow do we fix this?\nWell, by modifying the base of the logarithm with the variable a:\n\n \n\n\nHere, we show the differences in n_v for 25 \\leq a \\leq 35 when v=255.\nIt is important to twiddle a based on what the maximum count is expected for\n each experiment.\nAs an important note, the expected error estimate (variance) for each count will\n be\n\n\\sigma(n,a)^2 = \\frac{n(n-1)}{2a}.\n\nFinally, before ending the paper, Morris mentioned that it is possible to pre-compute all values \\Delta_j = (a/(a+1))^j for all j \\in [1,N] where N is the largest value possible integer with that bitstring (as an example, 255 for 8 bits).\nThis was probably more useful in 1978 than it is now, but it's still nice to keep in mind if you find yourself working on a machine with compute constrictions.\nVideo Explanation\nHere is a video describing the Approximate Counting Algorithm:\n\n\n\n\nExample Code\nFor this example, we have returned to the question asked above: how high can someone count on their fingers using the approximate counting algorithm?\nWe know from the formula that with a=30 and 10 bits, we should be able to count to 1.1\\times 10^{16}, but what happens when we perform the actual experiment?\nAs we do not have any objects to count, we will instead simulate the counting with a while loop that keeps going until out bitstring is 1023 (2^{10}).\nusing Test \n\n# This function takes \n# - v: value in register\n# - a: a scaling value for the logarithm based on Morris's paper\n# It returns n(v,a), the approximate count\nfunction n(v, a)\n a*((1+1/a)^v-1) \nend\n\n# This function takes\n# - v: value in register\n# - a: a scaling value for the logarithm based on Morris's paper\n# It returns a new value for v\nfunction increment(v, a)\n # delta is the probability of incrementing our counter\n delta = 1/(n(v+1, a)-n(v, a))\n\n if rand() \n#include \n#include \n#include \n#include \n#include \n\n// This function returns a pseudo-random number between 0 and 1\ndouble drand()\n{\n return (double)rand() / RAND_MAX;\n}\n\n// This function takes\n// - v: value in register\n// - a: a scaling value for the logarithm based on Morris's paper\n// It returns the approximate count\ndouble n(double v, double a)\n{\n return a * (pow(1 + 1 / a, v) - 1);\n}\n\n// This function takes\n// - v: value in register\n// - a: a scaling value for the logarithm based on Morris's paper\n// It returns a new value for v\ndouble increment(double v, double a)\n{\n // delta is the probability of incrementing our counter\n double delta = 1 / (n(v + 1, a) - n(v, a));\n\n if (drand() \n#include \n#include \n#include \n#include \n\n// Returns a pseudo-random number generator\nstd::default_random_engine& rng() {\n // Initialize static pseudo-random engine with non-deterministic random seed\n static std::default_random_engine randEngine(std::random_device{}());\n return randEngine;\n}\n\n// Returns a random double in [0, 1)\ndouble drand() {\n return std::uniform_real_distribution(0.0, 1.0)(rng());\n}\n\n// This function takes\n// - v: value in register\n// - a: a scaling value for the logarithm based on Morris's paper\n// It returns n(v,a), the approximate count\nauto n(double v, double a) { return a * (pow((1 + 1 / a), v) - 1); }\n\n// This function takes\n// - v: value in register\n// - a: a scaling value for the logarithm based on Morris's paper\n// It returns a new value for v\nauto increment(int v, double a) {\n // delta is the probability of incrementing our counter\n const auto delta = 1 / (n(v + 1, a) - n(v, a));\n return (drand() \nfrom random import random\n\n# This function takes\n# - v: value in register\n# - a: a scaling value for the logarithm based on Morris's paper\n# It returns n(v,a), the approximate_count\ndef n(v, a):\n return a*((1 + 1/a)**v - 1)\n\n# This function takes\n# - v: value in register\n# - a: a scaling value for the logarithm based on Morris's paper\n# It returns a new value for v\ndef increment(v, a):\n delta = 1/(n(v + 1, a) - n(v, a))\n if random() \n// This function takes\n// - v: value in register\n// - a: a scaling value for the logarithm based on Morris's paper\n// It returns n(v,a), the approximate count\nfn n(v: f64, a: f64) -> f64 {\n a * ((1_f64 + 1_f64 / a).powf(v) - 1_f64)\n}\n\n\n// This function takes\n// - v: value in register\n// - a: a scaling value for the logarithm based on Morris's paper\n// It returns a new value for v\nfn increment(v: f64, a: f64) -> f64 {\n // delta is the probability of incrementing our counter\n let delta = 1_f64 / (n(v + 1_f64, a) - n(v, a));\n\n if rand::random::() f64 {\n let mut v = 0_f64;\n\n for _ in 0..n_items {\n v = increment(v, a);\n }\n\n v\n}\n\n// This function takes\n// - n_trials: the number of counting trials\n// - n_items: the number of items to count to\n// - a: a scaling value for the logarithm based on Morris's paper\n// - threshold: the maximum percent error allowed\n// It returns a \"passed\" / \"failed\" test value\nfn test_approximate_count(n_trials: usize, n_items: usize, a: f64, threshold: f64) {\n let avg = std::iter::from_fn(|| Some(approximate_count(n_items, a)))\n .take(n_trials)\n .sum::() / n_trials as f64;\n\n let n_items_float = n_items as f64;\n\n if ((avg - n_items_float) / n_items_float) \nimport java.lang.Math;\nimport java.util.stream.DoubleStream;\n\npublic class ApproximateCounting {\n\n /*\n * This function taks\n * - v: value in register\n * - a: a scaling value for the logarithm based on Morris's paper\n * It returns the approximate count\n */\n static double n(double v, double a) {\n return a * (Math.pow(1 + 1 / a, v) - 1);\n }\n\n\n /*\n * This function takes\n * - v: value in register\n * - a: a scaling value for the logarithm based on Morris's paper\n * It returns the new value for v\n */\n static double increment(double v, double a) {\n double delta = 1 / (n(v + 1, a) - n(v, a));\n\n if (Math.random() approximateCount(nItems, a))\n .limit(nTrials)\n .average()\n .getAsDouble();\n\n if (Math.abs((avg - nItems) / nItems) \n\n\nBibliography\n1.Sanderson, G, How to count to 1000 on two hands, 2015.2.Morris, R, Counting large numbers of events in small registers, ACM New York, NY, USA, 1978.3.Flajolet, P, Approximate counting: a detailed analysis, Springer, 1985.4.Bhayani, A, Morris's Algorithm for Approximate Counting, 2020.5.Gundersen, G, Approximate Counting with Morris's Algorithm, 2019.\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nText\nThe text of this chapter was written by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nImages/Graphics\n\nThe image \"Finger Counting\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Approximate trials\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Histograms\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Delta v v\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Approximate trials Logarithm\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Histograms 10,000\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Histograms exp 10,000\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Histograms 500,000\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Histograms exp 500,000\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Histograms 1,000,000\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"Histograms exp 1,000,000\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\nThe image \"A from 25 to 35\" was created by James Schloss and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n"},"contents/metropolis/metropolis.html":{"url":"contents/metropolis/metropolis.html","title":"Metropolis","keywords":"","body":"The Metropolis Algorithm\nThe Monte Carlo Integration method uses random numbers to approximate the area of pretty much any shape we choose. \nThe Metropolis algorithm [1] is a slightly more advanced Monte Carlo method which uses random numbers to approximate a probability distribution:\n\nP(\\mathbf{x}) = \\frac{f(\\mathbf{x})}{\\displaystyle\\int_D f(\\mathbf{x})d\\mathbf{x}},\n\nwhere D is the domain of P(\\mathbf{x}), i.e., all possible values of the \\mathbf{x} for which P(\\mathbf{x}) is defined.\nf(\\mathbf{x}) is a function that is proportional to P(x), such as a statistical frequency distribution which counts the number of occurrences of each \\mathbf{x}.\nThe integral in the denominator is the normalization factor which ensures that the sum of all probabilities is unity, i.e.,\n\n\\int_D P(\\mathbf{x}) d\\mathbf{x} = 1.\n\nA one-dimensional example is the normal distribution, or Gaussian distribution, given by\n\nP(x) = \\frac{e^{-x^2}}{\\displaystyle\\int_{-\\infty}^{\\infty} e^{-x^2} dx} = \\frac{1}{\\sqrt{\\pi}} e^{-x^2}.\n\nIn practice, it's often easy for us to know f(x), but the integral in the denominator can be quite difficult to calculate, even numerically. \nThis is especially true when the coordinates (\\mathbf{x}) are multidimensional, and f(\\mathbf{x}) is an expensive calculation, as we shall see in the examples below.\nAn example application\nOne example of a complicated probability function arises when considering a physical system of N particles. \nThese could be atoms, molecules, or even star systems! \nFor such systems, we can usually describe the potential energy [2] of the system as a function of the coordinates of all particles, \\mathbf{x},\n\nE(\\mathbf{x}) = E(x_1, y_1, z_1, x_2, y_2, z_2, ... ,x_N, y_N, z_N),\n\nwhere x_i, y_i, z_i are the spatial coordinates of particle i. \nSo altogether there are 3N coordinates – making E(\\mathbf{x}) a 3N dimensional function, which can be a computationally intensive calculation on it's own. But it doesn't end there!\nThe physicist Ludwig Boltzmann [3] discovered that when such a system is in equilibrium at some temperature T, you can describe the probability density of the system for any set of coordinates \\mathbf{x} using, [4] \n\nP(\\mathbf{x}) = \\frac{\\displaystyle \\exp\\left[{\\displaystyle\\frac{-E(\\mathbf{x})}{T} } \\right]} {Q},\n\nwhere the numerator is called the Boltzmann factor, and Q is the normalization constant,\n\nQ = \\int_D \\exp\\left[{\\displaystyle\\frac{-E(\\mathbf{x})}{T} } \\right] d\\mathbf{x}.\n\nWe can see now that the probability density function is a difficult calculation, particularly because of Q. \nAlmost always, no analytical solution exists to the integral in Q, and the numerical integration is unfeasible. \nTo see that Q is unfeasible to calculate, imagine there are just 10 particles which all exist in a 1D world, restricted to a line segment.\n\n 1D particles\">\n\n\nLet's assume that the particles interact, meaning that the position of one particle affects that of another. \nThis could be the case, for example, if all the particles were charged, and so they would be repelling or attracting each other. \nThis means that the energy E(\\mathbf{x}) = E(x_1,...,x_{10}) of the system is a 10D function, and it would not be possible to simplify it any further due to the interactions. \nThus, the Boltzmann factor, \\exp\\left[-E(\\mathbf{x})/T\\right], is also a 10D function. To calculate Q, we would have to integrate the Boltzmann factor 10 times, one for each coordinate,\n\nQ = \\int_{x_1} \\dots \\int_{x_{10}} \\exp\\left[\\frac{-E(x_1,\\dots x_{10})}{T}\\right]\\ dx_1\\dots dx_{10}.\n\nIn most cases, there is no known analytical expression for the above integral, so it has to be done numerically.\nTo do so, imagine that we divide the 1D line segment into only 50 different intervals, allowing each particle to take on 50 different positions. \nThis is equivalent to dividing the length of a football field into intervals of about 2 meters – not a resolution you'd wanna watch a game in! \nEven with such poor resolution, the number of different combinations of positions is 10^{50} – a colossal number indeed. \nTo see how large this number is, imagine that a single computation of E(\\mathbf{x}) took only 1 nanosecond on a single processor, which is much faster than most energy calculations for physical systems in practice.\n With that speed, it would require 10^{41} seconds on a single processor to calculate Q – which means that even with all the processors in the world running in parallel (there could be billions or trillions of them), calculating Q would still take longer than the age of the universe – by many orders of magnitude!\nWhat's really powerful about the Metropolis approach is that you don't need to know the probability function itself.\nInstead, you just need a function which is proportional to it. \nWhat this means for the Boltzmann distribution is that you only need to know the term,\n\nf(\\mathbf{x}) = \\exp\\left[{\\displaystyle\\frac{-E(\\mathbf{x})}{T} } \\right].\n\nThe Metropolis algorithm can bypass the calculation of Q altogether and use f(x) to generate a distribution of x which follows the probability density P(x). \nIn other words, it can sample values of x in such away that the probability of sampling x will follow the actual distribution P(x). \nThus, if Metropolis was used to sample from x, the number of occurrences of x would be proportional to P(x).\nNumerical normalization can then be done by using the total number of samples instead of performing an integration. \nThis fact dramatically reduces the number of calculations needed to approximate the probability distribution.\nFinally, the Metropolis algorithm can be modified or implemented in other methods, and forms the basis of many advanced sampling algorithms. \nThe most popular is probably the Metropolis-Hastings algorithm [5] which is fundamentally the same. \nSome other algorithms that use this method are Metropolis-adjusted Langevin algorithm [6], and Hamiltonian Monte Carlo [7], to name a few. \nThey are often used for physical systems that follow a Boltzmann distribution.\nA Random Walk in One Dimension\nIn the rest of this chapter, we will look at 1D examples to understand the Metropolis algorithm. \nAlthough the algorithm is not particularly efficient in just one dimension, it is much easier to understand in one dimension than in multiple dimensions. \nThe Metropolis algorithm is very similar to a random walk, so let's first see how we can get a distribution from a random walk.\n\n\n \nYour browser does not support the video tag.\n\n\n\nThe dot in the figure above is a \"walker\", whose initial position is x=0. \nThe step size, g, is a random number in the interval (-1, 1). \nTo get the next position of the walker, we simply generate g and add it to the current position. \nTo get a distribution of x from this walk, we can divide the domain into discrete locations or \"bins\" and count how often the walker visits each bin. \nEach time it visits a bin, the frequency for that bin goes up by one. \nOver many iterations, we get a frequency distribution of x. \nA Random Walk With an Acceptance Criterion\nThe Metropolis algorithm works in a similar way to the random walk, but differs crucially in one way – after choosing a random step for the walker, a decision is made about whether to accept or reject the step based on the function f(x). \nTo understand how this works, let's call x_t the position before the step, and x' the position after it. \nWe then define the probability of accepting the step to be\n\nA = \\min \\left(\\frac{f(x')}{f(x_t)}, 1\\right).\n\nThe \\min function above implies that A=1 if f(x') \\gt f(x_t), which means that the move will always be accepted if it is toward a higher probability position. \nOtherwise, it will be accepted with a probability of f(x') / f(x_t). \nIf we create a histogram of this walk for some arbitrary target function P(x), we can see from the figure below that the frequency starts to look very much like it after many iterations! \n\n\n \nYour browser does not support the video tag.\n\n\n\nAlthough convergence occurs eventually, not all parts of the distribution achieve convergence quickly. \nNote from the animation above, that the walker very quickly replicates the distribution of the two peaks on the left, but takes quite a while to even reach the third peak to the right. \nThis is because there is a long low probability region between the third peak and second peak that acts as a \"barrier.\" \nThis may not necessarily be a bad thing – sometimes one might want to estimate how long something takes to transition from one state to another, and often these peaks represent such 'states'. \nSo averaging over many metropolis runs may give some estimate of these transition times. \nIf global sampling is the goal, the process of exploration could be sped up by choosing larger step sizes for the walker, for example by choosing step size g from an interval like (-3,3) instead of (-1,1). \nThe Algorithm for a One Dimensional Example\nNow let's dive into the actual algorithm with some example code!\nThe Initial Setup\nLet our target distribution be\n\nP(x) = \\frac{f(x)}{\\int_{-10}^{10} f(x)},\n\nwhere f(x) is the same function we have shown above and is given by\n\nf(x) = 10e^{-4(x+4)^2} + 3e^{-0.2(x+1)^2} + e^{-2(x-5)^2}.\n\nThe code for defining this function is given below.\ndef f(x, normalize=False):\n '''\n Function proportional to target distribution, a sum of Gaussians.\n For testing, set normalize to True, to get target distribution exactly.\n '''\n # Gaussian heights, width parameters, and mean positions respectively:\n a = np.array([10., 3., 1.]).reshape(3, 1)\n b = np.array([ 4., 0.2, 2.]).reshape(3, 1)\n xs = np.array([-4., -1., 5.]).reshape(3, 1)\n\n if normalize:\n norm = (np.sqrt(np.pi) * (a / np.sqrt(b))).sum()\n a /= norm\n\n return (a * np.exp(-b * (x - xs)**2)).sum(axis=0)\n\n\n\nSince this is an easy function to integrate, and hence get our target distribution P(x) directly, we can use it to verify the Metropolis algorithm. \nThe plot of P(x) in the figure below shows three different peaks of varying width and height, with some overlap as well.\n\n Plot of P(x)\" style=\"width:80%\">\n\n\nNext, we define our walker's symmetric step generating function. \nAs in the random walk example, we will use a random real number between -1 and +1 as the step size. \ndef g():\n '''Random step vector.'''\n return np.random.uniform(-1,1)\n\n\n\nHowever, g can be any function symmetric about 0 for the above algorithm to work. \nFor example, it can be a number chosen randomly from a discrete list, such as [ -3, -1, -1, +1, +1, +3]. \nIt can also be a number chosen from a symmetric continuous distribution, like the Gaussian, e^{-x^2}. \nIn higher dimensions, the function should be spherically symmetric, such as a multidimensional Gaussian function, e^{-(x^2 +y^2 + ...)}. \nWhatever function you choose, there are at least a couple of things to note:\n\nIf the function g is discrete, you will only sample discrete values. \nFor example, if g returns only -1 or +1, and nothing in between, you will sample only integer steps away from the initial x_0. \nThe average step size really matters! \nA small step-size means the walker will carefully sample nearby regions more, but will walk more slowly, so might not be good at exploring far and wide. \nOn the other hand, a walker with a large step size may not sample nearby regions accurately – and actually has a higher chance of being rejected if the walker is already in a high probability region, since the acceptance ratio is more drastic for large steps. \nThe effect of step-size on the walker's efficiency is far from obvious! \n\nThe question of how to choose an optimal g is a research area on its own, and depends largely on what the goal of the sampling is.\nSome techniques even use an \"adaptive\" method where g is \"trained\" on-the-fly using a learning algorithm! \nSome of these methods and others are discussed in Ref. [8] and Ref. [9]. \nIn a lot of cases, people just use trial and error, as the algorithm is not too difficult to implement.\nAfter choosing g, we are almost ready to iterate. \nWe just need to choose the domain of x, and an initial point for x_0 (x_t at t = 0) chosen randomly from the domain of x.\nxmin, xmax = -10, 10\nx0 = np.random.uniform(xmin, xmax)\n\n\n\nHow to Iterate\n\nGenerate new proposed position x' = x_t + g.\nCalculate the acceptance probability, \n\nA = \\min\\left(1, \\frac{f(x')}{f(x_t)}\\right).\n\nAccept proposal, x' with probability A. If your programming language doesn't have a built-in method for this,\nGenerate a random number u between 0 and 1.\nIf u \\leq A , then accept move, and set new position, x_{t+1} = x' .\nOtherwise, reject move, and set new position to current position, x_{t+1} = x_t .\n\n\nIncrement t \\rightarrow t + 1 and repeat from step 1.\n\nThe code for steps 1 to 3 is:\ndef metropolis_iterate(x0, num_steps):\n '''Iterate metropolis algorithm for num_steps using iniital position x_0'''\n\n for n in range(num_steps):\n if n == 0:\n x = x0\n else:\n x = metropolis_step(x)\n yield x\n\n\n\nThe following plot shows the result of running the algorithm for different numbers of iterations (N), with the same initial position. \nThe histograms are normalized so that they integrate to 1. \nWe can see the convergence toward P(x) as we increase N.\n\n multiple histograms\" style=\"width:80%\">\n\n\n\nExample Code\nThe following code puts everything together, and runs the Metropolis algorithm for a number of steps given by num_steps. \nAll the positions visited by the algorithm are then written to a file, which can be later read and fed into a histogram or other density calculating scheme. \nThe code also incorporates a few tests of the algorithm using the test_metropolis_iterate method. \nThis test will create a normalized density histogram from the generated data, and compare it to P(x) using the Root Mean Square Deviations metric [10].\nimport numpy as np\n\n\ndef f(x, normalize=False):\n '''\n Function proportional to target distribution, a sum of Gaussians.\n For testing, set normalize to True, to get target distribution exactly.\n '''\n # Gaussian heights, width parameters, and mean positions respectively:\n a = np.array([10., 3., 1.]).reshape(3, 1)\n b = np.array([ 4., 0.2, 2.]).reshape(3, 1)\n xs = np.array([-4., -1., 5.]).reshape(3, 1)\n\n if normalize:\n norm = (np.sqrt(np.pi) * (a / np.sqrt(b))).sum()\n a /= norm\n\n return (a * np.exp(-b * (x - xs)**2)).sum(axis=0)\n\ndef g():\n '''Random step vector.'''\n return np.random.uniform(-1,1)\n\ndef metropolis_step(x, f=f, g=g):\n '''Perform one full iteration and return new position.'''\n\n x_proposed = x + g()\n a = min(1, (f(x_proposed) / f(x)).item())\n\n x_new = np.random.choice([x_proposed, x], p=[a, 1-a])\n\n return x_new\n\ndef metropolis_iterate(x0, num_steps):\n '''Iterate metropolis algorithm for num_steps using iniital position x_0'''\n\n for n in range(num_steps):\n if n == 0:\n x = x0\n else:\n x = metropolis_step(x)\n yield x\n\n\ndef test_metropolis_iterate(num_steps, xmin, xmax, x0):\n '''\n Calculate error in normalized density histogram of data \n generated by metropolis_iterate() by using \n normalized-root-mean-square-deviation metric. \n '''\n\n bin_width = 0.25\n bins = np.arange(xmin, xmax + bin_width/2, bin_width)\n centers = np.arange(xmin + bin_width/2, xmax, bin_width)\n\n true_values = f(centers, normalize=True)\n mean_value = np.mean(true_values - min(true_values))\n\n x_dat = list(metropolis_iterate(x0, num_steps))\n heights, _ = np.histogram(x_dat, bins=bins, density=True)\n\n nmsd = np.average((heights - true_values)**2 / mean_value)\n nrmsd = np.sqrt(nmsd)\n\n return nrmsd\n\n\n\nif __name__ == \"__main__\":\n xmin, xmax = -10, 10\n x0 = np.random.uniform(xmin, xmax)\n\n num_steps = 50_000\n\n x_dat = list(metropolis_iterate(x0, 50_000))\n\n # Write data to file\n output_string = \"\\n\".join(str(x) for x in x_dat)\n\n with open(\"output.dat\", \"w\") as out:\n out.write(output_string)\n out.write(\"\\n\")\n\n\n # Testing\n print(f\"Testing with x0 = {x0:5.2f}\")\n print(f\"{'num_steps':>10s} {'NRMSD':10s}\")\n for num_steps in (500, 5_000, 50_000):\n nrmsd = test_metropolis_iterate(num_steps, xmin, xmax, x0)\n print(f\"{num_steps:10d} {nrmsd:5.1%}\")\n\n\n\n\n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nBibliography\n1.Metropolis,Nicholas et al., Equation of State Calculations by Fast Computing Machines, 1953.2.Wikipedia: Potential Energy, 2021.3.Wikipedia: Ludwig Boltzmann, 2021.4.Wikipedia: Boltzmann distribution, 2021.5.Hastings, W. K., Monte Carlo sampling methods using Markov chains and their applications, 1970.6.Wikipedia: Metropolis-adjusted Langevin Algorithm, 2021.7.Wikipedia: Hamiltonian Monte Carlo, 2021.8.Rosenthal, Jeffrey S and others, Optimal proposal distributions and adaptive MCMC, Chapman & Hall/CRC Boca Raton, FL, 2011.9.Gareth O. Roberts and Jeffrey S. Rosenthal, Optimal scaling for various Metropolis-Hastings algorithms, Institute of Mathematical Statistics, 2001.10.Wikipedia: Root Mean Square Deviation, 2021.\nLicense\nCode Examples\nThe code examples are licensed under the MIT license (found in LICENSE.md).\nImages/Graphics\n\nThe animation \"Animated Random Walk\" was created by K. Shudipto Amin and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nThe animation \"Animated Metropolis\" was created by K. Shudipto Amin and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nThe image \"Plot of P(x)\" was created by K. Shudipto Amin and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nThe image \"Multiple Histograms\" was created by K. Shudipto Amin and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n\nText\nThe text of this chapter was written by K. Shudipto Amin and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"},"contents/probability_distributions/distributions.html":{"url":"contents/probability_distributions/distributions.html","title":"Probability Distributions","keywords":"","body":"What's a probability distribution?\nProbability distributions are mathematical functions that give the probabilities of a range or set of outcomes. \nThese outcomes can be the result of an experiment or procedure, such as tossing a coin or rolling dice. \nThey can also be the result of a physical measurement, such as measuring the temperature of an object, counting how many electrons are spin up, etc.\nBroadly speaking, we can classify probability distributions into two categories - discrete probability distributions and continuous probability distributions.\nDiscrete Probability Distributions\nIt's intuitive for us to understand what a discrete probability distribution is. \nFor example, we understand the outcomes of a coin toss very well, and also that of a dice roll. \nFor a single coin toss, we know that the probability of getting heads (H) is half, or P(H) = \\frac{1}{2}. \nSimilarly, the probability of getting tails (T) is P(T) = \\frac{1}{2}. \nFormally, we can write the probability distribution for such a coin toss as,\n\nP(n) = \\begin{matrix}\n \\displaystyle \\frac 1 2 &;& n \\in \\left\\{H,T\\right\\}. \n \\end{matrix}\n\nHere, n denotes the outcome, and we used the \"set notation\", n \\in\\left\\{H,T\\right\\}, which means \"n belongs to a set containing H and T\". \nFrom the above equation, we can also assume that any other outcome for n (such as landing on an edge) is incredibly unlikely, impossible, or simply \"not allowed\" (for example, just toss again if it does land on its edge!).\nFor a probability distribution, it's important to take note of the set of possibilities, or the domain of the distribution. \nHere, \\left\\{H,T\\right\\} is the domain of P(n), telling us that n can only be either H or T.\nIf we use a different system, the outcome n could mean other things.\nFor example, it could be a number like the outcome of a die roll which has the probability distribution,\n\nP(n) = \\begin{matrix}\n \\displaystyle\\frac 1 6 &;& n \\in [\\![1,6]\\!] \n \\end{matrix}.\n\nThis is saying that the probability of n being a whole number between 1 and 6 is 1/6, and we assume that the probability of getting any other n is 0. \nThis is a discrete probability function because n is an integer, and thus only takes discrete values. \nBoth of the above examples are rather boring, because the value of P(n) is the same for all n. \nAn example of a discrete probability function where the probability actually depends on n, is when n is the sum of numbers on a roll of two dice. \nIn this case, P(n) is different for each n as some possibilities like n=2 can happen in only one possible way (by getting a 1 on both dice), whereas n=4 can happen in 3 ways (1 and 3; or 2 and 2; or 3 and 1). \nThe example of rolling two dice is a great case study for how we can construct a probability distribution, since the probability varies and it is not immediately obvious how it varies. \nSo let's go ahead and construct it! \nLet's first define the domain of our target P(n). \nWe know that the lowest sum of two dice is 2 (a 1 on both dice), so n \\geq 2 for sure. Similarly, the maximum is the sum of two sixes, or 12, so n \\leq 12 also. \nSo now we know the domain of possibilities, i.e., n \\in [\\![2,12]\\!]. \nNext, we take a very common approach - for each outcome n, we count up the number of different ways it can occur. \nLet's call this number the frequency of n, f(n). \nWe already mentioned that there is only one way to get n=2, by getting a pair of 1s. \nBy our definition of the function f, this means that f(2)=1. \nFor n=3, we see that there are two possible ways of getting this outcome: the first die shows a 1 and the second a 2, or the first die shows a 2 and the second a 1. \nThus, f(3)=2. \nIf you continue doing this for all n, you may see a pattern (homework for the reader!). \nOnce you have all the f(n), we can visualize it by plotting f(n) vs n, as shown below.\n\n Die Roll\" style=\"width:80%\"/>\n\n\nWe can see from the plot that the most common outcome for the sum of two dice is a n=7, and the further away from n=7 you get, the less likely the outcome. \nGood to know, for a prospective gambler!\nNormalization\nThe f(n) plotted above is technically NOT the probability P(n) – because we know that the sum of all probabilities should be 1, which clearly isn't the case for f(n). \nBut we can get the probability by dividing f(n) by the total number of possibilities, N. \nFor two dice, that is N = 6 \\times 6 = 36, but we could also express it as the sum of all frequencies,\n\nN = \\sum_n f(n),\n\nwhich would also equal to 36 in this case. \nSo, by dividing f(n) by \\sum_n f(n) we get our target probability distribution, P(n). \nThis process is called normalization and is crucial for determining almost any probability distribution. \nSo in general, if we have the function f(n), we can get the probability as\n\nP(n) = \\frac{f(n)}{\\displaystyle\\sum_{n} f(n)}.\n\nNote that f(n) does not necessarily have to be the frequency of n – it could be any function which is proportional to P(n), and the above definition of P(n) would still hold. \nIt's easy to check that the sum is now equal to 1, since\n\n\\sum_n P(n) = \\frac{\\displaystyle\\sum_{n}f(n)}{\\displaystyle\\sum_{n} f(n)} = 1.\n\nOnce we have the probability function P(n), we can calculate all sorts of probabilites. \nFor example, let's say we want to find the probability that n will be between two integers a and b, inclusively (also including a and b). \nFor brevity, we will use the notation \\mathbb{P}(a \\leq n \\leq b) to denote this probability. \nAnd to calculate it, we simply have to sum up all the probabilities for each value of n in that range, i.e.,\n\n\\mathbb{P}(a \\leq n \\leq b) = \\sum_{n=a}^{b} P(n).\n\nProbability Density Functions\nWhat if instead of a discrete variable n, we had a continuous variable x, like temperature or weight? \nIn that case, it doesn't make sense to ask what the probability is of x being exactly a particular number – there are infinite possible real numbers, after all, so the probability of x being exactly any one of them is essentially zero! \nBut it does make sense to ask what the probability is that x will be between a certain range of values. \nFor example, one might say that there is 50\\% chance that the temperature tomorrow at noon will be between 5 and 15, or 5\\% chance that it will be between 16 and 16.5. \nBut how do we put all that information, for every possible range, in a single function? \nThe answer is to use a probability density function. \n What does that mean? \nWell, suppose x is a continous quantity, and we have a probability density function, P(x) which looks like\n\n probability density\" style=\"width:100%\"/>\n\n\nNow, if we are interested in the probability of the range of values that lie between x_0 and x_0 + dx, all we have to do is calculate the area of the green sliver above. \nThis is the defining feature of a probability density function: \n the probability of a range of values is the area of the region under the probability density curve which is within that range. \nSo if dx is infinitesimally small, then the area of the green sliver becomes P(x)dx, and hence,\n\n\\mathbb{P}(x_0 \\leq x \\leq x_0 + dx) = P(x)dx.\n\nSo strictly speaking, P(x) itself is NOT a probability, but rather the probability is the quantity P(x)dx, or any area under the curve. \nThat is why we call P(x) the probability density at x, while the actual probability is only defined for ranges of x. \nThus, to obtain the probability of x lying within a range, we simply integrate P(x) between that range, i.e.,\n\n\\mathbb{P}(a \\leq x \\leq b ) = \\int_a^b P(x)dx.\n\nThis is analagous to finding the probability of a range of discrete values from the previous section:\n\n\\mathbb{P}(a \\leq n \\leq b) = \\sum_{n=a}^{b} P(n).\n\nThe fact that all probabilities must sum to 1 translates to\n\n\\int_D P(x)dx = 1.\n\nwhere D denotes the domain of P(x), i.e., the entire range of possible values of x for which P(x) is defined.\nNormalization of a Density Function\nJust like in the discrete case, we often first calculate some density or frequency function f(x), which is NOT P(x), but proportional to it. \nWe can get the probability density function by normalizing it in a similar way, except that we integrate instead of sum:\n\nP(\\mathbf{x}) = \\frac{f(\\mathbf{x})}{\\int_D f(\\mathbf{x})d\\mathbf{x}}.\n\nFor example, consider the following Gaussian function (popularly used in normal distributions), \n\nf(x) = e^{-x^2},\n\nwhich is defined for all real numbers x. \nWe first integrate it (or do a quick google search, as it is rather tricky) to get\n\nN = \\int_{-\\infty}^{\\infty} e^{-x^2} dx = \\sqrt{\\pi}.\n\nNow we have a Gaussian probability distribution,\n\nP(x) = \\frac{1}{N} e^{-x^2} = \\frac{1}{\\sqrt{\\pi}} e^{-x^2}.\n\nIn general, normalization can allow us to create a probability distribution out of almost any function f(\\mathbf{x}). \nThere are really only two rules that f(\\mathbf{x}) must satisfy to be a candidate for a probability density distribution:\n\nThe integral of f(\\mathbf{x}) over any subset of D (denoted by S) has to be non-negative (it can be zero):\n\n\\int_{S}f(\\mathbf{x})d\\mathbf{x} \\geq 0.\n \nThe following integral must be finite:\n\n\\int_{D} f(\\mathbf{x})d\\mathbf{x}.\n \n\n\nMathJax.Hub.Queue([\"Typeset\",MathJax.Hub]);\n\n\nLicense\nImages/Graphics\n\nThe image \"Frequency distribution of a double die roll\" was created by K. Shudipto Amin and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nThe image \"Probability Density\" was created by K. Shudipto Amin and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\n\nText\nThe text of this chapter was written by K. Shudipto Amin and is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.\n\nPull Requests\nAfter initial licensing (#560), the following pull requests have modified the text or graphics of this chapter:\n\nnone\n\n"}}} \ No newline at end of file